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%!PS-Adobe-2.0 %%Creator: dvips(k) 5.86 Copyright 1999 Radical Eye Software %%Title: aniso.dvi %%Pages: 10 %%PageOrder: Ascend %%BoundingBox: 0 0 612 792 %%DocumentFonts: Helvetica-Bold Helvetica Times-Bold Times-Roman %%+ Times-Italic CMR9 CMSY6 CMMI9 CMMI6 CMMI8 CMSY9 CMR6 CMEX10 MSAM10 %%+ CMBX9 CMBX6 CMR5 CMR8 MSAM7 CMMI5 %%EndComments %DVIPSWebPage: (www.radicaleye.com) %DVIPSCommandLine: dvips -D1200 -Pwww -oaniso.ps aniso.dvi %DVIPSParameters: dpi=1200, compressed %DVIPSSource: TeX output 2003.03.27:0149 %%BeginProcSet: texc.pro %! /TeXDict 300 dict def TeXDict begin/N{def}def/B{bind def}N/S{exch}N/X{S N}B/A{dup}B/TR{translate}N/isls false N/vsize 11 72 mul N/hsize 8.5 72 mul N/landplus90{false}def/@rigin{isls{[0 landplus90{1 -1}{-1 1}ifelse 0 0 0]concat}if 72 Resolution div 72 VResolution div neg scale isls{ landplus90{VResolution 72 div vsize mul 0 exch}{Resolution -72 div hsize mul 0}ifelse TR}if Resolution VResolution vsize -72 div 1 add mul TR[ matrix currentmatrix{A A round sub abs 0.00001 lt{round}if}forall round exch round exch]setmatrix}N/@landscape{/isls true N}B/@manualfeed{ statusdict/manualfeed true put}B/@copies{/#copies X}B/FMat[1 0 0 -1 0 0] N/FBB[0 0 0 0]N/nn 0 N/IEn 0 N/ctr 0 N/df-tail{/nn 8 dict N nn begin /FontType 3 N/FontMatrix fntrx N/FontBBox FBB N string/base X array /BitMaps X/BuildChar{CharBuilder}N/Encoding IEn N end A{/foo setfont}2 array copy cvx N load 0 nn put/ctr 0 N[}B/sf 0 N/df{/sf 1 N/fntrx FMat N df-tail}B/dfs{div/sf X/fntrx[sf 0 0 sf neg 0 0]N df-tail}B/E{pop nn A definefont setfont}B/Cw{Cd A length 5 sub get}B/Ch{Cd A length 4 sub get }B/Cx{128 Cd A length 3 sub get sub}B/Cy{Cd A length 2 sub get 127 sub} B/Cdx{Cd A length 1 sub get}B/Ci{Cd A type/stringtype ne{ctr get/ctr ctr 1 add N}if}B/id 0 N/rw 0 N/rc 0 N/gp 0 N/cp 0 N/G 0 N/CharBuilder{save 3 1 roll S A/base get 2 index get S/BitMaps get S get/Cd X pop/ctr 0 N Cdx 0 Cx Cy Ch sub Cx Cw add Cy setcachedevice Cw Ch true[1 0 0 -1 -.1 Cx sub Cy .1 sub]/id Ci N/rw Cw 7 add 8 idiv string N/rc 0 N/gp 0 N/cp 0 N{ rc 0 ne{rc 1 sub/rc X rw}{G}ifelse}imagemask restore}B/G{{id gp get/gp gp 1 add N A 18 mod S 18 idiv pl S get exec}loop}B/adv{cp add/cp X}B /chg{rw cp id gp 4 index getinterval putinterval A gp add/gp X adv}B/nd{ /cp 0 N rw exit}B/lsh{rw cp 2 copy get A 0 eq{pop 1}{A 255 eq{pop 254}{ A A add 255 and S 1 and or}ifelse}ifelse put 1 adv}B/rsh{rw cp 2 copy get A 0 eq{pop 128}{A 255 eq{pop 127}{A 2 idiv S 128 and or}ifelse} ifelse put 1 adv}B/clr{rw cp 2 index string putinterval adv}B/set{rw cp fillstr 0 4 index getinterval putinterval adv}B/fillstr 18 string 0 1 17 {2 copy 255 put pop}for N/pl[{adv 1 chg}{adv 1 chg nd}{1 add chg}{1 add chg nd}{adv lsh}{adv lsh nd}{adv rsh}{adv rsh nd}{1 add adv}{/rc X nd}{ 1 add set}{1 add clr}{adv 2 chg}{adv 2 chg nd}{pop nd}]A{bind pop} forall N/D{/cc X A type/stringtype ne{]}if nn/base get cc ctr put nn /BitMaps get S ctr S sf 1 ne{A A length 1 sub A 2 index S get sf div put }if put/ctr ctr 1 add N}B/I{cc 1 add D}B/bop{userdict/bop-hook known{ bop-hook}if/SI save N @rigin 0 0 moveto/V matrix currentmatrix A 1 get A mul exch 0 get A mul add .99 lt{/QV}{/RV}ifelse load def pop pop}N/eop{ SI restore userdict/eop-hook known{eop-hook}if showpage}N/@start{ userdict/start-hook known{start-hook}if pop/VResolution X/Resolution X 1000 div/DVImag X/IEn 256 array N 2 string 0 1 255{IEn S A 360 add 36 4 index cvrs cvn put}for pop 65781.76 div/vsize X 65781.76 div/hsize X}N /p{show}N/RMat[1 0 0 -1 0 0]N/BDot 260 string N/Rx 0 N/Ry 0 N/V{}B/RV/v{ /Ry X/Rx X V}B statusdict begin/product where{pop false[(Display)(NeXT) (LaserWriter 16/600)]{A length product length le{A length product exch 0 exch getinterval eq{pop true exit}if}{pop}ifelse}forall}{false}ifelse end{{gsave TR -.1 .1 TR 1 1 scale Rx Ry false RMat{BDot}imagemask grestore}}{{gsave TR -.1 .1 TR Rx Ry scale 1 1 false RMat{BDot} imagemask grestore}}ifelse B/QV{gsave newpath transform round exch round exch itransform moveto Rx 0 rlineto 0 Ry neg rlineto Rx neg 0 rlineto fill grestore}B/a{moveto}B/delta 0 N/tail{A/delta X 0 rmoveto}B/M{S p delta add tail}B/b{S p tail}B/c{-4 M}B/d{-3 M}B/e{-2 M}B/f{-1 M}B/g{0 M} B/h{1 M}B/i{2 M}B/j{3 M}B/k{4 M}B/w{0 rmoveto}B/l{p -4 w}B/m{p -3 w}B/n{ p -2 w}B/o{p -1 w}B/q{p 1 w}B/r{p 2 w}B/s{p 3 w}B/t{p 4 w}B/x{0 S rmoveto}B/y{3 2 roll p a}B/bos{/SS save N}B/eos{SS restore}B end %%EndProcSet %%BeginProcSet: 8r.enc % @@psencodingfile@{ % author = "S. 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All Rights Reserved) readonly def /FullName (MSAM7) readonly def /FamilyName (Euler) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /MSAM7 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 92 /angle put readonly def /FontBBox{0 -576 1569 1076}readonly def /UniqueXX 5032012 def currentdict end currentfile eexec bd2bc8312da7a34353963e088820ad4a2494871a5c866f8f44672a854e9e8a27 6fd3b21943b2867c3b30802d749780e1ebc10edad1e60864715c2b0d510d631b b3ea24b6ff392735adc334e1acc208f5ccbeb37a64e819267c12c01f65ce2874 139c00fa924304665e8e3b6caa150bdfd78b46291153c060657197929952dd84 82addc6c49f5d25d846cf29a9c369fdc1ce1c946d51ee4e7d9ccbb5bdfe9c7c3 a6580882b53120964199c2746ef2c9ea3ced8ce05368fe658f58459c2a6886f1 7c789209b30f9b93e74f5e019ac17509073328a8682797d746830f479a8e37cf ef4dd3d0a969af6601ed88c3f5da2b0415c21021eb3087080a055b3c606a43b6 97e4bb7b3990c55c4be557a4be0894a58e95c57ee60f448ec6f015ce7685030c d95b811e80f5dab0906d041dc606245ba655b7afb3416127adfca35b103b24e9 06ca962e00d3a07f24e9376a8cee5718c202eae8a11a4a53f41cad7b34fcb2a4 11b47a0de489195ee9ea72a2718bc6ea2b7074bc3a3ded23916fc900d0f1d17f 67359d48512d59703e5aea38c7cf6baf0326f9ece5db36d6864e7b55e36d0749 cf9bea28196bcc01ab02a3be5d1fdc611d1bc5bf26fceaf7472309b1f719d14e 7c313341089d6123d2647668f5f341150b5c4be4256bf275fd7af002614c84f5 8419b0d0a919f7ec918c9560ba8791f5689c72ef8ef24640989707df578af06b 79a3c5ef18d734209a3274c8242ee11d88885c3ea85c05609481d285d414210a 93ce5b8a05e4c9843b04b2c2da77035f113906e55b088c32b1eb27a45078e91d 994bee0b677775ec9cc4c8e285d39bdd188614c75929665b47210bf4bcf2bd27 38006d36aa619e4b023ce04c02c73305f72e2a74aac6789d7da24b495be899f5 888866192df45563080f7c64839aa1671946e1c7149c9ee6454c783e4edcf813 2a6166378f3b8b5d0b5c3a45aa38cccaf71bb5ce98e672daaf10b25cc169afd6 c5ddde5817983aa96909c1312dd6bd5e6faaabba55a9569259bb567e1471322c 39d916a7d96deb7cbc8e67d2d0bcebfadaaacf5a6b47e60f850121d48e3dd352 eb25c98058b68c3a64ace274aa38ecdbf9d97642a3c5f8f421a6780a70b780b6 1de05255c654b662cd1fd2e8b983827324c511274a17fd9805e62b0384aee70d a0fcbabc3b5d023fc620a42d565d63bd71fed96887f9f428312e57df8b009f75 ba8154af827033f1873c0bde3ecad721dc4f0da9eaabc0d112710e9b7c529fbf e65b72bfb724244a37be4e45656c21946c6be81d918ce28288366ce7aa16618d afa655d50dba8eeb144f26fd2df8f2680051ec2562852b222a597a507fec1138 5adcfac55f9890a04bb428d16590128a2995b3d94f2202268e1f08d1d6a4f918 0dfdf4fe02df3275c30653b4ef75e4fda2b325bb324ce1eb86825002d1378f8e 27c28bcdbd34cfc246c755a40c28e28ab9239a5be16f815fa2b73f7da26d01fa 1dc31252fce9713fe9c2 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMR8 %!PS-AdobeFont-1.1: CMR8 1.0 %%CreationDate: 1991 Aug 20 16:39:40 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR8) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR8 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 61 /equal put readonly def /FontBBox{-36 -250 1070 750}readonly def /UniqueXX 5000791 def currentdict end currentfile eexec 9b9c1569015f2c1d2bf560f4c0d52257bacdd6500abda5ed9835f6a016cfc8f0 0b6c052ed76a87856b50f4d80dfaeb508c97f8281f3f88b17e4d3b90c0f65ec3 79791aacdc162a66cbbc5be2f53aad8de72dd113b55a022fbfee658cb95f5bb3 2ba0357b5e050fddf264a07470bef1c52119b6fbd5c77ebed964ac5a2bbec9d8 b3e48ae5bb003a63d545774b922b9d5ff6b0066ece43645a131879b032137d6d 823385fe55f3402d557fd3b4486858b2a4b5a0cc2e1bf4e2a4a0e748483c3bcf 5de47cc5260a3a967cac70a7a35b88b54315191d0423b4065c7a432987938c6b edad3b72ad63c2918b6e5a2017457e0d4ebc204b094541f345ec367ae85ca9bd 24568a01d3b9f8095f7420e6c423c414b3dcce6da48dd1c89a56d078e0d0e2f2 62a13640a06d17e44ee3866c3471fb58fedf5a3b77294517651c16bdd7267d39 a54e7171752dbde63ac19bb4b3021ce95eb5fe67390b09ae4d9ed4d704a67443 f55dce17acd996c1f5e023c9e5a18cbeecc3097f23763acb86cdd7cd13381ae7 4e48495ec7fa520539d87f8a8dcb3c826275469b6800876a457e7d1e5be867c7 b1ccad69742a8c9b0ad943482bf2a4ad0aed40baeb69a0233bad36b4ca2d2da7 322956c70375d152653500b2f22d2ab6990cadde2da14b4917f7515e64bc3d96 bf775258fc7dae4e42a4c9b6da8eddec4a800c8aadc8d75e48cae52137e05c03 677f5d6a82fa46d9f2fc7f56d62e5c605a1b7898b8d1401c2cac1a0122a2c8a7 aae09607f2c5f29293a09b9959399283be89051452898238b777db9830ff4318 a298b221c4a820c700ca964fc99e6b1d9eb0bafc39be9aa9dffa2fa326b2a466 1e67261bb3dbc85844e76f9313ab533ee16bcb478166de5502b68e6ec1ea6110 f53206cf1cfea419571b0243244b32ea38b828a01e62b03bcf476a32c2341cec b8a0fa2a3f3f339315d5f3aa7704408f6617d026ffee4925aa48537a4b2e556d 225be09392546ad561cd46cf766f0ba14c6854c5af1a528c3842b0c5aeefefcf 19f19cbce5d967153c4f88e51c776cfbe10d39328466f7a3b83d85601ef4d1ce 0cc136610fa6a74d9676e4e99291d565cad27b9eb2337b0eba4148efd0eb2866 ebf0a4209ba135ad1376cf9cc2d4110f36121055caa3f2e62ddb460c33c83b70 83246b63b444a420449b61facc3205103f953809a6bd6526d31607e63a3cf827 06713bba9174b440fae925fdad0c8377043ca3ab64c71ddbb62fa81abe8626ae bf5ac3792ef771c2ed79c110db751a702a7efa45398be4a822ef7538f436df6f d7c86ff3eff4c4ae56e9eb3e5fadfb8a08266ecd31c3deb8ab82c69113d9fcbf 934a79d4008bdab0f584225679f5e019b0169e20f8b1e81952e9010c6e66f11b 64920b7a3a9e9d05c3a6b2468791d3506ae3db33dd4a19e9791861d3cdd78860 43f11baea4853c769f39352b5c3315a215d9f6f9c125f0bf22c879356b31d8be f78a2979e99f40d8281114be2ce264eea07b38e0c4 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMR5 %!PS-AdobeFont-1.1: CMR5 1.00B %%CreationDate: 1992 Feb 19 19:55:02 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00B) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR5) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR5 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 49 /one put dup 50 /two put dup 51 /three put readonly def /FontBBox{-341 -250 1304 965}readonly def /UniqueXX 5000788 def currentdict end currentfile eexec 8053514d28ec28da1630165fab262882d3fca78881823c5537fe6c3dda8ee5b8 97e17cb027f5c73fdbb56b0a7c25fc3512b55fe8f3acfbffcc7f4a382d8299cc 8fd37d3cea49dabdca92847af0560b404ef71134b0f3d99934fc9d0b4e602011 b9cfb856c23f958f3c5a2fbe0ef8587d1f5774879c324e51fcb22888b74f2415 50d7401eb990d4f3a7af635198422283cac1b6cd446ddbcbd915db9bff88844e 784c6bf7389803d9450b0c21756a017306457c7e62c1d269f306bd3402e266de fc3b5e7d8a8d2f5bf0fe6ddd40d07391df4fad4a6018dce29a2b8f692b29f202 3a7c0e66de8ed85c14f1f8492167357f51a7e84cc5d92e0fee4a71813d2ffb26 445026f89b4787516ecd1afc78f8bd19e91e9ccc9402e8c36d2449c1ff850a8a f61165aac3fe931332dd28e261b91b05edd18f44ea7d58a8f35fe88493b64aad 6bfac3a0136215fc2f4ca8e91d70c5010e6f4013e6d63b44f6fb00afdbd7cdb4 5ec5b1d9736f45cefc8a0124b815987cebd81bbe0d44dedb2d5ef37923b3d551 abb6a1cefca7868fc7bf3814ef7d7b6b1ae6e869cb77aa29e3d90b12b0dc3ff6 ec945922b5899bbf2f12e92731486d2ef1230c528bf8d7e0ae09ad7632a38966 5963de49d1ef3d65bc483e4a577b927c940f5e121169ba52f6576c85793e5fd7 7f5863c488e55bdefd5d8b2514795533aabbc12e7f51816c7e1484f1c441aa9a 66a5dc77158e79cd6692d299b95e8058b35e771a6972d2b5eb1cd6d2bb8e835d 361a6eac0c90c906aea1cd75c4412a1339dc1439f93e59917311bf20af4f2bc8 bba5a4626f75f28a47d4595c37f4019df480d9385975159142618e22e964f019 d88125210e2ef21d65baf500adf802297b24eebbf4e93c617a613f856bd0d45f e17a9480980ef83950bdb8ebf208c895ebc4a7132f0765b7c19a332ebbf8a3c9 ab65063a42e19ca9d43dec3de7aba46b9a5d24fb93d615c0a1726ab7e31c378e ab77150858535b91362ab0e2b968dee1c539964126d937f9d4980ccefa92bc81 b054996a65a13995c9c9d819ff05511cfc89cbfe67447c940405001d61be633b b771eff383fc6977ec06af30f981504260de7b9ec97359974734f495ac073935 fb30e3700679092ef5d971b6b2da0e15960f2391fa6b63c33e7f56b4a9b86951 1d3686a5e8e613a69a0add8b8c73b127ddcd397a48d785079e786d24b5f8ded8 78fe818b2419f9b46be91aae8e3562b4593b7f1388bcb4edb2ecd7ca58b930e4 bda34049d717b65b4c1a6cc2ceed86866d9a8b5922767de500ba61ee1ab8e120 f2c3b3ad4f1974adf96bb9436524a2d56895ab7fff29a07c52e4923a9cb0f41a 1e3e6fe6081d0abc7135756d4e6e4b593493b7bf168a2d8e58a336e108ba2faf a568f70d8c5c53f599e2f45bd57de55828fd7a9585378ad95027f2c8bd900f76 dec3b06dbe8a5bf133fb6ba28eb45cc16f9515ae6da7a6f250db499740cc03ea 3bb658ed1eeebd96b64535b94373e0ea52e8e8a4232f712ba61a842ad9e3459c b8d12ad1ede49d1cdf89f4a354f8e58296fdc3a33596183afcb27229c1657462 eac09b7ce0ba539a77a8df6013895820573565bb8499a916bc85b8ba733f0b6c 96081943bb46d54c399cda8885b4a74b19f33e0ddf88fc4a289e245374833fed 031de5cacd8f9cc3814fc3c04e1cd27cddf04f6028e36ee9cbd27f45ef2a5bc5 14862c22181798a6eee17592a5a03255d010541324b779791980043c29b04fcf 477f021bdab0369300d82173b68447ac99ac4b22c60482d6f9937244c6c3f525 05a17a53b1e3ac79708e0200f7fe4cbc35b82a22a0da283ddf64b1013cb3b306 b75226c7dc71f6ea243fdba1fbf135232799088314a5aab820fc88c9b69cb08a 03cec7b97fe6c1dec43d66ff9a64596fa3af82a0d7e42caf2a3fa7bd14bf51d6 1f728ef86d41d60755e0f4b2a3d441a12fcdbf655c90584f3c5ce7ed494e4f64 dcc6099d1d278df7514437068da690a38a309f724349d493bf7991bbaaaf7345 332611e645e4087ea1a0a91b722416fb38513450f1d59aed4bba2603d864b7d1 20b64e76fcbc5bce46198e2fe73e090fabd724bf 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMBX6 %!PS-AdobeFont-1.1: CMBX6 1.0 %%CreationDate: 1991 Aug 20 16:35:30 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMBX6) readonly def /FamilyName (Computer Modern) readonly def /Weight (Bold) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMBX6 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 115 /s put readonly def /FontBBox{-49 -250 1367 753}readonly def /UniqueXX 5000764 def currentdict end currentfile eexec 9b9c1569015f2c1d2bf560f4c0d52257bacdd6500abda5ed9835f6a016cfc8f0 0b6c052ed76a87856b50f4d80dfaeb508c97f8281f3f88b17e4d3b90c0f65ec3 79791aacdc162a66cbbc5be2f53aad8de72dd113b55a022fbfee658cb95f5bb3 2ba0357b5e050fddf264a07470bef1c52119b6fbd5c77ebed964ac5a2bbec9d8 b3e48ae5bb003a63d545774b922b9d5ff6b0066ece43645a131879b032137d6d 823385fe55f3402d557fd3b4486be1f91da738298311c1360c8158d61cb73427 3c21bce59b0f2e1d3c853547e19715d3d570cef600ee263180d3e7a38d50b375 8dd0cefd9101435d4abab6d6fc24a6e3b161ca0bc1bf52f71a10b608905028a2 2381239adcbc00060d6c1e7ef5829015a5afa1d1ab3473c01363d08e71452ff9 fc63cff9ce95e7afaf4e8a1722bd03fe5dd4048821cda268cc9ff1bb832da53f 174d9e4af1ba9d2b589b8b429ce7368ac70433b0ff5cc83a19f4048fe72e7708 d7a8660449ecec43435f71d329eca654dfd2d005e7e97113ef3fdea187a5b834 be9e2c464878232f477bedc0c5ab6629d49e7fcb218c5353d120c77a5988d359 3721bf0112b242344df6bb8204624de09d31e54700f4ae64872a0d8c6794f65d 5825f1dd4c2a95c1bd09358efed666b41467c451dacf553a7219a9b6f15c9e05 53d54ee3fc6fb3ab2600ff64cde6edc96e198f0655a6354613d9ee365ff117ea fbca446ea8a72885313152306723dfabb26561a0887f00184c5639975db79b5f cfb46295842fd49f43ca585f36c6322f3b062b09630dba1e9942d3bd7f998163 731692475cedfafc8c07dc96855dcadcaef131b0c7545c37f5b5e82f34fad7ae 9da5183f3bf5fc3a9534d0803e680198feac773a9b4cb8dd21574f71a5132e84 2bb805b079d9ef80aba443cc74ce606e48e3ebd33a3aed020ea919845dafc115 bcbc62c1bb2867d722037939b720ea1c2d87233d0c3463b13e48e2b08a45b825 4496aea4d0caf8afe2be8c52ea28d3ee8a9cd6410cfdfe1f7b2f2ee631bd20b0 64e2312cf06de8aa4e46e1286864fb0dad8b85ccc2020107ef45acd5a8e7fa08 1f1ca294726dc0d287f3e57b9104ca9106bcb78475e4ba3818be3d84d558ffcb 5ce3bba032ee1e079e6a53a6dc18df00cf15138e79b3ca2d53eb544b98adbe64 9ec4d0ec58fea8ab04813564210e2c2ccd3476ee0f8e57fd0031c26812068beb 5221cc2cb6f3d114f55f7f45673043e36d75f8f78d8350b7ae7e8e67f449a312 f6a3f6514f0979b1a4c9f364d59ebee1fc96da86702b67792105af8f4835dfc5 cbffaecc0c08b1cf55a1f7d021eb006418dff6bd22abe5c18c819acce5df4038 4cb2eb95591adaf447d40acc0e24052d682b0dd2ba5c0dc461dfe50cd856835b 5ebba1d250ad3408e38c9a675e249ffafba8d9a809b2e723bc932ea33a822d90 7ebabb5f8cc8b5a970d36f71466fc68a05088a4ee2dbe894debc90c5e95ca500 7926cfb01f22c6709aa318873420d3ad11f9bdcc04714aadb85f47cdf032201e 481d5ba5f159b897848fbbdb78668a83a3683c28000168ae7fecef7ee9bfe297 1840108d591aa1c60bce49d771ad13351f9fe73f74fd5d460b9f527c913cf66b 57bd60ea63db0a4980b4376ba5197fc4122a89989b7f52945e895db0 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMBX9 %!PS-AdobeFont-1.1: CMBX9 1.0 %%CreationDate: 1991 Aug 20 16:36:25 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMBX9) readonly def /FamilyName (Computer Modern) readonly def /Weight (Bold) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMBX9 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 115 /s put readonly def /FontBBox{-58 -250 1195 750}readonly def /UniqueXX 5000767 def currentdict end currentfile eexec 9b9c1569015f2c1d2bf560f4c0d52257bacdd6500abda5ed9835f6a016cfc8f0 0b6c052ed76a87856b50f4d80dfaeb508c97f8281f3f88b17e4d3b90c0f65ec3 79791aacdc162a66cbbc5be2f53aad8de72dd113b55a022fbfee658cb95f5bb3 2ba0357b5e050fddf264a07470bef1c52119b6fbd5c77ebed964ac5a2bbec9d8 b3e48ae5bb003a63d545774b922b9d5ff6b0066ece43645a131879b032137d6d 823385fe55f3402d557fd3b4486be79011d1f5bfae5c1f476ee6f05eb1d2caeb 269958b194521197b312fcced4867f3c8fbd030bd715d8ffda1dcd454b174e7a 1a97b59fe770e67702519d9d9b23d61ac08424d55fd4dda249cff0b56b9f3aff e9d0de215c02a52a6bc77155ff6b8cba5cd6646ba331254ac58ace650a967d3b 272331b87b6df06d5ab9d80fabe9f9ceac10139b61244814dd9fc295ed42d1b5 cd11c2e4beab318b20f51ca2c2930657e5343ab7bcf0e8870a0d12de4ffacb6c b3fdbdda481c2fcb84408d3d902e9a32070b2af6cd9317a33a42a43857c114b3 f4c3005cef9401f1c2bad3e69150d7145b79f95c9cfaf7a335b277e6435ab374 f6a3e78e124ac1e4615511f743ad65c5d778403a840310ac4902985f107fd33c 0049623e4c496cd353d2ae2a4804110c6a420a38ece5d5b235c5e35886a0987d 284e6110527b653b1b2c68c636ef423536180acadb954843eff4d9a82568a713 b682c574e30f793f093aef755c650e0e7175c2e3138695212d9fea7bd4b5805c a90985b134c6bc15a19afae0bfb3066363ca3e2568c2ac4559a69fc32feb443b 61243b4508b7524d974636855c83c8149d489b68fe18bd497116a953431251df bd09fa1d2ef66c85b997ab2f6b7c6d9d096cb43931379ff9782fa00c5f3cbd06 04265d16891ffc4f66e4a0307765d384c32aa83a4e4f89ac79ef8e76eed08450 e3466fbaf54f85324f0a4f04bd00ccc22d32e4132c51749bea28f112c2051857 423ea203df902ae80224d75efeb59094bdc5f4b6784ebeb01c38c34b695e681e 57a93ae18b657d13770300bde28833c732010ded4c8e79078d17acc3d4b521b1 6f2cac338c4f72e2e07c667227ef142d0273e5b501f24b02e9cad75fe9d18741 b36bbb29c9cd3d46964e00d8ba318912e69a6aa7ccf823c12a95b97e987a0b6b 15e12f5ea46aa8f9855fd0f5e6461fb6b786c67e58ab2f8b6c5aef667797c88e c185bf75ca6036917fc9944eb8db92019357d0d4c97e466026d5f54b3663ab67 a6221052b4dbd47384f1bf7d91f0ef9ef61f72bc85e2fbb25c249d75d490e8b3 79d2fe9df981a55599fd56a56c5615a29e4e7df242825cdda37befde8633178c 88955fddf1b8a42a67dc3c4b8c94efde19fb4a3022eb9781228174fc64628aff 25c12ce0ed863dc48ad0a2ab7e3fb21ea10860123d6893ebf8517d69d0acc737 69e3605b9d08ee648f62b35d21a6349ece684ab217ead8e149ad340ae229e4f5 0b7b4bf1119e5dc6747414170e8fd315c5a4fdfaf928ccdf085784f298a4fc5d 54547c0fd80b595dfebfa42eb858b4acdaafb552816a13c0ac05319c5a72878a c81eddbbeaa0123cc9c8466cd9145c74ad9d4f2eb757072479cc218768681bee 2a92f0a34929d59cf283dca7921df7ec 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: MSAM10 %!PS-AdobeFont-1.1: MSAM10 2.1 %%CreationDate: 1993 Sep 17 09:05:00 % Math Symbol fonts were designed by the American Mathematical Society. % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (2.1) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (MSAM10) readonly def /FamilyName (Euler) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /MSAM10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 4 /squaresolid put dup 92 /angle put readonly def /FontBBox{8 -463 1331 1003}readonly def /UniqueXX 5031981 def currentdict end currentfile eexec 80347982ab3942d930e069a70d0d48311d7190fa2d133a583138f76695558e7a e9348d37cac6651806d08527c1bb4a062a4835ac37784cc39ad8841404e438b4 d52d3901e47a1de4f7924e0fb3daf442499175bab1226edf692a4956739f8828 e80592f450c5d5c22ac88bcfbe9748f61d18243a16f4a4467f084e8e2be46ef4 7fc51c3a8199e3cda62ff9c4fb73956dab8b6683d2156377808cb35026073e80 523f59a30d195fcf9b9fce4ffafc6f33457e3200f0935ea98f1a0cfaff49cfa2 d877ff805620cba84126dfd175a82e1b4c6ec58461fce97cdd749a012e2c4243 86b199a97c306b282350cbe5af90cf1d8e7371dcaedbd5fa3346dd3e558072c5 fd51a2edfee6890f62efd1b552699123f4f52c2817dadd5ece30b3bc178a3ef4 f45fd8ad0ee5bf30db5f9eee9ddefe249f3c349a886cf9130cba68ae559ad719 c439930ece1d52d38366116c390cbeabb8fdb36811cf3b8e2416825e8c880b24 6521ec6880ebe7f127c8741c756b29e1f89e3fd5d638a7bbade8c3a0fdbbf7ba ec37cd372afb2d9dd25d509726d20a05914e418f6b7e759c440beb61519df02a 06734ec1226890d17c51f25f775e6879fdc231bc4d7fcb4b33d04fa273bdb8e8 f124171714614f8a94e98a6c2d6bdc1254913999f9c181e42c0886556cdf48af 92a265c1eb06bb30fb2745840c17bd31c7b8bdfd37dfb9643a418a2eaae14094 6752e0a315207aef85c3c2630538907971ec1b05687208571a3504bb3369b5c8 9a43e5abe343d0599fd8d41a1bf01de49f5856bdd67d63a2b3ecea75d721a6ca 0c8751ab41e892e9cf674218dd44acfd40019bf59f4d69ea40d5cf9068a6ff96 9f8cc772b920baf17334833d732431a2969b9a30fe38bd44772cef653935a957 af61dd568f041847ccce3c587656cba7bbf46d8cefec936c6d34dbe51bc04929 0440354f3b29ed8e6b4f21ad53b5809779d67339f284563d54ed4d2a504b014d 974a31c0ceb57b364af519bad4e85c41d521a3ffc26dbac555b42dc191367152 1d60c30b95b5bbafb3c7d87a1c043ea5f0e6dab83a4de99a742e75f02837b923 c50eb478ac4131ee604e3d7b784bd8c93eb9430291d452c21be0495718546333 66a602a9f142a563fdae3c8d40de6a8aa4f3118e6b59bd7a2c35420557fc465c b2c852523436519025d752360d7c8e87d39fd9ef06ecc50d3014f88a1eb44dcc 180eae9e8b878664d76285b9a9a3fe0fe6600bbffe555900e342dcf0f7365904 60c5aaa15e61b173c69e7f0fe0fe2084519734cf4337749735c8e3df91affee8 23ff89d30a72bda2568cd728fbb60072ddb4408691a64fa0bc0020b17e5f57db 2771d9cf9da40835e91109e24a794579735b32dccc21c67d988b50ca9c306cf3 c003e7a3a46d1dd84b1881c06ca5d012b9723f1ff7ec4a2eaf6c72c0b1401fc4 6b5d772f7881ed167d0e2ee79fc001e513ce877b504d5656144ddafb78ddff5b 8fecec1fc75db54a020c7c10d2d918af79bfe34ef706b46ee315ac3f11d1b68e 31e6b7f719fa2aa8a95c5fe3ba31de83ca88444ecd77a13f4f7b0fc659f8f7a5 9d8580dc37ef1e8532b540e6667a098a47120e8b306e1587a0e0a1fc1d 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMEX10 %!PS-AdobeFont-1.1: CMEX10 1.00 %%CreationDate: 1992 Jul 23 21:22:48 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMEX10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMEX10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 40 /braceleftBigg put dup 41 /bracerightBigg put dup 83 /uniontext put dup 84 /intersectiontext put dup 90 /integraldisplay put dup 112 /radicalbig put dup 114 /radicalbigg put readonly def /FontBBox{-24 -2960 1454 772}readonly def /UniqueXX 5000774 def currentdict end currentfile eexec 80347982ab3942d930e069a70d0d48311d7190fa2d133a583138f76695558e7a e9348d37cac6651806d08527c1bb4a062a4835ac37784cc39ad8841404e438b4 d52d3901e47a1de4f7924e0fb3daf442499175bab1226edf692a4956739f8828 e80592f450c5d5c22ac88bcfbe9748f61d18243a16f4a4467f084e8e2be46ef4 7fc51c3a8199e3cda62ff9c4fb73956dab8b6683d2156377808cb35026073e80 523f59a30d195fcf9b9fce4ffafc6d5649664203ab24acb938d58d246707ffe7 d62f04bec4b70c21ef75beb2b812622b3c74e969d72d3cd11bd7106294a99caf 0b1629bc7d4de6b96ca82930831d64575f23f4ad06a0e45e315b1d392411be8d 6d73c998789ff258a07a3c8c2057325784514c845500bfd1a971310cfc11d41c 1a167dbd5ff012c60add4e87325f6e5299032a839de65fb1473a166aae1876a4 414a434f22c1d241591fb36f857df6fa930608750ffc0c54f44994662b1f00f1 400bf752ea8d83ffc4cb77a290bc2d99981ae59a191748ba5c7ba1a9d2583fd2 1398452b6ff5d83a059f7eadcd2ef744e9dd22bdf9c79d049bf06835e878c32b 7765c69bdd8ef4deb4ea7cfff4cf9354a4ddffa689de961d16772491c7afbd7f ffde42400764c68e954ee5c455a5687959829bc3b319b2147deaab3628662c80 30c5e02fea09609abe4eaa12e217bc3af673f1bc36a7039eb13fcacb4218fe0f c5a3f9452d4edf46cc91db67b624d4f2d37502fb9f11af4da18ca40b61097f95 d44329375467ed13c5cb585ec53f62b83ef9502cc755af44bf32b87b8ae9f3f2 f8dbf72dab90acafbacd280db6aaffaefdff6d5eff26669bac56280a950560e3 d01714ba38659b0e4e28bf8cdc1f15ff7e3ea9d95a6afbbe3d8e6905aa6d531d 6b6dcab89e2036cc492c65f76ddcc3cfcff33fde3d9ffd10f7a90530fd5c7683 4329baa902e701ca42717476298c9ff511b1941244bb1dfd0e5cab92a43970cd 1bdb292eadd055c97972844fdcdb0aa06401e7b2632b9d134f96bce0064860f3 9859da7a9a82be0a840672a1331212752ae1b521b693b384a72dba8d37a86eaf a0341e7fc5f6ef7a8c566aacb91e8bf5005c18837894c4eacff41dba54e071ca 83f4d4be6c2568b5f01f2beefd6f5be299e4291b06e57d60300f382dbf9029a5 e5aa0d711d9722800171d1739ce680076cc79e7e632d6ff14c72180745244ac1 ba04f4f064a0ab9328fd9705fef70cebf1d33e9842640808697d0583ab51d0dc 17e178d8546e9451331b0054e13f9a7763d18e93de7d968b425242baf187b1a3 b9ebdecc6f3295007cf7dbf640cf63ba0113a639d85b7eb3650aba6bc22fc29c 5242680edd606268894ab64a74dbbd1ef236af9f30741edd40794d9f93873cc9 1c68f8e4fe3d1171c8715e86131665ca590727ba152118b65a4438ed65571cc1 27e8e37c17fc96862b796920336db3efee9aa8058e98008988331bdd165cb0ef a2bf061e64fae130e2390b0bc337be0c4b04489f69b6087ca956c5fe30bed353 d82eb8c23f6f1499c087e30675c348587c5cd8d5aa0e575ce1a2757e347ea92a a5e10cd60907d1d59e4c77b85a63596937f116ed6348583854a154da7691423d 7dd0ee4da812622b550bf5882b6cf3287c771795c1f55ca3fe3b5f8587198171 e481978f9ff2feff5f6031d2d1c817c746ad8e7c903d979bbfbb144f783b5130 abc90f7d4377db5fbf9edf260656365e7ddfbccca85b0eab95d806bacc37e2f5 bec6e488708765def9444efea05a93df95903f6cf638c053424444db5fb6d9a8 9c246abd122c6adcb066462f33bcb0afd6489b989b883eba2fba8415908d1791 406b211ef126d99d9c4952225b7c770f77bd397b2c62e693cd3771a5aac79255 fe4f1c310059c72aa3a944d46d0358e425d8caea209ab80cfa73dbbcd09ba1a9 12d85bbee6b5f0f74bcb52dd078896d5953442cad11ad1a2a26769f84aab4055 f60093225887358dd8d5edcb6cf84f0e1c6dbb1723c20bd83eb2cd2db021af93 0cd23af9c0bde6212b8d1495e8f50b331faa34bfad4e6319f1d29acc065bbb27 e5bfe698c954bec8f1f2d65cdf10fb390aba82e38a3fc32f99e4747afd9fe1d0 73f8973e7e63684724eaf4fe0576f67c5c07524244961acd2f1e0890d59c8f79 46d8f7223f3bd515f353a88fd91f5c5e97480db89accc358013a18a33918c8c3 3d4874d5e98e4642464955dc75b3afe529b16a6f91a092cfef9c8670220e25a1 680ff0b344e8b158eaa8b33acf7aee2b2d5360c199a80432403edd2033b04230 eb6d7389115dc2ed1ee0cf77ad07d17b18abb8bd1e8efa80d4628e84205ed816 dfca13f618fada259940d93dd8f3b1c5ba947bdea1a421a1ce1802df7d04e593 7c4565924cf6be53a02328920e09c62660bc3e2f865a3d45e485efdf15015cb5 69dc88b1bf853129595513542c411358d6512ecf9a2b1af844710a5a47dc3296 350ca9cdd31519e480e5923c67eca855881515cff7802edf1bf954717c1a8ca1 2392614429af53b69a941fc4e10a3fa537990a1efd9ee1257a0e914467445f07 3cc219bdf562e3bb100acbe2033b081a08ee27c2a1f448bc9aacfa77443c7291 5e598f74fa380adbe17073476fee359b94e5fba29842c17a98ed1eb2e0dcb5b8 33b9159ffc8d999893549a2d803c443f79755b15cf0589520270cfad90a3f3fb 16e98802b506ebb5de7c8786be6e45940d7e8533c020567e101f0bfd27140410 d9ba2d6913d0f62f4b72d53910de42f1b8067024f82fa31241945940ebb2fe43 e974112ec3f0107517e710da7ce8c395ef2975a669dc33c74b7c65da9839fff1 2a0def3d498e6a5d9881b97ff08617e4b2317ff61309aee811c18ec46a591271 c9fa67a1c12de78231026b5fefcd5293896dd75ec6670978bee2101aafc12d82 076983838dd7cac7105de0 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMR6 %!PS-AdobeFont-1.1: CMR6 1.0 %%CreationDate: 1991 Aug 20 16:39:02 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR6) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR6 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 10 /Omega put dup 40 /parenleft put dup 41 /parenright put dup 43 /plus put dup 48 /zero put dup 49 /one put dup 50 /two put dup 51 /three put dup 52 /four put dup 53 /five put dup 56 /eight put dup 61 /equal put dup 97 /a put dup 98 /b put dup 100 /d put dup 105 /i put dup 109 /m put dup 110 /n put dup 111 /o put dup 117 /u put dup 120 /x put readonly def /FontBBox{-20 -250 1193 750}readonly def /UniqueXX 5000789 def currentdict end currentfile eexec 9b9c1569015f2c1d2bf560f4c0d52257bacdd6500abda5ed9835f6a016cfc8f0 0b6c052ed76a87856b50f4d80dfaeb508c97f8281f3f88b17e4d3b90c0f65ec3 79791aacdc162a66cbbc5be2f53aad8de72dd113b55a022fbfee658cb95f5bb3 2ba0357b5e050fddf264a07470bef1c52119b6fbd5c77ebed964ac5a2bbec9d8 b3e48ae5bb003a63d545774b922b9d5ff6b0066ece43645a131879b032137d6d 823385fe55f3402d557fd3b4486858b2a4b5a0cc2e1bf4e2a4a0e748483c3bcf 5de47cc5260a3a967cac70a7a35b88b54315191d0423b4065c7a432987938c6b edad3b72ad63c2918b6e5a2017457e0d4ebc204b031f3fc6c13d7da7277a94ba 018e9998b3dd888011a5d7c4204989f30f908b95533bda845746b673ab71ea57 65a0d14f4350707e47c8276305b28513cbe1bb0dbd269a53719bda46e536685d df78ca0146b6b93e760256b74d939d4e35b5e77238f04c92298dfdd188feea30 e053eefbcbb52f2011772b3aae39f5805597bbc1e8bb75a446ce014030f4f2f0 f49f9e962ee4a1024a746fa92a3628db5270732b54e43fe5ecfa524f127e5fcc 788e77e66098336ad67fe4cccaf0253272d5df79864bf4b734cb9a5859d557d8 bc11b8e00221ebc12e97de4b1f466ead83a4c894709363bca9040410a52d592e 34ee40cc7e5efa920546b981aa659513a24b1b85c221a1875b62d0b89e57a368 321b8043a5b094e0379760a443d632892b14ad6d19dacc8c78093243ad67e6a3 08e56e6b68412ee690b10dac6e17708754a00d51fc957b500eb80175716eef4b 2ca1ef867614659bee3f2b7319e97b6fdf1efc847bf3cee3156f72f21751da8e 5fb6898919e6799820d3de0642d756e09d6fae4ff08dd3deda3173bff4bb11f7 9109c97ddc05897af709ea199a90fcee8ce4c7a3c15b18170c41c04de2d3fba8 f34296a95b8e1e8de3739b17273f8f2c85e914615e8eac5e8bd2387ba3b1edf4 7968f06e2067d836d0f9f3e085cdfd2de06a62c81d786b304326f7002e83160a 36598589228b4dddddc43c85e1d126f8fe81b828028e26317af5894aaccf4f69 6301e1a9fc45935d8a414957f08febebbc3a72ada80f101e47447d019ade56e9 f4fab969bba2b44e47399fedf5caa1bcea216d7ba713d523dfb4a28be726d326 668de841816f412bc43d643c5d80f178ca0ff4377980fed4efb318d7e15fd323 a3f485db0427b80222ae2df69db51bfb71f64226de391d5d45420cd104d2715a 5ded7a356df6046ad6f11c950f8a04faa4a90b785fae20dab1fe0793b5d7e1bc 98e3ca29679596ebd3ed76470bc3e4404f4fda0acbabcf0085426b616e1f6270 623ade31508b572f10264aa6a037d1151a65b94a3893ab18e489ab3ba43d7133 4707087ecb05da81c6f65acad0a5cdac00ac4e66a733b22d4f6324ba6257ed01 feae1028dc024090ed13e385b0a64795186dcb67c2304360d1a65812e83c42fd 2061f78045fc431116a5466c9efc5a74e99fdb314d9f5cd19dd25df736951363 8a86c1756ccf9e5a8189f704f21609dab08122b3e101e8197e937ea9714f51e2 427e88782a735d8f07bcb9dd1dc7096327f6a81a22e2e41455eded59fb4feed2 1987dd514d18c4f150c12e6ecd4912f38f73fb0126430f5281da5d7105e4922b a4d2b8bce37b6ec4e002cef6d99cd9d95d2de6742ddf53b31729d69c30477ec6 4b47680953ca79043c6ddb15d8b8f55c24c322bd223cd5f9995796d688ab76b3 6987e25c860d492d79b1b43687738a27372646673365fe3c0e2c5578e5e3a914 ffc45010ce42df9269e27d50e56fa97d9e36944ba55ac3159354c01a25cf53af bc8fe613a008f7eeedd454d3d2ce51475d7e01a31bd64f46afbcebfaf53d812c a020d21ce8401bcf5249f6f83beacfe1f8c45a332201f5f84fe158832e07f3ef 9d513dd5598f4231b5aa3a16404eb2604ad123b85dcad9c18964b0e9f65df804 25bb5ee03e040dff974fb8017400cfb6b3e412365042013bc179bec9fa9075c7 1ca6a62528bafc04ef453ce4f2a2a57e28ce90c642bc55ec69e97ffe209e831a 350b9fb354b3201b1aa779366f9bfa83047dcf620992627233a833bc645e4f49 7a4b198d32b243aaf2d1868c414be796f149a1186dd1ea00376afc7a6aac0fae 97c63f2e956ee74e65c20f5cbbea706e6a93cf458ed131fd7a9ed38b3182e004 a44b2162e2cd284375f918bb927e9eca781fd196d892e2b55b37fdb0494b99ad 6bca38ebfcfcf35f0bff26e1ad525bee16b3a3e52906324551759e3086fd3d45 2acb823903cc8a84fcbb7a2ee86d15e6a598c74a0f04601c19e9c8f79099f0b8 a7607e6d6177153a5cb830a0ea1fdb61f765352c7d61fb36f12e9ee971eba8c8 bd8e65f79bb0623bbfba0c43e595216646b59a12493a0f95efe7b98554cc0608 29e39124efe42fcbfdfc88b7b604133c723cf2c93bb66ba09a396ba66b7f8e22 049117ad990df803154185439e5dc6aa899d694fd5860beb8ef751ef6bf9327d 38c96540980d2d2aa84bae58644e874eb6bac527703c2f39697ec843a7a12174 580851c5ab9a278a91d2f7645e45f31401cb033341fee88c0b1161c939143bc0 b130f84f0bc9eaf14ed3c32f5434011b5b8df8ffbf410e729eade8038f14d2da 189374a2b7a3c560924a1c2e898458619b9874c88b3e27d84fcabbc14cc79be7 635549418419ea5e3896ce6a4ddd938c4351738169a6c49f406c55883d8d52cc 105428217852685b2f5e221c645115a85b8c80906a8d3c417435160e4d53794e 77ac645747cdaa37be87e2d353ea408ba4c11c80cf6715bd25ec3388d35ad8c8 7f5874f22f1040bffbc4a35f47a403da22ceb7eccc9446545902fd3f436120ce d596d6e4e6c3cd49a07d8e9b47e62c69b0b98f21de1c7064fbd9c0ad5eeabdf5 c2d62068b7ceff5187b779ea9c6f56e7cd7d0ece49fc72a3c3006cebc5dcaeef 7f9a93b42e0a4067c28268871db6387dd1e596bd3ea938b6a604814034f03953 2353cfbb0a8f098c26e2fc4183580384b280bd418d2f82855f3ac3262839836a 3c0ceb6515aa003f55eb6fd066f25c5ffd19cb3bf337da9761ef86f2aa4d5691 e4b2afee8f7d276ee15acb6dbda1b39fb1c3823c73978cefd56c066efd884b2a e700f30ce63cde6d1b7777a897caec6e5eeeab13be55dc897a3f8d74033cdf0b 0f27f82deb723bfbfcbf76373becef5ac7e7992803af0b1453cb0e94eac88ed2 31b63022e0ca0479d217c3428bd047607f39411217beda8ab6407911a22cf727 09690a063bb51caa68aa30ef50309a4fac9820d54ec449d5df4757b1ffc13d0b 7e1455ebd22bb4ece6f939a151a3acab5e69b4505eb3271658c12d5f67dc931a 9da8018c645844fbb9b9ac5676a1f00902f165d9ee6b446fe7836bebdf16d91d 546d5eda3de18296e8ab6b52788fee16b48e646255634994d6cb6b879445665d 26c9e5cf268722e3167dc289f5c4c647d8b6322a82a0a635245b90c193706438 ccb3980d740d78fd2a22c60b79330f5ece98859b09c8921b91c5b3e1d8bfea91 4c7347bb2e16ca162b69adfee0626a0c0a5efe1b28c95b7c9633eda87f46943d 041a91623633a409779b8d26f08143ba730418e7acf1551294eed5d15d1115f6 4c41849a30907f63d88679efcbe66fef887577b360ff8798801764a3edc07190 068b4cdf4e86aff04f82770b587ca56f962a7dc057cfa2a33506abf695be2cb8 590a5e07e23ba2c0980264f53efb6487ace7a21ca0fd3deaa8430a2c30815a74 783b7b1c9ddf375ac5b468ac37c3d40f54f68374d4221b769bcbe0641fa017b7 040b90a837de5988d28f72af728e635ef345e0c2eb19c690d217a48e45977a4c 57522866bd2a05891320b7651ad48e380859f53bcb643615fa2dd8e7c352759a 7c3bf710e8d7870972cb2863a231d33796970244d8f66a9df2fcc285432c273d 244153a970f57032625320926f8c75209f016ea07fb958d6b4d4091b58b053c7 3de06e64107d91bc3ff58097c73203ad739d69797ef35ea07661a3d2a97a9d6f fd2ce62f02bc90f6d2b1319c2f0066197db11557fe6c4a4e7e53bb9bd9d101da e8a810a57d486bffb3ac10964ef4dc9368d1a21c351b0638c2c7135efe2908a2 53a0ef8926f8bc80521337f34e4f2082fabfcf6ee7074b078e436270703b3f2e f79edaf27a7d76f9d14f971f4f93b5c587346724577932d25a4724b339dd6a7e b75d0da7a79d97b21c5d66641b84290510c75068c19deeccdc14867627e68f18 642d07480dce9eda147c4f746c94c10f63aebaf71c8b51be54f31b5a1f7121c0 621856331c34b46ced139cfa34073e0636704854dfcf19c1ba0ecc5a182b65bc 8ee86dfb4b61f7126c4ebd64c90e8a8b36dbc927de695589c6f6bcb094d6b522 e64a8ad50aae82c2e0d40ead9cbc68c5b14a7360f9ca22f5f8623e9e36d5cf46 87d169f6a73f348b019b38d663c892b70d1a1d322551e9461eb4fb61ed4058e6 978824df7306a9aca51cf85950798e4c010e34f7d79bf1b783bf61a0c22c8735 b78c25b797f7ca93b74e491b1373cbf76cedd0d3f72de34a92bcabfb34670f32 250526face5a7ef39682ea2ef28228fa25ceeac4eca21aca325d603271cfaa4a 39436a067e56134cc2486de4707ed3e475bd709abe3c2485618b756683c81f2a 0fc0a38e7e6a983f3841c322a25f970d8fadeb1534c60eb9b70b91a1e2de5dcc 9b04857af5a663941c3591943c28f47f79752ad37c9cc03151432b85ff66b9ca a81e19871fca0e552b09e057bc9e6c0619dc646f4021ee825f77753c508c93e4 b95fe986e391c49e7768916e06fcbd34d2db60e6b4d78a82d9f80964304cfb8f ce1fce1acf819dce88b319afd9cde07a5e4f264cc3c855c3fd800d833924c8da ece68e711c7b36ee56d8b241d2ef27879d14910a6daecd3a5f3c2600e3e067c5 4381fb56c07063b40251ef5ada7b45b2848c2c3013c8198497c20eb76bf71f52 c2b31296adb4e5b7a126e27c9f403b10c088fa6ccc6b2c05395d6f88c2064430 3aa0e3253e4e76b55c8cddb8ffbaae748bd2f164490c52262cc492425ef52352 a9f51b65ba135da1649239e4d82e966e1e13d1eba03e44c1fec99fea69c412b7 5017387f2d74fbde3a720fa062bfb5ef41e7f5932e4996634eb2db42b9615cc3 65ff66ab4970e9b87a653bbcf44fe36441f27997c609b6db9c12968ec9a2fe4e c7a51aaa269ccd2c0e756f848b7427666a8da86589ef565d53a3abc9f1b7bddc e6faaa862dcb09d65b449c8edd0bc9cee7353225f80f1f67a1123ba559a1ab7f 1099020b720aa0a8ba791d08098a352735f727d40397ccaef3b614e8a2d8d738 40acfb923680dbb0bff5fe8b1982333bebe536eb48a341be4efa9a6a20066cdd f83948c9b4e3ac8b3f41b814b8edbb4a40e2971ba0e629e7c8a6e7230a198723 9f68b7f172ade1eda76e0a71a04d04e89fb01da48c72bc8bc4d6f95b30e90eaf 72b7af8f7dcbd5bec7915c796eee333883d73163fd94a774b1468bc9fd845194 dd0475c3388a6690ca8136d949d3f9774a446079274b209ab30a8fffc217ab7f 7b6c97d15b61571a2b0ad30bddc4463add513095a6d1a793cb49c86759b54d36 e3ac7dc6c8523fb1f03fd7d167ca2e1f2f2c013248d72f8d973a335982ba94db d7607652a94ae9ecf5b92104ce3bd77cdaff79ab5256b43128fa3ff681d00879 ca1aa7d1827f7f8edf447f723b8bda201323d7208a72529d7527912b8ea4c794 fc69d045e9498d7b3d14df7db234afe048241c7da930f02304669c4c5cad36a3 4d5663f55f9f7a15a8e865f8c17aa3a9c97de8fcadf23820aaae3ef734cb3b08 bf9dd3745ca4b8fd6636756fe4e771eb149fe4dc250028275b3140452fd5f963 e21022fd1fb58376ea7581081583783ea758b3945a00ed505863f18d 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMSY9 %!PS-AdobeFont-1.1: CMSY9 1.0 %%CreationDate: 1991 Aug 15 07:22:27 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSY9) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY9 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /minus put dup 1 /periodcentered put dup 2 /multiply put dup 15 /bullet put dup 17 /equivalence put dup 18 /reflexsubset put dup 20 /lessequal put dup 21 /greaterequal put dup 26 /propersubset put dup 50 /element put dup 52 /triangle put dup 54 /negationslash put dup 59 /emptyset put dup 65 /A put dup 91 /union put dup 92 /intersection put dup 102 /braceleft put dup 103 /braceright put dup 106 /bar put dup 107 /bardbl put dup 110 /backslash put dup 112 /radical put readonly def /FontBBox{-30 -958 1146 777}readonly def /UniqueXX 5000819 def currentdict end currentfile eexec 9b9c1569015f2c1d2bf560f4c0d52257bac8ced9b09a275ab231194ecf829352 05826f4e975dcecec72b2cf3a18899ccde1fd935d09d813b096cc6b83cdf4f23 b9a60db41f9976ac333263c908dcefcdbd4c8402ed00a36e7487634d089fd45a f4a38a56a4412c3b0baffaeb717bf0de9ffb7a8460bf475a6718b0c73c571145 d026957276530530a2fbefc6c8f67052788e6703bb5ee49533870bca1f113ad8 3750d597b842d8d96c423ba1273ddc63eb43f34fa90ea73a234af35fd9b24eb7 4f19626e9124df7acb92629cc87b2cf81c4a89b27447806db34393ddf0402958 e2daee0b4bf315f9aa0a2650d2e11ee289ffaec940d0af160fe7f29411c1c458 69d1ac3bcfe2ae4da72422549095f1fc9fec606289316f106e719a4ae2fd45ee 868fddf07a80e9a626bb43cdfdaa9dcd208b88fd99af20b27f9d6b5cda6a3fa8 8d5acfce8b5eebb38854378cecc3bfdac526514f1be9fb28ae628918ba942a3e 05b78c3aff808cf416a5ed01be280231b75a7aee0c66b0549713bef6b3cbc188 e625ba81b3f94853e8d9a3c6f6e7c406bdca23d3fc0d769864658fa1c6d75c01 bee566adfda19c32a33f37c9f0b58b300b00f94ff61299be3471d78e1348007e 0b0db8ea7e3d5884a568c1d35535c90b39c60ae1cff3733c3ff62dc2a74ac832 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241da23109f936727817fa5bceebd145db8d79a531cdf8886a584981640129b1 61f7b383b8648199cb0ddbb985607643910fbd04931554b401b9db28f4e26e35 9eccad4a3515c000e32afbf65d7f70c36cf0d714c42b34bd441381a42c588544 5cd4e82e9584d901e55a51fb5fd9009f9d189446d4cc315ac8fff67b861d8b1c 3b8c1f648dc0a14ad708df8aff7244746d2492c20b452867a32b76549ffd6031 ae6b01319e274635b2d0bd6319f12dab04f0e54578741e3c806d7fedbe762ff5 4dd2019c497c784dccb3ce4d275f110071125d8f2676db9514b50dcb1d80b6db 1311f962ca7c28eddcd22857c0a82cd5d97c596bb336b21a903e1fc31f204ba9 713c12b2c6faf51992c80fa227be8aaaa273685a4d2c2afdece334c33b1d4d22 3120c64b4750bad030ee97bafe2f0432b19af3b80a22fa34d935f38cfd32eb45 54e8d2fa38cce504b846d1ff6c8da3e9ba70983a9673cf06d66dc08f8e333047 ac94534f413c4e89925cc720b645a53440b71ab40e689cf9805af9567e3f11d8 71eb6e5d70b411d7ee41db8963676262f02ea6f23146a26ef762d702e1b5e087 4a8472dca3acb620c38ff0fe625222ed4833335ad0d6bf59a76ed828c31db726 d424b3d7a1e1d9de12982c1b155607f28faa7364dfc4700dc58b1a98564b5428 958f1e9b6d9c9bee3f6409a239b4327831e6cb12aeee2e70b12b610098b2dd54 8fa2c7dfbee7952f7693ba838735460d7b8bad1fba512228ea26bc23c33858c3 d659538c1ef2f0a93fe3d50d720d7ec8debf4d4aed13c1085bd8b8a7fe6e123f caa0094bbdf15a767e2ac520bee8e1dfe5e315796f588bf68e9dd9b831bd05b9 ce0a3f6c6734bc779a0ef5f629d8eda34bc8814d45bc9c26e1f122c6013251a0 46254e43eb5100c1d4a5b21ba730e9a1e9aaad8423557d94385b6dd6fb2ad082 8a1d43579e6e5b65dcaab4f2ccffdc373ff7d1118c34e09c6bdaf85b62a2c659 c63878e1910901239138cef21b84527dc2d1e2fd739cb96a9b61589476640d3f f52851909847ece4fb4202ead9d9a21f46532c2e4a9abe55bc29c60ac9df21b7 74ee357f8d9ff0df10f06555066f085d53aa38830f04ce41d5532a5f83216db7 cf1b672b670ca56f91ab1f52284e76c8a627ec0225ebac54257b4e492e725e1e 7e9af18189a2ddf06ba910c4f2259beda0a4c9109f41488f9016ade020e6c14f e943decd56cefa1eb059c67ee39fb49ee40019dbe1d8f84686c525de4c1d3acf 75e5f89b0a83011286039b4a32c84b2dfc0fec4f499431cb40537d6050e8a0a7 b3ba236edfe52c5682e483e803bd302ea283365dbed9cbdca25259933b078c98 ea491c507e3b4da5b083c098884c675f5a0a23d7801403cb468c08146a6a2330 3eb5d7ae470e2a1da651e9b959b7a07ea3623bf8d92f1c9428edbfbb865929e9 d7f5727c0fa73bf5ae4d1b875e20a91c8fd430c59d82b19c6db033f72a91010b c32a26180c92fea84e66743a72ef04134700de08b361e8b343a7eb11427b77b5 9c0be43483bb2c634f60caf1eeb3dccbd9392bc8e3fee769abe9056f07e58bca be1c1db9a58083c88a73f6ffa1355b8bb0c1da5dcae23e4c2ec1d055c4815ad9 303c99c60aacfbc244aa865617e38f77294a1d1b137d60fbe2babf3514819509 14525a358b39ac9a5d1d73c5714ca0bce844cc87556653103a193048321d37ec 4c9d01c5af39806761a1cb3b34074345acfb037a072267d3d4f7248e51f8c1c8 07f4df4f93b14e70cc5a2d67a753b494e923e9ada3cfffcfc267f08568fbba28 a71d9c03efe0491be5aec3a11d5a9f7029e7cb3be1e01ef73ddaf97fe0a9cc7d 0bf1ef19f900647c16d38dc21c9d6a9587a3e5e56776ddf87c96531cec5e5fee 7feec9f08a9f761a76f871c611cd07191ed90fda677b70f537ab6d13b9622cf9 cdac1eea0233e08309484ae5bd74119581768df03a23a84875fbf3e8e577a78f e3a9d6777e232ee2317deadc25b9f1cf2427e7d2d0c9cbf9c1d1ec86fdc420d9 564066bc3b43f3856370debb855f6de5aa54a03596044687b76e1fd24eb42065 0070e3a2df59c2269e5374fb877845f3111cc73f1ff48ab6f2c2cfae91b93963 597a127568d4d19a6b5e670ce4e9487036b0b721a0dcb84927bcb879d718d556 50d35bb686b2a3882c87466a7da3168499a656c9b2f9841d51c6d0929df62277 f933726a952ead57 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMMI8 %!PS-AdobeFont-1.1: CMMI8 1.100 %%CreationDate: 1996 Jul 23 07:53:54 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.100) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMMI8) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI8 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 18 /theta put dup 70 /F put dup 112 /p put dup 118 /v put dup 119 /w put readonly def /FontBBox{-24 -250 1110 750}readonly def /UniqueXX 5087383 def currentdict end currentfile eexec 80347982ab3942d930e069a70d0d48311d725e830d1c76fba12e12486e989c98 74c2b527f0925722787027f44470d484262c360cdfdddf3657533a57bb16f730 48bfbbfcb73a650484015441fdc837add94ac8fbd2022e3ec8f115d4b4bb7b7f 15388f22cc6198efe768bd9fceb3446ee4a8dc27d6cd152485384ef5f59381ff da43f2d20c8fb08aa27ab2015b774db10dacfdcd33e60f178c461553146ab427 bdd7da12534ba078ad3d780414930e72218b3075925ce1192f11fc8530fcd5e3 038e3a6a6db2dcfbae3b4653e7e02730314e02b54a1e296d2bef8a79411d9225 dad7b4e6d6f9cf0688b69ba21193bf1495807e7a196cf14c95a4e02f9cd2da8c db2546c6df52e524745992e18d9ff87aa25e4e1800bbe4ebb357c6ef55ed6d03 6d3a00c1ee8073266c21d2f0ac85d656abf61d7e5a4fa87da8ec3b5329e434d0 d2adab706b42a2e5331be5295399d803ccac03f631f01f39a022fcdf63486b68 7d15ef284a77def7fde4898543e7b5f7ec267756103e477f547cfb8d2311c4b0 09deff56085f5d419697af1846c8b88c1bbbae149f0f19ca3c8dafe19cec48fe 6b38357246d8b5cef80b53bab4cbbbe8bc8318cc462a4158258f456e697f6058 86010493f252073ee4e4c9531f23485415ad6bc901bbaea659ef701f825f4b6d 5c9bed0dce7b63810f906b33ea4955531ca1ed1fc120cc56dc1e277a33222cc6 c3a97552607b865783faf0895cbeccd0df54f57bd162a88494768435eda71a39 69718c0c5912d3167bb0971546d733e735aa9bcd89f5aa154656031ab3f6fe41 94ec225ad03ab8b67a9da43ab365c4df17c23e79f685c3b6fd5b654e4a6f2603 6cec3a8641b0b57f93eb95f9e238832aeac2061f3153e0f375513c974f1c38f7 b59edcc94716f2862cf71c9a2be8430985da1cd813b1e1c1b9310564a2eb1aff 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f2d48ff044f2160141f24c6612b0b13f16d72fec74ff109dd5786cfe9c2f125a fc124a483aba9938259e6d2d673d5240119e216eb0d19b330f1ae644cebb48b9 80ee434af8c8f08fa87dced65c30e9c061682f768924e45f7dba868680ab24a6 9ce2c84ee663448cfc2c81364f26618e1bdb6d88d93ca9af98f83b72f08e1ca0 cd36cbdd71df8e248ef2b4809450b2d8f0278923fe654a84ddbfc8cd95b6f643 5706a7774434972b7cd56594d8a3a915d7afe1bbf57192e6e1088d0a2e020371 7cbd1c52886a444883e5b4fe00fed42bf082853ebd1196c6f9c2921e20bfb797 3de64e5f25ce1a559af9a53f63bea6a94b1bee76d63af5227addc8e3f2810bdf f82482df6752e7ffe8bac6e81daa72051247a64cd8a321283b05985aacac9145 17ce14ad6324e598c38ff0ecfe3b8db05d9f6eb6b3c0471c34ac1cf8d9a6380b 9d23e45a372ad76beae61c808da495b7312f322bae0c52a312485e4569df0b8c 0d365b2e9c813851c10f0aab4adff3a6a2b2 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMMI6 %!PS-AdobeFont-1.1: CMMI6 1.100 %%CreationDate: 1996 Jul 23 07:53:52 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.100) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMMI6) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI6 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 12 /beta put dup 15 /epsilon1 put dup 61 /slash put dup 84 /T put dup 87 /W put dup 97 /a put dup 98 /b put dup 100 /d put dup 105 /i put dup 106 /j put dup 107 /k put dup 112 /p put dup 113 /q put dup 116 /t put dup 117 /u put dup 118 /v put dup 119 /w put dup 120 /x put dup 122 /z put readonly def /FontBBox{11 -250 1241 750}readonly def /UniqueXX 5087381 def currentdict end currentfile eexec 80347982ab3942d930e069a70d0d48311d725e830d1c76fba12e12486e989c98 74c2b527f0925722787027f44470d484262c360cdfdddf3657533a57bb16f730 48bfbbfcb73a650484015441fdc837add94ac8fbd2022e3ec8f115d4b4bb7b7f 15388f22cc6198efe768bd9fceb3446ee4a8dc27d6cd152485384ef5f59381ff da43f2d20c8fb08aa27ab2015b774db10dacfdcd33e60f178c461553146ab427 bdd7da12534ba078ad3d780414930e72218b3075925ce1192f11fc8530fcd5e3 038e3a6a6db2dcfbae3b4653e7e02730314e02b54a1e296d2bef8a79411d9225 dad7b4e6d6f9cf0688b69ba21193bf1495807e7a1e67ed7e41cc25acc04702f6 8ef703e3d45722c1a91fdef7100a48631a02a6f02a08c6b1f9b4df8310385b86 8632718fd87119a233f219d9411383b7fa9f3e4780d8c27e2e89e0cae883d664 c3eac57a3aef8988a2e9f0f8c7f53e0a80bdfc4620e21287d0390e1975398544 7f3ea66401024bea75e1b4c4437b7bb188f76f96b918ac7c6ad7e8ae7f21d8c2 790f08cccec904fe48ef39e597ed4d4237c1d1f596f5906b19ea308020f7a35c 168e327ec3246b1dfabe912f6b6daac09974876d3996e57d180261110db05f15 e3e8eebba3d90b5764c03df3033a1ed678ebc679569a2fb297378b25434c0f20 5313ecb8a952f07242d3ee731b0cdc086a4481178a3d65129c47c09b22e9c431 e11b3747b94c26a757c38d06001798c6a568303d541385244b967d3b1786edea f65bb53c4c2fe75e4b1b15c2c78d930b4296c80f08bad86012451edc8e9f0854 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07167b88d3b1175676255dd178f71922fa6d839323543a10dac94dc0d4247c7d ab5ac6332485a5cff6003a548cdd808f5b3883c1f990574f702cb2569d1d1b94 5e1af5a8d746c917824569ef011c9939f9e10dca40beedae421201ad65630c12 41c4eafaf1ac02ef2289b8528fa6f7be5b499218e2667e0f82c33b3a00460e71 2f7c4fde556b635bca1eba60b6c4370d4da2068a518a56200020a418df408df2 f33712af10bda9e6a06b4cdc0c1694124bf800cab6f5b9948a54d0c8d022f6ab ecebe179cc165badd5370abd1383b2aa54e10083d4bb023985eaf7cbecee4ffd 65fdfdde7ec99c228bcfa24245ea9d607ab5d0e8dec8b12a9d22afa8f44a6bf7 8931c68f345a988f01bc7ae1833c505cafd64e1898ef429f0b3f534079db6dce d564020fc60efd06c66c564ebca0c3be23bb55e560ab30e37fbcbafbdce3df44 1b91ebb24b865f21171e11484c5de2c2a8dcfc4e775b6cee3eafc072dd678d57 b27e4fb5a81c43ac8acf700653f6bcd7b3d04dd2d87e9d82edf5498ad8cb632e a9d13956cfae65de76dd8a67c180643899a4a5dc03f2f58d066152b5f2c629f1 dea05ede6e9576e18d05fe35227106b2cf2a11ea02df4778edaaf98fa8223ff6 aea4cfb6f3a94b301b04c1e22c70206c8cc85ff0613e07a1df91ee610da773ca 74810a7a85033ccfcd83846b76ab0c56d56010c2b390cf30cf0b763d293c32f9 f3274915aac728fa7a419906d4540b5f1bbb78b091ee5c480e1cdb578ae2edfb a8b7f9d766fad01bd1778767b1cf1af5bdd1355c1bda78f30f4d031968087ec0 34240bc052b03da333b3c0e3254d62706e3436e20dacc105d1599f09be8cd565 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMMI9 %!PS-AdobeFont-1.1: CMMI9 1.100 %%CreationDate: 1996 Jul 23 07:53:55 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.100) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMMI9) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI9 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 12 /beta put dup 13 /gamma put dup 15 /epsilon1 put dup 18 /theta put dup 21 /lambda put dup 22 /mu put dup 28 /tau put dup 30 /phi put dup 31 /chi put dup 58 /period put dup 59 /comma put dup 60 /less put dup 61 /slash put dup 62 /greater put dup 65 /A put dup 66 /B put dup 67 /C put dup 68 /D put dup 69 /E put dup 70 /F put dup 71 /G put dup 73 /I put dup 76 /L put dup 77 /M put dup 79 /O put dup 81 /Q put dup 82 /R put dup 84 /T put dup 86 /V put dup 87 /W put dup 88 /X put dup 96 /lscript put dup 97 /a put dup 98 /b put dup 99 /c put dup 100 /d put dup 102 /f put dup 103 /g put dup 104 /h put dup 105 /i put dup 106 /j 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68cc268d0ce29183b4c54e937ace82d86d453b0d1110510d398d13d56d08017e a9b2de1eb90271cc3e5e68313aa22e11bd68ac1f9a8204f0c5b7d2c33d142146 e5506f01b0413f58ff3acd67ced9474f0c1e58342c65043748ae6ae3a5b822ce bf4baf11c9e02dff242c1fe92c6ebe9a7fdeb753615c5ef524c4554ab24ec975 42cb8f30ffbab3e160f1b51ed34bfd2913d8793e680f37a449171b8559888ef1 546263edd8ff7cacc4d569 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMSY6 %!PS-AdobeFont-1.1: CMSY6 1.0 %%CreationDate: 1991 Aug 15 07:21:34 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSY6) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY6 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /minus put dup 14 /openbullet put dup 48 /prime put dup 50 /element put dup 54 /negationslash put dup 112 /radical put readonly def /FontBBox{-4 -948 1329 786}readonly def /UniqueXX 5000816 def currentdict end currentfile eexec 9b9c1569015f2c1d2bf560f4c0d52257bac8ced9b09a275ab231194ecf829352 05826f4e975dcecec72b2cf3a18899ccde1fd935d09d813b096cc6b83cdf4f23 b9a60db41f9976ac333263c908dcefcdbd4c8402ed00a36e7487634d089fd45a f4a38a56a4412c3b0baffaeb717bf0de9ffb7a8460bf475a6718b0c73c571145 d026957276530530a2fbefc6c8f059084178f5ab59e11b6a18979f258b8c6ed3 ccafbc21aca420c9c83eea371adc20e038b4d7b8ac303004b0aa205f04135140 76407216032fdd22e6219da8f16b28ca12524deb7bca073cc5eba65c102a5e85 fd48e6d062cd4283ee570a7774597e5bf0e3400b6be72db0115f3cb12db70ce0 83722870cddfadee715f10f1fcaf20e06f3c54afe5ca238539bfe2b596116e83 f5371ff18fa5003d8543226cfd4025f9940365b392a858d27f078d3abcffe4a1 54e78c7692d1a32bf935967c64f01b24788ff8325d61145e2d4a489fd986fb77 38e6b254522c77ca2797a504a9ce4676a77ebacb026eca94dde5922c936f8e90 c43e285193c6a23bfb15f4811c1e6bfeb0a0eb1ab6a3f0629c739721823fefb0 27a600be4755a103f761196118807d4a0f4d43db6905bbd669538debe505fbfd b5844ca395bd5f3093cd6aaca0c1f41a258b94d5e59168c32532b1fedebead78 29642e646f6835483c6b3ccafce21c00c05eb9c9548d931ae43e1888f01eb9c3 9d3cd5b15fc4c9921ac85a6e5e52cec74193c318a2d9da64adf100bca4fb8da0 2485144631669d8b85ef7b5111f0b565ee4a0bfc308f5ef4cebaa32cc7bc94f3 f757582182acead6709e1c027886572438f588ba93a64f1c3fad3a66bc6c44a7 21998f88cb773f4f5133449788f278b3c3f5c1dff7586c5947dbf4401051bd50 fb0940ccdce262fad65113a8db726b372ef7eaeb375f445623fdef14b1683445 fe65595d2fb84b76b538c757649d5bfa7f16ad888a847a0a5427dff9d8014e34 32e4bb5910f275ef517f5addd632d5497c731b0ec42981294fe925b71357d94d 1644c0120f6b6ab3a2e96b149c0dbe30df09b09cb57bd15e9addcd3693fe5991 d14301cd3fbdf5b6056b1063712f41f678415685bcb37f5307fae8a3578d9d83 ba68aebecaa5d3e467160b0f8e23ff0b40391b54247534644cb09b172f844132 7c3a4ff7600eaed95f82e2ba3a865cb8ead678150ab9e3b1450a2eeae77099e6 e356956202d1bd6470e5c4e1e49f970137631629419eb8636c405f6a0677e630 1e0d6ff59cf734537e4f4f2f7ab907fe87adc12cbc9be83df2cb453949e19cff 60dc54464c572181e4742d70c4ba93c8d25f11bcb6729ae0fa671d16ae9b1b85 491a17f1ebee3f9cf541b396b48b42eeb46e61180294e50567e4d676551c78c4 38516459fcfc577139450fcb76057e12c702ef8499391ed67bf9ffeea3c50499 59e40f97ddb2f48f5ef645c042156dc574682e9ee0795bdf4dc2802e4946b1b5 537b586d27a33a98848c981962636cc46d67d4918063c7778c4dc26b55e2d50a e81ce5eaff89465e5ad63fb316b4be0645a18818ba0a73c8cbecd81deef44158 ff73abdb05a03f18e84c69bf47f868ae7f2392975eff0343ac56cd0545201f3c cc8b054ed2e9d12a7a6b3095370144 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMR9 %!PS-AdobeFont-1.1: CMR9 1.0 %%CreationDate: 1991 Aug 20 16:39:59 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR9) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR9 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 10 /Omega put dup 40 /parenleft put dup 41 /parenright put dup 43 /plus put dup 48 /zero put dup 49 /one put dup 50 /two put dup 51 /three put dup 54 /six put dup 55 /seven put dup 56 /eight put dup 57 /nine put dup 58 /colon put dup 61 /equal put dup 86 /V put dup 91 /bracketleft put dup 93 /bracketright put dup 97 /a put dup 98 /b put dup 99 /c put dup 100 /d put dup 101 /e put dup 102 /f put dup 103 /g put dup 105 /i put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 114 /r put dup 115 /s put dup 116 /t put dup 119 /w put dup 120 /x put readonly def /FontBBox{-39 -250 1036 750}readonly def /UniqueXX 5000792 def currentdict end currentfile eexec 9b9c1569015f2c1d2bf560f4c0d52257bacdd6500abda5ed9835f6a016cfc8f0 0b6c052ed76a87856b50f4d80dfaeb508c97f8281f3f88b17e4d3b90c0f65ec3 79791aacdc162a66cbbc5be2f53aad8de72dd113b55a022fbfee658cb95f5bb3 2ba0357b5e050fddf264a07470bef1c52119b6fbd5c77ebed964ac5a2bbec9d8 b3e48ae5bb003a63d545774b922b9d5ff6b0066ece43645a131879b032137d6d 823385fe55f3402d557fd3b448685bdd20eb05d5e7c2126132e33a59a7170609 dcf4871a5d023c9ef57d3362d9f2d7a440bb69bf653364105f16f4d0f03582f9 aced3d05cc76489b16e3fa8a446094d30038b06ecceda269f2eab9d19a99c7f9 39f9548f206c5a457a19270b2b82c43b091dfc5573468eaa3e7a4a32f8042891 d85e4b180fcbcb3091d2800e54c87d84ce9cad6869b5aabbbe47f40c68799893 d22b765295e1e69e33aa048b7ed98ba480ceca91f3ebf8ef85fe9a3976909626 b95ac5940d53f9b02215d84a44837ba25ed15cce0d504f1d335065594f3bc824 5405407591cccb11cfd4645da60d960c0b93f187b0cf7b105543c0b70f89af5d 264b6c026e3ae646acf145950202ec73282111e3e601cf2bcde22ce3edf6db23 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566.714 399.116 550.068 399.117 533.423 curveto closepath fill 0.116 0.882 0.059 setrgbcolor 287.723 655.048 moveto 287.582 656.352 287.438 657.683 287.292 659.041 curveto 286.878 658.324 286.468 657.821 286.060 657.532 curveto 285.856 657.387 285.652 657.296 285.448 657.257 curveto 285.276 657.225 285.105 657.231 284.934 657.274 curveto 284.718 657.328 284.501 657.442 284.284 657.617 curveto 283.851 654.358 283.435 651.314 283.036 648.471 curveto 282.673 639.474 282.352 630.601 282.072 621.829 curveto 282.846 611.674 283.517 601.927 284.091 592.505 curveto 284.393 592.448 284.694 592.433 284.996 592.460 curveto 285.313 592.488 285.631 592.562 285.949 592.683 curveto 286.436 595.716 286.946 598.910 287.481 602.275 curveto 287.542 619.860 287.622 637.450 287.723 655.048 curveto closepath fill 0.138 0.868 0.088 setrgbcolor 281.061 683.748 moveto 281.281 676.187 281.483 668.691 281.665 661.249 curveto 282.150 656.689 282.605 652.438 283.036 648.471 curveto 283.435 651.314 283.851 654.358 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708.986 204.080 743.580 curveto stroke 210.792 598.103 moveto 208.991 609.846 206.884 623.568 204.384 639.824 curveto stroke 219.886 614.601 moveto 217.607 606.959 215.525 602.100 213.527 599.759 curveto 212.965 599.101 212.409 598.641 211.855 598.375 curveto 211.500 598.204 211.146 598.114 210.792 598.103 curveto stroke 219.561 743.580 moveto 219.719 700.576 219.827 657.585 219.886 614.601 curveto stroke 172.090 573.655 moveto 168.272 611.272 161.611 662.099 149.819 743.580 curveto stroke 171.592 549.708 moveto 162.698 525.216 156.076 511.658 150.251 506.011 curveto 148.789 504.593 147.361 503.659 145.949 503.195 curveto 144.960 502.870 143.977 502.775 142.992 502.909 curveto 141.853 503.064 140.709 503.526 139.551 504.298 curveto 137.007 505.992 134.367 509.201 131.517 514.058 curveto stroke 191.711 515.908 moveto 189.983 476.350 189.054 436.990 188.918 397.673 curveto stroke 171.592 549.708 moveto 179.468 531.277 185.865 520.530 191.711 515.908 curveto stroke 187.380 392.720 moveto 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moveto 352.680 397.788 360.302 390.165 367.208 383.260 curveto stroke 344.223 406.245 moveto 348.224 416.239 352.771 426.526 357.893 437.163 curveto stroke 367.208 383.260 moveto 379.818 378.673 391.720 375.985 403.390 375.088 curveto 413.975 374.275 424.490 374.926 435.281 377.062 curveto stroke 374.349 342.709 moveto 398.545 343.122 423.146 346.903 449.843 354.313 curveto stroke 320.191 324.681 moveto 336.972 329.508 354.890 335.472 374.349 342.709 curveto stroke 297.334 330.439 moveto 299.576 333.865 301.926 337.317 304.384 340.796 curveto stroke 307.611 325.789 moveto 304.253 327.295 300.828 328.845 297.334 330.439 curveto stroke 280.024 328.218 moveto 285.741 328.820 291.506 329.560 297.334 330.439 curveto stroke 280.024 328.218 moveto 276.590 320.456 273.480 312.732 270.692 305.040 curveto stroke 131.517 361.055 moveto 179.188 344.903 219.658 337.515 259.262 337.737 curveto stroke 270.692 305.040 moveto 226.106 303.972 181.355 308.313 131.517 318.540 curveto stroke 270.692 305.040 moveto 277.466 303.123 284.075 301.324 290.535 299.640 curveto stroke 131.517 285.161 moveto 182.737 278.515 230.440 275.839 278.237 276.931 curveto stroke 281.598 254.357 moveto 232.319 253.477 183.172 255.292 131.517 259.898 curveto stroke 131.517 239.515 moveto 176.753 236.574 220.537 235.202 264.191 235.357 curveto stroke 289.221 219.527 moveto 237.043 218.860 185.039 219.836 131.517 222.487 curveto stroke 297.535 212.697 moveto 294.844 214.970 292.073 217.246 289.221 219.527 curveto stroke 297.535 212.697 moveto 357.971 211.919 418.179 213.087 480.483 216.249 curveto stroke 290.319 205.548 moveto 292.648 207.928 295.054 210.311 297.535 212.697 curveto stroke 307.442 200.952 moveto 301.849 202.469 296.142 204.001 290.319 205.548 curveto stroke 131.517 207.862 moveto 185.207 205.768 237.688 205.003 290.319 205.548 curveto stroke 296.968 193.147 moveto 242.042 192.596 187.305 193.194 131.517 194.954 curveto stroke 131.517 183.385 moveto 185.490 181.985 238.646 181.480 291.913 181.862 curveto stroke 275.333 167.609 moveto 227.571 167.470 179.808 167.892 131.517 168.880 curveto stroke 289.602 151.626 moveto 295.718 152.262 301.884 152.904 308.104 153.554 curveto stroke 312.465 140.829 moveto 305.200 144.419 297.579 148.017 289.602 151.626 curveto stroke 305.492 140.194 moveto 247.576 139.913 189.777 140.141 131.517 140.879 curveto stroke 131.517 132.735 moveto 184.771 132.148 237.684 131.932 290.639 132.086 curveto stroke 281.771 124.147 moveto 231.767 124.054 181.777 124.249 131.517 124.733 curveto stroke 297.899 122.484 moveto 292.561 123.035 287.185 123.589 281.771 124.147 curveto stroke 297.899 122.484 moveto 358.616 122.354 419.314 122.635 480.483 123.330 curveto stroke 285.159 116.099 moveto 289.287 118.226 293.534 120.354 297.899 122.484 curveto stroke 285.159 116.099 moveto 286.820 115.973 288.478 115.848 290.133 115.722 curveto stroke 294.544 108.291 moveto 240.007 107.824 185.757 107.615 131.517 107.664 curveto stroke 296.756 107.367 moveto 296.021 107.675 295.284 107.983 294.544 108.291 curveto stroke 331.216 103.280 moveto 319.931 104.632 308.445 105.994 296.756 107.367 curveto stroke 296.756 107.367 moveto 292.314 105.970 287.951 104.575 283.667 103.182 curveto stroke 283.667 103.182 moveto 288.196 102.388 292.678 101.595 297.113 100.804 curveto stroke 283.667 103.182 moveto 232.813 102.826 182.164 102.674 131.517 102.724 curveto stroke 131.517 99.829 moveto 181.547 99.768 231.568 99.899 281.769 100.221 curveto stroke 159.343 92.530 moveto 150.054 92.415 140.779 92.305 131.517 92.202 curveto stroke 307.695 89.131 moveto 248.932 88.920 190.288 88.924 131.517 89.143 curveto stroke 308.902 86.764 moveto 249.741 86.561 190.696 86.572 131.517 86.798 curveto stroke 131.517 85.221 moveto 190.776 85.019 249.915 85.016 309.163 85.211 curveto stroke 131.517 80.968 moveto 190.257 80.764 248.877 80.747 307.592 80.918 curveto stroke 307.592 80.918 moveto 365.396 80.551 422.958 80.365 480.483 80.360 curveto stroke 307.592 80.918 moveto 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86.262 309.788 85.761 310.226 85.260 curveto stroke 309.163 85.211 moveto 309.518 85.227 309.872 85.243 310.226 85.260 curveto stroke 301.100 108.819 moveto 360.496 109.097 420.168 109.688 480.483 110.595 curveto stroke 480.483 117.863 moveto 416.363 116.749 353.078 116.038 290.133 115.722 curveto stroke 290.133 115.722 moveto 293.898 113.420 297.554 111.119 301.100 108.819 curveto stroke 301.100 108.819 moveto 298.909 108.643 296.724 108.466 294.544 108.291 curveto stroke 131.517 116.600 moveto 182.887 116.172 234.014 116.006 285.159 116.099 curveto stroke 303.911 130.441 moveto 363.062 129.728 421.749 129.459 480.483 129.633 curveto stroke 480.483 139.799 moveto 424.640 139.662 368.810 140.004 312.465 140.829 curveto stroke 312.465 140.829 moveto 310.135 140.617 307.810 140.405 305.492 140.194 curveto stroke 305.492 140.194 moveto 300.368 137.488 295.417 134.786 290.639 132.086 curveto stroke 290.639 132.086 moveto 295.095 131.535 299.519 130.987 303.911 130.441 curveto stroke 281.771 124.147 moveto 288.949 126.238 296.329 128.337 303.911 130.441 curveto stroke 131.517 152.544 moveto 184.511 151.722 237.029 151.417 289.602 151.626 curveto stroke 308.104 153.554 moveto 365.425 153.264 422.648 153.606 480.483 154.584 curveto stroke 299.621 163.363 moveto 358.925 164.008 418.891 165.469 480.483 167.768 curveto stroke 311.057 174.306 moveto 367.275 174.001 423.429 174.566 480.483 176.012 curveto stroke 311.057 174.306 moveto 304.887 176.813 298.506 179.331 291.913 181.862 curveto stroke 303.432 185.974 moveto 363.351 183.943 421.921 183.076 480.483 183.353 curveto stroke 303.432 185.974 moveto 302.549 187.971 301.643 189.968 300.714 191.965 curveto stroke 300.714 191.965 moveto 360.403 191.271 419.809 191.901 480.483 193.872 curveto stroke 307.442 200.952 moveto 363.317 202.326 420.463 205.113 480.483 209.391 curveto stroke 296.968 193.147 moveto 300.341 195.744 303.832 198.345 307.442 200.952 curveto stroke 300.714 191.965 moveto 299.472 192.359 298.223 192.752 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562.837 256.499 559.790 curveto 257.644 558.665 258.773 557.876 259.893 557.419 curveto 260.674 557.101 261.451 556.943 262.228 556.944 curveto stroke 262.228 556.944 moveto 262.832 560.849 263.469 564.850 264.140 568.955 curveto stroke 264.140 568.955 moveto 264.059 589.495 263.951 610.039 263.816 630.587 curveto stroke 263.816 630.587 moveto 262.755 627.879 261.728 626.092 260.716 625.193 curveto 260.352 624.869 259.989 624.660 259.627 624.565 curveto 259.351 624.493 259.075 624.487 258.799 624.548 curveto 258.453 624.624 258.106 624.804 257.758 625.089 curveto 256.880 625.809 255.991 627.199 255.079 629.277 curveto stroke 255.079 629.277 moveto 254.451 665.933 253.359 703.682 251.771 743.580 curveto stroke 264.683 639.961 moveto 264.382 636.767 264.093 633.644 263.816 630.587 curveto stroke 263.995 743.580 moveto 264.323 708.926 264.552 674.408 264.683 639.961 curveto stroke 262.066 517.756 moveto 262.110 530.818 262.164 543.881 262.228 556.944 curveto stroke 262.066 517.756 moveto 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651.013 293.116 648.791 curveto stroke 300.836 597.234 moveto 300.266 597.552 299.693 598.069 299.114 598.785 curveto 297.172 601.189 295.147 605.873 292.940 613.067 curveto stroke 291.313 660.951 moveto 290.517 658.499 289.744 656.823 288.982 655.898 curveto 288.725 655.585 288.468 655.358 288.212 655.216 curveto 288.049 655.125 287.886 655.069 287.723 655.048 curveto stroke 291.313 660.951 moveto 291.299 668.615 291.282 676.279 291.264 683.944 curveto stroke 290.569 697.977 moveto 290.537 713.175 290.499 728.375 290.454 743.580 curveto stroke 287.195 743.580 moveto 287.248 726.128 287.292 708.681 287.328 691.239 curveto stroke 283.836 698.114 moveto 283.802 713.266 283.761 728.421 283.712 743.580 curveto stroke 281.061 683.748 moveto 280.773 685.629 280.479 687.672 280.176 689.883 curveto stroke 281.665 661.249 moveto 281.483 668.691 281.281 676.187 281.061 683.748 curveto stroke 280.176 689.883 moveto 279.722 685.631 279.290 681.749 278.879 678.209 curveto stroke 278.879 678.209 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lineto 540 587 lineto 72 587 lineto closepath clip newpath 452 474 moveto 443 473 lineto 455 457 lineto 452 474 lineto stroke 450 454 moveto 455 457 lineto 443 473 lineto 450 454 lineto stroke 455 457 moveto 469 445 lineto 452 474 lineto 455 457 lineto stroke 461 476 moveto 452 474 lineto 469 445 lineto 461 476 lineto stroke 455 457 moveto 459 437 lineto 469 445 lineto 455 457 lineto stroke 469 405 moveto 469 445 lineto 459 437 lineto 469 405 lineto stroke 444 442 moveto 459 437 lineto 450 454 lineto 444 442 lineto stroke 455 457 moveto 450 454 lineto 459 437 lineto 455 457 lineto stroke 437 472 moveto 450 454 lineto 443 473 lineto 437 472 lineto stroke 442 453 moveto 450 454 lineto 437 472 lineto 442 453 lineto stroke 435 463 moveto 437 472 lineto 432 471 lineto 435 463 lineto stroke 430 471 moveto 435 463 lineto 432 471 lineto 430 471 lineto stroke 442 453 moveto 437 472 lineto 435 463 lineto 442 453 lineto stroke 428 470 moveto 435 463 lineto 430 471 lineto 428 470 lineto stroke 423 462 moveto 428 470 lineto 420 478 lineto 423 462 lineto stroke 426 476 moveto 420 478 lineto 428 470 lineto 426 476 lineto stroke 406 496 moveto 412 482 lineto 420 478 lineto 406 496 lineto stroke 423 462 moveto 420 478 lineto 412 482 lineto 423 462 lineto stroke 388 509 moveto 412 482 lineto 406 496 lineto 388 509 lineto stroke 419 488 moveto 406 496 lineto 420 478 lineto 419 488 lineto stroke 412 500 moveto 406 496 lineto 419 488 lineto 412 500 lineto stroke 426 476 moveto 419 488 lineto 420 478 lineto 426 476 lineto stroke 395 513 moveto 406 496 lineto 412 500 lineto 395 513 lineto stroke 395 513 moveto 412 500 lineto 402 516 lineto 395 513 lineto stroke 366 537 moveto 402 516 lineto 393 530 lineto 366 537 lineto stroke 356 558 moveto 366 537 lineto 393 530 lineto 356 558 lineto stroke 327 541 moveto 366 537 lineto 331 555 lineto 327 541 lineto stroke 356 558 moveto 331 555 lineto 366 537 lineto 356 558 lineto stroke 327 541 moveto 331 555 lineto 295 554 lineto 327 541 lineto stroke 297 562 moveto 295 554 lineto 331 555 lineto 297 562 lineto stroke 266 536 moveto 327 541 lineto 295 554 lineto 266 536 lineto stroke 354 528 moveto 327 541 lineto 326 529 lineto 354 528 lineto stroke 285 528 moveto 326 529 lineto 327 541 lineto 285 528 lineto stroke 314 515 moveto 326 529 lineto 285 528 lineto 314 515 lineto stroke 250 513 moveto 275 506 lineto 285 528 lineto 250 513 lineto stroke 314 515 moveto 285 528 lineto 275 506 lineto 314 515 lineto stroke 250 513 moveto 235 483 lineto 275 506 lineto 250 513 lineto stroke 262 482 moveto 275 506 lineto 235 483 lineto 262 482 lineto stroke 250 513 moveto 216 483 lineto 235 483 lineto 250 513 lineto stroke 209 458 moveto 235 483 lineto 216 483 lineto 209 458 lineto stroke 192 455 moveto 216 483 lineto 213 498 lineto 192 455 lineto stroke 250 513 moveto 213 498 lineto 216 483 lineto 250 513 lineto stroke 213 513 moveto 213 498 lineto 240 521 lineto 213 513 lineto stroke 250 513 moveto 240 521 lineto 213 498 lineto 250 513 lineto stroke 213 513 moveto 240 521 lineto 234 530 lineto 213 513 lineto stroke 266 536 moveto 234 530 lineto 240 521 lineto 266 536 lineto stroke 263 555 moveto 234 530 lineto 266 536 lineto 263 555 lineto stroke 285 528 moveto 266 536 lineto 240 521 lineto 285 528 lineto stroke 327 541 moveto 266 536 lineto 285 528 lineto 327 541 lineto stroke 263 555 moveto 266 536 lineto 295 554 lineto 263 555 lineto stroke 297 562 moveto 263 555 lineto 295 554 lineto 297 562 lineto stroke 271 568 moveto 263 555 lineto 297 562 lineto 271 568 lineto stroke 316 567 moveto 300 570 lineto 297 562 lineto 316 567 lineto stroke 271 568 moveto 297 562 lineto 300 570 lineto 271 568 lineto stroke 356 558 moveto 316 567 lineto 331 555 lineto 356 558 lineto stroke 297 562 moveto 331 555 lineto 316 567 lineto 297 562 lineto stroke 345 569 moveto 316 567 lineto 356 558 lineto 345 569 lineto stroke 396 549 moveto 356 558 lineto 393 530 lineto 396 549 lineto stroke 366 561 moveto 356 558 lineto 396 549 lineto 366 561 lineto stroke 388 558 moveto 396 549 lineto 397 552 lineto 388 558 lineto stroke 470 464 moveto 463 481 lineto 461 476 lineto 470 464 lineto stroke 470 464 moveto 461 476 lineto 469 445 lineto 470 464 lineto stroke 478 452 moveto 470 464 lineto 469 445 lineto 478 452 lineto stroke 470 481 moveto 470 464 lineto 478 452 lineto 470 481 lineto stroke 482 464 moveto 478 452 lineto 486 445 lineto 482 464 lineto stroke 488 403 moveto 486 445 lineto 478 452 lineto 488 403 lineto stroke 495 446 moveto 486 445 lineto 503 398 lineto 495 446 lineto stroke 488 403 moveto 503 398 lineto 486 445 lineto 488 403 lineto stroke 513 385 moveto 503 398 lineto 495 344 lineto 513 385 lineto stroke 488 403 moveto 495 344 lineto 503 398 lineto 488 403 lineto stroke 480 354 moveto 495 344 lineto 488 403 lineto 480 354 lineto stroke 469 445 moveto 469 405 lineto 488 403 lineto 469 445 lineto stroke 469 362 moveto 488 403 lineto 469 405 lineto 469 362 lineto stroke 454 366 moveto 469 405 lineto 456 400 lineto 454 366 lineto stroke 459 437 moveto 456 400 lineto 469 405 lineto 459 437 lineto stroke 454 366 moveto 456 400 lineto 445 373 lineto 454 366 lineto stroke 441 418 moveto 445 373 lineto 456 400 lineto 441 418 lineto stroke 432 336 moveto 454 366 lineto 445 373 lineto 432 336 lineto stroke 432 336 moveto 447 336 lineto 454 366 lineto 432 336 lineto stroke 469 362 moveto 454 366 lineto 447 336 lineto 469 362 lineto stroke 428 283 moveto 447 336 lineto 410 302 lineto 428 283 lineto stroke 432 336 moveto 410 302 lineto 447 336 lineto 432 336 lineto stroke 424 353 moveto 392 310 lineto 410 302 lineto 424 353 lineto stroke 355 269 moveto 410 302 lineto 392 310 lineto 355 269 lineto stroke 369 322 moveto 338 283 lineto 392 310 lineto 369 322 lineto stroke 355 269 moveto 392 310 lineto 338 283 lineto 355 269 lineto stroke 355 269 moveto 338 283 lineto 302 273 lineto 355 269 lineto stroke 308 285 moveto 302 273 lineto 338 283 lineto 308 285 lineto stroke 270 275 moveto 302 273 lineto 308 285 lineto 270 275 lineto stroke 314 300 moveto 308 285 lineto 338 283 lineto 314 300 lineto stroke 271 300 moveto 308 285 lineto 314 300 lineto 271 300 lineto stroke 369 322 moveto 302 328 lineto 314 300 lineto 369 322 lineto stroke 292 312 moveto 314 300 lineto 302 328 lineto 292 312 lineto stroke 369 322 moveto 343 356 lineto 302 328 lineto 369 322 lineto stroke 288 358 moveto 302 328 lineto 343 356 lineto 288 358 lineto stroke 312 398 moveto 343 356 lineto 350 397 lineto 312 398 lineto stroke 383 369 moveto 350 397 lineto 343 356 lineto 383 369 lineto stroke 383 369 moveto 377 434 lineto 350 397 lineto 383 369 lineto stroke 336 442 moveto 350 397 lineto 377 434 lineto 336 442 lineto stroke 396 437 moveto 377 434 lineto 401 403 lineto 396 437 lineto stroke 383 369 moveto 401 403 lineto 377 434 lineto 383 369 lineto stroke 415 422 moveto 396 437 lineto 401 403 lineto 415 422 lineto stroke 401 456 moveto 372 480 lineto 396 437 lineto 401 456 lineto stroke 363 469 moveto 396 437 lineto 372 480 lineto 363 469 lineto stroke 339 488 moveto 363 469 lineto 372 480 lineto 339 488 lineto stroke 329 476 moveto 363 469 lineto 339 488 lineto 329 476 lineto stroke 341 502 moveto 339 488 lineto 372 480 lineto 341 502 lineto stroke 303 500 moveto 339 488 lineto 341 502 lineto 303 500 lineto stroke 362 511 moveto 341 502 lineto 372 480 lineto 362 511 lineto stroke 314 515 moveto 341 502 lineto 362 511 lineto 314 515 lineto stroke 326 529 moveto 362 511 lineto 354 528 lineto 326 529 lineto stroke 388 509 moveto 354 528 lineto 362 511 lineto 388 509 lineto stroke 395 513 moveto 354 528 lineto 388 509 lineto 395 513 lineto stroke 362 511 moveto 398 485 lineto 388 509 lineto 362 511 lineto stroke 412 482 moveto 388 509 lineto 398 485 lineto 412 482 lineto stroke 362 511 moveto 372 480 lineto 398 485 lineto 362 511 lineto stroke 401 456 moveto 398 485 lineto 372 480 lineto 401 456 lineto stroke 423 462 moveto 398 485 lineto 401 456 lineto 423 462 lineto stroke 396 437 moveto 415 422 lineto 401 456 lineto 396 437 lineto stroke 426 433 moveto 401 456 lineto 415 422 lineto 426 433 lineto stroke 407 375 moveto 415 422 lineto 401 403 lineto 407 375 lineto stroke 433 393 moveto 415 422 lineto 407 375 lineto 433 393 lineto stroke 383 369 moveto 407 375 lineto 401 403 lineto 383 369 lineto stroke 369 322 moveto 407 375 lineto 383 369 lineto 369 322 lineto stroke 369 322 moveto 383 369 lineto 343 356 lineto 369 322 lineto stroke 338 283 moveto 369 322 lineto 314 300 lineto 338 283 lineto stroke 407 375 moveto 369 322 lineto 392 310 lineto 407 375 lineto stroke 424 353 moveto 407 375 lineto 392 310 lineto 424 353 lineto stroke 433 393 moveto 407 375 lineto 424 353 lineto 433 393 lineto stroke 432 336 moveto 424 353 lineto 410 302 lineto 432 336 lineto stroke 445 373 moveto 424 353 lineto 432 336 lineto 445 373 lineto stroke 433 393 moveto 424 353 lineto 445 373 lineto 433 393 lineto stroke 441 418 moveto 433 393 lineto 445 373 lineto 441 418 lineto stroke 426 433 moveto 433 393 lineto 441 418 lineto 426 433 lineto stroke 437 441 moveto 441 418 lineto 444 442 lineto 437 441 lineto stroke 456 400 moveto 444 442 lineto 441 418 lineto 456 400 lineto stroke 459 437 moveto 444 442 lineto 456 400 lineto 459 437 lineto stroke 442 453 moveto 444 442 lineto 450 454 lineto 442 453 lineto stroke 437 455 moveto 444 442 lineto 442 453 lineto 437 455 lineto stroke 437 455 moveto 442 453 lineto 435 463 lineto 437 455 lineto stroke 428 470 moveto 437 455 lineto 435 463 lineto 428 470 lineto stroke 423 462 moveto 437 455 lineto 428 470 lineto 423 462 lineto stroke 437 441 moveto 437 455 lineto 423 462 lineto 437 441 lineto stroke 398 485 moveto 423 462 lineto 412 482 lineto 398 485 lineto stroke 426 433 moveto 423 462 lineto 401 456 lineto 426 433 lineto stroke 437 441 moveto 423 462 lineto 426 433 lineto 437 441 lineto stroke 433 393 moveto 426 433 lineto 415 422 lineto 433 393 lineto stroke 437 441 moveto 426 433 lineto 441 418 lineto 437 441 lineto stroke 437 455 moveto 437 441 lineto 444 442 lineto 437 455 lineto stroke 395 513 moveto 388 509 lineto 406 496 lineto 395 513 lineto stroke 366 537 moveto 354 528 lineto 395 513 lineto 366 537 lineto stroke 366 537 moveto 395 513 lineto 402 516 lineto 366 537 lineto stroke 327 541 moveto 354 528 lineto 366 537 lineto 327 541 lineto stroke 314 515 moveto 362 511 lineto 326 529 lineto 314 515 lineto stroke 303 500 moveto 341 502 lineto 314 515 lineto 303 500 lineto stroke 303 500 moveto 314 515 lineto 275 506 lineto 303 500 lineto stroke 262 482 moveto 303 500 lineto 275 506 lineto 262 482 lineto stroke 298 475 moveto 303 500 lineto 262 482 lineto 298 475 lineto stroke 228 459 moveto 262 482 lineto 235 483 lineto 228 459 lineto stroke 237 437 moveto 262 482 lineto 228 459 lineto 237 437 lineto stroke 207 421 moveto 237 437 lineto 228 459 lineto 207 421 lineto stroke 207 421 moveto 214 397 lineto 237 437 lineto 207 421 lineto stroke 235 396 moveto 237 437 lineto 214 397 lineto 235 396 lineto stroke 235 396 moveto 214 397 lineto 226 365 lineto 235 396 lineto stroke 208 381 moveto 226 365 lineto 214 397 lineto 208 381 lineto stroke 237 328 moveto 226 365 lineto 218 353 lineto 237 328 lineto stroke 208 381 moveto 218 353 lineto 226 365 lineto 208 381 lineto stroke 227 323 moveto 237 328 lineto 218 353 lineto 227 323 lineto stroke 292 312 moveto 237 328 lineto 271 300 lineto 292 312 lineto stroke 227 323 moveto 271 300 lineto 237 328 lineto 227 323 lineto stroke 270 275 moveto 308 285 lineto 271 300 lineto 270 275 lineto stroke 292 312 moveto 271 300 lineto 314 300 lineto 292 312 lineto stroke 261 338 moveto 292 312 lineto 302 328 lineto 261 338 lineto stroke 237 328 moveto 292 312 lineto 261 338 lineto 237 328 lineto stroke 288 358 moveto 261 338 lineto 302 328 lineto 288 358 lineto stroke 248 366 moveto 261 338 lineto 288 358 lineto 248 366 lineto stroke 312 398 moveto 288 358 lineto 343 356 lineto 312 398 lineto stroke 260 397 moveto 288 358 lineto 312 398 lineto 260 397 lineto stroke 284 423 moveto 260 397 lineto 312 398 lineto 284 423 lineto stroke 263 437 moveto 260 397 lineto 284 423 lineto 263 437 lineto stroke 316 430 moveto 284 423 lineto 312 398 lineto 316 430 lineto stroke 301 448 moveto 284 423 lineto 316 430 lineto 301 448 lineto stroke 301 448 moveto 316 430 lineto 336 442 lineto 301 448 lineto stroke 350 397 moveto 336 442 lineto 316 430 lineto 350 397 lineto stroke 377 434 moveto 348 455 lineto 336 442 lineto 377 434 lineto stroke 319 465 moveto 336 442 lineto 348 455 lineto 319 465 lineto stroke 329 476 moveto 319 465 lineto 348 455 lineto 329 476 lineto stroke 329 476 moveto 298 475 lineto 319 465 lineto 329 476 lineto stroke 301 448 moveto 319 465 lineto 298 475 lineto 301 448 lineto stroke 301 448 moveto 298 475 lineto 266 459 lineto 301 448 lineto stroke 262 482 moveto 266 459 lineto 298 475 lineto 262 482 lineto stroke 237 437 moveto 266 459 lineto 262 482 lineto 237 437 lineto stroke 263 437 moveto 266 459 lineto 237 437 lineto 263 437 lineto stroke 301 448 moveto 266 459 lineto 263 437 lineto 301 448 lineto stroke 235 396 moveto 263 437 lineto 237 437 lineto 235 396 lineto stroke 260 397 moveto 263 437 lineto 235 396 lineto 260 397 lineto stroke 248 366 moveto 235 396 lineto 226 365 lineto 248 366 lineto stroke 260 397 moveto 235 396 lineto 248 366 lineto 260 397 lineto stroke 260 397 moveto 248 366 lineto 288 358 lineto 260 397 lineto stroke 261 338 moveto 248 366 lineto 226 365 lineto 261 338 lineto stroke 301 448 moveto 263 437 lineto 284 423 lineto 301 448 lineto stroke 319 465 moveto 301 448 lineto 336 442 lineto 319 465 lineto stroke 303 500 moveto 298 475 lineto 329 476 lineto 303 500 lineto stroke 303 500 moveto 329 476 lineto 339 488 lineto 303 500 lineto stroke 363 469 moveto 329 476 lineto 348 455 lineto 363 469 lineto stroke 363 469 moveto 348 455 lineto 377 434 lineto 363 469 lineto stroke 350 397 moveto 316 430 lineto 312 398 lineto 350 397 lineto stroke 237 328 moveto 261 338 lineto 226 365 lineto 237 328 lineto stroke 235 300 moveto 271 300 lineto 227 323 lineto 235 300 lineto stroke 209 335 moveto 227 323 lineto 218 353 lineto 209 335 lineto stroke 214 323 moveto 227 323 lineto 209 335 lineto 214 323 lineto stroke 201 379 moveto 209 335 lineto 218 353 lineto 201 379 lineto stroke 218 353 moveto 208 381 lineto 201 379 lineto 218 353 lineto stroke 205 395 moveto 208 381 lineto 214 397 lineto 205 395 lineto stroke 209 458 moveto 192 425 lineto 207 421 lineto 209 458 lineto stroke 192 455 moveto 180 423 lineto 192 425 lineto 192 455 lineto stroke 179 445 moveto 180 423 lineto 192 455 lineto 179 445 lineto stroke 189 482 moveto 192 455 lineto 213 498 lineto 189 482 lineto stroke 179 445 moveto 192 455 lineto 189 482 lineto 179 445 lineto stroke 213 513 moveto 189 482 lineto 213 498 lineto 213 513 lineto stroke 185 497 moveto 189 482 lineto 213 513 lineto 185 497 lineto stroke 212 523 moveto 213 513 lineto 234 530 lineto 212 523 lineto stroke 185 497 moveto 213 513 lineto 212 523 lineto 185 497 lineto stroke 178 511 moveto 185 497 lineto 212 523 lineto 178 511 lineto stroke 168 459 moveto 189 482 lineto 185 497 lineto 168 459 lineto stroke 153 473 moveto 185 497 lineto 178 511 lineto 153 473 lineto stroke 168 519 moveto 153 473 lineto 178 511 lineto 168 519 lineto stroke 128 453 moveto 153 473 lineto 168 519 lineto 128 453 lineto stroke 199 544 moveto 168 519 lineto 178 511 lineto 199 544 lineto stroke 202 567 moveto 168 519 lineto 199 544 lineto 202 567 lineto stroke 223 548 moveto 235 565 lineto 199 544 lineto 223 548 lineto stroke 202 567 moveto 199 544 lineto 235 565 lineto 202 567 lineto stroke 329 578 moveto 338 577 lineto 333 582 lineto 329 578 lineto stroke 325 575 moveto 338 577 lineto 329 578 lineto 325 575 lineto stroke 338 577 moveto 325 575 lineto 345 569 lineto 338 577 lineto stroke 316 567 moveto 345 569 lineto 325 575 lineto 316 567 lineto stroke 396 549 moveto 388 558 lineto 366 561 lineto 396 549 lineto stroke 378 564 moveto 366 561 lineto 388 558 lineto 378 564 lineto stroke 392 561 moveto 388 558 lineto 398 556 lineto 392 561 lineto stroke 397 552 moveto 398 556 lineto 388 558 lineto 397 552 lineto stroke 463 481 moveto 470 464 lineto 470 481 lineto 463 481 lineto stroke 482 464 moveto 470 481 lineto 478 452 lineto 482 464 lineto stroke 479 482 moveto 470 481 lineto 482 464 lineto 479 482 lineto stroke 489 455 moveto 482 464 lineto 486 445 lineto 489 455 lineto stroke 495 446 moveto 489 455 lineto 486 445 lineto 495 446 lineto stroke 479 482 moveto 485 469 lineto 488 474 lineto 479 482 lineto stroke 513 385 moveto 512 423 lineto 503 398 lineto 513 385 lineto stroke 495 446 moveto 503 398 lineto 512 423 lineto 495 446 lineto stroke 527 402 moveto 512 423 lineto 513 385 lineto 527 402 lineto stroke 513 353 moveto 513 385 lineto 495 344 lineto 513 353 lineto stroke 527 402 moveto 513 385 lineto 513 353 lineto 527 402 lineto stroke 497 305 moveto 513 353 lineto 495 344 lineto 497 305 lineto stroke 516 316 moveto 513 353 lineto 497 305 lineto 516 316 lineto stroke 477 294 moveto 497 305 lineto 495 344 lineto 477 294 lineto stroke 201 247 moveto 197 249 lineto 198 246 lineto 201 247 lineto stroke 200 249 moveto 197 249 lineto 201 247 lineto 200 249 lineto stroke 200 249 moveto 201 247 lineto 202 247 lineto 200 249 lineto stroke 203 246 moveto 204 246 lineto 207 244 lineto 203 246 lineto stroke 204 244 moveto 207 244 lineto 204 246 lineto 204 244 lineto stroke 203 247 moveto 203 246 lineto 207 244 lineto 203 247 lineto stroke 202 249 moveto 203 247 lineto 207 244 lineto 202 249 lineto stroke 200 249 moveto 203 247 lineto 202 249 lineto 200 249 lineto stroke 203 251 moveto 197 252 lineto 202 249 lineto 203 251 lineto stroke 200 249 moveto 202 249 lineto 197 252 lineto 200 249 lineto stroke 196 258 moveto 197 252 lineto 203 251 lineto 196 258 lineto stroke 211 244 moveto 203 251 lineto 202 249 lineto 211 244 lineto stroke 213 248 moveto 203 251 lineto 211 244 lineto 213 248 lineto stroke 219 239 moveto 213 248 lineto 211 244 lineto 219 239 lineto stroke 236 236 moveto 213 248 lineto 219 239 lineto 236 236 lineto stroke 209 242 moveto 219 239 lineto 211 244 lineto 209 242 lineto stroke 213 238 moveto 219 239 lineto 209 242 lineto 213 238 lineto stroke 204 244 moveto 209 242 lineto 207 244 lineto 204 244 lineto stroke 211 244 moveto 207 244 lineto 209 242 lineto 211 244 lineto stroke 213 238 moveto 209 242 lineto 204 244 lineto 213 238 lineto stroke 207 238 moveto 213 238 lineto 204 244 lineto 207 238 lineto stroke 267 228 moveto 236 236 lineto 243 223 lineto 267 228 lineto stroke 219 239 moveto 243 223 lineto 236 236 lineto 219 239 lineto stroke 249 244 moveto 236 236 lineto 267 228 lineto 249 244 lineto stroke 315 220 moveto 300 232 lineto 267 228 lineto 315 220 lineto stroke 249 244 moveto 267 228 lineto 300 232 lineto 249 244 lineto stroke 282 248 moveto 249 244 lineto 300 232 lineto 282 248 lineto stroke 219 251 moveto 249 244 lineto 234 257 lineto 219 251 lineto stroke 242 263 moveto 234 257 lineto 249 244 lineto 242 263 lineto stroke 219 274 moveto 234 257 lineto 242 263 lineto 219 274 lineto stroke 229 277 moveto 242 263 lineto 256 267 lineto 229 277 lineto stroke 282 248 moveto 256 267 lineto 242 263 lineto 282 248 lineto stroke 311 257 moveto 256 267 lineto 282 248 lineto 311 257 lineto stroke 316 246 moveto 311 257 lineto 282 248 lineto 316 246 lineto stroke 349 254 moveto 311 257 lineto 316 246 lineto 349 254 lineto stroke 300 232 moveto 346 238 lineto 316 246 lineto 300 232 lineto stroke 349 254 moveto 316 246 lineto 346 238 lineto 349 254 lineto stroke 381 251 moveto 349 254 lineto 346 238 lineto 381 251 lineto stroke 355 269 moveto 311 257 lineto 349 254 lineto 355 269 lineto stroke 385 271 moveto 349 254 lineto 381 251 lineto 385 271 lineto stroke 385 240 moveto 381 251 lineto 366 238 lineto 385 240 lineto stroke 346 238 moveto 366 238 lineto 381 251 lineto 346 238 lineto stroke 346 238 moveto 353 229 lineto 366 238 lineto 346 238 lineto stroke 368 232 moveto 366 238 lineto 353 229 lineto 368 232 lineto stroke 368 232 moveto 353 229 lineto 352 223 lineto 368 232 lineto stroke 315 220 moveto 352 223 lineto 353 229 lineto 315 220 lineto stroke 371 222 moveto 380 234 lineto 352 223 lineto 371 222 lineto stroke 368 232 moveto 352 223 lineto 380 234 lineto 368 232 lineto stroke 383 237 moveto 368 232 lineto 380 234 lineto 383 237 lineto stroke 385 240 moveto 368 232 lineto 383 237 lineto 385 240 lineto stroke 381 251 moveto 385 240 lineto 398 249 lineto 381 251 lineto stroke 396 245 moveto 398 249 lineto 385 240 lineto 396 245 lineto stroke 389 240 moveto 396 245 lineto 385 240 lineto 389 240 lineto stroke 393 239 moveto 396 245 lineto 389 240 lineto 393 239 lineto stroke 338 216 moveto 371 222 lineto 352 223 lineto 338 216 lineto stroke 363 212 moveto 371 222 lineto 338 216 lineto 363 212 lineto stroke 315 220 moveto 338 216 lineto 352 223 lineto 315 220 lineto stroke 267 228 moveto 280 213 lineto 315 220 lineto 267 228 lineto stroke 243 223 moveto 280 213 lineto 267 228 lineto 243 223 lineto stroke 263 209 moveto 280 213 lineto 243 223 lineto 263 209 lineto stroke 346 238 moveto 315 220 lineto 353 229 lineto 346 238 lineto stroke 300 232 moveto 315 220 lineto 346 238 lineto 300 232 lineto stroke 428 283 moveto 398 249 lineto 449 278 lineto 428 283 lineto stroke 468 312 moveto 449 278 lineto 477 294 lineto 468 312 lineto stroke 460 325 moveto 449 278 lineto 468 312 lineto 460 325 lineto stroke 480 354 moveto 460 325 lineto 468 312 lineto 480 354 lineto stroke 469 362 moveto 447 336 lineto 460 325 lineto 469 362 lineto stroke 428 283 moveto 460 325 lineto 447 336 lineto 428 283 lineto stroke 449 278 moveto 460 325 lineto 428 283 lineto 449 278 lineto stroke 385 271 moveto 428 283 lineto 410 302 lineto 385 271 lineto stroke 381 251 moveto 428 283 lineto 385 271 lineto 381 251 lineto stroke 355 269 moveto 349 254 lineto 385 271 lineto 355 269 lineto stroke 355 269 moveto 385 271 lineto 410 302 lineto 355 269 lineto stroke 311 257 moveto 355 269 lineto 302 273 lineto 311 257 lineto stroke 398 249 moveto 428 283 lineto 381 251 lineto 398 249 lineto stroke 469 362 moveto 460 325 lineto 480 354 lineto 469 362 lineto stroke 495 344 moveto 480 354 lineto 468 312 lineto 495 344 lineto stroke 469 362 moveto 480 354 lineto 488 403 lineto 469 362 lineto stroke 454 366 moveto 469 362 lineto 469 405 lineto 454 366 lineto stroke 495 344 moveto 468 312 lineto 477 294 lineto 495 344 lineto stroke 368 232 moveto 385 240 lineto 366 238 lineto 368 232 lineto stroke 300 232 moveto 316 246 lineto 282 248 lineto 300 232 lineto stroke 270 275 moveto 311 257 lineto 302 273 lineto 270 275 lineto stroke 256 267 moveto 311 257 lineto 270 275 lineto 256 267 lineto stroke 235 300 moveto 270 275 lineto 271 300 lineto 235 300 lineto stroke 219 295 moveto 270 275 lineto 235 300 lineto 219 295 lineto stroke 218 310 moveto 235 300 lineto 214 323 lineto 218 310 lineto stroke 227 323 moveto 214 323 lineto 235 300 lineto 227 323 lineto stroke 205 334 moveto 214 323 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295 lineto 256 267 lineto 270 275 lineto stroke 218 310 moveto 219 295 lineto 235 300 lineto 218 310 lineto stroke 209 311 moveto 219 295 lineto 218 310 lineto 209 311 lineto stroke 207 324 moveto 218 310 lineto 214 323 lineto 207 324 lineto stroke 209 311 moveto 218 310 lineto 207 324 lineto 209 311 lineto stroke 219 295 moveto 209 311 lineto 205 311 lineto 219 295 lineto stroke 208 298 moveto 219 295 lineto 205 311 lineto 208 298 lineto stroke 208 298 moveto 200 293 lineto 229 277 lineto 208 298 lineto stroke 168 433 moveto 162 420 lineto 171 421 lineto 168 433 lineto stroke 161 427 moveto 162 420 lineto 168 433 lineto 161 427 lineto stroke 153 473 moveto 139 428 lineto 168 459 lineto 153 473 lineto stroke 128 453 moveto 139 428 lineto 153 473 lineto 128 453 lineto stroke 193 272 moveto 196 258 lineto 219 251 lineto 193 272 lineto stroke 213 248 moveto 219 251 lineto 196 258 lineto 213 248 lineto stroke 236 236 moveto 219 251 lineto 213 248 lineto 236 236 lineto stroke 249 244 moveto 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moveto 453.580 441.034 454.572 444.867 454.986 449.265 curveto stroke 450.816 439.996 moveto 451.193 439.186 451.572 438.369 451.953 437.545 curveto stroke 441.130 449.591 moveto 444.472 447.257 447.633 444.126 450.816 439.996 curveto stroke 438.613 457.231 moveto 439.486 454.630 440.325 452.084 441.130 449.591 curveto stroke 439.512 445.318 moveto 436.746 449.360 434.041 452.895 431.345 455.990 curveto stroke 431.345 455.990 moveto 431.175 451.959 430.387 448.366 428.933 444.992 curveto stroke 412.193 472.997 moveto 412.458 469.192 412.083 465.568 411.049 461.935 curveto stroke 397.442 495.417 moveto 403.221 487.267 408.100 479.852 412.193 472.997 curveto stroke 419.549 472.537 moveto 417.215 473.068 414.797 473.219 412.193 472.997 curveto stroke 412.439 487.699 moveto 415.298 482.248 417.653 477.227 419.549 472.537 curveto stroke 423.683 475.617 moveto 422.595 477.802 421.451 480.043 420.248 482.344 curveto stroke 426.477 481.134 moveto 427.213 479.187 427.883 477.304 428.490 475.480 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443.000 482.690 449.294 470.349 curveto stroke 429.056 519.680 moveto 430.144 515.862 430.244 512.345 429.367 508.719 curveto stroke 383.491 546.098 moveto 397.924 537.920 413.083 529.131 429.056 519.680 curveto stroke 381.876 548.961 moveto 382.463 548.019 383.001 547.066 383.491 546.098 curveto stroke 337.001 565.259 moveto 341.933 564.820 347.171 564.227 352.756 563.477 curveto stroke 362.510 567.731 moveto 358.786 566.973 355.622 565.593 352.756 563.477 curveto stroke 352.756 563.477 moveto 363.870 558.407 373.490 553.612 381.876 548.961 curveto stroke 381.908 556.294 moveto 382.227 554.114 382.217 551.710 381.876 548.961 curveto stroke 381.908 556.294 moveto 380.649 557.440 379.311 558.591 377.890 559.751 curveto stroke 389.716 554.221 moveto 387.006 555.015 384.408 555.705 381.908 556.294 curveto stroke 394.642 555.659 moveto 392.944 555.362 391.313 554.885 389.716 554.221 curveto stroke 389.716 554.221 moveto 405.792 545.489 422.657 536.132 440.402 526.098 curveto stroke 440.402 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558.238 curveto stroke 374.088 572.783 moveto 379.179 568.890 383.208 565.219 386.372 561.589 curveto stroke 358.223 571.374 moveto 359.375 573.855 360.445 575.729 361.525 577.159 curveto stroke 361.525 577.159 moveto 351.507 578.082 342.276 578.789 333.730 579.287 curveto stroke 366.211 581.589 moveto 364.599 583.963 362.463 586.180 359.684 588.365 curveto 351.275 594.975 336.056 602.011 305.058 613.616 curveto stroke 411.212 601.055 moveto 404.929 605.129 397.596 610.767 388.556 618.476 curveto stroke 411.212 601.055 moveto 408.261 606.769 405.251 612.575 402.181 618.476 curveto stroke 456.119 552.655 moveto 452.435 557.605 443.568 567.163 411.212 601.055 curveto stroke 456.119 552.655 moveto 448.479 571.124 439.161 592.737 427.740 618.476 curveto stroke 458.881 545.935 moveto 458.313 548.001 457.406 550.209 456.119 552.655 curveto stroke 483.849 476.366 moveto 478.955 494.084 470.977 516.313 458.881 545.935 curveto stroke 491.254 461.107 moveto 488.737 466.354 486.270 471.438 483.849 476.366 curveto stroke 502.984 451.029 moveto 500.887 453.905 498.792 456.159 496.592 457.907 curveto 494.910 459.244 493.148 460.300 491.254 461.107 curveto stroke 504.192 423.589 moveto 502.244 422.869 499.780 422.176 496.586 421.451 curveto stroke 496.586 421.451 moveto 496.187 419.878 495.741 418.379 495.246 416.948 curveto stroke 494.970 372.863 moveto 495.165 386.920 495.257 401.598 495.246 416.948 curveto stroke 504.989 369.626 moveto 502.623 370.781 499.432 371.812 494.970 372.863 curveto stroke 508.868 404.914 moveto 507.692 391.993 506.406 380.290 504.989 369.626 curveto stroke 520.669 383.169 moveto 520.231 390.440 519.749 397.334 519.221 403.882 curveto stroke 519.221 403.882 moveto 521.241 445.706 518.812 508.927 510.979 618.476 curveto stroke 469.384 618.476 moveto 497.976 510.788 505.643 472.579 502.984 451.029 curveto stroke 504.192 423.589 moveto 504.224 431.654 503.826 440.716 502.984 451.029 curveto stroke 508.868 404.914 moveto 507.382 411.781 505.831 417.973 504.192 423.589 curveto stroke 519.221 403.882 moveto 516.867 404.454 513.629 404.776 508.868 404.914 curveto stroke 520.669 383.169 moveto 521.072 382.045 521.451 380.879 521.806 379.668 curveto stroke 518.206 348.282 moveto 516.350 341.708 514.523 335.351 512.719 329.202 curveto stroke 527.746 330.946 moveto 540.732 370.914 555.100 418.419 571.579 475.876 curveto stroke 480.791 173.524 moveto 502.707 241.363 517.709 291.658 527.746 330.946 curveto stroke 527.746 330.946 moveto 526.418 330.120 524.967 329.545 523.321 329.190 curveto 520.582 328.601 517.206 328.605 512.719 329.202 curveto stroke 512.719 329.202 moveto 512.355 328.508 511.990 327.824 511.627 327.151 curveto stroke 511.627 327.151 moveto 500.634 290.933 482.835 242.812 454.803 173.524 curveto stroke 511.627 327.151 moveto 509.184 328.179 505.750 329.470 500.634 331.284 curveto stroke 495.354 321.805 moveto 497.081 324.780 498.838 327.935 500.634 331.284 curveto stroke 428.009 173.524 moveto 463.856 244.382 484.253 289.291 495.354 321.805 curveto stroke 495.354 321.805 moveto 493.388 320.323 491.353 319.235 489.164 318.494 curveto 486.749 317.678 484.105 317.271 481.095 317.252 curveto stroke 481.095 317.252 moveto 476.939 310.446 472.893 303.900 468.949 297.600 curveto stroke 468.949 297.600 moveto 462.019 281.466 451.202 261.664 434.997 235.442 curveto stroke 423.612 232.612 moveto 422.472 233.940 420.859 236.035 418.200 239.640 curveto stroke 352.541 214.861 moveto 371.438 218.384 394.442 224.130 423.612 232.612 curveto stroke 434.997 235.442 moveto 435.725 232.555 435.926 229.927 435.612 227.388 curveto 435.297 224.840 434.458 222.327 433.038 219.684 curveto 428.964 212.099 419.638 202.557 399.210 185.073 curveto stroke 423.612 232.612 moveto 426.957 232.881 430.662 233.802 434.997 235.442 curveto stroke 318.990 201.890 moveto 332.267 206.439 343.284 210.698 352.541 214.861 curveto stroke 352.541 214.861 moveto 353.930 216.390 355.071 218.005 355.992 219.749 curveto stroke 335.085 221.870 moveto 340.936 220.394 347.753 219.703 355.992 219.749 curveto stroke 335.669 222.854 moveto 335.481 222.520 335.287 222.192 335.085 221.870 curveto stroke 329.766 228.760 moveto 331.537 226.303 333.469 224.370 335.669 222.854 curveto stroke 348.570 234.396 moveto 342.424 232.531 336.157 230.653 329.766 228.760 curveto stroke 326.118 229.023 moveto 327.308 228.924 328.523 228.836 329.766 228.760 curveto stroke 364.356 244.778 moveto 360.029 241.305 354.835 237.889 348.570 234.396 curveto stroke 383.623 246.846 moveto 376.283 245.328 369.977 244.652 364.356 244.778 curveto stroke 405.117 272.490 moveto 406.317 269.590 407.064 267.036 407.399 264.687 curveto stroke 407.399 264.687 moveto 414.092 264.472 421.188 266.371 429.902 270.709 curveto stroke 386.378 248.254 moveto 394.278 254.063 401.243 259.507 407.399 264.687 curveto stroke 386.378 248.254 moveto 388.212 247.165 390.042 246.355 391.921 245.802 curveto stroke 376.368 237.616 moveto 375.841 238.088 375.312 238.601 374.780 239.159 curveto stroke 363.382 234.766 moveto 367.186 236.226 370.985 237.691 374.780 239.159 curveto stroke 363.382 234.766 moveto 361.909 232.477 360.079 230.318 357.838 228.224 curveto stroke 367.095 227.975 moveto 363.758 227.864 360.689 227.946 357.838 228.224 curveto stroke 367.095 227.975 moveto 370.351 230.323 373.211 232.612 375.723 234.881 curveto stroke 383.152 230.880 moveto 384.973 233.211 386.331 235.546 387.282 237.980 curveto stroke 394.580 242.904 moveto 403.654 246.793 413.615 251.388 424.668 256.784 curveto stroke 424.668 256.784 moveto 425.524 258.732 426.201 260.637 426.707 262.524 curveto stroke 426.707 262.524 moveto 413.624 255.746 402.156 250.234 391.921 245.802 curveto stroke 391.921 245.802 moveto 391.689 245.168 391.432 244.540 391.149 243.916 curveto stroke 394.580 242.904 moveto 393.412 243.145 392.272 243.482 391.149 243.916 curveto stroke 387.282 237.980 moveto 386.884 237.949 386.490 237.922 386.099 237.900 curveto stroke 387.282 237.980 moveto 389.785 239.648 392.217 241.289 394.580 242.904 curveto stroke 391.149 243.916 moveto 389.391 242.744 387.594 241.558 385.756 240.357 curveto stroke 386.099 237.900 moveto 386.031 238.675 385.917 239.492 385.756 240.357 curveto stroke 385.756 240.357 moveto 382.490 239.336 379.366 238.424 376.368 237.616 curveto stroke 375.723 234.881 moveto 375.994 235.761 376.208 236.670 376.368 237.616 curveto stroke 375.723 234.881 moveto 379.030 235.774 382.483 236.779 386.099 237.900 curveto stroke 418.200 239.640 moveto 403.450 234.563 392.279 231.772 383.152 230.880 curveto stroke 424.668 256.784 moveto 424.613 254.414 424.211 252.094 423.448 249.742 curveto 422.415 246.561 420.703 243.264 418.200 239.640 curveto stroke 368.073 226.905 moveto 367.746 227.240 367.421 227.596 367.095 227.975 curveto stroke 368.073 226.905 moveto 372.810 228.044 377.824 229.366 383.152 230.880 curveto stroke 383.623 246.846 moveto 384.541 247.315 385.459 247.784 386.378 248.254 curveto stroke 374.780 239.159 moveto 378.112 241.765 381.044 244.314 383.623 246.846 curveto stroke 429.902 270.709 moveto 429.131 268.039 428.072 265.327 426.707 262.524 curveto stroke 429.902 270.709 moveto 436.131 278.396 442.105 285.855 447.838 293.102 curveto stroke 443.968 310.112 moveto 445.821 307.259 447.016 304.517 447.631 301.708 curveto 448.221 299.010 448.289 296.198 447.838 293.102 curveto stroke 426.353 301.481 moveto 432.341 302.803 438.020 305.585 443.968 310.112 curveto stroke 421.256 295.890 moveto 422.955 297.750 424.654 299.614 426.353 301.481 curveto stroke 426.353 301.481 moveto 427.618 304.681 428.693 307.687 429.590 310.530 curveto stroke 416.677 323.249 moveto 422.869 318.645 426.238 315.681 428.077 313.220 curveto 428.770 312.294 429.265 311.412 429.590 310.530 curveto stroke 429.590 310.530 moveto 435.226 324.310 440.413 337.368 445.181 349.782 curveto stroke 445.181 349.782 moveto 445.201 350.524 445.213 351.255 445.215 351.974 curveto stroke 445.215 351.974 moveto 443.010 353.488 439.810 355.051 435.000 356.963 curveto stroke 435.960 371.040 moveto 437.826 377.745 439.598 385.151 441.305 393.382 curveto stroke 434.240 414.666 moveto 432.185 414.035 429.607 413.399 426.295 412.706 curveto stroke 434.240 414.666 moveto 434.259 420.102 434.009 426.023 433.487 432.529 curveto stroke 441.305 393.382 moveto 439.186 401.778 436.868 408.761 434.240 414.666 curveto stroke 448.072 398.577 moveto 446.250 396.505 444.039 394.808 441.305 393.382 curveto stroke 449.029 417.811 moveto 448.865 410.862 448.547 404.476 448.072 398.577 curveto stroke 445.864 424.942 moveto 446.914 422.690 447.968 420.316 449.029 417.811 curveto stroke 433.487 432.529 moveto 436.027 431.892 438.260 430.975 440.279 429.737 curveto 442.302 428.498 444.138 426.922 445.864 424.942 curveto stroke 433.487 432.529 moveto 431.962 436.743 430.444 440.896 428.933 444.992 curveto stroke 428.933 444.992 moveto 423.487 451.595 418.170 456.248 412.468 459.401 curveto stroke 412.468 459.401 moveto 414.133 453.056 415.290 447.385 415.972 442.225 curveto stroke 411.049 461.935 moveto 401.636 471.021 393.352 477.920 385.660 483.081 curveto stroke 385.660 483.081 moveto 387.533 478.865 388.537 475.090 388.753 471.464 curveto 388.936 468.372 388.549 465.327 387.570 462.156 curveto stroke 376.178 493.099 moveto 379.483 489.666 382.641 486.330 385.660 483.081 curveto stroke 374.794 493.751 moveto 375.253 493.535 375.714 493.318 376.178 493.099 curveto stroke 343.084 511.906 moveto 355.293 505.520 365.757 499.529 374.794 493.751 curveto stroke 318.917 506.585 moveto 322.072 504.481 324.633 502.156 326.724 499.500 curveto stroke 277.452 496.994 moveto 280.062 496.225 282.404 495.161 284.564 493.762 curveto 286.884 492.258 289.023 490.349 291.069 487.955 curveto stroke 246.505 464.040 moveto 243.876 469.484 242.752 473.754 242.920 477.653 curveto stroke 223.451 466.512 moveto 218.893 458.962 214.811 451.877 211.163 445.185 curveto stroke 196.541 446.351 moveto 198.089 443.675 200.616 441.125 204.512 438.309 curveto stroke 204.512 438.309 moveto 201.701 427.781 198.969 417.230 196.314 406.648 curveto stroke 220.251 424.844 moveto 216.303 420.662 212.920 415.497 209.872 408.993 curveto stroke 210.425 390.951 moveto 210.205 396.839 210.021 402.851 209.872 408.993 curveto stroke 204.211 385.325 moveto 201.690 390.608 199.490 396.963 197.486 404.755 curveto stroke 196.314 406.648 moveto 191.041 400.358 187.403 391.390 184.510 377.549 curveto stroke 190.477 367.654 moveto 188.543 370.553 186.566 373.832 184.510 377.549 curveto stroke 184.510 377.549 moveto 182.392 377.361 180.581 377.239 179.012 377.178 curveto stroke 172.878 368.106 moveto 174.287 371.637 176.278 374.582 179.012 377.178 curveto stroke 167.562 361.342 moveto 170.063 382.662 173.386 405.812 177.590 431.190 curveto stroke 167.148 420.908 moveto 163.754 396.959 161.027 374.795 158.933 354.142 curveto stroke 158.933 354.142 moveto 158.367 352.836 157.892 351.464 157.503 350.012 curveto stroke 213.741 304.059 moveto 212.580 303.472 211.482 303.007 210.429 302.656 curveto stroke 233.633 292.872 moveto 236.332 290.403 239.108 287.889 241.962 285.328 curveto stroke 241.962 285.328 moveto 246.390 284.888 250.270 285.109 253.851 286.005 curveto 257.111 286.820 260.184 288.210 263.234 290.248 curveto stroke 241.962 285.328 moveto 242.121 284.219 242.348 283.142 242.643 282.091 curveto stroke 284.728 262.830 moveto 268.433 269.647 254.568 275.992 242.643 282.091 curveto stroke 242.643 282.091 moveto 241.822 281.588 241.006 281.141 240.191 280.747 curveto stroke 240.191 280.747 moveto 240.679 276.418 242.054 272.580 244.443 268.877 curveto stroke 221.168 288.186 moveto 218.617 287.591 216.072 287.433 213.420 287.705 curveto stroke 213.420 287.705 moveto 193.376 308.466 174.306 328.787 156.122 348.763 curveto stroke 156.122 348.763 moveto 151.167 347.397 147.670 346.549 145.040 346.077 curveto stroke 145.040 346.077 moveto 163.280 325.807 182.306 305.226 202.189 284.256 curveto stroke 145.040 346.077 moveto 142.744 347.054 140.644 348.348 138.665 350.007 curveto stroke 138.665 350.007 moveto 138.178 350.217 137.703 350.441 137.238 350.682 curveto stroke 151.726 431.116 moveto 154.523 435.515 157.271 438.750 160.210 441.104 curveto 162.326 442.798 164.578 444.066 167.067 444.963 curveto stroke 178.493 460.648 moveto 177.592 466.602 178.152 473.128 180.236 480.961 curveto stroke 180.236 480.961 moveto 185.605 487.026 190.775 492.757 195.767 498.177 curveto stroke 170.079 490.617 moveto 177.649 498.737 184.967 506.481 192.057 513.871 curveto stroke 198.539 532.782 moveto 200.030 531.832 201.625 530.614 203.382 529.082 curveto stroke 203.382 529.082 moveto 206.429 530.616 209.380 532.070 212.242 533.447 curveto stroke 212.242 533.447 moveto 215.763 534.198 218.907 534.479 221.820 534.303 curveto 224.146 534.162 226.352 533.728 228.503 532.988 curveto stroke 240.783 551.109 moveto 230.324 544.894 220.851 539.032 212.242 533.447 curveto stroke 228.503 532.988 moveto 239.313 537.392 249.301 541.243 258.592 544.589 curveto stroke 228.503 532.988 moveto 224.872 529.225 221.907 525.655 219.519 522.172 curveto stroke 229.463 521.064 moveto 226.291 522.051 223.040 522.413 219.519 522.172 curveto stroke 200.760 509.204 moveto 198.607 505.327 196.957 501.684 195.767 498.177 curveto stroke 195.767 498.177 moveto 198.633 498.858 201.425 499.026 204.287 498.690 curveto stroke 204.287 498.690 moveto 210.814 503.404 217.010 507.754 222.915 511.767 curveto stroke 198.454 477.865 moveto 199.754 478.543 201.038 479.137 202.312 479.652 curveto stroke 183.960 440.323 moveto 185.447 439.401 187.249 438.427 189.448 437.355 curveto stroke 189.448 437.355 moveto 191.831 440.738 194.182 443.721 196.541 446.351 curveto stroke 196.541 446.351 moveto 199.178 452.415 202.094 458.804 205.311 465.561 curveto stroke 205.311 465.561 moveto 203.872 468.026 202.942 470.382 202.469 472.760 curveto 202.031 474.966 201.980 477.227 202.312 479.652 curveto stroke 239.621 498.299 moveto 232.348 490.425 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269.741 546.547 curveto stroke 296.396 544.333 moveto 302.129 546.805 308.874 548.737 317.002 550.235 curveto stroke 317.002 550.235 moveto 315.587 553.549 313.797 556.187 311.494 558.355 curveto stroke 282.211 557.469 moveto 292.232 557.823 301.989 558.118 311.494 558.355 curveto stroke 311.494 558.355 moveto 313.039 559.373 314.713 560.282 316.537 561.095 curveto stroke 316.537 561.095 moveto 312.641 563.026 308.183 564.680 303.017 566.113 curveto stroke 303.017 566.113 moveto 297.278 566.096 291.426 566.058 285.457 566.000 curveto stroke 285.457 566.000 moveto 285.906 569.850 286.728 572.714 288.033 574.973 curveto 288.980 576.613 290.208 577.977 291.799 579.159 curveto stroke 303.017 566.113 moveto 306.748 568.337 311.157 570.141 316.477 571.621 curveto stroke 291.799 579.159 moveto 302.158 577.088 310.135 574.651 316.477 571.621 curveto stroke 276.895 562.539 moveto 279.544 563.729 282.391 564.879 285.457 566.000 curveto stroke 276.895 562.539 moveto 278.893 561.243 280.633 559.583 282.211 557.469 curveto stroke 247.080 530.645 moveto 250.503 535.356 255.395 539.842 262.259 544.565 curveto stroke 261.394 526.335 moveto 257.160 528.966 252.567 530.349 247.080 530.645 curveto stroke 231.802 509.647 moveto 241.034 514.867 250.736 520.225 260.945 525.743 curveto stroke 228.076 501.284 moveto 228.911 504.090 230.141 506.850 231.802 509.647 curveto stroke 228.076 501.284 moveto 232.028 501.251 235.754 500.288 239.621 498.299 curveto stroke 239.621 498.299 moveto 242.400 499.441 245.077 500.485 247.663 501.433 curveto stroke 247.663 501.433 moveto 255.028 506.340 263.720 511.363 274.063 516.688 curveto stroke 274.063 516.688 moveto 271.963 519.368 269.819 521.399 267.499 522.908 curveto 265.508 524.203 263.356 525.134 260.945 525.743 curveto stroke 260.945 525.743 moveto 261.092 525.941 261.242 526.139 261.394 526.335 curveto stroke 229.463 521.064 moveto 235.274 524.248 241.146 527.442 247.080 530.645 curveto stroke 222.915 511.767 moveto 224.641 514.805 226.806 517.878 229.463 521.064 curveto stroke 222.915 511.767 moveto 225.964 511.653 228.866 510.961 231.802 509.647 curveto stroke 297.516 539.687 moveto 283.219 535.130 271.366 530.749 261.394 526.335 curveto stroke 297.516 539.687 moveto 297.160 541.441 296.790 542.978 296.396 544.333 curveto stroke 278.849 589.962 moveto 279.496 588.591 280.093 586.866 280.686 584.653 curveto stroke 333.730 579.287 moveto 317.460 582.772 299.291 586.307 278.849 589.962 curveto stroke 280.686 584.653 moveto 300.622 581.407 318.254 578.226 333.975 575.041 curveto stroke 333.975 575.041 moveto 333.958 576.639 333.877 578.041 333.730 579.287 curveto stroke 278.849 589.962 moveto 277.444 591.008 275.872 591.859 274.081 592.544 curveto 271.368 593.581 268.095 594.258 264.010 594.628 curveto stroke 210.508 560.553 moveto 224.129 570.444 241.490 581.501 264.010 594.628 curveto stroke 264.010 594.628 moveto 265.674 597.520 267.860 600.035 270.697 602.325 curveto 276.202 606.767 284.467 610.608 297.455 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535.882 90.914 539.611 91.419 543.762 curveto 92.963 556.439 102.539 575.148 129.662 618.476 curveto stroke 40.421 537.338 moveto 43.570 532.756 45.256 528.440 45.692 523.841 curveto 46.276 517.670 44.647 510.598 40.421 500.958 curveto stroke 80.003 505.582 moveto 68.947 488.523 56.256 465.888 40.421 434.986 curveto stroke 88.918 505.332 moveto 71.199 458.692 55.079 414.792 40.421 373.254 curveto stroke 97.685 512.794 moveto 94.438 501.414 92.880 492.228 92.857 484.322 curveto stroke 121.963 519.359 moveto 120.172 523.355 119.370 527.268 119.487 531.442 curveto stroke 121.963 519.359 moveto 131.148 529.302 139.611 538.134 147.487 546.000 curveto stroke 111.669 500.138 moveto 114.848 506.244 118.274 512.641 121.963 519.359 curveto stroke 110.852 494.156 moveto 111.030 496.068 111.302 498.058 111.669 500.138 curveto stroke 92.857 484.322 moveto 99.174 492.062 105.170 497.103 111.669 500.138 curveto stroke 92.857 484.322 moveto 77.470 448.073 60.268 405.079 40.421 353.265 curveto stroke 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256.430 181.349 258.899 181.490 261.654 181.358 curveto stroke 261.654 181.358 moveto 259.451 181.117 256.975 180.975 254.163 180.930 curveto stroke 314.030 198.935 moveto 313.388 195.480 312.456 192.997 311.091 191.110 curveto 310.062 189.688 308.756 188.560 307.060 187.629 curveto 301.492 184.573 290.686 183.081 261.654 181.358 curveto stroke 261.279 216.645 moveto 273.947 210.708 290.776 205.058 314.030 198.935 curveto stroke 314.030 198.935 moveto 315.865 199.851 317.509 200.831 318.990 201.890 curveto stroke 318.990 201.890 moveto 316.666 202.837 314.835 204.038 313.346 205.592 curveto 311.703 207.307 310.426 209.505 309.388 212.406 curveto stroke 309.388 212.406 moveto 301.020 214.567 294.354 217.086 288.907 220.147 curveto stroke 264.064 222.159 moveto 272.953 221.290 281.208 220.621 288.907 220.147 curveto stroke 255.329 226.108 moveto 258.106 224.808 261.014 223.492 264.064 222.159 curveto stroke 225.125 228.607 moveto 226.049 225.243 227.833 222.190 230.674 219.108 curveto 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199.719 253.445 200.126 252.634 200.567 251.819 curveto stroke 200.567 251.819 moveto 201.308 251.160 202.057 250.496 202.815 249.829 curveto stroke 202.815 249.829 moveto 204.319 248.976 205.804 248.141 207.270 247.323 curveto stroke 203.811 248.021 moveto 203.320 248.427 202.832 248.831 202.347 249.234 curveto stroke 200.743 249.523 moveto 201.283 249.416 201.818 249.320 202.347 249.234 curveto stroke 200.743 249.523 moveto 201.469 248.915 202.200 248.304 202.939 247.690 curveto stroke 202.939 247.690 moveto 203.156 247.626 203.372 247.564 203.587 247.503 curveto stroke 203.811 248.021 moveto 203.734 247.846 203.659 247.673 203.587 247.503 curveto stroke 203.587 247.503 moveto 204.368 247.096 205.142 246.694 205.910 246.298 curveto stroke 205.975 246.894 moveto 205.950 246.693 205.929 246.495 205.910 246.298 curveto stroke 205.975 246.894 moveto 205.259 247.264 204.538 247.640 203.811 248.021 curveto stroke 207.270 247.323 moveto 206.839 247.165 206.407 247.022 205.975 246.894 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406.138 338.462 moveto 410.979 349.483 415.900 361.897 421.013 375.992 curveto stroke 406.138 338.462 moveto 403.670 336.886 401.176 335.631 398.601 334.672 curveto stroke 421.010 389.683 moveto 421.069 385.316 421.070 380.758 421.013 375.992 curveto stroke 421.010 389.683 moveto 418.634 395.872 415.566 400.410 411.395 403.905 curveto stroke 426.295 412.706 moveto 425.245 403.581 423.522 396.074 421.010 389.683 curveto stroke 415.972 442.225 moveto 419.348 433.031 422.781 423.215 426.295 412.706 curveto stroke 405.282 438.048 moveto 410.254 440.071 413.575 441.369 415.972 442.225 curveto stroke 408.039 415.784 moveto 407.683 422.412 406.773 429.757 405.282 438.048 curveto stroke 408.039 415.784 moveto 406.145 417.859 404.105 419.436 401.799 420.604 curveto 399.170 421.936 396.136 422.767 392.471 423.159 curveto stroke 397.055 377.787 moveto 399.692 380.138 401.971 382.866 403.978 386.071 curveto 406.901 390.743 409.309 396.533 411.395 403.905 curveto stroke 411.395 403.905 moveto 410.280 408.055 409.163 412.010 408.039 415.784 curveto stroke 392.471 423.159 moveto 392.024 414.856 390.221 408.142 386.843 402.205 curveto stroke 362.927 434.179 moveto 364.513 437.970 365.332 441.517 365.439 445.058 curveto 365.548 448.648 364.928 452.311 363.535 456.302 curveto stroke 363.535 456.302 moveto 359.716 459.388 355.826 462.491 351.861 465.614 curveto stroke 363.535 456.302 moveto 369.145 455.417 374.722 453.134 380.849 449.215 curveto stroke 383.220 462.551 moveto 383.463 460.346 383.411 458.227 383.063 456.129 curveto 382.686 453.856 381.957 451.579 380.849 449.215 curveto stroke 383.220 462.551 moveto 375.442 468.718 367.638 474.808 359.803 480.825 curveto stroke 359.803 480.825 moveto 356.877 481.055 354.192 480.922 351.650 480.421 curveto 349.304 479.959 347.053 479.180 344.828 478.057 curveto stroke 326.724 499.500 moveto 324.184 498.555 321.945 497.339 319.925 495.803 curveto 317.782 494.175 315.854 492.166 314.061 489.691 curveto stroke 344.828 478.057 moveto 335.153 481.891 324.917 485.762 314.061 489.691 curveto stroke 315.910 473.499 moveto 322.465 471.378 328.637 469.266 334.461 467.150 curveto stroke 334.061 455.297 moveto 335.074 460.299 335.200 464.037 334.461 467.150 curveto stroke 315.910 473.499 moveto 310.014 472.148 305.107 470.377 300.908 468.084 curveto 297.633 466.295 294.745 464.166 292.145 461.622 curveto stroke 302.146 488.218 moveto 306.262 486.574 309.226 484.654 311.418 482.211 curveto 313.451 479.944 314.896 477.143 315.910 473.499 curveto stroke 302.146 488.218 moveto 298.496 488.146 294.805 488.059 291.069 487.955 curveto stroke 291.069 487.955 moveto 281.967 483.252 275.118 478.582 269.898 473.523 curveto stroke 291.571 461.567 moveto 288.304 465.918 285.068 468.855 281.466 470.736 curveto 278.161 472.462 274.433 473.360 269.898 473.523 curveto stroke 284.727 457.312 moveto 286.848 458.727 289.125 460.142 291.571 461.567 curveto stroke 292.145 461.622 moveto 302.403 459.898 311.118 457.925 318.654 455.622 curveto stroke 291.571 461.567 moveto 291.763 461.585 291.954 461.604 292.145 461.622 curveto stroke 280.713 437.791 moveto 280.005 442.549 280.083 446.394 280.956 449.759 curveto 281.656 452.455 282.883 454.914 284.727 457.312 curveto stroke 280.713 437.791 moveto 275.427 432.655 270.441 427.611 265.733 422.637 curveto stroke 265.733 422.637 moveto 265.775 418.684 266.586 415.196 268.242 411.849 curveto 270.852 406.572 275.720 401.328 284.012 394.859 curveto stroke 261.726 368.920 moveto 256.625 373.547 252.213 379.589 248.058 387.637 curveto stroke 235.228 371.491 moveto 236.953 366.620 238.796 361.604 240.761 356.430 curveto stroke 225.052 389.431 moveto 228.205 382.076 231.524 376.225 235.228 371.491 curveto stroke 248.058 387.637 moveto 243.847 385.129 240.868 382.574 238.783 379.680 curveto 237.074 377.309 235.918 374.646 235.228 371.491 curveto stroke 248.058 387.637 moveto 247.991 395.826 248.046 404.108 248.224 412.499 curveto stroke 248.224 412.499 moveto 245.337 415.633 243.351 418.780 242.110 422.189 curveto stroke 242.110 422.189 moveto 238.846 421.276 235.988 419.963 233.396 418.185 curveto 230.542 416.227 227.958 413.668 225.491 410.357 curveto stroke 253.578 465.422 moveto 251.225 460.947 250.057 457.030 249.930 453.200 curveto 249.809 449.560 250.626 445.866 252.467 441.717 curveto stroke 253.578 465.422 moveto 251.263 465.179 248.917 464.720 246.505 464.040 curveto stroke 222.801 436.347 moveto 231.209 446.744 239.061 455.918 246.505 464.040 curveto stroke 222.801 436.347 moveto 221.803 432.310 220.955 428.484 220.251 424.844 curveto stroke 220.251 424.844 moveto 221.021 419.226 222.712 414.550 225.491 410.357 curveto stroke 252.467 441.717 moveto 248.388 434.739 244.958 428.272 242.110 422.189 curveto stroke 225.491 410.357 moveto 225.291 403.419 225.145 396.445 225.052 389.431 curveto stroke 225.052 389.431 moveto 221.042 386.144 218.314 382.418 216.532 377.796 curveto stroke 216.532 377.796 moveto 216.594 375.321 216.719 372.741 216.907 370.047 curveto stroke 207.862 363.043 moveto 206.608 370.426 205.391 377.852 204.211 385.325 curveto stroke 216.907 370.047 moveto 212.510 367.692 209.670 365.493 207.862 363.043 curveto stroke 207.862 363.043 moveto 207.616 360.162 207.578 357.034 207.747 353.599 curveto stroke 207.747 353.599 moveto 210.615 349.285 213.410 345.177 216.139 341.260 curveto stroke 219.529 325.539 moveto 216.644 326.668 213.753 328.191 210.778 330.147 curveto stroke 225.240 311.893 moveto 221.833 313.566 218.299 315.640 214.567 318.157 curveto stroke 210.762 316.783 moveto 213.908 312.019 217.434 306.986 221.378 301.630 curveto stroke 192.101 333.741 moveto 198.911 326.979 205.061 321.390 210.762 316.783 curveto stroke 214.567 318.157 moveto 213.209 317.553 211.950 317.098 210.762 316.783 curveto stroke 209.242 327.634 moveto 210.893 324.586 212.667 321.431 214.567 318.157 curveto stroke 209.242 327.634 moveto 199.211 335.971 187.801 348.670 172.878 368.106 curveto stroke 172.878 368.106 moveto 170.670 366.130 169.059 363.939 167.921 361.365 curveto stroke 167.921 361.365 moveto 176.630 351.109 184.648 341.949 192.101 333.741 curveto stroke 213.741 304.059 moveto 205.736 314.622 198.552 324.476 192.101 333.741 curveto stroke 221.378 301.630 moveto 218.901 302.177 216.370 302.982 213.741 304.059 curveto stroke 221.378 301.630 moveto 225.627 298.485 229.705 295.571 233.633 292.872 curveto stroke 233.633 292.872 moveto 228.788 299.868 226.120 305.914 225.240 311.893 curveto stroke 225.240 311.893 moveto 226.105 312.353 227.008 312.884 227.958 313.491 curveto stroke 219.529 325.539 moveto 222.161 321.669 224.967 317.658 227.958 313.491 curveto stroke 227.958 313.491 moveto 235.142 309.226 241.623 306.018 247.672 303.732 curveto stroke 247.672 303.732 moveto 247.058 305.901 246.797 308.139 246.880 310.536 curveto stroke 261.349 315.656 moveto 258.705 313.793 256.172 312.480 253.622 311.649 curveto 251.443 310.940 249.223 310.573 246.880 310.536 curveto stroke 230.905 344.795 moveto 234.501 343.004 238.130 341.898 241.978 341.421 curveto stroke 224.412 335.713 moveto 225.494 338.459 227.546 341.329 230.905 344.795 curveto stroke 246.880 310.536 moveto 238.981 319.189 231.501 327.571 224.412 335.713 curveto stroke 261.349 315.656 moveto 260.588 317.988 260.133 320.442 259.969 323.093 curveto stroke 281.816 323.458 moveto 275.718 321.721 268.768 321.605 259.969 323.093 curveto stroke 240.761 356.430 moveto 245.812 353.102 250.344 351.225 254.899 350.577 curveto 259.196 349.965 263.665 350.425 268.777 352.005 curveto stroke 241.978 341.421 moveto 240.496 346.857 240.102 351.719 240.761 356.430 curveto stroke 259.969 323.093 moveto 253.527 329.447 247.543 335.543 241.978 341.421 curveto stroke 281.409 342.650 moveto 280.325 336.909 280.003 332.540 280.402 328.971 curveto 280.629 326.937 281.094 325.125 281.816 323.458 curveto stroke 323.295 315.630 moveto 307.926 318.074 294.197 320.665 281.816 323.458 curveto stroke 341.047 317.939 moveto 335.371 317.102 329.461 316.333 323.295 315.630 curveto stroke 333.938 293.877 moveto 320.264 293.626 307.533 293.605 295.625 293.814 curveto stroke 274.529 286.986 moveto 277.201 285.003 280.178 283.156 283.510 281.414 curveto stroke 316.595 279.266 moveto 304.885 279.860 293.882 280.574 283.510 281.414 curveto stroke 316.595 279.266 moveto 321.118 281.509 324.797 283.930 327.819 286.652 curveto 330.224 288.818 332.242 291.201 333.938 293.877 curveto stroke 346.222 298.188 moveto 352.298 298.516 359.023 299.755 366.775 301.975 curveto stroke 366.775 301.975 moveto 378.180 313.347 388.763 324.220 398.601 334.672 curveto stroke 398.601 334.672 moveto 398.609 337.391 398.177 339.890 397.280 342.306 curveto 396.195 345.230 394.405 348.100 391.765 351.149 curveto stroke 357.309 339.555 moveto 363.453 338.773 368.840 339.133 373.956 340.668 curveto 379.813 342.426 385.523 345.786 391.765 351.149 curveto stroke 373.824 400.788 moveto 373.108 397.836 372.385 394.974 371.656 392.196 curveto stroke 332.268 409.493 moveto 333.735 397.264 334.213 385.795 333.719 374.736 curveto stroke 302.116 420.245 moveto 311.835 419.380 321.374 415.979 332.268 409.493 curveto stroke 343.853 424.164 moveto 341.779 420.035 338.142 415.430 332.268 409.493 curveto stroke 320.204 441.987 moveto 329.719 435.876 337.474 430.031 343.853 424.164 curveto stroke 343.853 424.164 moveto 348.361 424.512 352.242 424.049 355.854 422.731 curveto 359.918 421.249 363.788 418.632 367.920 414.573 curveto stroke 367.920 414.573 moveto 367.392 420.892 365.761 427.299 362.927 434.179 curveto stroke 362.927 434.179 moveto 353.668 441.239 344.058 448.270 334.061 455.297 curveto stroke 318.654 455.622 moveto 323.287 456.097 328.352 455.990 334.061 455.297 curveto stroke 318.654 455.622 moveto 320.115 452.353 320.595 448.129 320.204 441.987 curveto stroke 320.204 441.987 moveto 311.398 441.321 304.106 440.023 297.845 438.007 curveto stroke 297.845 438.007 moveto 298.950 434.535 300.227 429.224 302.116 420.245 curveto stroke 284.012 394.859 moveto 290.101 406.100 295.900 414.232 302.116 420.245 curveto stroke 284.012 394.859 moveto 284.183 392.148 284.390 389.400 284.634 386.610 curveto stroke 319.677 362.601 moveto 308.729 367.745 297.438 375.481 284.634 386.610 curveto stroke 268.777 352.005 moveto 265.328 358.023 263.025 363.547 261.726 368.920 curveto stroke 268.777 352.005 moveto 272.780 348.936 276.985 345.821 281.409 342.650 curveto stroke 315.951 341.612 moveto 306.172 340.718 294.929 341.056 281.409 342.650 curveto stroke 315.951 341.612 moveto 318.255 346.607 319.420 353.173 319.677 362.601 curveto stroke 350.843 333.884 moveto 341.240 332.361 334.129 332.493 328.201 334.305 curveto 323.753 335.664 319.803 338.020 315.951 341.612 curveto stroke 357.309 339.555 moveto 355.153 337.650 352.998 335.760 350.843 333.884 curveto stroke 371.656 392.196 moveto 372.114 377.845 367.723 361.733 357.309 339.555 curveto stroke 333.719 374.736 moveto 341.072 373.548 346.637 373.497 351.261 374.572 curveto 354.343 375.289 357.090 376.527 359.681 378.366 curveto 363.670 381.198 367.459 385.574 371.656 392.196 curveto stroke 319.677 362.601 moveto 324.750 366.041 329.377 370.040 333.719 374.736 curveto stroke 284.634 386.610 moveto 272.198 378.227 265.506 373.060 261.726 368.920 curveto stroke 373.824 400.788 moveto 371.845 405.717 369.882 410.300 367.920 414.573 curveto stroke 391.765 351.149 moveto 393.776 360.541 395.536 369.400 397.055 377.787 curveto stroke 397.055 377.787 moveto 396.101 383.766 394.663 388.778 392.657 393.112 curveto 391.102 396.474 389.186 399.470 386.843 402.205 curveto stroke 386.843 402.205 moveto 383.406 401.784 379.169 401.323 373.824 400.788 curveto stroke 350.843 333.884 moveto 348.692 327.953 345.509 322.773 341.047 317.939 curveto stroke 341.047 317.939 moveto 344.696 307.910 346.194 302.193 346.222 298.188 curveto stroke 333.938 293.877 moveto 338.251 295.306 342.340 296.741 346.222 298.188 curveto stroke 334.353 271.609 moveto 329.892 272.324 326.197 273.409 323.041 274.930 curveto 320.636 276.090 318.512 277.518 316.595 279.266 curveto stroke 368.215 286.143 moveto 357.933 281.455 346.693 276.630 334.353 271.609 curveto stroke 366.775 301.975 moveto 368.035 297.976 368.685 294.625 368.775 291.659 curveto 368.834 289.699 368.649 287.881 368.215 286.143 curveto stroke 295.625 293.814 moveto 293.375 292.189 290.907 290.880 288.144 289.844 curveto 284.326 288.413 279.878 287.479 274.529 286.986 curveto stroke 289.429 302.819 moveto 298.828 304.270 306.296 306.285 312.451 309.029 curveto 316.543 310.854 320.115 313.028 323.295 315.630 curveto stroke 295.625 293.814 moveto 292.919 296.286 290.912 299.204 289.429 302.819 curveto stroke 289.429 302.819 moveto 278.542 307.139 269.294 311.367 261.349 315.656 curveto stroke 247.672 303.732 moveto 251.952 299.439 257.083 294.993 263.234 290.248 curveto stroke 263.234 290.248 moveto 267.044 289.133 270.808 288.046 274.529 286.986 curveto stroke 224.412 335.713 moveto 221.716 337.189 218.979 339.025 216.139 341.260 curveto stroke 216.139 341.260 moveto 216.373 336.379 217.481 331.239 219.529 325.539 curveto stroke 210.778 330.147 moveto 210.182 329.289 209.672 328.455 209.242 327.634 curveto stroke 207.747 353.599 moveto 204.941 354.512 202.381 355.829 199.956 357.606 curveto 196.702 359.991 193.622 363.256 190.477 367.654 curveto stroke 210.778 330.147 moveto 203.333 343.368 196.586 355.834 190.477 367.654 curveto stroke 230.905 344.795 moveto 226.392 352.437 221.746 360.819 216.907 370.047 curveto stroke 216.532 377.796 moveto 214.248 381.567 212.235 385.903 210.425 390.951 curveto stroke 210.425 390.951 moveto 207.831 389.357 205.807 387.524 204.211 385.325 curveto stroke 248.224 412.499 moveto 251.119 415.524 254.019 417.816 257.081 419.501 curveto 259.762 420.976 262.606 422.007 265.733 422.637 curveto stroke 297.845 438.007 moveto 292.809 438.725 287.218 438.654 280.713 437.791 curveto stroke 284.727 457.312 moveto 275.273 454.230 264.828 449.181 252.467 441.717 curveto stroke 269.898 473.523 moveto 264.584 470.945 259.148 468.246 253.578 465.422 curveto stroke 334.461 467.150 moveto 339.544 467.530 345.210 467.029 351.861 465.614 curveto stroke 351.861 465.614 moveto 350.474 469.972 348.187 474.019 344.828 478.057 curveto stroke 314.061 489.691 moveto 309.807 489.330 305.849 488.840 302.146 488.218 curveto stroke 359.803 480.825 moveto 358.104 484.350 355.743 487.792 352.606 491.314 curveto stroke 326.724 499.500 moveto 335.199 496.892 343.823 494.165 352.606 491.314 curveto stroke 380.849 449.215 moveto 384.963 440.265 388.833 431.588 392.471 423.159 curveto stroke 387.570 462.156 moveto 393.161 455.216 399.018 447.244 405.282 438.048 curveto stroke 387.570 462.156 moveto 386.139 462.408 384.694 462.539 383.220 462.551 curveto stroke 416.677 323.249 moveto 415.948 322.820 415.220 322.417 414.490 322.040 curveto stroke 435.000 356.963 moveto 428.540 344.252 422.478 333.098 416.677 323.249 curveto stroke 435.960 371.040 moveto 435.804 366.663 435.486 361.987 435.000 356.963 curveto stroke 414.490 322.040 moveto 405.195 311.187 395.314 299.924 384.798 288.195 curveto stroke 283.510 281.414 moveto 284.298 277.337 285.555 274.108 287.400 271.420 curveto 289.103 268.939 291.353 266.852 294.331 264.989 curveto stroke 294.331 264.989 moveto 291.412 264.110 288.228 263.395 284.728 262.830 curveto stroke 282.906 257.667 moveto 283.516 259.127 284.117 260.829 284.728 262.830 curveto stroke 330.874 254.359 moveto 320.766 253.346 310.274 252.381 299.370 251.460 curveto stroke 264.885 257.461 moveto 271.606 257.093 277.552 257.160 282.906 257.667 curveto stroke 257.302 250.457 moveto 260.072 251.890 262.498 254.131 264.885 257.461 curveto stroke 256.607 250.669 moveto 247.672 255.546 239.144 260.284 230.996 264.896 curveto stroke 257.302 250.457 moveto 257.071 250.528 256.840 250.598 256.607 250.669 curveto stroke 244.443 268.877 moveto 250.683 265.220 257.474 261.427 264.885 257.461 curveto stroke 230.518 271.870 moveto 235.573 270.427 240.175 269.438 244.443 268.877 curveto stroke 230.996 264.896 moveto 230.447 267.052 230.291 269.335 230.518 271.870 curveto stroke 202.189 284.256 moveto 204.643 280.214 207.638 275.947 211.246 271.351 curveto stroke 230.996 264.896 moveto 225.146 266.248 218.656 268.369 211.246 271.351 curveto stroke 230.518 271.870 moveto 224.786 276.437 219.400 280.831 214.335 285.073 curveto stroke 214.335 285.073 moveto 212.289 284.358 210.300 283.940 208.303 283.807 curveto 206.314 283.674 204.297 283.822 202.189 284.256 curveto stroke 321.768 238.763 moveto 327.425 240.635 332.499 242.527 337.071 244.469 curveto stroke 294.793 225.292 moveto 286.269 228.347 279.668 231.649 274.444 235.472 curveto stroke 294.793 225.292 moveto 306.328 226.392 316.710 227.629 326.118 229.023 curveto stroke 229.251 253.122 moveto 231.646 249.810 234.659 246.529 238.397 243.160 curveto stroke 238.397 243.160 moveto 242.267 241.276 246.248 239.364 250.344 237.419 curveto stroke 211.246 271.351 moveto 210.840 269.779 210.603 268.307 210.528 266.900 curveto stroke 255.329 226.108 moveto 249.285 227.725 242.914 229.538 236.175 231.556 curveto stroke 250.344 237.419 moveto 250.692 235.100 251.285 233.025 252.146 231.122 curveto 252.952 229.337 254.002 227.682 255.329 226.108 curveto stroke 228.918 231.005 moveto 224.148 234.340 219.687 237.547 215.511 240.645 curveto stroke 228.918 231.005 moveto 227.670 230.008 226.417 229.215 225.125 228.607 curveto stroke 75.436 311.299 moveto 73.298 306.987 72.080 302.250 71.694 296.742 curveto stroke 230.674 219.108 moveto 242.909 217.210 252.864 216.409 261.279 216.645 curveto stroke 264.064 222.159 moveto 263.118 219.962 262.203 218.150 261.279 216.645 curveto stroke 288.907 220.147 moveto 291.150 221.530 293.083 223.221 294.793 225.292 curveto stroke 62.227 258.626 moveto 57.367 252.978 54.421 247.660 53.028 242.022 curveto 51.579 236.157 51.752 229.702 53.569 221.802 curveto stroke 110.852 494.156 moveto 113.253 491.361 117.346 488.331 124.376 484.145 curveto stroke 165.265 551.582 moveto 162.671 545.627 161.606 540.076 161.957 534.344 curveto stroke 165.265 551.582 moveto 159.569 551.036 153.800 549.225 147.487 546.000 curveto stroke 147.487 546.000 moveto 147.792 550.442 148.967 554.916 151.083 559.701 curveto stroke 151.083 559.701 moveto 146.976 560.224 142.932 559.701 138.523 558.078 curveto stroke 138.523 558.078 moveto 131.515 548.563 125.192 539.716 119.487 531.442 curveto stroke 119.487 531.442 moveto 113.913 529.163 108.257 525.304 101.907 519.449 curveto stroke 141.486 565.031 moveto 140.282 562.615 139.299 560.307 138.523 558.078 curveto stroke 110.536 538.840 moveto 122.302 549.947 132.407 558.498 141.486 565.031 curveto stroke 101.907 519.449 moveto 104.171 525.365 107.025 531.779 110.536 538.840 curveto stroke 111.310 549.169 moveto 110.468 545.495 110.214 542.110 110.536 538.840 curveto stroke 111.310 549.169 moveto 105.512 544.863 99.321 539.318 92.430 532.257 curveto stroke 92.430 532.257 moveto 87.835 522.737 83.705 513.874 80.003 505.582 curveto stroke 80.003 505.582 moveto 82.509 506.137 85.365 506.057 88.918 505.332 curveto stroke 88.918 505.332 moveto 91.873 508.302 94.772 510.769 97.685 512.794 curveto stroke 101.907 519.449 moveto 100.507 517.247 99.100 515.029 97.685 512.794 curveto stroke 113.007 551.496 moveto 112.436 550.716 111.871 549.940 111.310 549.169 curveto stroke 198.826 618.476 moveto 179.723 601.389 161.936 585.255 145.340 569.963 curveto stroke 337.815 573.381 moveto 335.223 572.294 332.937 570.899 330.867 569.144 curveto stroke 333.975 575.041 moveto 335.299 574.494 336.578 573.941 337.815 573.381 curveto stroke 334.555 561.558 moveto 335.338 562.968 336.147 564.192 337.001 565.259 curveto stroke 330.867 569.144 moveto 333.110 567.908 335.147 566.618 337.001 565.259 curveto stroke 341.875 546.057 moveto 346.615 547.742 352.036 548.581 358.546 548.637 curveto stroke 384.525 526.384 moveto 380.990 526.706 377.728 526.584 374.619 526.014 curveto stroke 403.225 504.193 moveto 403.763 506.111 404.034 507.917 404.047 509.675 curveto stroke 404.047 509.675 moveto 410.403 506.983 417.440 503.062 425.606 497.659 curveto stroke 404.047 509.675 moveto 397.818 515.084 391.316 520.649 384.525 526.384 curveto stroke 425.606 497.659 moveto 425.891 497.703 426.173 497.740 426.453 497.770 curveto stroke 426.453 497.770 moveto 427.009 499.478 427.325 501.152 427.409 502.840 curveto 427.495 504.575 427.337 506.343 426.931 508.199 curveto stroke 426.931 508.199 moveto 410.062 518.068 396.774 524.534 385.483 528.369 curveto stroke 385.483 528.369 moveto 385.191 527.745 384.872 527.084 384.525 526.384 curveto stroke 411.589 495.358 moveto 408.833 498.283 406.045 501.227 403.225 504.193 curveto stroke 396.592 506.528 moveto 398.727 505.913 400.931 505.138 403.225 504.193 curveto stroke 396.592 506.528 moveto 397.790 502.898 398.189 499.340 397.817 495.586 curveto stroke 376.257 522.887 moveto 383.291 517.299 390.064 511.850 396.592 506.528 curveto stroke 368.554 517.038 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404.069 200.388 -18.274 -108.892 -95.878 ellipsearc stroke 261.181 433.549 437.741 217.087 -18.274 -106.554 -97.139 ellipsearc stroke 261.181 433.549 471.414 233.787 -18.274 -104.587 -98.218 ellipsearc stroke 261.181 433.549 505.086 250.486 -18.274 -102.906 -99.361 ellipsearc stroke 350.039 315.108 13.570 30.392 -23.208 0 360 ellipsearc closepath stroke 350.039 315.108 27.139 60.783 -23.208 0 360 ellipsearc closepath stroke 350.039 315.108 40.709 91.175 -23.208 0 360 ellipsearc closepath stroke 350.039 315.108 54.278 121.566 -23.208 -41.855 105.789 ellipsearc stroke 350.039 315.108 54.278 121.566 -23.208 169.013 243.530 ellipsearc stroke 350.039 315.108 67.848 151.958 -23.208 -28.680 107.449 ellipsearc stroke 350.039 315.108 67.848 151.958 -23.208 -179.874 -129.645 ellipsearc stroke 350.039 315.108 81.418 182.350 -23.208 41.222 112.701 ellipsearc stroke 350.039 315.108 81.418 182.350 -23.208 -173.474 -137.139 ellipsearc stroke 350.039 315.108 81.418 182.350 -23.208 -21.186 26.543 ellipsearc stroke 350.039 315.108 94.987 212.741 -23.208 45.653 117.493 ellipsearc stroke 350.039 315.108 94.987 212.741 -23.208 -169.219 -142.129 ellipsearc stroke 350.039 315.108 94.987 212.741 -23.208 -16.196 13.065 ellipsearc stroke 350.039 315.108 108.557 243.133 -23.208 45.772 121.368 ellipsearc stroke 350.039 315.108 108.557 243.133 -23.208 -166.163 -145.728 ellipsearc stroke 350.039 315.108 108.557 243.133 -23.208 -12.597 6.015 ellipsearc stroke 350.039 315.108 122.126 273.525 -23.208 45.164 91.098 ellipsearc stroke 350.039 315.108 122.126 273.525 -23.208 110.577 124.478 ellipsearc stroke 350.039 315.108 122.126 273.525 -23.208 -163.856 -148.461 ellipsearc stroke 350.039 315.108 122.126 273.525 -23.208 -9.865 1.207 ellipsearc stroke 350.039 315.108 135.696 303.916 -23.208 44.403 73.340 ellipsearc stroke 350.039 315.108 135.696 303.916 -23.208 -162.050 -150.611 ellipsearc stroke 350.039 315.108 135.696 303.916 -23.208 -7.714 -2.365 ellipsearc stroke 350.039 315.108 149.266 334.308 -23.208 57.948 64.582 ellipsearc stroke 350.039 315.108 149.266 334.308 -23.208 -160.596 -152.351 ellipsearc stroke 350.039 315.108 149.266 334.308 -23.208 -5.975 -5.151 ellipsearc stroke 350.039 315.108 162.835 364.699 -23.208 -159.401 -153.788 ellipsearc stroke 350.039 315.108 176.405 395.091 -23.208 -158.400 -154.996 ellipsearc stroke 350.039 315.108 189.975 425.483 -23.208 -157.550 -156.027 ellipsearc stroke 261.181 433.549 202.034 100.194 -18.274 -5.546 17.332 ellipsearc stroke 261.181 433.549 235.707 116.893 -18.274 -22.454 31.605 ellipsearc stroke 261.181 433.549 269.379 133.592 -18.274 -30.850 38.116 ellipsearc stroke 261.181 433.549 303.052 150.291 -18.274 29.697 42.345 ellipsearc stroke 261.181 433.549 303.052 150.291 -18.274 -36.485 -11.096 ellipsearc stroke 261.181 433.549 336.724 166.990 -18.274 41.781 45.410 ellipsearc stroke 261.181 433.549 336.724 166.990 -18.274 -40.639 -23.180 ellipsearc stroke 261.181 433.549 370.396 183.689 -18.274 -43.865 -30.624 ellipsearc stroke } if % *** draw the Voronoi diagram arcs voronoiarc_flag { voronoiarc_linewidth setlinewidth voronoiarc_color setrgbcolor 108.467 224.625 moveto 305.681 350.558 355.977 386.540 375.643 415.764 curveto 381.527 424.508 385.173 433.395 387.046 443.562 curveto 391.271 466.502 387.097 499.354 371.312 567.375 curveto stroke 534.500 480.605 moveto 491.861 450.545 471.062 432.076 460.183 414.616 curveto 454.883 406.109 451.628 397.344 450.025 387.266 curveto 445.825 360.847 452.222 320.645 475.908 224.625 curveto stroke } if % *** draw the border border_flag { border_linewidth 2 mul setlinewidth border_color setrgbcolor 77.500 224.625 moveto 534.500 224.625 lineto 534.500 567.375 lineto 77.500 567.375 lineto closepath stroke } if % draw a normal diagram over the wedge 494.227 567.375 moveto 77.500 567.375 lineto 77.500 224.625 lineto 298.322 224.625 lineto closepath clip newpath 77.500 429.762 moveto 77.500 224.625 lineto 534.500 224.625 lineto 534.500 439.182 lineto closepath clip 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414.616 curveto 471.062 432.076 491.861 450.545 534.500 480.605 curveto closepath fill 0.254 0.218 0.741 setrgbcolor 534.500 224.625 moveto 534.500 309.952 534.500 395.278 534.500 480.605 curveto 491.861 450.545 471.062 432.076 460.183 414.616 curveto 454.883 406.109 451.628 397.344 450.025 387.266 curveto 445.825 360.847 452.222 320.645 475.908 224.625 curveto 495.438 224.625 514.969 224.625 534.500 224.625 curveto closepath fill } if % *** draw the isocontour arcs isocontour_flag { isocontour_linewidth setlinewidth isocontour_color setrgbcolor % function to draw ellipse arcs % params: xcenter ycenter xradius yradius rotationangle startangle endangle /ellipsearc { /endangle exch def % store function parameters /startangle exch def /rotationangle exch def /yradius exch def /xradius exch def /ycenter exch def /xcenter exch def matrix currentmatrix % preserve matrix xcenter ycenter translate rotationangle rotate xradius yradius scale 0 0 1 startangle endangle arc setmatrix % restore 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336.724 166.990 -18.274 -40.639 -23.180 ellipsearc stroke 261.181 433.549 370.396 183.689 -18.274 -43.865 -30.624 ellipsearc stroke } if % *** draw the Voronoi diagram arcs voronoiarc_flag { voronoiarc_linewidth setlinewidth voronoiarc_color setrgbcolor 108.467 224.625 moveto 305.681 350.558 355.977 386.540 375.643 415.764 curveto 381.527 424.508 385.173 433.395 387.046 443.562 curveto 391.271 466.502 387.097 499.354 371.312 567.375 curveto stroke 534.500 480.605 moveto 491.861 450.545 471.062 432.076 460.183 414.616 curveto 454.883 406.109 451.628 397.344 450.025 387.266 curveto 445.825 360.847 452.222 320.645 475.908 224.625 curveto stroke } if % *** draw the border border_flag { border_linewidth 2 mul setlinewidth border_color setrgbcolor 77.500 224.625 moveto 534.500 224.625 lineto 534.500 567.375 lineto 77.500 567.375 lineto closepath stroke } if grestore % draw the wedge voronoiarc_linewidth setlinewidth voronoiarc_color setrgbcolor 298.322 224.625 moveto 419.602 436.814 lineto 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Fq(v)5 b Ft(\))p Fq(:)4080 10581 y Fv(Let)52 b Fq(q)57 b Fv(be)52 b(an)n(y)f(point)f(that)h (satis\002es)h(these)g(inequalities.)88 b(The)52 b(visibility)4080 10755 y(claim)34 b(is)f(that)g Fq(q)4911 10692 y Fs(0)4998 10755 y Ft(=)43 b Fq(\025q)25 b Ft(+)20 b(\(1)g Fk(\000)g Fq(\025)p Ft(\))p Fq(v)38 b Fv(satis\002es)c(these)g(inequalities)d(as) k(well,)p eop %%Page: 4 4 4 3 bop -303 -137 a Fv(for)40 b Ft(0)51 b Fq(<)g(\025)f(<)h Ft(1)p Fv(.)59 b(This)42 b(claim)f(can)h(be)g(v)n(eri\002ed)f(by)g (substituting)d Fq(q)3306 -201 y Fs(0)3392 -137 y Fv(for)j Fq(q)-303 37 y Fv(and)k(sho)l(wing)f(that)h(the)g(inequalities)f(hold)g (for)h Fq(q)2344 -26 y Fs(0)2389 37 y Fv(,)j(gi)l(v)n(en)d(that)f(the)n (y)h(hold)-303 211 y(for)36 b Fq(q)5 b Fv(.)47 b(The)38 b(result)e(holds)g(for)h Fq(w)k Fv(by)c(symmetry)-10 b(.)1284 b Fh(\004)-154 423 y Fv(Lemma)45 b(3)e(is)g(tight.)63 b(The)44 b(visibility)c(property)h(stops)i(precisely)g(where)-303 598 y(the)37 b(V)-19 b(oronoi)35 b(surf)o(ace)i(e)n(xits)f(the)h (wedge.)-133 864 y(D)8 b Fg(E)g(FI)g(N)g(I)g(T)g(I)g(O)g(N)82 b Fv(3.)75 b Fu(A)65 b(V)-17 b(or)-7 b(onoi)64 b Fq(k)t Fu(-face)h Fq(f)111 b Fk(\022)96 b Ft(V)-13 b(or\()p Fq(W)21 b Ft(\))p Fu(,)72 b(with)63 b Ft(0)95 b Fk(\024)-303 1039 y Fq(k)g(<)d(d)p Fu(,)69 b(is)63 b(said)f(to)g(be)h Fv(wedged)f Fu(if)g(for)h(e)n(very)h(pair)e(of)g(distinct)f(sites)-303 1213 y Fq(v)-228 1230 y Fj(1)-160 1213 y Fq(;)26 b(v)-16 1230 y Fj(2)95 1213 y Fk(2)43 b Fq(W)21 b Fu(,)38 b(e)n(very)f(point)e Fq(q)42 b Fu(on)35 b Fq(f)53 b Fu(falls)35 b(inside)g Ft(w)l(edge)q(\()p Fq(v)2834 1230 y Fj(1)2902 1213 y Fq(;)25 b(v)3045 1230 y Fj(2)3114 1213 y Ft(\))p Fu(.)46 b(F)-16 b(or)37 b(e)m(x-)-303 1387 y(ample)o(,)43 b Fq(f)68 b Fk(\022)53 b Ft(V)-13 b(or\()p Fk(f)p Fq(v)908 1404 y Fj(1)976 1387 y Fq(;)26 b(v)1120 1404 y Fj(2)1189 1387 y Fq(;)f(v)1332 1404 y Fj(3)1401 1387 y Fk(g)p Ft(\))42 b Fu(is)g(wedg)o(ed)f(if)h Fq(f)68 b Fk(\022)53 b Ft(w)l(edge)q(\()p Fq(v)3201 1404 y Fj(1)3269 1387 y Fq(;)26 b(v)3413 1404 y Fj(2)3481 1387 y Ft(\))38 b Fk(\\)-303 1562 y Ft(w)l(edge\()p Fq(v)237 1579 y Fj(2)306 1562 y Fq(;)25 b(v)449 1579 y Fj(3)518 1562 y Ft(\))33 b Fk(\\)i Ft(w)l(edge\()p Fq(v)1288 1579 y Fj(3)1357 1562 y Fq(;)25 b(v)1500 1579 y Fj(1)1569 1562 y Ft(\))p Fu(.)-133 1828 y Fv(T)8 b Fg(H)g(E)g(O)g(R)g(E)g(M)42 b Fv(4)165 b(\()8 b(V)g Fg(I)g(S)g(I)g(B)g (I)g(L)g(I)g(T)g(Y)38 b Fv(T)8 b Fg(H)g(E)g(O)g(R)g(E)g(M)g Fv(\))t(.)79 b Fu(If)27 b(e)n(very)j(lower)m(-dimen-)-303 2003 y(sional)j(face)i(of)g(a)g Fq(d)p Fu(-face)f(of)g Ft(V)-13 b(or)q(\()p Fq(v)5 b Ft(\))34 b Fu(is)h(wedg)o(ed,)g(then)f (the)h Fq(d)p Fu(-face)g(is)f(star)m(-)-303 2177 y(shaped)i(and)h(e)n (very)i(point)c(in)i(the)g Fq(d)p Fu(-face)f(is)h(visible)g(fr)-7 b(om)37 b Fq(v)5 b Fu(.)-150 2444 y Fv(P)j Fg(R)s(O)g(O)g(F)m Fv(.)68 b(F)n(or)44 b(the)f(sak)o(e)h(of)g(contradiction,)f(let)h Fq(p)g Fv(be)g(a)g(point)f(in)g(the)g Fq(d)p Fv(-)-303 2618 y(f)o(ace)35 b(that)g(is)f(not)h(visible)e(from)i Fq(v)5 b Fv(.)46 b(Let)36 b Fq(q)k Fv(be)35 b(the)g(point)e(furthest)h (from)h Fq(p)g Fv(on)-303 2792 y(the)k(line)g(se)n(gment)h Fq(pv)45 b Fv(that)39 b(is)h(visible)e(from)i Fq(p)p Fv(.)55 b(Because)40 b Fq(p)h Fv(is)e(not)g(visible)-303 2967 y(from)29 b Fq(v)5 b Fv(,)31 b(neither)d(is)h Fq(q)5 b Fv(.)44 b(Let)30 b Fq(w)j Fv(be)d(the)f(o)l(wner)g(of)g(the)g (\002rst)g(f)o(ace)g(encountered)-303 3141 y(strictly)36 b(after)h Fq(q)43 b Fv(on)38 b(the)f(ray)65 b Fq(~)-104 b(q)5 b(v)g Fv(.)48 b(Then)38 b Fq(q)43 b Fv(lies)37 b(on)h(a)g(f)o(ace)g(o)l(wned)g(by)f Fq(v)43 b Fv(and)-303 3315 y Fq(w)t Fv(.)j(By)37 b(assumption)f(this)g(f)o(ace)h(is)g (wedged.)46 b(Imagine)37 b(a)g(V)-19 b(oronoi)35 b(diagram)-303 3490 y(with)56 b(sites)i Fq(v)63 b Fv(and)57 b Fq(w)62 b Fv(only)-10 b(.)107 b(In)58 b(this)e(diagram)i Fq(q)63 b Fv(is)57 b(in)g Ft(V)-13 b(or)q(\()p Fq(v)5 b Ft(\))57 b Fv(and)g(in)-303 3664 y Ft(w)l(edge\()p Fq(v)5 b(;)25 b(w)t Ft(\))p Fv(,)31 b(b)m(ut)d Fq(q)35 b Fv(is)28 b(not)h(visible)e (from)i Fq(v)5 b Fv(,)31 b(contradicting)c(Lemma)k(3.)e Fh(\004)-154 4050 y Fv(The)60 b(follo)l(wing)d(lemma)k(implies)e(that)g (if)g(a)h(V)-19 b(oronoi)58 b(surf)o(ace)h(is)h(not)-303 4225 y(wedged,)32 b(we)f(can)h(insert)e(a)h(ne)l(w)h(site)e(on)h(it)f (that)g(is)h(not)f(close)h(to)g(an)g(e)n(xisting)-303 4399 y(site\227a)37 b(handy)g(tool)f(for)g(mesh)i(generation.)-133 4666 y(L)8 b Fg(E)g(M)g(M)g(A)85 b Fv(5.)75 b Fu(Let)28 b Fq(q)34 b Fu(be)29 b(a)f(point)f(in)h Ft(V)-13 b(or\()p Fq(v)5 b Ft(\))q Fk(\\)q Ft(V)-13 b(or\()p Fq(w)t Ft(\))28 b Fu(that)f(lies)h(outside)-303 4840 y Ft(w)l(edge\()p Fq(v)5 b(;)25 b(w)t Ft(\))42 b Fu(on)g(the)g(side)g(of)f Fq(w)t Fu(.)62 b(Let)42 b Fq(\015)61 b Fk(\025)53 b Ft(1)42 b Fu(be)g(a)g(constant)f(for)h(whic)n(h)-303 5014 y Fq(\034)17 b Ft(\()p Fq(v)5 b(;)24 b(w)t Ft(\))65 b Fk(\024)f Fq(\015)9 b Fu(.)81 b(Then)49 b(the)f(pr)-7 b(oximity)48 b(of)g Fq(q)54 b Fu(to)48 b Fq(v)54 b Fu(and)48 b Fq(w)53 b Fu(is)48 b(bounded)g(by)-303 5210 y Fq(d)-223 5227 y Fp(v)-150 5210 y Ft(\()p Fq(q)5 b Ft(\))42 b(=)i Fq(d)329 5227 y Fp(w)428 5210 y Ft(\()p Fq(q)5 b Ft(\))42 b Fk(\025)h Fq(d)906 5227 y Fp(w)1006 5210 y Ft(\()p Fq(v)5 b Ft(\))p Fq(=)1283 5081 y Fi(p)p 1436 5081 422 7 v 1436 5210 a Fq(\015)1524 5168 y Fj(2)1627 5210 y Fk(\000)35 b Ft(1)o Fu(.)-150 5477 y Fv(P)8 b Fg(R)s(O)g(O)g(F)m Fv(.)59 b(Because)42 b Fq(q)j Fv(is)c(on)f Fq(w)t Fv(')-8 b(s)41 b(side)f(of)g Ft(w)l(edge)q(\()p Fq(v)5 b(;)25 b(w)t Ft(\))p Fv(,)42 b Fq(d)3003 5494 y Fp(w)3102 5477 y Ft(\()p Fq(q)5 b(;)25 b(v)5 b Ft(\))3444 5413 y Fj(2)3562 5477 y Fk(\025)-303 5651 y Fq(d)-223 5668 y Fp(w)-124 5651 y Ft(\()p Fq(q)g Ft(\))70 5588 y Fj(2)194 5651 y Ft(+)55 b Fq(d)448 5668 y Fp(w)547 5651 y Ft(\()p Fq(v)5 b Ft(\))747 5588 y Fj(2)880 5651 y Fv(by)64 b(Pythagoras')g(Theorem.)128 b(By)64 b(Proposition)e(1,)-303 5826 y Fq(d)-223 5843 y Fp(w)-124 5826 y Ft(\()p Fq(q)5 b(;)25 b(v)5 b Ft(\))218 5762 y Fj(2)330 5826 y Fk(\024)44 b Fq(\034)17 b Ft(\()p Fq(v)5 b(;)24 b(w)t Ft(\))959 5762 y Fj(2)1028 5826 y Fq(d)1108 5843 y Fp(v)1182 5826 y Ft(\()p Fq(q)5 b Ft(\))1376 5762 y Fj(2)1488 5826 y Fk(\024)43 b Fq(\015)1738 5762 y Fj(2)1807 5826 y Fq(d)1887 5843 y Fp(v)1961 5826 y Ft(\()p Fq(q)5 b Ft(\))2155 5762 y Fj(2)2224 5826 y Fv(.)47 b(Because)39 b Fq(q)48 b Fk(2)43 b Ft(V)-13 b(or)q(\()p Fq(v)5 b Ft(\))33 b Fk(\\)-303 6000 y Ft(V)-13 b(or\()p Fq(w)t Ft(\))p Fv(,)31 b Fq(d)318 6017 y Fp(v)392 6000 y Ft(\()p Fq(q)5 b Ft(\))42 b(=)h Fq(d)870 6017 y Fp(w)970 6000 y Ft(\()p Fq(q)5 b Ft(\))p Fv(.)43 b(The)31 b(result)e(follo)l(ws) f(by)i(combining)e(inequal-)-303 6174 y(ities)36 b(and)h(rearranging)f (terms.)2231 b Fh(\004)-154 6561 y Fv(The)35 b(rest)g(of)f(this)g (section)g(applies)g(to)g(the)h(tw)o(o-dimensional)c(case)36 b(only)-10 b(.)-133 6827 y(L)8 b Fg(E)g(M)g(M)g(A)43 b Fv(6)165 b(\()8 b(T)g Fg(R)g(I)g(A)g(N)g(G)g(L)g(E)41 b Fv(O)8 b Fg(R)g(I)g(E)g(N)g(T)m(A)-5 b(T)8 b(I)g(O)g(N)39 b Fv(L)8 b Fg(E)g(M)g(M)g(A)g Fv(\))d(.)79 b Fu(Let)63 b Fq(q)k Fu(be)c(a)-303 7002 y(V)-17 b(or)-7 b(onoi)47 b(verte)m(x)i(owned)e(by)g(the)h(sites)f Fq(v)1866 7019 y Fj(1)1935 7002 y Fq(;)25 b(v)2078 7019 y Fj(2)2147 7002 y Fq(;)g(v)2290 7019 y Fj(3)2359 7002 y Fu(.)78 b(If)47 b Fq(q)52 b Fu(is)c(wedg)o(ed,)h(then)-303 7176 y(the)44 b(orientation)e(of)i(the)h(triangle)e Fq(v)1615 7193 y Fj(1)1684 7176 y Fq(v)1759 7193 y Fj(2)1827 7176 y Fq(v)1902 7193 y Fj(3)2016 7176 y Fu(matc)n(hes)h(the)h(or)-6 b(dering)44 b(of)g(the)-303 7350 y(cells)39 b Ft(V)-13 b(or\()p Fq(v)384 7367 y Fj(1)452 7350 y Ft(\))p Fq(;)25 b Ft(V)-13 b(or)q(\()p Fq(v)955 7367 y Fj(2)1023 7350 y Ft(\))p Fq(;)25 b Ft(V)-13 b(or\()p Fq(v)1525 7367 y Fj(3)1594 7350 y Ft(\))39 b Fu(locally)f(ar)-7 b(ound)38 b Fq(q)5 b Fu(.)52 b(In)39 b(other)f(wor)-6 b(ds,)-303 7525 y(if)48 b(at)h Fq(q)55 b Fu(the)49 b(cells)g Ft(V)-13 b(or)q(\()p Fq(v)1049 7542 y Fj(1)1117 7525 y Ft(\))p Fq(;)25 b Ft(V)-13 b(or\()p Fq(v)1619 7542 y Fj(2)1688 7525 y Ft(\))p Fq(;)25 b 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Fv(from)f Fq(v)3613 6065 y Fj(2)-303 6222 y Fv(\(b)m(ut)46 b(on)h(the)g(triangle-side)f(of) h(edges)h Fq(v)1839 6239 y Fj(1)1908 6222 y Fq(v)1983 6239 y Fj(2)2099 6222 y Fv(and)g Fq(v)2438 6239 y Fj(2)2507 6222 y Fq(v)2582 6239 y Fj(3)2650 6222 y Fv(\))g(as)g(illustrated)d(in) -303 6397 y(Figure)j(5)g(\(left\).)80 b(As)49 b(measured)g(by)g Fq(v)1786 6414 y Fj(2)1854 6397 y Fv(,)j Fh(\\)p Fq(v)2129 6414 y Fj(2)2198 6397 y Fq(q)5 b(v)2347 6414 y Fj(1)2459 6397 y Ft(+)43 b Fh(\\)p Fq(v)2807 6414 y Fj(2)2876 6397 y Fq(q)5 b(v)3025 6414 y Fj(3)3158 6397 y Fq(<)65 b Ft(180)3573 6333 y Fs(\016)3644 6397 y Fv(.)-303 6571 y(Assume)38 b(without)d(loss)i(of)g(generality)f(that)g Fh(\\)p Fq(v)2224 6588 y Fj(2)2293 6571 y Fq(q)5 b(v)2442 6588 y Fj(1)2554 6571 y Fq(<)43 b Ft(90)2870 6507 y Fs(\016)2942 6571 y Fv(.)k(If)37 b(we)h(com-)-303 6745 y(pute)54 b(the)h(angle)f Fq(\036)77 b Ft(=)f Fh(\\)p Fq(q)5 b(v)1248 6762 y Fj(1)1317 6745 y Fq(v)1392 6762 y Fj(2)1516 6745 y Fv(as)55 b(before,)60 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7443 y Fq(q)5 b(v)2360 7460 y Fj(1)2488 7443 y Fq(<)61 b Ft(90)2822 7379 y Fs(\016)2893 7443 y Fv(,)49 b(this)d(implies)-303 7617 y(that)g Ft(sin)26 b Fh(\\)p Fq(v)369 7634 y Fj(1)437 7617 y Fq(v)512 7634 y Fj(2)581 7617 y Fq(q)67 b Fk(\025)c Fq(\037)p Fv(,)50 b(which)d(in)g(turn)g(implies)f(that)h Fq(\022)67 b Fk(\025)62 b Fh(\\)p Fq(v)3213 7634 y Fj(1)3282 7617 y Fq(v)3357 7634 y Fj(2)3426 7617 y Fq(q)67 b Fk(\025)-303 7791 y Ft(arcsin)25 b Fq(\037)37 b Fv(as)h(measured)g(by)f Fq(v)1283 7808 y Fj(2)1351 7791 y Fv(.)-154 7966 y(The)51 b(proof)f(of)g(Lemma)i (6)e(tells)g(us)h(there)f(are)h(only)f(tw)o(o)f(other)h(cases:)-303 8140 y(either)38 b Fq(q)43 b Fv(lies)38 b(in)g Fq(t)p Fv(,)i(or)e Fq(q)44 b Fv(lies)38 b(on)g(the)g(opposite)f(side)i(of)f(e) n(xactly)g(one)g(edge,)-303 8314 y Fq(v)-228 8331 y Fj(1)-160 8314 y Fq(v)-85 8331 y Fj(2)35 8314 y Fv(or)51 b Fq(v)286 8331 y Fj(2)354 8314 y Fq(v)429 8331 y Fj(3)498 8314 y Fv(\227assume)i(without)48 b(loss)j(of)f(generality)g Fq(v)2829 8331 y Fj(2)2898 8314 y Fq(v)2973 8331 y Fj(3)3041 8314 y Fv(.)88 b(In)50 b(either)-303 8489 y(case)32 b(the)e(line)g Fq(v)528 8506 y Fj(1)597 8489 y Fq(q)36 b Fv(cuts)30 b(the)h(angle)g Fh(\\)p Fq(v)1728 8506 y Fj(3)1796 8489 y Fq(v)1871 8506 y Fj(1)1940 8489 y Fq(v)2015 8506 y Fj(2)2084 8489 y Fv(.)44 b(Consider)30 b(Figure)g(5)h(\(right\),)-303 8663 y(dra)n(wn)51 b(from)i Fq(v)539 8680 y Fj(1)607 8663 y Fv(')-8 b(s)53 b(perspecti)l(v)n(e,)j(where)d Fq(t)g Fv(achie)l(v)n(es)g Ft(sin)25 b Fq(\022)76 b Ft(=)c(cos)25 b Fq(\036)72 b Ft(=)-303 8837 y Fq(\037)p Fv(.)96 b(In)54 b(the)g(\002gure,)k(imagine)c Fq(v)1397 8854 y Fj(1)1520 8837 y Fv(and)g Fq(q)59 b Fv(are)54 b(\002x)n(ed.)97 b(W)-12 b(e)55 b(claim)f(that)f(the)-303 9012 y(illustrated)35 b(positions)g(of)i Fq(v)1146 9029 y Fj(2)1252 9012 y Fv(and)g Fq(v)1580 9029 y Fj(3)1686 9012 y Fv(minimize)g Fq(\022)t Fv(.)-154 9186 y(F)n(or)32 b(the)g(case)i(where)f Fq(q)38 b Fv(lies)32 b(on)g(the)g(opposite)g(side)g(of)g Fq(v)2776 9203 y Fj(2)2845 9186 y Fq(v)2920 9203 y Fj(3)2989 9186 y Fv(,)i(we)f(choose)-303 9360 y(to)27 b(measure)j Fq(\022)46 b Ft(=)e Fh(\\)p Fq(v)835 9377 y Fj(1)903 9360 y Fq(v)978 9377 y Fj(2)1047 9360 y Fq(v)1122 9377 y Fj(3)1219 9360 y Fv(from)28 b Fq(v)1613 9377 y Fj(1)1682 9360 y Fv(')-8 b(s)28 b(perspecti)l(v)n(e.)43 b(Because)30 b Fq(d)3172 9377 y Fp(v)3234 9396 y Fd(1)3307 9360 y Ft(\()p Fq(v)3442 9377 y Fj(2)3510 9360 y Ft(\))42 b Fk(\025)-303 9535 y Fq(r)t(=\014)51 b Fv(and)43 b Fq(d)324 9552 y Fp(v)386 9571 y Fd(1)458 9535 y Ft(\()p Fq(v)593 9552 y Fj(2)662 9535 y Fq(;)25 b(q)5 b Ft(\))54 b Fk(\024)g Fq(\015)9 b(r)t Fv(,)45 b Fq(v)1409 9552 y Fj(2)1521 9535 y Fv(is)e(constrained)f(to)h(lie)f Fu(inside)h Fv(the)f(illus-) -303 9709 y(trated)g(circle)h(\(which)f(circumscribes)i(our)e(proposed) g(w)o(orst-case)h Fq(t)p Fv(\).)64 b(By)-303 9883 y(circle)47 b(geometry)-10 b(,)50 b(mo)n(ving)c Fq(v)1295 9900 y Fj(2)1412 9883 y Fv(subject)h(to)g(this)f(constraint)g(can)i(only)f (in-)-303 10058 y(crease)h Fq(\022)t Fv(.)75 b(Once)47 b Fq(v)742 10075 y Fj(2)858 10058 y Fv(is)g(\002x)n(ed,)i(mo)n(ving)c Fq(v)1964 10075 y Fj(3)2080 10058 y Fv(subject)h(to)g(the)h (symmetrical)-303 10232 y(constraints)35 b Fq(d)461 10249 y Fp(v)523 10268 y Fd(1)596 10232 y Ft(\()p Fq(v)731 10249 y Fj(3)799 10232 y Ft(\))42 b Fk(\025)i Fq(r)t(=\014)g Fv(and)36 b Fq(d)1677 10249 y Fp(v)1739 10268 y Fd(1)1812 10232 y Ft(\()p Fq(v)1947 10249 y Fj(3)2015 10232 y Fq(;)26 b(q)5 b Ft(\))42 b Fk(\024)h Fq(\015)9 b(r)41 b Fv(cannot)36 b(decrease)i Fq(\022)-303 10406 y Fv(either)-8 b(.)45 b(Therefore)38 b(from)f Fq(v)1142 10423 y Fj(1)1210 10406 y Fv(')-8 b(s)38 b(perspecti)l(v)n(e,)f Fq(\022)47 b Fk(\025)c Ft(arcsin)25 b Fq(\037)p Fv(.)-154 10581 y(F)n(or)38 b(the)h(case)h(where)f Fq(q)44 b Fv(lies)39 b(in)f Fq(t)p Fv(,)j(there)d(are)i(tw)o(o)d(other)i(con\002gurations)-303 10755 y(of)f(the)g(v)n(ertices)g(that)f(sometimes)i(locally)e(minimize) h Fq(\022)t Fv(,)i(b)m(ut)d(the)h(case)i(just)4080 -137 y(described)h(is)g(al)o(w)o(ays)f(the)h(global)e(minimum)i(for)f(the)h (ranges)g(of)g Fq(\015)50 b Fv(and)41 b Fq(\014)4080 37 y Fv(speci\002ed)d(in)e(the)h(theorem.)47 b(Details)37 b(are)g(omitted.)4230 211 y(Rotate)57 b(the)h(v)n(erte)n(x)f(labels)h (and)g(repeat)h(the)f(ar)m(gument)g(to)f(pro)n(vide)g(a)4080 386 y(lo)l(wer)37 b(bound)f(for)h(all)f(three)i(angles)f(of)g Fq(t)p Fv(.)1673 b Fh(\004)4250 649 y Fv(C)8 b Fg(O)g(R)s(O)g(L)g(L)g (A)g(RY)83 b Fv(10.)74 b Fu(Let)43 b Fq(q)5 b Fu(,)44 b Fq(v)5859 666 y Fj(1)5928 649 y Fu(,)h Fq(v)6085 666 y Fj(2)6153 649 y Fu(,)g Fq(v)6310 666 y Fj(3)6379 649 y Fu(,)f Fq(\015)9 b Fu(,)44 b(and)e Fq(\014)50 b Fu(satisfy)42 b(the)g(condi-)4080 824 y(tions)30 b(of)g(Theor)-6 b(em)32 b(9.)44 b(Let)31 b Fq(p)g Fu(be)g(an)g(arbitr)n(ary)f(point)f(suc)n(h)i (that)e Fq(\034)17 b Ft(\()p Fq(p;)25 b(v)7791 841 y Fp(i)7843 824 y Ft(\))43 b Fk(\024)4080 998 y Fq(\015)54 b Fu(for)44 b Fq(i)56 b Fk(2)i(f)p Ft(1)p Fq(;)25 b Ft(2)p Fq(;)g Ft(3)p Fk(g)p 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y(the)c(same)h(angle)e(as)i(measured)f(by)g Fq(v)6103 1802 y Fp(i)6155 1785 y Fv(.)79 b(By)47 b(Theorem)h(9,)j(for) c(some)i Fq(j)71 b Fk(2)4080 1959 y(f)p Ft(1)p Fq(;)25 b Ft(2)p Fq(;)g Ft(3)p Fk(g)p Fv(,)44 b(either)e Ft(sin)25 b Fq(\022)5351 1976 y Fp(v)5413 1997 y Fa(j)5536 1959 y Fk(\025)53 b Fq(\037)43 b Fv(or)f Fq(\022)6086 1976 y Fp(v)6148 1997 y Fa(j)6271 1959 y Fk(\025)53 b Ft(90)6597 1896 y Fs(\016)6669 1959 y Fv(.)62 b(Let)43 b Fq(A)7125 1976 y Fp(p)7240 1959 y Fv(be)g(the)f(area)i(of)4080 2134 y Fq(t)39 b Fv(as)g(measured)h(by)e Fq(p)p Fv(,)h(and)f Fq(A)5659 2151 y Fp(v)5721 2172 y Fa(j)5831 2134 y Fv(the)g(area)h(of)f Fq(t)i Fv(as)f(measured)g(by)f Fq(v)7634 2151 y Fp(j)7699 2134 y Fv(.)50 b(By)38 b(a)4080 2308 y(well-kno)l(wn)e(formula)g(for)h (the)g(sine)g(of)g(an)g(angle,)4269 2694 y Ft(sin)25 b Fq(\022)4555 2711 y Fp(p)4777 2694 y Ft(=)5561 2598 y(2)p Fq(A)5753 2615 y Fp(p)p 5066 2660 1255 7 v 5066 2796 a Fq(d)5146 2813 y Fp(p)5218 2796 y Ft(\()p Fq(v)5353 2813 y Fj(1)5421 2796 y Fq(;)g(v)5564 2813 y Fj(2)5633 2796 y Ft(\))p Fq(d)5773 2813 y Fp(p)5845 2796 y Ft(\()p Fq(v)5980 2813 y Fj(2)6048 2796 y Fq(;)h(v)6192 2813 y Fj(3)6260 2796 y Ft(\))6383 2694 y(=)6623 2572 y(2)p Fq(A)6815 2589 y Fp(v)6877 2610 y Fa(j)6973 2572 y Ft(det)q(\()p Fq(F)7345 2589 y Fp(p)7417 2572 y Fq(F)7536 2508 y Fs(\000)p Fj(1)7515 2598 y Fp(v)7577 2619 y Fa(j)7701 2572 y Ft(\))p 6565 2660 V 6565 2796 a Fq(d)6645 2813 y Fp(p)6717 2796 y Ft(\()p Fq(v)6852 2813 y Fj(1)6920 2796 y Fq(;)f(v)7063 2813 y Fj(2)7132 2796 y Ft(\))p Fq(d)7272 2813 y Fp(p)7344 2796 y Ft(\()p Fq(v)7479 2813 y Fj(2)7547 2796 y Fq(;)h(v)7691 2813 y Fj(3)7759 2796 y Ft(\))4777 3150 y Fk(\025)5184 3027 y Ft(2)p Fq(A)5376 3044 y Fp(v)5438 3065 y Fa(j)5508 3027 y Fk(k)p Fq(F)5683 3044 y Fp(p)5755 3027 y Fq(F)5874 2964 y Fs(\000)p Fj(1)5853 3054 y Fp(v)5915 3075 y Fa(j)6040 3027 y Fk(k)6117 3044 y Fj(2)6186 3027 y Fq(=)p Fk(k)p Fq(F)6438 3044 y Fp(v)6500 3065 y Fa(j)6570 3027 y Fq(F)6689 2964 y Fs(\000)p 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9545 4909 l 9556 4888 l 9566 4868 l 9575 4850 l 9583 4834 l 9589 4822 l 9594 4812 l 9597 4805 l 9599 4802 l 9600 4800 l gs col0 s gr % Polyline n 600 4800 m 601 4801 l 602 4803 l 604 4807 l 608 4814 l 613 4823 l 621 4836 l 630 4852 l 641 4871 l 655 4894 l 671 4921 l 689 4950 l 710 4984 l 732 5020 l 757 5058 l 783 5099 l 811 5142 l 841 5186 l 872 5232 l 904 5278 l 938 5325 l 972 5372 l 1008 5419 l 1045 5465 l 1083 5511 l 1121 5555 l 1161 5599 l 1202 5641 l 1245 5683 l 1288 5722 l 1333 5760 l 1380 5796 l 1428 5830 l 1479 5862 l 1531 5891 l 1585 5917 l 1642 5941 l 1700 5961 l 1760 5977 l 1822 5990 l 1886 5997 l 1950 6000 l 2014 5997 l 2078 5990 l 2140 5977 l 2200 5961 l 2258 5941 l 2315 5917 l 2369 5891 l 2421 5862 l 2472 5830 l 2520 5796 l 2567 5760 l 2612 5722 l 2655 5683 l 2698 5641 l 2739 5599 l 2779 5555 l 2817 5511 l 2855 5465 l 2892 5419 l 2928 5372 l 2963 5325 l 2996 5278 l 3028 5232 l 3059 5186 l 3089 5142 l 3117 5099 l 3143 5058 l 3168 5020 l 3190 4984 l 3211 4950 l 3229 4921 l 3245 4894 l 3259 4871 l 3270 4852 l 3279 4836 l 3287 4823 l 3292 4814 l 3296 4807 l 3298 4803 l 3299 4801 l 3300 4800 l gs col0 s gr % Polyline n 2325 5325 m 2325 5327 l 2326 5332 l 2328 5341 l 2330 5355 l 2333 5374 l 2338 5398 l 2343 5427 l 2349 5460 l 2356 5497 l 2364 5537 l 2372 5578 l 2381 5620 l 2391 5663 l 2401 5705 l 2411 5746 l 2422 5786 l 2433 5823 l 2445 5858 l 2457 5891 l 2471 5921 l 2485 5947 l 2500 5969 l 2516 5985 l 2533 5996 l 2550 6000 l 2567 5996 l 2584 5985 l 2600 5969 l 2615 5947 l 2629 5921 l 2643 5891 l 2655 5858 l 2667 5823 l 2678 5786 l 2689 5746 l 2699 5705 l 2709 5663 l 2719 5620 l 2728 5578 l 2736 5537 l 2744 5497 l 2751 5460 l 2757 5427 l 2762 5398 l 2767 5374 l 2770 5355 l 2772 5341 l 2774 5332 l 2775 5327 l 2775 5325 l gs col0 s gr % Polyline 0 slj 0.000 slw n 6075 5775 m 5925 5625 l 6075 5625 l cp gs col7 1.00 shd ef gr % Polyline n 6300 4800 m 6525 4800 l 6525 5100 l 6300 5100 l cp gs col7 1.00 shd ef gr % Polyline n 7575 4800 m 8325 4800 l 8325 5775 l 7575 5775 l cp gs col7 1.00 shd ef gr % Polyline n 8700 5400 m 9000 5400 l 9000 5798 l 8700 5798 l cp gs col7 1.00 shd ef gr % Polyline n 5400 4800 m 6225 4800 l 6225 5699 l 5400 5699 l cp gs col7 1.00 shd ef gr % Polyline n 525 4725 m 1350 4725 l 1350 5850 l 525 5850 l cp gs col7 1.00 shd ef gr % Polyline n 2250 5250 m 2250 5850 l 2613 5869 l 2706 5614 l 2850 5416 l 2850 5250 l cp gs col7 1.00 shd ef gr % Polyline n 3300 4725 m 4071 4725 l 4071 5925 l 3300 5925 l cp gs col7 1.00 shd ef gr % Polyline 2 slj 30.000 slw n 3300 4800 m 3300 4802 l 3301 4805 l 3303 4811 l 3305 4822 l 3309 4836 l 3314 4855 l 3320 4878 l 3328 4907 l 3337 4940 l 3347 4978 l 3359 5020 l 3371 5065 l 3385 5113 l 3400 5164 l 3416 5217 l 3433 5270 l 3450 5325 l 3468 5380 l 3487 5434 l 3506 5488 l 3526 5540 l 3546 5592 l 3568 5641 l 3590 5689 l 3613 5735 l 3636 5778 l 3661 5819 l 3687 5856 l 3714 5891 l 3742 5921 l 3771 5948 l 3802 5970 l 3834 5986 l 3867 5996 l 3900 6000 l 3933 5996 l 3966 5986 l 3998 5970 l 4029 5948 l 4058 5921 l 4086 5891 l 4113 5856 l 4139 5819 l 4164 5778 l 4187 5735 l 4210 5689 l 4232 5641 l 4254 5592 l 4274 5540 l 4294 5488 l 4313 5434 l 4332 5380 l 4350 5325 l 4367 5270 l 4384 5217 l 4400 5164 l 4415 5113 l 4429 5065 l 4441 5020 l 4453 4978 l 4463 4940 l 4472 4907 l 4480 4878 l 4486 4855 l 4491 4836 l 4495 4822 l 4497 4811 l 4499 4805 l 4500 4802 l 4500 4800 l gs col0 s gr % Polyline n 900 4800 m 900 4802 l 901 4806 l 903 4813 l 905 4825 l 908 4842 l 912 4864 l 918 4891 l 924 4924 l 932 4962 l 941 5004 l 951 5051 l 961 5102 l 973 5155 l 986 5210 l 999 5267 l 1013 5325 l 1027 5383 l 1042 5440 l 1057 5497 l 1073 5553 l 1089 5607 l 1107 5659 l 1124 5708 l 1143 5756 l 1162 5800 l 1182 5841 l 1203 5879 l 1225 5913 l 1248 5942 l 1273 5966 l 1298 5984 l 1324 5996 l 1350 6000 l 1376 5996 l 1402 5984 l 1427 5966 l 1452 5942 l 1475 5913 l 1497 5879 l 1518 5841 l 1538 5800 l 1557 5756 l 1576 5708 l 1593 5659 l 1611 5607 l 1627 5553 l 1643 5497 l 1658 5440 l 1673 5383 l 1688 5325 l 1701 5267 l 1714 5210 l 1727 5155 l 1739 5102 l 1749 5051 l 1759 5004 l 1768 4962 l 1776 4924 l 1782 4891 l 1788 4864 l 1792 4842 l 1795 4825 l 1797 4813 l 1799 4806 l 1800 4802 l 1800 4800 l gs col0 s gr % Polyline 0 slj 0.000 slw n 1275 4725 m 1875 4725 l 1875 5875 l 1275 5875 l cp gs col7 1.00 shd ef gr % Polyline n 3975 4725 m 4650 4725 l 4650 5884 l 3975 5884 l cp gs col7 1.00 shd ef gr 7.500 slw % Ellipse n 4800 6000 75 75 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col0 s gr % Ellipse n 6150 6000 75 75 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col0 s gr % Ellipse n 6675 6000 75 75 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col0 s gr % Ellipse n 7650 6000 75 75 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col0 s gr % Ellipse n 8400 6000 75 75 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col0 s gr % Ellipse n 9000 6000 75 75 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col0 s gr % Ellipse n 4800 6450 75 75 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col0 s gr % Ellipse n 6150 6450 75 75 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col0 s gr % Ellipse n 6675 6450 75 75 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col0 s gr % Ellipse n 7650 6450 75 75 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col0 s gr % Ellipse n 8400 6450 75 75 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col0 s gr % Ellipse n 9000 6450 75 75 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col0 s gr % Ellipse n 4800 3300 75 75 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col0 s gr % Ellipse n 6150 3300 75 75 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col0 s gr % Ellipse n 6675 3300 75 75 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col0 s gr % Ellipse n 7650 3300 75 75 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col0 s gr % Ellipse n 8400 3300 75 75 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col0 s gr % Ellipse n 9000 3300 75 75 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col0 s gr % Ellipse n 1950 6000 75 75 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col0 s gr % Ellipse n 1350 6000 75 75 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col0 s gr % Ellipse n 2550 6000 75 75 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col0 s gr % Ellipse n 3900 6000 75 75 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col0 s gr % Ellipse n 4800 3750 75 75 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col0 s gr % Ellipse n 6150 3750 75 75 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col0 s gr % Ellipse n 6675 3750 75 75 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col0 s gr % Ellipse n 7650 3750 75 75 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col0 s gr % Ellipse n 8400 3750 75 75 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col0 s gr % Ellipse n 9000 3750 75 75 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col0 s gr % Ellipse n 1950 3300 75 75 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col0 s gr % Ellipse n 1350 3300 75 75 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col0 s gr % Ellipse n 2550 3300 75 75 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col0 s gr % Ellipse n 3900 3300 75 75 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col0 s gr % Ellipse n 1350 3750 75 75 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col0 s gr % Ellipse n 1950 3750 75 75 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col0 s gr % Ellipse n 2550 3750 75 75 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col0 s gr % Ellipse n 3900 3750 75 75 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col0 s gr % Ellipse n 3900 6450 75 75 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col0 s gr % Ellipse n 2550 6450 75 75 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col0 s gr % Ellipse n 1950 6450 75 75 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col0 s gr % Ellipse n 1350 6450 75 75 0 360 DrawEllipse gs col7 0.00 shd ef gr gs col0 s gr % Polyline 15.000 slw gs clippath 9915 6510 m 9915 6390 l 9628 6390 l 9868 6450 l 9628 6510 l cp 285 6390 m 285 6510 l 572 6510 l 332 6450 l 572 6390 l cp eoclip n 300 6450 m 9900 6450 l gs col0 s gr gr % arrowhead n 572 6390 m 332 6450 l 572 6510 l 572 6390 l cp gs col7 1.00 shd ef gr col0 s % arrowhead n 9628 6510 m 9868 6450 l 9628 6390 l 9628 6510 l cp gs col7 1.00 shd ef gr col0 s % Polyline gs clippath 9915 3810 m 9915 3690 l 9628 3690 l 9868 3750 l 9628 3810 l cp 285 3690 m 285 3810 l 572 3810 l 332 3750 l 572 3690 l cp eoclip n 300 3750 m 9900 3750 l gs col0 s gr gr % arrowhead n 572 3690 m 332 3750 l 572 3810 l 572 3690 l cp gs col7 1.00 shd ef gr col0 s % arrowhead n 9628 3810 m 9868 3750 l 9628 3690 l 9628 3810 l cp gs col7 1.00 shd ef gr col0 s % Polyline 2 slj 7.500 slw [60] 0 sd n 2400 4800 m 2401 4801 l 2402 4802 l 2404 4804 l 2409 4808 l 2414 4814 l 2422 4822 l 2433 4832 l 2446 4844 l 2461 4859 l 2479 4876 l 2500 4896 l 2524 4918 l 2551 4943 l 2580 4970 l 2612 4999 l 2647 5030 l 2684 5063 l 2723 5097 l 2765 5133 l 2808 5170 l 2854 5208 l 2901 5247 l 2950 5286 l 3000 5325 l 3052 5364 l 3105 5404 l 3159 5443 l 3215 5481 l 3272 5520 l 3330 5557 l 3389 5594 l 3450 5630 l 3513 5665 l 3577 5699 l 3643 5731 l 3710 5763 l 3780 5793 l 3852 5822 l 3926 5849 l 4003 5875 l 4082 5898 l 4163 5920 l 4248 5940 l 4334 5957 l 4424 5972 l 4516 5984 l 4609 5993 l 4704 5998 l 4800 6000 l 4896 5998 l 4991 5993 l 5084 5984 l 5176 5972 l 5266 5957 l 5352 5940 l 5437 5920 l 5518 5898 l 5597 5875 l 5674 5849 l 5748 5822 l 5820 5793 l 5890 5763 l 5957 5731 l 6023 5699 l 6087 5665 l 6150 5630 l 6211 5594 l 6270 5557 l 6328 5520 l 6385 5481 l 6441 5443 l 6495 5404 l 6548 5364 l 6600 5325 l 6650 5286 l 6699 5247 l 6746 5208 l 6792 5170 l 6835 5133 l 6877 5097 l 6916 5063 l 6953 5030 l 6988 4999 l 7020 4970 l 7049 4943 l 7076 4918 l 7100 4896 l 7121 4876 l 7139 4859 l 7154 4844 l 7167 4832 l 7178 4822 l 7186 4814 l 7191 4808 l 7196 4804 l 7198 4802 l 7199 4801 l 7200 4800 l gs col0 s gr [] 0 sd % Polyline [60] 0 sd n 5850 4800 m 5850 4802 l 5851 4806 l 5852 4813 l 5853 4825 l 5855 4842 l 5858 4864 l 5862 4891 l 5866 4924 l 5871 4962 l 5877 5004 l 5884 5051 l 5891 5102 l 5899 5155 l 5907 5210 l 5916 5267 l 5925 5325 l 5935 5383 l 5944 5440 l 5955 5497 l 5965 5553 l 5976 5607 l 5988 5659 l 5999 5708 l 6012 5756 l 6025 5800 l 6038 5841 l 6052 5879 l 6067 5913 l 6082 5942 l 6098 5966 l 6115 5984 l 6132 5996 l 6150 6000 l 6168 5996 l 6185 5984 l 6202 5966 l 6218 5942 l 6233 5913 l 6248 5879 l 6262 5841 l 6275 5800 l 6288 5756 l 6301 5708 l 6312 5659 l 6324 5607 l 6335 5553 l 6345 5497 l 6356 5440 l 6365 5383 l 6375 5325 l 6384 5267 l 6393 5210 l 6401 5155 l 6409 5102 l 6416 5051 l 6423 5004 l 6429 4962 l 6434 4924 l 6438 4891 l 6442 4864 l 6445 4842 l 6447 4825 l 6448 4813 l 6449 4806 l 6450 4802 l 6450 4800 l gs col0 s gr [] 0 sd % Polyline [60] 0 sd n 6375 4800 m 6375 4802 l 6376 4806 l 6377 4813 l 6378 4825 l 6380 4842 l 6383 4864 l 6387 4891 l 6391 4924 l 6396 4962 l 6402 5004 l 6409 5051 l 6416 5102 l 6424 5155 l 6432 5210 l 6441 5267 l 6450 5325 l 6460 5383 l 6469 5440 l 6480 5497 l 6490 5553 l 6501 5607 l 6513 5659 l 6524 5708 l 6537 5756 l 6550 5800 l 6563 5841 l 6577 5879 l 6592 5913 l 6607 5942 l 6623 5966 l 6640 5984 l 6657 5996 l 6675 6000 l 6693 5996 l 6710 5984 l 6727 5966 l 6743 5942 l 6758 5913 l 6773 5879 l 6787 5841 l 6800 5800 l 6813 5756 l 6826 5708 l 6837 5659 l 6849 5607 l 6860 5553 l 6870 5497 l 6881 5440 l 6890 5383 l 6900 5325 l 6909 5267 l 6918 5210 l 6926 5155 l 6934 5102 l 6941 5051 l 6948 5004 l 6954 4962 l 6959 4924 l 6963 4891 l 6967 4864 l 6970 4842 l 6972 4825 l 6973 4813 l 6974 4806 l 6975 4802 l 6975 4800 l gs col0 s gr [] 0 sd % Polyline [60] 0 sd n 7050 4800 m 7050 4802 l 7051 4805 l 7053 4811 l 7055 4822 l 7059 4836 l 7064 4855 l 7070 4878 l 7078 4907 l 7087 4940 l 7097 4978 l 7109 5020 l 7121 5065 l 7135 5113 l 7150 5164 l 7166 5217 l 7183 5270 l 7200 5325 l 7218 5380 l 7237 5434 l 7256 5488 l 7276 5540 l 7296 5592 l 7318 5641 l 7340 5689 l 7363 5735 l 7386 5778 l 7411 5819 l 7437 5856 l 7464 5891 l 7492 5921 l 7521 5948 l 7552 5970 l 7584 5986 l 7617 5996 l 7650 6000 l 7683 5996 l 7716 5986 l 7748 5970 l 7779 5948 l 7808 5921 l 7836 5891 l 7863 5856 l 7889 5819 l 7914 5778 l 7937 5735 l 7960 5689 l 7982 5641 l 8004 5592 l 8024 5540 l 8044 5488 l 8063 5434 l 8082 5380 l 8100 5325 l 8117 5270 l 8134 5217 l 8150 5164 l 8165 5113 l 8179 5065 l 8191 5020 l 8203 4978 l 8213 4940 l 8222 4907 l 8230 4878 l 8236 4855 l 8241 4836 l 8245 4822 l 8247 4811 l 8249 4805 l 8250 4802 l 8250 4800 l gs col0 s gr [] 0 sd % Polyline [60] 0 sd n 7200 4800 m 7201 4801 l 7202 4804 l 7204 4808 l 7208 4816 l 7214 4827 l 7221 4841 l 7231 4859 l 7242 4881 l 7256 4907 l 7272 4937 l 7290 4970 l 7310 5007 l 7332 5046 l 7357 5089 l 7382 5133 l 7410 5180 l 7439 5227 l 7469 5276 l 7500 5325 l 7532 5374 l 7566 5423 l 7600 5472 l 7636 5520 l 7672 5566 l 7710 5612 l 7748 5656 l 7788 5699 l 7830 5739 l 7872 5778 l 7917 5815 l 7963 5849 l 8011 5881 l 8061 5910 l 8113 5935 l 8167 5957 l 8223 5975 l 8281 5989 l 8340 5997 l 8400 6000 l 8460 5997 l 8519 5989 l 8577 5975 l 8633 5957 l 8687 5935 l 8739 5910 l 8789 5881 l 8837 5849 l 8883 5815 l 8928 5778 l 8970 5739 l 9012 5699 l 9052 5656 l 9090 5612 l 9128 5566 l 9164 5520 l 9200 5472 l 9234 5423 l 9268 5374 l 9300 5325 l 9331 5276 l 9361 5227 l 9390 5180 l 9418 5133 l 9443 5089 l 9468 5046 l 9490 5007 l 9510 4970 l 9528 4937 l 9544 4907 l 9558 4881 l 9569 4859 l 9579 4841 l 9586 4827 l 9592 4816 l 9596 4808 l 9598 4804 l 9599 4801 l 9600 4800 l gs col0 s gr [] 0 sd % Polyline [60] 0 sd n 8700 4800 m 8700 4802 l 8701 4806 l 8702 4813 l 8703 4825 l 8705 4842 l 8708 4864 l 8712 4891 l 8716 4924 l 8721 4962 l 8727 5004 l 8734 5051 l 8741 5102 l 8749 5155 l 8757 5210 l 8766 5267 l 8775 5325 l 8785 5383 l 8794 5440 l 8805 5497 l 8815 5553 l 8826 5607 l 8838 5659 l 8849 5708 l 8862 5756 l 8875 5800 l 8888 5841 l 8902 5879 l 8917 5913 l 8932 5942 l 8948 5966 l 8965 5984 l 8982 5996 l 9000 6000 l 9018 5996 l 9035 5984 l 9052 5966 l 9068 5942 l 9083 5913 l 9098 5879 l 9112 5841 l 9125 5800 l 9138 5756 l 9151 5708 l 9162 5659 l 9174 5607 l 9185 5553 l 9195 5497 l 9206 5440 l 9215 5383 l 9225 5325 l 9234 5267 l 9243 5210 l 9251 5155 l 9259 5102 l 9266 5051 l 9273 5004 l 9279 4962 l 9284 4924 l 9288 4891 l 9292 4864 l 9295 4842 l 9297 4825 l 9298 4813 l 9299 4806 l 9300 4802 l 9300 4800 l gs col0 s gr [] 0 sd % Polyline 15.000 slw n 2400 2100 m 2401 2101 l 2402 2102 l 2404 2104 l 2409 2108 l 2414 2114 l 2422 2122 l 2433 2132 l 2446 2144 l 2461 2159 l 2479 2176 l 2500 2196 l 2524 2218 l 2551 2243 l 2580 2270 l 2612 2299 l 2647 2330 l 2684 2363 l 2723 2397 l 2765 2433 l 2808 2470 l 2854 2508 l 2901 2547 l 2950 2586 l 3000 2625 l 3052 2664 l 3105 2704 l 3159 2743 l 3215 2781 l 3272 2820 l 3330 2857 l 3389 2894 l 3450 2930 l 3513 2965 l 3577 2999 l 3643 3031 l 3710 3063 l 3780 3093 l 3852 3122 l 3926 3149 l 4003 3175 l 4082 3198 l 4163 3220 l 4248 3240 l 4334 3257 l 4424 3272 l 4516 3284 l 4609 3293 l 4704 3298 l 4800 3300 l 4896 3298 l 4991 3293 l 5084 3284 l 5176 3272 l 5266 3257 l 5352 3240 l 5437 3220 l 5518 3198 l 5597 3175 l 5674 3149 l 5748 3122 l 5820 3093 l 5890 3063 l 5957 3031 l 6023 2999 l 6087 2965 l 6150 2930 l 6211 2894 l 6270 2857 l 6328 2820 l 6385 2781 l 6441 2743 l 6495 2704 l 6548 2664 l 6600 2625 l 6650 2586 l 6699 2547 l 6746 2508 l 6792 2470 l 6835 2433 l 6877 2397 l 6916 2363 l 6953 2330 l 6988 2299 l 7020 2270 l 7049 2243 l 7076 2218 l 7100 2196 l 7121 2176 l 7139 2159 l 7154 2144 l 7167 2132 l 7178 2122 l 7186 2114 l 7191 2108 l 7196 2104 l 7198 2102 l 7199 2101 l 7200 2100 l gs col0 s gr % Polyline n 5850 2100 m 5850 2102 l 5851 2106 l 5852 2113 l 5853 2125 l 5855 2142 l 5858 2164 l 5862 2191 l 5866 2224 l 5871 2262 l 5877 2304 l 5884 2351 l 5891 2402 l 5899 2455 l 5907 2510 l 5916 2567 l 5925 2625 l 5935 2683 l 5944 2740 l 5955 2797 l 5965 2853 l 5976 2907 l 5988 2959 l 5999 3008 l 6012 3056 l 6025 3100 l 6038 3141 l 6052 3179 l 6067 3213 l 6082 3242 l 6098 3266 l 6115 3284 l 6132 3296 l 6150 3300 l 6168 3296 l 6185 3284 l 6202 3266 l 6218 3242 l 6233 3213 l 6248 3179 l 6262 3141 l 6275 3100 l 6288 3056 l 6301 3008 l 6312 2959 l 6324 2907 l 6335 2853 l 6345 2797 l 6356 2740 l 6365 2683 l 6375 2625 l 6384 2567 l 6393 2510 l 6401 2455 l 6409 2402 l 6416 2351 l 6423 2304 l 6429 2262 l 6434 2224 l 6438 2191 l 6442 2164 l 6445 2142 l 6447 2125 l 6448 2113 l 6449 2106 l 6450 2102 l 6450 2100 l gs col0 s gr % Polyline n 7050 2100 m 7050 2102 l 7051 2105 l 7053 2111 l 7055 2122 l 7059 2136 l 7064 2155 l 7070 2178 l 7078 2207 l 7087 2240 l 7097 2278 l 7109 2320 l 7121 2365 l 7135 2413 l 7150 2464 l 7166 2517 l 7183 2570 l 7200 2625 l 7218 2680 l 7237 2734 l 7256 2788 l 7276 2840 l 7296 2892 l 7318 2941 l 7340 2989 l 7363 3035 l 7386 3078 l 7411 3119 l 7437 3156 l 7464 3191 l 7492 3221 l 7521 3248 l 7552 3270 l 7584 3286 l 7617 3296 l 7650 3300 l 7683 3296 l 7716 3286 l 7748 3270 l 7779 3248 l 7808 3221 l 7836 3191 l 7863 3156 l 7889 3119 l 7914 3078 l 7937 3035 l 7960 2989 l 7982 2941 l 8004 2892 l 8024 2840 l 8044 2788 l 8063 2734 l 8082 2680 l 8100 2625 l 8117 2570 l 8134 2517 l 8150 2464 l 8165 2413 l 8179 2365 l 8191 2320 l 8203 2278 l 8213 2240 l 8222 2207 l 8230 2178 l 8236 2155 l 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1083 2811 l 1121 2855 l 1161 2899 l 1202 2941 l 1245 2983 l 1288 3022 l 1333 3060 l 1380 3096 l 1428 3130 l 1479 3162 l 1531 3191 l 1585 3217 l 1642 3241 l 1700 3261 l 1760 3277 l 1822 3290 l 1886 3297 l 1950 3300 l 2014 3297 l 2078 3290 l 2140 3277 l 2200 3261 l 2258 3241 l 2315 3217 l 2369 3191 l 2421 3162 l 2472 3130 l 2520 3096 l 2567 3060 l 2612 3022 l 2655 2983 l 2698 2941 l 2739 2899 l 2779 2855 l 2817 2811 l 2855 2765 l 2892 2719 l 2928 2672 l 2963 2625 l 2996 2578 l 3028 2532 l 3059 2486 l 3089 2442 l 3117 2399 l 3143 2358 l 3168 2320 l 3190 2284 l 3211 2250 l 3229 2221 l 3245 2194 l 3259 2171 l 3270 2152 l 3279 2136 l 3287 2123 l 3292 2114 l 3296 2107 l 3298 2103 l 3299 2101 l 3300 2100 l gs col0 s gr % Polyline n 900 2100 m 900 2102 l 901 2106 l 903 2113 l 905 2125 l 908 2142 l 912 2164 l 918 2191 l 924 2224 l 932 2262 l 941 2304 l 951 2351 l 961 2402 l 973 2455 l 986 2510 l 999 2567 l 1013 2625 l 1027 2683 l 1042 2740 l 1057 2797 l 1073 2853 l 1089 2907 l 1107 2959 l 1124 3008 l 1143 3056 l 1162 3100 l 1182 3141 l 1203 3179 l 1225 3213 l 1248 3242 l 1273 3266 l 1298 3284 l 1324 3296 l 1350 3300 l 1376 3296 l 1402 3284 l 1427 3266 l 1452 3242 l 1475 3213 l 1497 3179 l 1518 3141 l 1538 3100 l 1557 3056 l 1576 3008 l 1593 2959 l 1611 2907 l 1627 2853 l 1643 2797 l 1658 2740 l 1673 2683 l 1688 2625 l 1701 2567 l 1714 2510 l 1727 2455 l 1739 2402 l 1749 2351 l 1759 2304 l 1768 2262 l 1776 2224 l 1782 2191 l 1788 2164 l 1792 2142 l 1795 2125 l 1797 2113 l 1799 2106 l 1800 2102 l 1800 2100 l gs col0 s gr % Polyline n 2250 2100 m 2250 2102 l 2251 2106 l 2252 2113 l 2253 2125 l 2255 2142 l 2258 2164 l 2262 2191 l 2266 2224 l 2271 2262 l 2277 2304 l 2284 2351 l 2291 2402 l 2299 2455 l 2307 2510 l 2316 2567 l 2325 2625 l 2335 2683 l 2344 2740 l 2355 2797 l 2365 2853 l 2376 2907 l 2388 2959 l 2399 3008 l 2412 3056 l 2425 3100 l 2438 3141 l 2452 3179 l 2467 3213 l 2482 3242 l 2498 3266 l 2515 3284 l 2532 3296 l 2550 3300 l 2568 3296 l 2585 3284 l 2602 3266 l 2618 3242 l 2633 3213 l 2648 3179 l 2662 3141 l 2675 3100 l 2688 3056 l 2701 3008 l 2712 2959 l 2724 2907 l 2735 2853 l 2745 2797 l 2756 2740 l 2765 2683 l 2775 2625 l 2784 2567 l 2793 2510 l 2801 2455 l 2809 2402 l 2816 2351 l 2823 2304 l 2829 2262 l 2834 2224 l 2838 2191 l 2842 2164 l 2845 2142 l 2847 2125 l 2848 2113 l 2849 2106 l 2850 2102 l 2850 2100 l gs col0 s gr % Polyline n 3300 2100 m 3300 2102 l 3301 2105 l 3303 2111 l 3305 2122 l 3309 2136 l 3314 2155 l 3320 2178 l 3328 2207 l 3337 2240 l 3347 2278 l 3359 2320 l 3371 2365 l 3385 2413 l 3400 2464 l 3416 2517 l 3433 2570 l 3450 2625 l 3468 2680 l 3487 2734 l 3506 2788 l 3526 2840 l 3546 2892 l 3568 2941 l 3590 2989 l 3613 3035 l 3636 3078 l 3661 3119 l 3687 3156 l 3714 3191 l 3742 3221 l 3771 3248 l 3802 3270 l 3834 3286 l 3867 3296 l 3900 3300 l 3933 3296 l 3966 3286 l 3998 3270 l 4029 3248 l 4058 3221 l 4086 3191 l 4113 3156 l 4139 3119 l 4164 3078 l 4187 3035 l 4210 2989 l 4232 2941 l 4254 2892 l 4274 2840 l 4294 2788 l 4313 2734 l 4332 2680 l 4350 2625 l 4367 2570 l 4384 2517 l 4400 2464 l 4415 2413 l 4429 2365 l 4441 2320 l 4453 2278 l 4463 2240 l 4472 2207 l 4480 2178 l 4486 2155 l 4491 2136 l 4495 2122 l 4497 2111 l 4499 2105 l 4500 2102 l 4500 2100 l gs col0 s gr % Polyline 7.500 slw [60] 0 sd n 900 4800 m 900 4802 l 901 4806 l 903 4813 l 905 4825 l 908 4842 l 912 4864 l 918 4891 l 924 4924 l 932 4962 l 941 5004 l 951 5051 l 961 5102 l 973 5155 l 986 5210 l 999 5267 l 1013 5325 l 1027 5383 l 1042 5440 l 1057 5497 l 1073 5553 l 1089 5607 l 1107 5659 l 1124 5708 l 1143 5756 l 1162 5800 l 1182 5841 l 1203 5879 l 1225 5913 l 1248 5942 l 1273 5966 l 1298 5984 l 1324 5996 l 1350 6000 l 1376 5996 l 1402 5984 l 1427 5966 l 1452 5942 l 1475 5913 l 1497 5879 l 1518 5841 l 1538 5800 l 1557 5756 l 1576 5708 l 1593 5659 l 1611 5607 l 1627 5553 l 1643 5497 l 1658 5440 l 1673 5383 l 1688 5325 l 1701 5267 l 1714 5210 l 1727 5155 l 1739 5102 l 1749 5051 l 1759 5004 l 1768 4962 l 1776 4924 l 1782 4891 l 1788 4864 l 1792 4842 l 1795 4825 l 1797 4813 l 1799 4806 l 1800 4802 l 1800 4800 l gs col0 s gr [] 0 sd % Polyline [60] 0 sd n 2250 4800 m 2250 4802 l 2251 4806 l 2252 4813 l 2253 4825 l 2255 4842 l 2258 4864 l 2262 4891 l 2266 4924 l 2271 4962 l 2277 5004 l 2284 5051 l 2291 5102 l 2299 5155 l 2307 5210 l 2316 5267 l 2325 5325 l 2335 5383 l 2344 5440 l 2355 5497 l 2365 5553 l 2376 5607 l 2388 5659 l 2399 5708 l 2412 5756 l 2425 5800 l 2438 5841 l 2452 5879 l 2467 5913 l 2482 5942 l 2498 5966 l 2515 5984 l 2532 5996 l 2550 6000 l 2568 5996 l 2585 5984 l 2602 5966 l 2618 5942 l 2633 5913 l 2648 5879 l 2662 5841 l 2675 5800 l 2688 5756 l 2701 5708 l 2712 5659 l 2724 5607 l 2735 5553 l 2745 5497 l 2756 5440 l 2765 5383 l 2775 5325 l 2784 5267 l 2793 5210 l 2801 5155 l 2809 5102 l 2816 5051 l 2823 5004 l 2829 4962 l 2834 4924 l 2838 4891 l 2842 4864 l 2845 4842 l 2847 4825 l 2848 4813 l 2849 4806 l 2850 4802 l 2850 4800 l gs col0 s gr [] 0 sd % Polyline [60] 0 sd n 3300 4800 m 3300 4802 l 3301 4805 l 3303 4811 l 3305 4822 l 3309 4836 l 3314 4855 l 3320 4878 l 3328 4907 l 3337 4940 l 3347 4978 l 3359 5020 l 3371 5065 l 3385 5113 l 3400 5164 l 3416 5217 l 3433 5270 l 3450 5325 l 3468 5380 l 3487 5434 l 3506 5488 l 3526 5540 l 3546 5592 l 3568 5641 l 3590 5689 l 3613 5735 l 3636 5778 l 3661 5819 l 3687 5856 l 3714 5891 l 3742 5921 l 3771 5948 l 3802 5970 l 3834 5986 l 3867 5996 l 3900 6000 l 3933 5996 l 3966 5986 l 3998 5970 l 4029 5948 l 4058 5921 l 4086 5891 l 4113 5856 l 4139 5819 l 4164 5778 l 4187 5735 l 4210 5689 l 4232 5641 l 4254 5592 l 4274 5540 l 4294 5488 l 4313 5434 l 4332 5380 l 4350 5325 l 4367 5270 l 4384 5217 l 4400 5164 l 4415 5113 l 4429 5065 l 4441 5020 l 4453 4978 l 4463 4940 l 4472 4907 l 4480 4878 l 4486 4855 l 4491 4836 l 4495 4822 l 4497 4811 l 4499 4805 l 4500 4802 l 4500 4800 l gs col0 s gr [] 0 sd % Polyline [60] 0 sd n 600 4800 m 601 4801 l 602 4803 l 604 4807 l 608 4814 l 613 4823 l 621 4836 l 630 4852 l 641 4871 l 655 4894 l 671 4921 l 689 4950 l 710 4984 l 732 5020 l 757 5058 l 783 5099 l 811 5142 l 841 5186 l 872 5232 l 904 5278 l 938 5325 l 972 5372 l 1008 5419 l 1045 5465 l 1083 5511 l 1121 5555 l 1161 5599 l 1202 5641 l 1245 5683 l 1288 5722 l 1333 5760 l 1380 5796 l 1428 5830 l 1479 5862 l 1531 5891 l 1585 5917 l 1642 5941 l 1700 5961 l 1760 5977 l 1822 5990 l 1886 5997 l 1950 6000 l 2014 5997 l 2078 5990 l 2140 5977 l 2200 5961 l 2258 5941 l 2315 5917 l 2369 5891 l 2421 5862 l 2472 5830 l 2520 5796 l 2567 5760 l 2612 5722 l 2655 5683 l 2698 5641 l 2739 5599 l 2779 5555 l 2817 5511 l 2855 5465 l 2892 5419 l 2928 5372 l 2963 5325 l 2996 5278 l 3028 5232 l 3059 5186 l 3089 5142 l 3117 5099 l 3143 5058 l 3168 5020 l 3190 4984 l 3211 4950 l 3229 4921 l 3245 4894 l 3259 4871 l 3270 4852 l 3279 4836 l 3287 4823 l 3292 4814 l 3296 4807 l 3298 4803 l 3299 4801 l 3300 4800 l gs col0 s gr [] 0 sd % Ellipse n 4087 6450 75 75 0 360 DrawEllipse gs col7 1.00 shd ef gr gs col0 s gr % Ellipse n 2426 6450 75 75 0 360 DrawEllipse gs col7 1.00 shd ef gr gs col0 s gr % Ellipse n 1507 6450 75 75 0 360 DrawEllipse gs col7 1.00 shd ef gr gs col0 s gr % Ellipse n 8850 6450 75 75 0 360 DrawEllipse gs col7 1.00 shd ef gr gs col0 s gr % Ellipse n 5995 6450 75 75 0 360 DrawEllipse gs col7 1.00 shd ef gr gs col0 s gr % Ellipse n 7900 6450 75 75 0 360 DrawEllipse gs col7 1.00 shd ef gr gs col0 s gr % Ellipse n 9200 6450 75 75 0 360 DrawEllipse gs col7 1.00 shd ef gr gs col0 s gr % Ellipse n 6412 6450 75 75 0 360 DrawEllipse gs col7 1.00 shd ef gr gs col0 s gr % Ellipse n 7001 6450 75 75 0 360 DrawEllipse gs col7 1.00 shd ef gr gs col0 s gr % Ellipse n 8850 3750 75 75 0 360 DrawEllipse gs col7 1.00 shd ef gr gs col0 s gr % Ellipse n 5995 3750 75 75 0 360 DrawEllipse gs col7 1.00 shd ef gr gs col0 s gr % Ellipse n 6350 3750 75 75 0 360 DrawEllipse gs col7 1.00 shd ef gr gs col0 s gr % Ellipse n 6475 3750 75 75 0 360 DrawEllipse gs col7 1.00 shd ef gr gs col0 s gr % Ellipse n 6945 3750 75 75 0 360 DrawEllipse gs col7 1.00 shd ef gr gs col0 s gr % Ellipse n 7080 3750 75 75 0 360 DrawEllipse gs col7 1.00 shd ef gr gs col0 s gr % Ellipse n 7900 3750 75 75 0 360 DrawEllipse gs col7 1.00 shd ef gr gs col0 s gr % Ellipse n 9200 3750 75 75 0 360 DrawEllipse gs col7 1.00 shd ef gr gs col0 s gr % Ellipse n 3300 6450 75 75 0 360 DrawEllipse gs col7 1.00 shd ef gr gs col0 s gr % Ellipse n 4087 3750 75 75 0 360 DrawEllipse gs col7 1.00 shd ef gr gs col0 s gr % Ellipse n 2426 3750 75 75 0 360 DrawEllipse gs col7 1.00 shd ef gr gs col0 s gr % Ellipse n 1507 3750 75 75 0 360 DrawEllipse gs col7 1.00 shd ef gr gs col0 s gr % Ellipse n 3600 3750 75 75 0 360 DrawEllipse gs col7 1.00 shd ef gr gs col0 s gr % Ellipse n 2687 3750 75 75 0 360 DrawEllipse gs col7 1.00 shd ef gr gs col0 s gr % Ellipse n 1047 3750 75 75 0 360 DrawEllipse gs col7 1.00 shd ef gr gs col0 s gr % Ellipse n 2977 3750 75 75 0 360 DrawEllipse gs col7 1.00 shd ef gr gs col0 s gr /Helvetica-iso ff 300.00 scf sf 600 6900 m gs 1 -1 sc (Loose anisotropic Voronoi Diagram) col0 sh gr /Helvetica-iso ff 300.00 scf sf 600 4200 m gs 1 -1 sc (Anisotropic Voronoi Diagram \(one-dimensional\)) col0 sh gr F2psBegin10setmiterlimit0.060000.06000scF2psEnd rs %%EndDocument @endspecial -303 1932 a Fr(Figur)m(e)47 b(6:)64 b Fm(A)45 b(loose)i(anisotropic)g(V)-11 b(oronoi)46 b(diag)o(r)o(am)f(often)h (has)g(f)l(e)m(w)o(er)f(or-)-303 2107 y(phans)k(than)g(the)g(tr)r(ue)g (anisotropic)h(V)-11 b(oronoi)50 b(diag)o(r)o(am.)82 b(Blac)m(k)50 b(points)g(are)-303 2281 y(sites;)38 b(white)f(points)g (are)g(V)-11 b(oronoi)37 b(v)m(er)5 b(tices)n(.)-303 2789 y Fv(w)o(ords,)42 b(if)f Fq(f)16 b Ft(\()p Fq(p)p Ft(\))41 b Fv(is)g(a)h(function)e(that)h(maps)h(each)g(point)e Fq(p)i Fv(in)f Fq(E)3078 2725 y Fp(d)3192 2789 y Fv(to)g(a)h(real)-303 2963 y(number)33 b Fq(h)h Fv(such)g(that)f Ft(\()p Fq(p;)25 b(h)p Ft(\))43 b Fk(2)1416 2851 y Fi(S)1570 2963 y Fq(F)21 b Fv(,)35 b(then)e Fq(f)50 b Fv(is)33 b(single-v)l(alued,)h(continu-) -303 3137 y(ous,)40 b(and)f(de\002ned)h(e)l(v)n(erywhere)f(in)g Fq(E)1725 3074 y Fp(d)1797 3137 y Fv(.)53 b(See)41 b(the)e(lo)l(wer)g (half)g(of)g(Figure)g(6)-303 3312 y(for)i(an)i(e)n(xample.)62 b(F)n(or)42 b(an)n(y)g Fq(F)64 b Fv(that)41 b(satis\002es)i(these)g (conditions,)f(let)g Fq(L)g Fv(be)-303 3486 y(the)h(arrangement)i (formed)e(by)h(projecting)e(the)i Fq(d)p Fv(-f)o(aces)g(in)f Fq(F)66 b Fv(to)43 b Fq(E)3346 3422 y Fp(d)3418 3486 y Fv(;)k(we)-303 3660 y(call)37 b Fq(L)g Fv(a)g Fu(loose)g(V)-17 b(or)-7 b(onoi)37 b(dia)o(gr)n(am)e Fv(of)i Fq(V)d Fv(.)-154 3835 y(F)n(or)42 b(a)h(loose)g(V)-19 b(oronoi)40 b(diagram)j Fq(L)p Fv(,)h(a)f(site)f Fq(v)48 b Fu(owns)42 b Fv(a)h(f)o(ace)g Fq(g)48 b Fv(of)43 b Fq(L)f Fv(if)g Fq(g)-303 4009 y Fv(is)37 b(the)g(projection)e(of)i(a)h(f)o(ace)f(of)g Fq(F)59 b Fv(that)36 b(lies)h(on)g Fq(v)5 b Fv(')-8 b(s)37 b(paraboloid.)-154 4183 y(In)49 b(general,)k(a)d(set)f(of)g(sites)g Fq(V)83 b Fv(may)50 b(ha)m(v)n(e)g(man)n(y)f(loose)g(V)-19 b(oronoi)47 b(dia-)-303 4358 y(grams;)i(the)c(true)g(anisotropic)f(V) -19 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Ft(\))38 b Fv(as)g(possible.)-154 3477 y(If)i(the)f(V)-19 b(oronoi)38 b(re\002nement)i(algorithm)f(terminates,)h(the)g(dual)g(of) f Fq(D)t Fk(j)3587 3494 y Fj(\012)-303 3652 y Fv(is)f(a)h (triangulation)c(of)j Ft(\012)g Fv(by)g(Theorem)h(7,)g(and)f(the)g (triangles)f(are)i(of)f(good)-303 3826 y(quality)31 b(\(because)k (otherwise)d(the)h(algorithm)f(w)o(ould)g(not)g(stop\).)44 b(But)33 b(does)-303 4000 y(it)g(terminate?)46 b(Section)34 b(10)g(sho)l(ws)g(that,)h(with)f(reasonable)g(restrictions)f(on)-303 4175 y Fq(M)54 b Fv(and)37 b Fq(\022)224 4193 y Fj(b)s(ound)565 4175 y Fv(,)h(it)e(does.)-154 4349 y(T)-12 b(o)37 b(simplify)f (programming,)g(an)i(implementation)d(only)h(needs)i(to)e(\002nd)-303 4524 y(V)-19 b(oronoi)36 b(\223arcs\224)k(that)e(are)h(ellipses)f (\(which)g(al)o(w)o(ays)f(ha)m(v)n(e)i(violators\),)e(and)-303 4698 y(V)-19 b(oronoi)45 b(v)n(ertices)h(that)h(dualize)g(to)f(in)-6 b(v)n(erted)46 b(or)h(poor)m(-quality)d(triangles.)-303 4872 y(\(F)n(or)d(this)h(purpose,)h(the)f(\223dual\224)h(of)f(an)g (orphan)g(is)g(the)g(site)h(that)e(o)l(wns)h(it.\))-303 5047 y(An)59 b(attack)h(on)f(these)h(violators)e(will)g(also)i (eliminate)f(all)g(orphans)g(and)-303 5221 y(\223island\224)d(V)-19 b(oronoi)55 b(cells)h(\(enclosed)g(in)g(other)g(V)-19 b(oronoi)55 b(cells,)61 b(possibly)-303 5395 y(adjoining)33 b(other)j(islands\))f(without)f(an)n(y)h(need)i(to)e(e)n(xplicitly)f (test)h(for)h(their)-303 5570 y(e)n(xistence.)46 b(W)-12 b(e)38 b(omit)e(the)h(proof.)-154 5744 y(Because)30 b(the)e(V)-19 b(oronoi)27 b(re\002nement)i(algorithm)e(re\002nes)i(the)f(mesh)i(hea)m (v-)-303 5918 y(ily)54 b(in)g(re)n(gions)g(where)h Fq(M)72 b Fv(v)l(aries)56 b(rapidly)-10 b(,)58 b(we)e(suggest)e(the)h(follo)l (wing)-303 6093 y(v)l(ariation.)98 b(F)n(or)54 b(an)n(y)g(point)f Fq(p)p Fv(,)60 b(let)55 b Fq(M)1794 6029 y Fs(0)1778 6119 y Fp(p)1926 6093 y Ft(=)77 b(\(det)26 b Fq(M)2569 6110 y Fp(p)2641 6093 y Ft(\))2701 6029 y Fs(\000)p Fj(1)p Fp(=d)2994 6093 y Fq(M)3142 6110 y Fp(p)3215 6093 y Fv(,)59 b(so)c(the)-303 6267 y(metric)50 b(tensor)f Fq(M)708 6204 y Fs(0)692 6293 y Fp(p)815 6267 y Fv(has)i(determinant)e(one.)85 b(The)51 b(tensors)f Fq(M)3072 6284 y Fp(p)3195 6267 y Fv(and)g Fq(M)3625 6204 y Fs(0)3609 6293 y Fp(p)-303 6441 y Fv(measure)32 b(angles)g(identically)e(b)m(ut)g(lengths)h(dif)l (ferently)-10 b(.)43 b(Use)32 b Fq(M)3097 6458 y Fp(p)3202 6441 y Fv(to)f(judge)-303 6616 y(whether)g(a)h(triangle)e(is)i(too)f (lar)m(ge)g(\(as)i(before\),)f(b)m(ut)f(de\002ne)h(the)g(anisotropic) -303 6790 y(V)-19 b(oronoi)42 b(diagram)i(using)f(the)h(tensor)f (\002eld)h Fq(M)2232 6727 y Fs(0)2216 6816 y Fp(p)2289 6790 y Fv(.)67 b(Then)44 b(the)g(relati)l(v)n(e)g(dis-)-303 6964 y(tortion)50 b(between)i(tw)o(o)g(points)f(is)h(solely)g(attrib)m (utable)e(to)i(dif)l(ferences)g(in)-303 7139 y(ho)l(w)36 b(the)n(y)g(measure)i(angles,)f(and)g(not)f(dif)l(ferences)h(in)f(ho)l (w)h(the)n(y)f(measure)-303 7313 y(areas.)46 b(In)32 b(our)h(e)n(xperiments,)g(the)g(modi\002ed)f(algorithm)f(produces)i (meshes)-303 7487 y(with)j(fe)l(wer)h(triangles.)-303 7870 y Fw(10.)198 b(Pr)l(oof)50 b(of)g(T)-18 b(ermination)-154 8086 y Fv(Intuiti)l(v)n(ely)-10 b(,)31 b(the)i(V)-19 b(oronoi)30 b(re\002nement)j(algorithm)e(inserts)h(sites)h(for)f(one) -303 8261 y(of)k(tw)o(o)f(reasons:)46 b(either)36 b(the)g(spacing)h(of) f(sites)g(is)h(not)e(uniform)h(enough)f(to)-303 8435 y(guarantee)45 b(good-quality)c(triangles,)46 b(or)f(neighboring)d (sites)j(ha)m(v)n(e)g(metric)-303 8609 y(tensors)58 b(that)h(strongly)e (disagree)i(with)f(each)i(other)-8 b(.)111 b(The)60 b(distances)f(at) -303 8784 y(which)47 b(these)g(ef)l(fects)i(occur)e(are)i(called)e(the) g Fu(local)g(featur)-6 b(e)48 b(size)g Fv(and)f(the)-303 8958 y Fu(bounded)36 b(distortion)e(r)n(adius)p Fv(.)-133 9246 y(D)8 b Fg(E)g(FI)g(N)g(I)g(T)g(I)g(O)g(N)82 b Fv(4.)75 b Fu(F)-16 b(or)52 b(a)f(metric)h(tensor)f(\002eld)g Fq(M)68 b Fu(and)51 b(a)h(\002xed)f Fq(\015)79 b(>)-303 9421 y Ft(1)p Fu(,)64 b(the)58 b Fv(bounded)g(distortion)d(radius)j Ft(b)t(dr)q(\()p Fq(p;)25 b(\015)9 b Ft(\))59 b Fu(at)f(a)g(point)f Fq(p)84 b Fk(2)f Ft(\012)59 b Fu(is)-303 9595 y(the)48 b(gr)-6 b(eatest)50 b(number)e(suc)n(h)h(that)f(for)g(e)n(very)j(point) c Fq(q)70 b Fk(2)c Ft(\012)p Fu(,)52 b(if)d Fq(d)3232 9612 y Fp(p)3304 9595 y Ft(\()p Fq(q)5 b Ft(\))64 b Fk(\024)-303 9769 y Ft(b)t(dr)q(\()p Fq(p;)25 b(\015)9 b Ft(\))p Fu(,)40 b(then)f Fq(\034)17 b Ft(\()p Fq(p;)25 b(q)5 b Ft(\))46 b Fk(\024)i Fq(\015)9 b Fu(.)53 b(\(Note)39 b(that)f Ft(b)t(dr)q(\()p Fq(p;)25 b(\015)9 b Ft(\))40 b Fu(can)f(be)h (in\002nite)n(.\))-303 9944 y(The)49 b Fv(distortion)e(disk)i Fu(center)-6 b(ed)51 b(at)e Fq(p)g Fu(is)h(the)f(elliptical)e(disk)j Fk(f)p Fq(q)71 b Fk(2)66 b Fq(E)3504 9880 y Fj(2)3639 9944 y Ft(:)-303 10118 y Fq(d)-223 10135 y Fp(p)-151 10118 y Ft(\()p Fq(q)5 b Ft(\))42 b Fk(\024)h Ft(b)t(dr)q(\()p Fq(p;)25 b(\015)9 b Ft(\))p Fk(g)p Fu(.)46 b(Let)37 b Ft(b)t(dr)1458 10135 y Fj(min)1669 10118 y Ft(\()p Fq(\015)9 b Ft(\))42 b(=)h(inf)2267 10135 y Fp(p)p Fs(2)p Fj(\012)2535 10118 y Ft(b)t(dr)q(\()p Fq(p;)25 b(\015)9 b Ft(\))p Fu(.)-154 10406 y Fv(Ev)n(ery)48 b(point)f(in)h Fq(p)p Fv(')-8 b(s)49 b(distortion)c(disk)j(has)h(a)g(similar)e(vie)l(w)i(of)f (lengths)-303 10581 y(and)36 b(angles.)47 b(The)37 b(V)-19 b(oronoi)35 b(re\002nement)i(algorithm)f(is)g(guaranteed)h(to)f(ter)m (-)-303 10755 y(minate)48 b(if)g Ft(b)t(dr)527 10772 y Fj(min)737 10755 y Ft(\()p Fq(\015)9 b Ft(\))48 b Fv(is)g(positi)l(v) n(e.)78 b(This)48 b(is)h(al)o(w)o(ays)e(true)h(if)g(the)g(metric)4080 -137 y(tensor)53 b(\002eld)g Fq(M)70 b Fv(is)53 b(continuous)f(o)n(v)n (er)g Ft(\012)h Fv(with)g(bounded)f(spatial)g(gradi-)4080 37 y(ents,)c(b)m(ut)d(is)g(sometimes)h(true)f(e)l(v)n(en)h(with)e (minor)h(discontinuities)d(in)j Fq(M)16 b Fv(.)4080 211 y(The)58 b(v)l(alue)f(of)f Fq(\015)66 b Fv(depends)57 b(on)f(ho)l(w)h(strong)e(an)i(angle)g(bound)f(the)g(user)4080 386 y(demands;)37 b(see)i(Theorem)e(11)g(belo)l(w)-10 b(.)4230 560 y(Let)55 b Fq(q)k Fv(and)c Fq(q)4957 497 y Fs(0)5057 560 y Fv(be)g(tw)o(o)e(distinct)g Fu(featur)-6 b(e)55 b(points)p Fv(\227points)d(that)i(lie)g(on)4080 734 y(input)45 b(sites)h(or)g(se)n(gments)g(in)g Fq(X)12 b Fv(.)73 b(Say)47 b(that)e Fq(q)52 b Fv(and)46 b Fq(q)6927 671 y Fs(0)7018 734 y Fv(are)h Fu(intertwined)d Fv(if)4080 909 y(the)n(y)i(lie)f(on)h(a)h(common)f(se)n(gment)g(of)g Fq(X)12 b Fv(,)48 b(or)e(if)g(the)n(y)f(lie)h(on)f(se)n(gments)i Fq(s)4080 1083 y Fv(and)33 b Fq(s)4401 1020 y Fs(0)4445 1083 y Fv(,)h(respecti)l(v)n(ely)-10 b(,)33 b(where)g Fq(s)f Fv(and)h Fq(s)6116 1020 y Fs(0)6193 1083 y Fv(share)g(a)g (common)f(endpoint)f Fq(b)h Fv(and)4080 1257 y Fq(\034)17 b Ft(\()p Fq(q)5 b(;)25 b(b)p Ft(\))42 b Fk(\024)h Fq(\015)j Fv(and)38 b Fq(\034)17 b Ft(\()p Fq(q)5295 1194 y Fs(0)5339 1257 y Fq(;)25 b(b)p Ft(\))42 b Fk(\024)h Fq(\015)9 b Fv(.)4250 1597 y(D)f Fg(E)g(FI)g(N)g(I)g(T)g(I)g(O)g(N)83 b Fv(5.)74 b Fu(F)-16 b(or)32 b(a)f(PSLG)g Fq(X)42 b Fu(and)31 b(a)f(\002xed)i Fq(\015)51 b(>)43 b Ft(1)p Fu(,)33 b(the)d Fv(local)h(fea-)4080 1771 y(ture)k(size)h Ft(lfs)o(\()p Fq(p)p Ft(\))f Fu(at)f(a)i(point)d Fq(p)43 b Fk(2)g Ft(\012)35 b Fu(is)g(the)g(r)n(adius)f(\(as)h(measur)-6 b(ed)36 b(by)g Fq(p)p Fu(\))f(of)4080 1946 y(the)40 b(smallest)f (elliptical)f(disk)i(\(cir)-6 b(cular)40 b(fr)-7 b(om)40 b Fq(p)p Fu(')-6 b(s)40 b(per)o(spective\))g(center)-6 b(ed)4080 2120 y(at)33 b Fq(p)g Fu(that)f(inter)o(sects)g(two)g(featur) -6 b(e)33 b(points)f(of)g Fq(X)45 b Fu(that)32 b(ar)-6 b(e)34 b(not)e(intertwined.)4080 2294 y(In)49 b(other)g(wor)-6 b(ds,)53 b(ther)-6 b(e)50 b(ar)-6 b(e)50 b(non-intertwined)c(featur)-6 b(e)50 b(points)d Fq(q)55 b Fu(and)49 b Fq(q)8021 2231 y Fs(0)4080 2469 y Fu(suc)n(h)44 b(that)e Fq(d)4752 2486 y Fp(p)4824 2469 y Ft(\()p Fq(q)5 b Ft(\))54 b(=)i(lfs)o(\()p Fq(p)p Ft(\))43 b Fu(and)g Fq(d)5985 2486 y Fp(p)6057 2469 y Ft(\()p Fq(q)6191 2405 y Fs(0)6236 2469 y Ft(\))55 b Fk(\024)g Ft(lfs)o(\()p Fq(p)p Ft(\))p Fu(,)46 b(b)m(ut)c(this)h(is)h (not)f(true)4080 2643 y(for)37 b(any)g(r)n(adius)f(smaller)h(than)f Ft(lfs)o(\()p Fq(p)p Ft(\))p Fu(.)46 b(Let)38 b Ft(lfs)6560 2660 y Fj(min)6813 2643 y Ft(=)43 b(inf)7162 2660 y Fp(p)p Fs(2)p Fj(\012)7429 2643 y Ft(lfs)o(\()p Fq(p)p Ft(\))p Fu(.)4230 2983 y Fv(This)49 b(de\002nition)e(of)i(local)g(feature)g (size)h(is)f(similar)g(to)f(Ruppert')-8 b(s,)51 b(b)m(ut)4080 3157 y(it)h(is)g(adjusted)f(to)h(account)g(for)f(the)h(f)o(act)g(that)g (tw)o(o)f(se)n(gments)h(that)g(meet)4080 3331 y(at)d(an)g(angle)g (greater)f(than)h Ft(90)5724 3268 y Fs(\016)5795 3331 y Fv(,)j(from)d(the)f(perspecti)l(v)n(e)h(of)f(their)g(shared)4080 3506 y(endpoint,)60 b(might)55 b(meet)i(at)f(an)h(angle)f(of)g Ft(1)6454 3442 y Fs(\016)6525 3506 y Fv(,)62 b(from)56 b(the)g(perspecti)l(v)n(e)g(of)4080 3680 y(points)f Fq(q)61 b Fv(and)56 b Fq(q)4978 3617 y Fs(0)5079 3680 y Fv(on)f(each)i(se)n (gment.)103 b(In)56 b(this)f(case,)63 b Fq(q)e Fv(and)56 b Fq(q)7535 3617 y Fs(0)7636 3680 y Fv(are)g(not)4080 3854 y(intertwined,)61 b(and)c(the)g(distance)g(between)h(them)f(\(as)h (the)n(y)e(measure)i(it\))4080 4029 y(in\003uences)44 b(the)g(local)f(feature)h(size)g(nearby)-10 b(.)66 b(Ho)l(we)l(v)n(er) -6 b(,)46 b(if)d Ft(b)t(dr)7511 4046 y Fj(min)7777 4029 y Fq(>)55 b Ft(0)p Fv(,)4080 4203 y(then)37 b Ft(lfs)4525 4220 y Fj(min)4778 4203 y Fq(>)43 b Ft(0)p Fv(.)4230 4377 y(F)n(or)28 b(bre)l(vity)-10 b(,)29 b(the)f(follo)l(wing)e (theorem)j(applies)f(only)f(when)h(the)g(V)-19 b(oronoi)4080 4552 y(re\002nement)31 b(algorithm)e(does)i(not)f(re\002ne)i(triangles) d(for)h(being)g(too)g(lar)m(ge.)45 b(It)4080 4726 y(is)31 b(straightforw)o(ard)d(\(if)j(tedious\))f(to)g(adapt)i(the)f(proof)f (to)g(co)n(v)n(er)h(re\002nement)4080 4901 y(of)37 b(o)n(v)n(ersized)g (triangles)f(as)h(well.)4250 5240 y(T)8 b Fg(H)g(E)g(O)g(R)g(E)g(M)84 b Fv(11.)75 b Fu(Let)47 b Fq(\022)5549 5258 y Fj(b)s(ound)5952 5240 y Fq(<)62 b Ft(arcsin)6653 5179 y Fj(1)p 6572 5206 222 7 v 6572 5305 a(2)6633 5223 y Fs(p)p 6733 5223 61 6 v 82 x Fj(2)6861 5240 y Fu(be)47 b(a)g(constant.)75 b(Sup-)4080 5436 y(pose)33 b(a)g(triangle)e Fq(t)j Fu(is)e(consider)-6 b(ed)33 b(to)g(be)g Fv(poorly)e(shaped)i Fu(\(thus)f(its)g(cir)-6 b(cum-)4080 5610 y(center)34 b(is)f(a)h(violator\))d(if)i Fq(t)h Fu(has)f(an)g(angle)g(less)h(than)e Fq(\022)6910 5628 y Fj(b)s(ound)7252 5610 y Fu(,)i(as)g(measur)-6 b(ed)4080 5785 y(by)38 b(an)e(arbitr)n(ary)h(point)e Fq(p)j Fu(in)e Fq(t)p Fu(.)47 b(Let)38 b Fq(\015)46 b Fu(be)37 b(the)g(r)-6 b(eal)38 b(r)-7 b(oot)37 b(of)4724 6089 y Fq(\015)4812 6018 y Fj(8)4915 6089 y Ft(+)d(2)p Fq(\015)5233 6018 y Fj(4)5302 5953 y Fi(p)p 5456 5953 422 7 v 136 x Fq(\015)5544 6046 y Fj(2)5647 6089 y Ft(+)h(1)25 b(sin)g Fq(\022)6189 6107 y Fj(b)s(ound)6565 6089 y Fk(\000)35 b Fq(\015)6807 6018 y Fj(4)6910 6089 y Fk(\000)f Ft(1)43 b(=)g(0)4080 6372 y Fu(that)49 b(is)i(gr)-6 b(eater)50 b(than)g(one)n(.)86 b(Suppose)49 b(any)i(two)e(adjoining)f(se)-6 b(gments)50 b(of)4080 6546 y Fq(X)60 b Fu(ar)-6 b(e)49 b(separ)n(ated)e(by)i(an)e(angle)g(of)h(at)f(least)h Ft(2)25 b(arcsin\()p Fq(\015)7215 6483 y Fj(2)7284 6546 y Fq(=)p Ft(2\))p Fu(,)50 b(as)f(mea-)4080 6720 y(sur)-6 b(ed)55 b(fr)-7 b(om)54 b(the)h(per)o(spective)f(of)g(the)g(inter)o (section)f(point.)96 b(\(This)54 b(angle)4080 6895 y(is)g(less)h(than)e Ft(79)4987 6831 y Fs(\016)5058 6895 y Fu(,)59 b(and)54 b(can)g(be)h(r)-6 b(educed)55 b(arbitr)n(arily)d(close)j(to)e Ft(60)7798 6831 y Fs(\016)7924 6895 y Fu(by)4080 7069 y(c)n(hoosing)39 b Fq(\015)50 b Fu(closer)41 b(to)g(one)n(.\))56 b(If)40 b Ft(b)t(dr)6075 7086 y Fj(min)6286 7069 y Ft(\()p Fq(\015)9 b Ft(\))48 b Fq(>)i Ft(0)p Fu(,)42 b(then)f(the)f(V)-17 b(or)-7 b(onoi)41 b(r)-6 b(e-)4080 7243 y(\002nement)29 b(algorithm)e(described)j(in)f(Section)f(9)h(g)o(ener)n(ates)g(a)g (triangulation)4080 7418 y Fq(T)56 b Fu(wher)-6 b(ein)35 b(no)f(triangle)f Fq(t)j Fu(has)e(an)h(angle)f(less)h(than)e Fq(\022)6945 7436 y Fj(b)s(ound)7322 7418 y Fu(as)i(measur)-6 b(ed)4080 7592 y(by)38 b(any)f(point)e Fq(p)43 b Fk(2)g Fq(t)p Fu(,)38 b(and)f(e)n(very)i(pair)d(of)h(sites)g Fq(u)43 b Fk(6)p Ft(=)g Fq(v)f Fu(in)37 b Fq(T)58 b Fu(satis\002es)4639 8009 y Fq(d)4719 8026 y Fp(u)4800 8009 y Ft(\()p Fq(v)5 b Ft(\))42 b Fk(\025)h Ft(min)5486 7754 y Fi(\()5630 7912 y Ft(lfs)5780 7929 y Fj(min)p 5630 7975 361 7 v 5766 8110 a Fq(\015)6010 8009 y(;)6370 7912 y Ft(b)t(dr)6605 7929 y Fj(min)6815 7912 y Ft(\()p Fq(\015)9 b Ft(\))p 6098 7975 1197 7 v 6098 8136 a(\()p Fq(\015)6246 8093 y Fj(5)6349 8136 y Ft(+)35 b Fq(\015)6591 8093 y Fj(3)6660 8136 y Ft(\))6720 8006 y Fi(p)p 6873 8006 422 7 v 6873 8136 a Fq(\015)6961 8093 y Fj(2)7064 8136 y Ft(+)g(1)7315 7754 y Fi(\))7464 8009 y Fq(:)4230 8489 y Fv(If)41 b Fq(\022)4443 8507 y Fj(b)s(ound)4837 8489 y Ft(=)52 b(0)5085 8425 y Fs(\016)5157 8489 y Fv(\227the)42 b(minimum)f(requirement)h(for) f(a)h(geometrically)4080 8663 y(v)l(alid)c(triangulation\227then)e Fq(\015)5796 8577 y(:)5758 8663 y Ft(=)47 b(1)p Fq(:)p Ft(1278)p Fv(.)j(This)39 b(suggests)g(that)f(if)g(neigh-)4080 8837 y(boring)f(sites)h(measure)h(lengths)e(more)i(than)f(about)f Ft(12)p Fv(\045)i(dif)l(ferently)-10 b(,)37 b(that)4080 9012 y(may)47 b(be)g(enough)f(to)f(trigger)h(re\002nement)g(to)g (reduce)h(the)f(disparity)-10 b(,)48 b(e)l(v)n(en)4080 9186 y(if)f(the)g(sites)f(are)i(uniformly)d(spaced.)77 b(If)47 b Fq(\022)6375 9204 y Fj(b)s(ound)6778 9186 y Ft(=)62 b(10)7113 9123 y Fs(\016)7184 9186 y Fv(,)50 b Fq(\015)7459 9101 y(:)7420 9186 y Ft(=)62 b(1)p Fq(:)p Ft(0629)p Fv(.)4080 9360 y Fq(\022)4152 9378 y Fj(b)s(ound)4549 9360 y Fv(may)55 b(be)f(as)i(high)d(as)i(about)f Ft(20)p Fq(:)p Ft(7)6396 9297 y Fs(\016)6522 9360 y Fv(\(as)h(it)e(is)i(for)f (Ruppert')-8 b(s)53 b(al-)4080 9535 y(gorithm\),)43 b(b)m(ut)e(as)i Fq(\022)5154 9553 y Fj(b)s(ound)5539 9535 y Fv(approaches)g(this)e (upper)h(limit,)h(the)f(algorithm)4080 9709 y(may)e(ha)m(v)n(e)f(to)f (re\002ne)h(the)g(edges)g(to)g(v)n(ery)f(short)g(lengths)g(to)g(k)o (eep)h(the)f(rela-)4080 9883 y(ti)l(v)n(e)f(distortion)d(locally)i (small)h(enough.)4230 10058 y(Our)56 b(proof)h(of)f(Theorem)i(11)f (proceeds)h(through)d(man)n(y)i(lemmas,)64 b(in)4080 10232 y(which)34 b(all)f(references)i(to)f(V)-19 b(oronoi)32 b(cells)i(refer)g(to)g(cells)g(of)g(the)f(true)h(aniso-)4080 10406 y(tropic)46 b(V)-19 b(oronoi)45 b(diagram,)50 b(e)l(v)n(en)e(if)e (the)h(V)-19 b(oronoi)46 b(re\002nement)h(algorithm)4080 10581 y(uses)32 b(a)g(loose)f(V)-19 b(oronoi)29 b(diagram)j(instead.)44 b(Lemma)33 b(20)e(sho)l(ws)g(that)g(it)f(does)4080 10755 y(no)37 b(harm)g(for)g(the)g(algorithm)f(to)g(w)o(ork)g(with)g(the)h (latter)-8 b(.)p eop %%Page: 8 8 8 7 bop -133 -137 a Fv(L)8 b Fg(E)g(M)g(M)g(A)85 b Fv(12.)75 b Fu(Let)41 b Fq(v)47 b Fu(be)42 b(a)g(site)f(of)g(a)h(V)-17 b(or)-7 b(onoi)41 b(dia)o(gr)n(am)f Fq(D)t Fu(,)j(and)e(let)h Fq(q)-303 37 y Fu(be)30 b(a)g(point)e(in)h Ft(V)-13 b(or)q(\()p Fq(v)5 b Ft(\))p Fu(.)43 b(F)-16 b(or)31 b(some)f Fq(\015)51 b Fk(\025)44 b Ft(1)p Fu(,)31 b(suppose)f Fq(d)2582 54 y Fp(v)2656 37 y Ft(\()p Fq(q)5 b Ft(\))42 b Fk(\025)h Ft(b)t(dr)q(\()p Fq(v)5 b(;)25 b(\015)9 b Ft(\))p Fu(.)-303 211 y(Then)33 b(for)g(any)h(site)f Fq(w)k Fu(of)c Fq(D)t Fu(,)i Fq(d)p Ft(\()p Fq(w)t(;)25 b(q)5 b Ft(\))42 b Fk(\025)h Ft(b)t(dr)2123 228 y Fj(min)2333 211 y Ft(\()p Fq(\015)9 b Ft(\))p Fq(=\015)g Fu(.)45 b(Thus,)34 b(inserting)-303 386 y Fq(q)42 b Fu(into)36 b Fq(D)41 b Fu(cr)-6 b(eates)39 b(no)d(inter)m(-site)g(distance)h(shorter)g(than)f Ft(b)t(dr)3013 403 y Fj(min)3223 386 y Ft(\()p Fq(\015)9 b Ft(\))p Fq(=\015)g Fu(.)-150 673 y Fv(P)f Fg(R)s(O)g(O)g(F)m Fv(.)122 b(Suppose)61 b(for)g(the)g(sak)o(e)h(of)f(contradiction)e(that)i(for)g(some)-303 847 y(site)i Fq(w)69 b Fv(of)64 b Fq(D)t Fv(,)71 b Fq(d)p Ft(\()p Fq(w)t(;)25 b(q)5 b Ft(\))93 b Fq(<)i Ft(b)t(dr)1573 864 y Fj(min)1783 847 y Ft(\()p Fq(\015)9 b Ft(\))p Fq(=\015)g Fv(.)126 b(Then)65 b(either)e Fq(d)3175 864 y Fp(w)3275 847 y Ft(\()p Fq(q)5 b Ft(\))93 b Fq(<)-303 1022 y Ft(b)t(dr)q(\()p Fq(w)t(;)25 b(\015)9 b Ft(\))p Fq(=\015)60 b Fv(or)52 b Fq(d)795 1039 y Fp(q)863 1022 y Ft(\()p Fq(w)t Ft(\))70 b Fq(<)i Ft(b)t(dr)q(\()p Fq(q)5 b(;)25 b(\015)9 b Ft(\))p Fq(=\015)g Fv(,)55 b(so)d Fq(\034)17 b Ft(\()p Fq(w)t(;)25 b(q)5 b Ft(\))70 b Fk(\024)i Fq(\015)9 b Fv(.)90 b(In)52 b(the)-303 1196 y(former)34 b(case)h Fq(d)509 1213 y Fp(w)609 1196 y Ft(\()p Fq(q)5 b Ft(\))42 b Fq(<)h Ft(b)t(dr)1242 1213 y Fj(min)1452 1196 y Ft(\()p Fq(\015)9 b Ft(\))p Fq(=\015)g Fv(,)34 b(and)g(in)g(the)g(latter)f(case)j Fq(d)3227 1213 y Fp(w)3326 1196 y Ft(\()p Fq(q)5 b Ft(\))42 b Fk(\024)-303 1370 y Fq(\015)9 b(d)-135 1387 y Fp(q)-67 1370 y Ft(\()p Fq(w)t Ft(\))42 b Fq(<)h Ft(b)t(dr)606 1387 y Fj(min)816 1370 y Ft(\()p Fq(\015)9 b Ft(\))p Fv(.)-154 1545 y(Because)50 b Fq(q)k Fv(is)48 b(in)g Ft(V)-13 b(or)q(\()p Fq(v)5 b Ft(\))p Fv(,)51 b Fq(d)1437 1562 y Fp(v)1511 1545 y Ft(\()p Fq(q)5 b Ft(\))64 b Fk(\024)h Fq(d)2033 1562 y Fp(w)2133 1545 y Ft(\()p Fq(q)5 b Ft(\))64 b Fq(<)h Ft(b)t(dr)2810 1562 y Fj(min)3020 1545 y Ft(\()p Fq(\015)9 b Ft(\))p Fv(,)51 b(which)-303 1719 y(contradicts)36 b(the)h(assumption)f(that)g Fq(d)1669 1736 y Fp(v)1743 1719 y Ft(\()p Fq(q)5 b Ft(\))42 b Fk(\025)h Ft(b)t(dr)q(\()p Fq(v)5 b(;)25 b(\015)9 b Ft(\))p Fv(.)793 b Fh(\004)-133 2006 y Fv(L)8 b Fg(E)g(M)g(M)g(A)85 b Fv(13.)75 b Fu(Let)41 b Fq(D)46 b Fu(be)41 b(a)h(V)-17 b(or)-7 b(onoi)41 b(dia)o(gr)n(am,)g (and)g(let)g Fq(q)46 b Fu(be)c(a)f(point)-303 2181 y(wher)-6 b(e)45 b(no)f(site)h(of)f Fq(D)49 b Fu(lies.)68 b(Let)45 b Fq(z)52 b Fu(be)45 b(a)f(point)f(that)h(would)f(be)i(in)f Ft(V)-13 b(or\()p Fq(q)5 b Ft(\))-303 2355 y Fu(if)56 b Fq(q)63 b Fu(wer)-6 b(e)59 b(inserted)e(into)g Fq(D)t Fu(.)107 b(F)-16 b(or)59 b(some)e Fq(\015)91 b Fk(\025)82 b Ft(1)p Fu(,)63 b(suppose)57 b Fq(d)3215 2372 y Fp(q)3283 2355 y Ft(\()p Fq(z)6 b Ft(\))82 b Fk(\025)-303 2529 y Ft(b)t(dr)q(\()p Fq(q)5 b(;)25 b(\015)9 b Ft(\))p Fu(.)46 b(Then)37 b(for)g(any)g(site)g Fq(w)k Fu(of)c Fq(D)t Fu(,)h Fq(d)p Ft(\()p Fq(w)t(;)24 b(z)6 b Ft(\))44 b Fk(\025)f Ft(b)t(dr)2821 2546 y Fj(min)3031 2529 y Ft(\()p Fq(\015)9 b Ft(\))p Fq(=\015)g Fu(.)-150 2817 y Fv(P)f Fg(R)s(O)g(O)g(F)m Fv(.)81 b(Essentially)47 b(the)g(same)i(as)g(the)f (proof)e(of)i(Lemma)h(12.)79 b(\(Ob-)-303 2991 y(serv)n(e)29 b(that)f(because)j Fq(z)36 b Fv(w)o(ould)27 b(lie)i(in)f Ft(V)-13 b(or\()p Fq(q)5 b Ft(\))29 b Fv(if)g Fq(q)34 b Fv(were)c(inserted,)g Fq(d)3254 3008 y Fp(q)3322 2991 y Ft(\()p Fq(z)6 b Ft(\))43 b Fk(\024)-303 3165 y Fq(d)-223 3182 y Fp(w)-124 3165 y Ft(\()p Fq(z)6 b Ft(\))38 b Fv(for)f(an)n(y)f (site)h Fq(w)42 b Fv(of)37 b Fq(D)t Fv(.\))2212 b Fh(\004)-133 3453 y Fv(L)8 b Fg(E)g(M)g(M)g(A)85 b Fv(14.)75 b Fu(Let)40 b Fq(u)h Fu(and)f Fq(v)46 b Fu(be)41 b(sites)f(of)h(a)f(V)-17 b(or)-7 b(onoi)40 b(dia)o(gr)n(am)f Fq(D)t Fu(.)57 b(Let)-303 3627 y Fq(q)k Fu(be)56 b(a)h(point)d(on)i(the)g(V)-17 b(or)-7 b(onoi)56 b(1-cell)g Ft(V)-13 b(or\()p Fq(u)p Ft(\))48 b Fk(\\)h Ft(V)-13 b(or)q(\()p Fq(v)5 b Ft(\))p Fu(.)103 b(F)-16 b(or)57 b(some)-303 3801 y Fq(\015)77 b Fk(\025)69 b Ft(1)p Fu(,)54 b(suppose)c Fq(d)821 3818 y Fp(u)903 3801 y Ft(\()p Fq(v)5 b Ft(\))67 b Fk(\025)i Ft(b)t(dr)q(\()p Fq(u;)26 b(\015)9 b Ft(\))p Fu(.)86 b(Then)51 b(for)f(any)h(site)f Fq(w)55 b Fu(of)50 b Fq(D)t Fu(,)-303 3976 y Fq(d)p Ft(\()p Fq(w)t(;)24 b(q)5 b Ft(\))43 b Fk(\025)g Ft(b)t(dr)592 3993 y Fj(min)802 3976 y Ft(\()p Fq(\015)9 b Ft(\))p Fq(=)p Ft(\()p Fq(\015)1235 3912 y Fj(3)1337 3976 y Ft(+)35 b Fq(\015)9 b Ft(\))p Fu(.)-150 4263 y Fv(P)f Fg(R)s(O)g(O)g(F)m Fv(.)59 b(If)41 b Fq(d)592 4280 y Fp(u)673 4263 y Ft(\()p Fq(q)5 b Ft(\))49 b Fk(\025)h Ft(b)t(dr)q(\()p Fq(u;)26 b(\015)9 b Ft(\))40 b Fv(or)h Fq(d)1971 4280 y Fp(v)2044 4263 y Ft(\()p Fq(q)5 b Ft(\))49 b Fk(\025)h Ft(b)t(dr)q(\()p Fq(v)5 b(;)25 b(\015)9 b Ft(\))p Fv(,)42 b(the)f(result)-303 4437 y(follo)l(ws)54 b(by)h(Lemma)i(12.)102 b(Otherwise,)60 b(by)55 b(the)g(de\002nition)f (of)h(bounded)-303 4612 y(distortion)34 b(radius,)j Fq(\034)17 b Ft(\()p Fq(u;)25 b(q)5 b Ft(\))42 b Fk(\024)h Fq(\015)k Fv(and)37 b Fq(\034)17 b Ft(\()p Fq(v)5 b(;)25 b(q)5 b Ft(\))42 b Fk(\024)h Fq(\015)9 b Fv(,)38 b(so)f Fq(\034)17 b Ft(\()p Fq(u;)25 b(v)5 b Ft(\))42 b Fk(\024)h Fq(\015)3462 4548 y Fj(2)3531 4612 y Fv(.)-154 4786 y(Suppose)38 b(for)h(the)f(sak)o (e)h(of)f(contradiction)f(that)h(for)g(some)i(site)e Fq(w)43 b Fv(of)38 b Fq(D)t Fv(,)-303 4960 y Fq(d)p Ft(\()p Fq(w)t(;)24 b(q)5 b Ft(\))43 b Fq(<)g Ft(b)t(dr)592 4977 y Fj(min)802 4960 y Ft(\()p Fq(\015)9 b Ft(\))p Fq(=)p Ft(\()p Fq(\015)1235 4897 y Fj(3)1321 4960 y Ft(+)18 b Fq(\015)9 b Ft(\))p Fv(.)46 b(Then)33 b(either)f Fq(d)2482 4977 y Fp(w)2582 4960 y Ft(\()p Fq(q)5 b Ft(\))42 b Fq(<)h Ft(b)t(dr)q(\()p Fq(w)t(;)25 b(\015)9 b Ft(\))p Fq(=)-303 5135 y Ft(\()p Fq(\015)-155 5071 y Fj(3)-52 5135 y Ft(+)35 b Fq(\015)9 b Ft(\))37 b Fv(or)g Fq(d)529 5152 y Fp(q)598 5135 y Ft(\()p Fq(w)t Ft(\))43 b Fq(<)g Ft(b)t(dr)q(\()p Fq(q)5 b(;)25 b(\015)9 b Ft(\))p Fq(=)p Ft(\()p Fq(\015)1847 5071 y Fj(3)1950 5135 y Ft(+)35 b Fq(\015)9 b Ft(\))p Fv(,)38 b(so)f Fq(\034)17 b Ft(\()p Fq(w)t(;)25 b(q)5 b Ft(\))43 b Fk(\024)h Fq(\015)9 b Fv(.)48 b(In)37 b(the)-303 5309 y(former)43 b(case)j Fq(d)529 5326 y Fp(w)628 5309 y Ft(\()p Fq(q)5 b Ft(\))55 b Fq(<)h Ft(b)t(dr)1287 5326 y Fj(min)1497 5309 y Ft(\()p Fq(\015)9 b Ft(\))p Fq(=)p Ft(\()p Fq(\015)1930 5245 y Fj(3)2037 5309 y Ft(+)40 b Fq(\015)9 b Ft(\))p Fv(,)46 b(and)d(in)h(the)f(latter)h(case)-303 5483 y Fq(d)-223 5500 y Fp(w)-124 5483 y Ft(\()p Fq(q)5 b Ft(\))42 b Fk(\024)h Fq(\015)9 b(d)442 5500 y Fp(q)511 5483 y Ft(\()p Fq(w)t Ft(\))42 b Fq(<)h Ft(b)t(dr)1184 5500 y Fj(min)1394 5483 y Ft(\()p Fq(\015)9 b Ft(\))p Fq(=)p Ft(\()p Fq(\015)1827 5420 y Fj(2)1929 5483 y Ft(+)35 b(1\))p Fv(.)-154 5658 y(Because)46 b Fq(q)k Fv(is)44 b(in)g Ft(V)-13 b(or\()p Fq(u)p Ft(\))40 b Fk(\\)g Ft(V)-13 b(or\()p Fq(v)5 b Ft(\))p Fv(,)47 b Fq(d)2045 5675 y Fp(u)2126 5658 y Ft(\()p Fq(q)5 b Ft(\))56 b(=)h Fq(d)2632 5675 y Fp(v)2706 5658 y Ft(\()p Fq(q)5 b Ft(\))56 b Fk(\024)h Fq(d)3212 5675 y Fp(w)3312 5658 y Ft(\()p Fq(q)5 b Ft(\))56 b Fq(<)-303 5832 y Ft(b)t(dr)-68 5849 y Fj(min)142 5832 y Ft(\()p Fq(\015)9 b Ft(\))p Fq(=)p Ft(\()p Fq(\015)575 5768 y Fj(2)689 5832 y Ft(+)48 b(1\))p Fv(.)95 b(Recall)54 b(that)e Fq(\034)17 b Ft(\()p Fq(u;)26 b(v)5 b Ft(\))73 b Fk(\024)h Fq(\015)2634 5768 y Fj(2)2704 5832 y Fv(,)58 b(so)53 b Fq(d)3065 5849 y Fp(u)3147 5832 y Ft(\()p Fq(v)5 b(;)25 b(q)5 b Ft(\))73 b Fk(\024)-303 6006 y Fq(\015)-215 5943 y Fj(2)-146 6006 y Fq(d)-66 6023 y Fp(v)7 6006 y Ft(\()p Fq(q)5 b Ft(\))78 b Fq(<)h(\015)565 5943 y Fj(2)635 6006 y Ft(b)t(dr)870 6023 y Fj(min)1080 6006 y Ft(\()p Fq(\015)9 b Ft(\))p Fq(=)p Ft(\()p Fq(\015)1513 5943 y Fj(2)1629 6006 y Ft(+)49 b(1\))p Fv(.)103 b(By)56 b(the)g(triangle)e (inequality)-10 b(,)-303 6181 y Fq(d)-223 6198 y Fp(u)-142 6181 y Ft(\()p Fq(v)5 b Ft(\))67 b Fk(\024)h Fq(d)392 6198 y Fp(u)474 6181 y Ft(\()p Fq(q)5 b Ft(\))43 b(+)i Fq(d)955 6198 y Fp(u)1036 6181 y Ft(\()p Fq(v)5 b(;)25 b(q)5 b Ft(\))68 b Fq(<)g Ft(b)t(dr)1868 6198 y Fj(min)2078 6181 y Ft(\()p Fq(\015)9 b Ft(\))p Fv(,)54 b(which)c(contradicts)f(the) -303 6355 y(assumption)36 b(that)g Fq(d)756 6372 y Fp(u)838 6355 y Ft(\()p Fq(v)5 b Ft(\))42 b Fk(\025)h Ft(b)t(dr)q(\()p Fq(u;)25 b(\015)9 b Ft(\))p Fv(.)47 b(The)37 b(result)g(follo)l(ws.)515 b Fh(\004)-133 6642 y Fv(L)8 b Fg(E)g(M)g(M)g(A)85 b Fv(15.)75 b Fu(Let)41 b Fq(v)47 b Fu(be)42 b(a)g(site)f(of)g(a)h(V)-17 b(or)-7 b(onoi)41 b(dia)o(gr)n(am)f Fq(D)t Fu(,)j(and)e(let)h Fq(q)-303 6817 y Fu(be)f(a)g(point)e(wher)-6 b(e)42 b(no)e(site)h(of)f Fq(D)45 b Fu(lies.)58 b(Let)41 b Fq(z)48 b Fu(be)41 b(a)g(point)e(in)h Ft(V)-13 b(or)q(\()p Fq(v)5 b Ft(\))40 b Fu(that)-303 6991 y(would)48 b(be)i(in)f Ft(V)-13 b(or)q(\()p Fq(q)5 b Ft(\))49 b Fu(if)g Fq(q)55 b Fu(wer)-6 b(e)51 b(inserted)f(into)e Fq(D)t Fu(.)85 b(F)-16 b(or)51 b(some)f Fq(\015)75 b Fk(\025)68 b Ft(1)p Fu(,)-303 7165 y(suppose)40 b Fq(d)299 7182 y Fp(q)368 7165 y Ft(\()p Fq(v)5 b Ft(\))49 b Fk(\025)i Ft(b)t(dr)q(\()p Fq(q)5 b(;)25 b(\015)9 b Ft(\))p Fu(.)58 b(Then)41 b(for)g(any)g(site)g Fq(w)46 b Fu(of)40 b Fq(D)t Fu(,)j Fq(d)p Ft(\()p Fq(w)t(;)24 b(z)6 b Ft(\))51 b Fk(\025)-303 7340 y Ft(b)t(dr)-68 7357 y Fj(min)142 7340 y Ft(\()p Fq(\015)9 b Ft(\))p Fq(=)p Ft(\()p Fq(\015)575 7276 y Fj(3)677 7340 y Ft(+)35 b Fq(\015)9 b Ft(\))p Fu(.)-150 7627 y Fv(P)f Fg(R)s(O)g(O)g(F)m Fv(.)59 b(Omitted.)d (Similar)40 b(to)g(the)g(proof)g(of)g(Lemma)i(14,)g(b)m(ut)d(it)h(uses) -303 7801 y(Lemma)f(13)d(as)i(well)f(as)h(Lemma)h(12.)1885 b Fh(\004)-133 8089 y Fv(L)8 b Fg(E)g(M)g(M)g(A)85 b Fv(16.)75 b Fu(Let)41 b Fq(D)46 b Fu(be)41 b(a)h(V)-17 b(or)-7 b(onoi)41 b(dia)o(gr)n(am,)g(and)g(let)g Fq(q)46 b Fu(be)c(a)f(point)-303 8263 y(in)66 b Ft(\012)p Fu(.)137 b(F)-16 b(or)68 b(any)f Fq(\015)109 b Fk(\025)100 b Ft(1)67 b Fu(and)g(for)g(e)n(very)h(site)f Fq(w)72 b Fu(of)66 b Fq(D)t Fu(,)76 b Fq(d)3161 8280 y Fp(q)3229 8263 y Ft(\()p Fq(w)t Ft(\))99 b Fk(\025)-303 8437 y Ft(min)p Fk(f)p Fq(d)110 8454 y Fp(w)209 8437 y Ft(\()p Fq(q)5 b Ft(\))p Fq(=\015)k(;)36 b Ft(b)t(dr)q(\()p Fq(q)5 b(;)25 b(\015)9 b Ft(\))p Fk(g)p Fu(.)-150 8724 y Fv(P)f Fg(R)s(O)g(O)g(F)m Fv(.)75 b(F)n(or)46 b(each)h(site)f Fq(w)t Fv(,)j(either)c Fq(d)1879 8741 y Fp(q)1948 8724 y Ft(\()p Fq(w)t Ft(\))59 b Fk(\025)h Ft(b)t(dr)q(\()p Fq(q)5 b(;)25 b(\015)9 b Ft(\))46 b Fv(\(satisfying)-303 8899 y(the)39 b(lemma\))h(or)g Fq(d)660 8916 y Fp(q)728 8899 y Ft(\()p Fq(w)t Ft(\))47 b Fq(<)g Ft(b)t(dr)q(\()p Fq(q)5 b(;)25 b(\015)9 b Ft(\))p Fv(.)54 b(In)39 b(the)h(latter)e(case,)k Fq(\034)17 b Ft(\()p Fq(q)5 b(;)25 b(w)t Ft(\))47 b Fk(\024)h Fq(\015)-303 9073 y Fv(by)36 b(the)h(de\002nition)f(of)h Ft(b)t(dr)h Fv(and)f Fq(d)1481 9090 y Fp(q)1549 9073 y Ft(\()p Fq(w)t Ft(\))43 b Fk(\025)g Fq(d)2068 9090 y Fp(w)2167 9073 y Ft(\()p Fq(q)5 b Ft(\))p Fq(=\015)k Fv(.)999 b Fh(\004)-133 9360 y Fv(L)8 b Fg(E)g(M)g(M)g(A)85 b Fv(17.)75 b Fu(Let)28 b Fq(X)40 b Fu(be)29 b(a)f(PSLG)g(whose)h(inter)o(secting)d(se)-6 b(gments)29 b(sat-)-303 9535 y(isfy)h(the)h(angle)f(condition)e (speci\002ed)j(in)f(Theor)-6 b(em)32 b(11.)44 b(Let)31 b Fq(s)f Fu(be)h(a)g(se)-6 b(gment)-303 9709 y(in)43 b Fq(X)57 b Fu(with)43 b(endpoints)f Fq(a)j Fu(and)f Fq(b)p Fu(.)68 b(Let)44 b Fq(D)49 b Fu(be)c(a)f(V)-17 b(or)-7 b(onoi)44 b(dia)o(gr)n(am)e(whose)-303 9883 y(sites)i(include)g (the)g(sites)g(in)g Fq(X)56 b Fu(\(including)42 b Fq(a)j Fu(and)f Fq(b)p Fu(\).)68 b(Let)45 b Fq(v)k Fu(be)c(a)f(site)g(of)-303 10058 y Fq(D)56 b Fu(that)50 b(encr)-7 b(oac)n(hes)53 b(upon)e Fq(s)p Fu(.)91 b(Let)52 b Fq(z)59 b Fu(be)52 b(a)g(point)e(in)h Ft(V)-13 b(or)q(\()p Fq(v)5 b Ft(\))44 b Fk(\\)i Fq(s)p Fu(.)91 b(Let)-303 10232 y Fq(m)43 b Ft(=)g(min)p Fk(f)p Fq(d)450 10249 y Fp(a)525 10232 y Ft(\()p Fq(v)5 b Ft(\))p Fq(;)24 b(d)872 10250 y Fp(b)935 10232 y Ft(\()p Fq(v)5 b Ft(\))p Fk(g)p Fu(.)-154 10406 y(Then)83 b(for)g(any)h(site)f Fq(w)k Fu(of)c Fq(D)t Fu(,)96 b Fq(d)p Ft(\()p Fq(w)t(;)24 b(z)6 b Ft(\))132 b Fk(\025)f Ft(min)p Fk(f)p Fq(m;)25 b Ft(lfs)3264 10423 y Fj(min)3474 10406 y Fq(=\015)9 b(;)-303 10581 y Ft(b)t(dr)-68 10598 y Fj(min)142 10581 y Ft(\()p Fq(\015)g Ft(\))p Fk(g)p Fu(.)44 b(Thus,)34 b(inserting)d Fq(z)40 b Fu(into)31 b Fq(D)36 b Fu(cr)-6 b(eates)34 b(no)e(inter)m(-site)g(distance)-303 10755 y(shorter)37 b(than)f Ft(min)p Fk(f)p Fq(m;)25 b Ft(lfs)1155 10772 y Fj(min)1366 10755 y Fq(=\015)9 b(;)25 b Ft(b)t(dr)1834 10772 y Fj(min)2044 10755 y Ft(\()p Fq(\015)9 b Ft(\))p Fk(g)p Fu(.)4234 -137 y Fv(P)f Fg(R)s(O)g(O)g(F)m Fv(.)50 b(Either)37 b Fq(v)43 b Fv(is)37 b(a)i(site)e(in)g Fq(X)50 b Fv(or)37 b Fq(v)43 b Fv(lies)38 b(on)f(a)h(se)n(gment)g(of)f Fq(X)50 b Fv(\(oth-)4080 37 y(erwise)c Fq(v)51 b Fv(w)o(ould)44 b(not)i(ha)m(v)n(e)g(been)g(inserted\).)71 b(Suppose)46 b Fq(v)51 b Fv(and)46 b Fq(z)53 b Fv(are)46 b(not)4080 211 y(intertwined.)j(Then)39 b Fq(d)5275 228 y Fp(v)5348 211 y Ft(\()p Fq(z)6 b Ft(\))46 b Fk(\025)g Ft(lfs)o(\()p Fq(v)5 b Ft(\))38 b Fv(by)h(the)f(de\002nition)f(of)h Ft(lfs)o Fv(.)51 b(Because)4080 386 y Fq(z)64 b Fv(is)57 b(in)f Ft(V)-13 b(or)q(\()p Fq(v)5 b Ft(\))p Fv(,)61 b Fq(d)5163 403 y Fp(w)5263 386 y Ft(\()p Fq(z)6 b Ft(\))80 b Fk(\025)h Fq(d)5820 403 y Fp(v)5894 386 y Ft(\()p Fq(z)6 b Ft(\))80 b Fk(\025)h Ft(lfs)o(\()p Fq(v)5 b Ft(\))57 b Fv(for)f(an)n(y)h(site)f Fq(w)61 b Fv(of)c Fq(D)t Fv(.)4080 560 y(By)38 b(Lemma)i(16,)f Fq(d)5094 577 y Fp(z)5165 560 y Ft(\()p Fq(w)t Ft(\))45 b Fk(\025)h Ft(min)p Fk(f)p Ft(lfs)o(\()p Fq(v)5 b Ft(\))p Fq(=\015)k(;)24 b Ft(b)t(dr)q(\()p Fq(z)6 b(;)26 b(\015)9 b Ft(\))p Fk(g)p Fv(,)39 b(so)f(the)g(lemma)4080 734 y(holds.)4230 909 y(If)47 b Fq(v)53 b Fv(and)48 b Fq(z)55 b Fv(are)48 b(intertwined,)h(then)e Fq(v)53 b Fv(lies)48 b(on)f(a)h(se)n(gment)g Fq(s)7510 845 y Fs(0)7602 909 y Fv(that)f(ad-)4080 1083 y(joins)57 b Fq(s)p Fv(.)108 b(Assume)59 b(without)c(loss)j(of)f(generality)g(that)g(the)h(shared)g (end-)4080 1257 y(point)44 b(of)h Fq(s)g Fv(and)g Fq(s)5053 1194 y Fs(0)5142 1257 y Fv(is)g Fq(b)p Fv(;)k(then)c Fq(\034)17 b Ft(\()p Fq(v)5 b(;)25 b(b)p Ft(\))57 b Fk(\024)h Fq(\015)d Fv(by)44 b(the)h(de\002nition)f(of)h(inter)m(-)4080 1432 y(twined.)68 b(W)-12 b(e)45 b(claim)g(that)e Fq(d)5558 1450 y Fp(b)5621 1432 y Ft(\()p Fq(v)5 b(;)25 b(z)6 b Ft(\))57 b Fq(>)g(\015)6287 1368 y Fj(2)6356 1432 y Fq(d)6436 1450 y Fp(b)6499 1432 y Ft(\()p Fq(v)5 b Ft(\))p Fv(.)68 b(Suppose)44 b(for)g(the)g(sak)o(e)4080 1606 y(of)c(contradiction)e (that)i Fq(d)5419 1624 y Fp(b)5481 1606 y Ft(\()p Fq(v)5 b(;)25 b(z)6 b Ft(\))50 b Fk(\024)f Fq(\015)6132 1543 y Fj(2)6201 1606 y Fq(d)6281 1624 y Fp(b)6343 1606 y Ft(\()p Fq(v)5 b Ft(\))p Fv(.)56 b(Because)41 b Fq(z)47 b Fv(is)40 b(in)g Ft(V)-13 b(or\()p Fq(v)5 b Ft(\))p Fv(,)4080 1780 y Fq(d)4160 1798 y Fp(b)4223 1780 y Ft(\()p Fq(z)h Ft(\))43 b Fk(\025)g Fq(d)4705 1797 y Fp(v)4779 1780 y Ft(\()p Fq(z)6 b Ft(\))43 b Fk(\025)g Fq(d)5261 1798 y Fp(b)5323 1780 y Ft(\()p Fq(v)5 b(;)25 b(z)6 b Ft(\))p Fq(=\015)j Fv(,)38 b(so)f Fq(d)6158 1798 y Fp(b)6221 1780 y Ft(\()p Fq(v)5 b(;)25 b(z)6 b Ft(\))43 b Fk(\024)g Fq(\015)9 b(d)6939 1798 y Fp(b)7001 1780 y Ft(\()p Fq(z)d Ft(\))43 b Fq(<)g(\015)7491 1717 y Fj(2)7561 1780 y Fq(d)7641 1798 y Fp(b)7703 1780 y Ft(\()p Fq(z)6 b Ft(\))p Fv(.)4230 1955 y(Let)36 b Fq(\022)k Fv(be)35 b(the)h(angle)f Fh(\\)p Fq(v)5 b(bz)43 b Fv(as)36 b(measured)g(by)f Fq(b)p Fv(.)46 b(Gi)l(v)n(en)35 b(the)h(constraints)4080 2129 y Fq(d)4160 2147 y Fp(b)4223 2129 y Ft(\()p Fq(v)5 b(;)25 b(z)6 b Ft(\))67 b Fk(\024)h Fq(\015)4910 2066 y Fj(2)4979 2129 y Fq(d)5059 2147 y Fp(b)5122 2129 y Ft(\()p Fq(v)5 b Ft(\))49 b Fv(and)h Fq(d)5717 2147 y Fp(b)5780 2129 y Ft(\()p Fq(v)5 b(;)25 b(z)6 b Ft(\))67 b Fq(<)h(\015)6467 2066 y Fj(2)6536 2129 y Fq(d)6616 2147 y Fp(b)6679 2129 y Ft(\()p Fq(z)6 b Ft(\))p Fv(,)54 b Fq(\022)g Fv(is)c(maximized)g(at) 4080 2304 y Fq(\022)d Ft(=)c(2)26 b(arcsin)o(\()p Fq(\015)5005 2240 y Fj(2)5074 2304 y Fq(=)p Ft(2\))36 b Fv(when)g(the)h(constraints) e(achie)l(v)n(e)i(equality)-10 b(.)45 b(But)36 b(the)4080 2478 y(second)42 b(constraint)e(cannot)i(achie)l(v)n(e)g(equality)-10 b(,)42 b(and)g(the)f(angle)h(condition)4080 2652 y(is)37 b Fq(\022)47 b Fk(\025)c Ft(2)26 b(arcsin)o(\()p Fq(\015)5142 2589 y Fj(2)5211 2652 y Fq(=)p Ft(2\))p Fv(,)37 b(so)g(the)g(claim)h (holds)e(by)h(contradiction.)4230 2827 y(Therefore,)g(for)e(an)n(y)h (site)g Fq(w)k Fv(of)c Fq(D)t Fv(,)h Fq(d)6193 2844 y Fp(w)6292 2827 y Ft(\()p Fq(z)6 b Ft(\))43 b Fk(\025)h Fq(d)6775 2844 y Fp(v)6848 2827 y Ft(\()p Fq(z)6 b Ft(\))43 b Fk(\025)g Fq(d)7330 2845 y Fp(b)7393 2827 y Ft(\()p Fq(v)5 b(;)25 b(z)6 b Ft(\))p Fq(=\015)52 b(>)4080 3001 y(\015)9 b(d)4248 3019 y Fp(b)4311 3001 y Ft(\()p Fq(v)c Ft(\))42 b Fk(\025)h Fq(\015)9 b(m)p Fv(.)47 b(By)36 b(Lemma)j(16,)e Fq(d)6031 3018 y Fp(z)6103 3001 y Ft(\()p Fq(w)t Ft(\))42 b Fk(\025)h Ft(min)p Fk(f)p Fq(m;)25 b Ft(b)t(dr)q(\()p Fq(z)6 b(;)26 b(\015)9 b Ft(\))p Fk(g)p Fv(.)166 b Fh(\004)4250 3323 y Fv(L)8 b Fg(E)g(M)g(M)g(A)86 b Fv(18.)74 b Fu(Let)36 b Fq(q)41 b Fu(be)c(a)e(V)-17 b(or)-7 b(onoi)36 b(verte)m(x)h(that)e(dualizes)g(to)g(a)h(poorly)4080 3497 y(shaped)46 b(triangle)f Fq(t)61 b Ft(=)f Fk(4)p Fq(v)5577 3514 y Fj(1)5646 3497 y Fq(v)5721 3514 y Fj(2)5790 3497 y Fq(v)5865 3514 y Fj(3)5933 3497 y Fu(.)75 b(De\002ne)46 b Fq(\015)56 b Fu(as)46 b(in)g(Theor)-6 b(em)47 b(11.)74 b(Sup-)4080 3672 y(pose)43 b(that)f Fq(d)4753 3689 y Fp(v)4815 3710 y Fa(i)4876 3672 y Ft(\()p Fq(v)5011 3689 y Fp(j)5075 3672 y Ft(\))54 b Fq(<)g Ft(b)t(dr)q(\()p Fq(v)5732 3689 y Fp(i)5784 3672 y Fq(;)25 b(\015)9 b Ft(\))43 b Fu(for)f(e)n(very)j Fq(i;)25 b(j)62 b Fk(2)54 b(f)p Ft(1)p Fq(;)25 b Ft(2)p Fq(;)g Ft(3)p Fk(g)p Fu(.)63 b(Let)44 b(the)4080 3846 y Fv(shortest)33 b(edge)i(length)e Fq(`)h Fu(of)g Fq(t)h Fu(be)f Ft(min)p Fk(f)p Fq(d)p Ft(\()p Fq(v)6365 3863 y Fj(1)6433 3846 y Fq(;)25 b(v)6576 3863 y Fj(2)6645 3846 y Ft(\))p Fq(;)g(d)p Ft(\()p Fq(v)6988 3863 y Fj(2)7056 3846 y Fq(;)g(v)7199 3863 y Fj(3)7268 3846 y Ft(\))p Fq(;)g(d)p Ft(\()p Fq(v)7611 3863 y Fj(3)7679 3846 y Fq(;)h(v)7823 3863 y Fj(1)7891 3846 y Ft(\))p Fk(g)p Fu(.)4230 4042 y(Then)37 b(for)g(e)n(very)h(site)f Fq(w)42 b Fu(of)36 b Fq(D)t Fu(,)i Fq(d)5972 4059 y Fp(w)6071 4042 y Ft(\()p Fq(q)5 b Ft(\))43 b Fq(>)g(\015)6558 3979 y Fj(2)6627 3913 y Fi(p)p 6780 3913 422 7 v 6780 4042 a Fq(\015)6868 3999 y Fj(2)6972 4042 y Ft(+)34 b(1)p Fq(`)p Fu(.)4234 4364 y Fv(P)8 b Fg(R)s(O)g(O)g(F)m Fv(.)54 b(F)n(or)38 b(each)i(v)n(erte)n(x)e Fq(v)5790 4381 y Fp(i)5882 4364 y Fv(of)g Fq(t)p Fv(,)j(the)e(distortion)d(disk)i(of)h Fq(v)7539 4381 y Fp(i)7630 4364 y Fv(is)g(lar)m(ge)4080 4539 y(enough)47 b(to)g(enclose)g(the)g(other)g(tw)o(o)f(v)n(ertices,)k (so)e(it)e(encloses)i Fq(t)p Fv(.)78 b(There-)4080 4713 y(fore,)42 b Fq(\034)17 b Ft(\()p Fq(v)4620 4730 y Fp(i)4672 4713 y Fq(;)25 b(p)p Ft(\))50 b Fk(\024)g Fq(\015)g Fv(for)41 b(an)n(y)f(v)n(erte)n(x)g Fq(v)6180 4730 y Fp(i)6274 4713 y Fv(of)g Fq(t)i Fv(and)f(point)e Fq(p)i Fv(in)g Fq(t)p Fv(.)58 b(Because)4080 4887 y Fq(t)41 b Fv(is)f(poorly)e (shaped,)k(there)e(is)f(a)i(point)e Fq(p)h Fv(in)f Fq(t)i Fv(from)f(whose)g(perspecti)l(v)n(e)g Fq(t)4080 5062 y Fv(has)d(an)g(angle)g Fq(\022)47 b(<)c(\022)5208 5080 y Fj(b)s(ound)5550 5062 y Fv(.)j(Let)37 b Fq(r)48 b Ft(=)43 b Fq(d)6228 5079 y Fp(v)6290 5098 y Fd(1)6363 5062 y Ft(\()p Fq(q)5 b Ft(\))42 b(=)h Fq(d)6841 5079 y Fp(v)6903 5098 y Fd(2)6976 5062 y Ft(\()p Fq(q)5 b Ft(\))42 b(=)h Fq(d)7454 5079 y Fp(v)7516 5098 y Fd(3)7589 5062 y Ft(\()p Fq(q)5 b Ft(\))p Fv(.)46 b(Let)4080 5258 y Fq(\014)62 b Ft(=)55 b Fq(\015)4491 5194 y Fj(2)4560 5128 y Fi(p)p 4714 5128 V 130 x Fq(\015)4802 5215 y Fj(2)4905 5258 y Ft(+)34 b(1)p Fv(.)65 b(If)43 b Fq(\014)62 b Fk(\025)55 b Fq(r)t(=`)p Fv(,)46 b(then)d(by)g(Corollary)f(10,)j Ft(2)p Fq(\015)7507 5194 y Fj(2)7601 5258 y Ft(sin)25 b Fq(\022)59 b Fk(\025)4080 5460 y Ft(1)p Fq(=\014)18 b Fk(\000)10 b Ft(\()p Fq(\015)4616 5397 y Fj(2)4696 5460 y Fk(\000)g Ft(1\))p Fq(\014)e Fv(.)44 b(Substitution)28 b(of)i Fq(\014)39 b Fv(gi)l(v)n(es)30 b Fq(\015)6601 5397 y Fj(8)6681 5460 y Ft(+)10 b(2)p Fq(\015)6975 5397 y Fj(4)7044 5331 y Fi(p)p 7198 5331 V 129 x Fq(\015)7286 5417 y Fj(2)7389 5460 y Ft(+)35 b(1)25 b(sin)g Fq(\022)15 b Fk(\000)4080 5662 y Fq(\015)4168 5599 y Fj(4)4262 5662 y Fk(\000)24 b Ft(1)43 b Fk(\025)g Ft(0)p Fv(.)i(By)35 b(assumption,)f Fq(\015)5897 5599 y Fj(8)5990 5662 y Ft(+)24 b(2)p Fq(\015)6298 5599 y Fj(4)6368 5533 y Fi(p)p 6522 5533 V 129 x Fq(\015)6610 5619 y Fj(2)6713 5662 y Ft(+)34 b(1)26 b(sin)f Fq(\022)7255 5680 y Fj(b)s(ound)7621 5662 y Fk(\000)f Fq(\015)7852 5599 y Fj(4)7946 5662 y Fk(\000)4080 5837 y Ft(1)43 b(=)g(0)p Fv(,)37 b(so)h Ft(sin)25 b Fq(\022)47 b Fk(\025)c Ft(sin)25 b Fq(\022)5465 5855 y Fj(b)s(ound)5806 5837 y Fv(,)38 b(a)g(contradiction;)c(hence)k Fq(\014)50 b(<)43 b(r)t(=`)p Fv(.)4230 6033 y(F)n(or)36 b(e)l(v)n(ery)i(site)f Fq(w)k Fv(of)c Fq(D)t Fv(,)g Fq(d)5679 6050 y Fp(w)5779 6033 y Ft(\()p Fq(q)5 b Ft(\))42 b Fk(\025)h Fq(r)k(>)d(\014)8 b(`)42 b Ft(=)h Fq(\015)6906 5969 y Fj(2)6975 5903 y Fi(p)p 7129 5903 V 130 x Fq(\015)7217 5990 y Fj(2)7320 6033 y Ft(+)35 b(1)o Fq(`)p Fv(.)296 b Fh(\004)4250 6355 y Fv(L)8 b Fg(E)g(M)g(M)g(A)86 b Fv(19.)74 b Fu(Let)66 b Fq(u)g Fu(and)e Fq(v)71 b Fu(be)65 b(sites)h(of)e(a)i(V)-17 b(or)-7 b(onoi)65 b(dia)o(gr)n(am)e Fq(D)t Fu(.)4080 6529 y(Let)k Fq(q)72 b Fu(be)67 b(a)g(wedg)o(e)f (violator)f(in)h Ft(V)-13 b(or\()p Fq(u)p Ft(\))57 b Fk(\\)g Ft(V)-13 b(or\()p Fq(v)5 b Ft(\))67 b Fu(that)e(is)i(outside) 4080 6704 y Ft(w)l(edge)q(\()p Fq(u;)25 b(v)5 b Ft(\))p Fu(.)87 b(De\002ne)51 b Fq(\015)59 b Fu(as)51 b(in)f(Theor)-6 b(em)51 b(11.)87 b(Then)51 b(for)f(e)n(very)i(site)e Fq(w)4080 6900 y Fu(of)37 b Fq(D)t Fu(,)g Fq(d)4519 6917 y Fp(w)4619 6900 y Ft(\()p Fq(q)5 b Ft(\))42 b Fk(\025)h Ft(min)p Fk(f)p Fq(\015)5438 6836 y Fj(2)5507 6770 y Fi(p)p 5661 6770 V 130 x Fq(\015)5749 6857 y Fj(2)5852 6900 y Ft(+)34 b(1)26 b Fq(d)p Ft(\()p Fq(u;)f(v)5 b Ft(\))p Fq(;)25 b Ft(b)t(dr)6847 6917 y Fj(min)7057 6900 y Fq(=)p Ft(\()p Fq(\015)7282 6836 y Fj(3)7385 6900 y Ft(+)34 b Fq(\015)9 b Ft(\))p Fk(g)p Fu(.)4234 7222 y Fv(P)f Fg(R)s(O)g(O)g(F)m Fv(.)97 b(If)54 b Fq(\034)17 b Ft(\()p Fq(u;)25 b(v)5 b Ft(\))73 b Fq(>)i(\015)9 b Fv(,)58 b(then)53 b Fq(d)6229 7239 y Fp(v)6302 7222 y Ft(\()p Fq(q)5 b Ft(\))74 b Fk(\025)g Ft(b)t(dr)6998 7239 y Fj(min)7208 7222 y Fq(=)p Ft(\()p Fq(\015)7433 7158 y Fj(3)7548 7222 y Ft(+)47 b Fq(\015)9 b Ft(\))54 b Fv(by)4080 7396 y(Lemma)c(14.)80 b(If)49 b Fq(\034)17 b Ft(\()p Fq(u;)25 b(v)5 b Ft(\))63 b Fk(\024)i Fq(\015)9 b Fv(,)52 b(assume)d Fq(q)54 b Fv(is)48 b(outside)g Ft(w)l(edge\()p Fq(u;)25 b(v)5 b Ft(\))49 b Fv(on)4080 7592 y(the)41 b(side)g(of)g Fq(u)p Fv(.)59 b(From)41 b(Lemma)i(5)e(we)g(ha)m(v)n(e)g Fq(d)6528 7609 y Fp(v)6602 7592 y Ft(\()p Fq(q)5 b Ft(\))50 b Fk(\025)g Fq(d)7095 7609 y Fp(u)7177 7592 y Ft(\()p Fq(v)5 b Ft(\))p Fq(=)7454 7463 y Fi(p)p 7606 7463 V 7606 7592 a Fq(\015)7694 7549 y Fj(2)7798 7592 y Fk(\000)34 b Ft(1)p Fv(.)4080 7795 y(By)78 b(assumption,)89 b Fq(\015)5229 7731 y Fj(8)5364 7795 y Fk(\000)66 b Fq(\015)5637 7731 y Fj(4)5772 7795 y Fk(\000)g Ft(1)121 b Fk(\024)h Ft(0)p Fv(,)90 b(so)78 b Fq(d)6891 7812 y Fp(u)6973 7795 y Ft(\()p Fq(v)5 b Ft(\))p Fq(=)7250 7665 y Fi(p)p 7403 7665 V 7403 7795 a Fq(\015)7491 7752 y Fj(2)7594 7795 y Fk(\000)34 b Ft(1)122 b Fk(\025)4080 7997 y Fq(\015)4168 7933 y Fj(2)4237 7867 y Fi(p)p 4391 7867 V 130 x Fq(\015)4479 7954 y Fj(2)4582 7997 y Ft(+)35 b(1)o Fq(d)4892 8014 y Fp(u)4974 7997 y Ft(\()p Fq(v)5 b Ft(\))42 b Fk(\025)h Fq(\015)5466 7933 y Fj(2)5535 7867 y Fi(p)p 5689 7867 V 130 x Fq(\015)5777 7954 y Fj(2)5880 7997 y Ft(+)34 b(1)26 b Fq(d)p Ft(\()p Fq(u;)f(v)5 b Ft(\))p Fv(.)4230 8171 y(Because)43 b Fq(q)59 b Fk(2)53 b Ft(V)-13 b(or\()p Fq(v)5 b Ft(\))p Fv(,)44 b(for)f(e)l(v)n(ery)f(site)h Fq(w)k Fv(of)42 b Fq(D)t Fv(,)j Fq(d)7027 8188 y Fp(w)7126 8171 y Ft(\()p Fq(q)5 b Ft(\))53 b Fk(\025)g Fq(d)7625 8188 y Fp(v)7699 8171 y Ft(\()p Fq(q)5 b Ft(\))53 b Fk(\025)4080 8367 y Ft(min)p Fk(f)p Fq(\015)4501 8304 y Fj(2)4570 8238 y Fi(p)p 4724 8238 V 129 x Fq(\015)4812 8324 y Fj(2)4915 8367 y Ft(+)34 b(1)26 b Fq(d)p Ft(\()p Fq(u;)f(v)5 b Ft(\))p Fq(;)25 b Ft(b)t(dr)5910 8384 y Fj(min)6120 8367 y Fq(=)p Ft(\()p Fq(\015)6345 8304 y Fj(3)6448 8367 y Ft(+)34 b Fq(\015)9 b Ft(\))p Fk(g)p Fv(.)1083 b Fh(\004)4250 8689 y Fv(L)8 b Fg(E)g(M)g(M)g(A)86 b Fv(20.)74 b Fu(Suppose)52 b(the)g(V)-17 b(or)-7 b(onoi)52 b(r)-6 b(e\002nement)53 b(algorithm)e(main-)4080 8864 y(tains)k(a)g(loose)g(anisotr)-7 b(opic)54 b(V)-17 b(or)-7 b(onoi)55 b(dia)o(gr)n(am)e(instead)i(of)g(a) g(true)h(ani-)4080 9038 y(sotr)-7 b(opic)63 b(V)-17 b(or)-7 b(onoi)64 b(dia)o(gr)n(am.)124 b(Let)64 b Fq(q)69 b Fu(be)64 b(a)g(point)f(that)f(the)i(algorithm)4080 9213 y(identi\002es)49 b(as)h(a)g(violator)-17 b(,)52 b(b)m(ut)d(is)h(not)f(r)-6 b(eally)50 b(a)g(violator)-17 b(.)84 b(The)50 b(bound)f(of)4080 9387 y(Lemma)38 b(19)e(applies)g(to)h Fq(q)42 b Fu(\(for)37 b(some)g(pair)g(of)f(sites)h Fq(u)h Fu(and)f Fq(v)5 b Fu(\).)4234 9709 y Fv(P)j Fg(R)s(O)g(O)g(F)m Fv(.)67 b(Let)44 b Fq(L)g Fv(be)g(the)f(loose)g(V)-19 b(oronoi)42 b(diagram)h(maintained)g(by)h(the)4080 9883 y(algorithm)d(at)i(the)g (moment)g Fq(q)48 b Fv(is)43 b(identi\002ed)e(as)j(a)f(violator)-6 b(,)43 b(and)g(let)f Fq(D)47 b Fv(be)4080 10058 y(the)c(true)f (anisotropic)f(V)-19 b(oronoi)40 b(diagram)j(of)f(the)h(same)h(sites.) 63 b(Because)43 b Fq(q)4080 10232 y Fv(is)35 b(incorrectly)e (identi\002ed)h(as)i(a)f(violator)-6 b(,)34 b Fq(q)40 b Fv(lies)35 b(in)f(a)h(2-cell)g Fq(c)g Fv(of)g Fq(L)g Fv(o)l(wned)4080 10406 y(by)i(some)h(site)f Fq(z)44 b Fv(whose)37 b(V)-19 b(oronoi)35 b(cell)i(\(in)g Fq(D)t Fv(\))g(does)g(not)g(contain)f Fq(z)6 b Fv(.)4230 10581 y(Consider)40 b(\002rst)g(the)h(case)i(where)e Fq(q)46 b Fv(lies)41 b(in)g(the)f(interior)g(of)g Fq(c)p Fv(.)59 b(Because)4080 10755 y Fq(q)48 b Fk(62)43 b Ft(V)-13 b(or\()p Fq(z)6 b Ft(\))p Fv(,)35 b(there)e(must)f(be)h(some)h(other)e (site)h Fq(v)38 b Fv(for)32 b(which)h Fq(q)47 b Fk(2)c Ft(V)-13 b(or\()p Fq(v)5 b Ft(\))p Fv(.)p eop %%Page: 9 9 9 8 bop -303 -137 a Fv(The)53 b(2-cell)g(of)g Fq(L)g Fv(o)l(wned)g(by)g Fq(v)58 b Fv(includes)53 b(e)l(v)n(ery)g(point)f(of) g Ft(V)-13 b(or)q(\()p Fq(v)5 b Ft(\))53 b Fv(that)-303 37 y(is)64 b(visible)f(to)h Fq(v)70 b Fv(within)63 b Ft(V)-13 b(or\()p Fq(v)5 b Ft(\))p Fv(.)128 b(Therefore,)72 b Fq(q)d Fv(is)c(not)f(visible)f(to)h Fq(v)-303 211 y Fv(within)50 b Ft(V)-13 b(or\()p Fq(v)5 b Ft(\))p Fv(.)91 b(Let)52 b Fq(p)g Fv(be)g(the)g(point)f(nearest)h Fq(v)57 b Fv(on)52 b(the)g(line)f(se)n(gment)-303 386 y Fq(q)5 b(v)44 b Fv(such)39 b(that)g(the)g(line)f(se)n(gment)i Fq(q)5 b(p)39 b Fv(lies)g(entirely)f(in)g Ft(V)-13 b(or)q(\()p Fq(v)5 b Ft(\))p Fv(.)52 b(\(It)38 b(is)h(pos-)-303 560 y(sible)56 b(that)g Fq(p)80 b Ft(=)g Fq(q)5 b Fv(.\))104 b(Let)58 b Fq(u)80 b Fk(6)p Ft(=)g Fq(v)62 b Fv(be)56 b(a)i(site)e(such)h(that)f Fq(p)80 b Fk(2)g Ft(V)-13 b(or\()p Fq(u)p Ft(\))-303 734 y Fv(and)46 b(some)i(point)d(of)h Ft(V)-13 b(or\()p Fq(u)p Ft(\))47 b Fv(lies)f(between)h Fq(p)g Fv(and)g Fq(v)5 b Fv(.)75 b(By)46 b(Lemma)i(3,)i Fq(p)-303 909 y Fv(is)f(outside)e Ft(w)l(edge)q(\()p Fq(u;)25 b(v)5 b Ft(\))p Fv(,)53 b(so)c Fq(p)g Fv(is)g(a)g(wedge)h (violator)-8 b(.)80 b(By)48 b(Lemma)j(19,)-303 1105 y Fq(d)-223 1122 y Fp(v)-150 1105 y Ft(\()p Fq(p)p Ft(\))43 b Fk(\025)g Ft(min)p Fk(f)p Fq(\015)673 1041 y Fj(2)742 975 y Fi(p)p 895 975 422 7 v 895 1105 a Fq(\015)983 1062 y Fj(2)1086 1105 y Ft(+)35 b(1)25 b Fq(d)p Ft(\()p Fq(u;)g(v)5 b Ft(\))p Fq(;)25 b Ft(b)t(dr)2081 1122 y Fj(min)2292 1105 y Fq(=)p Ft(\()p Fq(\015)2517 1041 y Fj(3)2614 1105 y Ft(+)30 b Fq(\015)9 b Ft(\))p Fk(g)p Fv(.)46 b(Because)37 b Fq(p)-303 1279 y Fv(lies)48 b(between)i Fq(q)k Fv(and)49 b Fq(v)5 b Fv(,)52 b Fq(d)1138 1296 y Fp(v)1212 1279 y Ft(\()p Fq(q)5 b Ft(\))65 b Fk(\025)h Fq(d)1736 1296 y Fp(v)1809 1279 y Ft(\()p Fq(p)p Ft(\))p Fv(.)82 b(Because)50 b Fq(q)71 b Fk(2)65 b Ft(V)-13 b(or\()p Fq(v)5 b Ft(\))p Fv(,)52 b(for)-303 1454 y(e)l(v)n(ery)37 b(site)g Fq(w)k Fv(of)c Fq(D)t Fv(,)h Fq(d)904 1471 y Fp(w)1003 1454 y Ft(\()p Fq(q)5 b Ft(\))42 b Fk(\025)i Fq(d)1482 1471 y Fp(v)1555 1454 y Ft(\()p Fq(q)5 b Ft(\))p Fv(.)46 b(The)38 b(result)f(follo)l(ws.)-154 1628 y(No)l(w)50 b(consider)f(the)g(case)i (where)f Fq(q)55 b Fv(lies)49 b(on)h(the)f(boundary)g(of)g Fq(c)p Fv(.)84 b(Let)-303 1802 y Fq(c)-237 1739 y Fs(0)-147 1802 y Ft(=)47 b Fq(c)26 b Fk(n)p Ft(V)-13 b(or\()p Fq(z)6 b Ft(\))p Fv(,)40 b(and)e(observ)n(e)h(that)f Fq(q)50 b Fk(2)c Fq(c)2053 1739 y Fs(0)2099 1802 y Fv(.)51 b(Because)40 b(the)e(bound)g(holds)-303 1977 y(for)43 b(e)l(v)n(ery)h(point)e(in)i (the)g(interior)e(of)h Fq(c)1742 1913 y Fs(0)1787 1977 y Fv(,)k(it)c(holds)g(for)g(e)l(v)n(ery)h(point)f(on)g(the)-303 2151 y(boundary)35 b(of)i Fq(c)526 2087 y Fs(0)609 2151 y Fv(by)g(the)g(continuity)d(of)j(distances.)1156 b Fh(\004)-133 2466 y Fv(L)8 b Fg(E)g(M)g(M)g(A)85 b Fv(21.)75 b Fu(Let)31 b Fq(q)37 b Fu(be)32 b(a)g(site)f(inserted)g(at)g(a)h(violator)e(by)i (the)f(V)-17 b(or)-7 b(onoi)-303 2641 y(r)h(e\002nement)43 b(algorithm.)62 b(Let)43 b Fq(D)k Fu(be)c(the)g(V)-17 b(or)-7 b(onoi)42 b(dia)o(gr)n(am)f(just)h(befor)-6 b(e)44 b Fq(q)-303 2815 y Fu(is)k(inserted.)79 b(Let)49 b Fq(m)64 b Ft(=)g(min)1321 2833 y Fp(u)p Fs(6)p Fj(=)p Fp(v)1587 2815 y Fq(d)1667 2832 y Fp(u)1749 2815 y Ft(\()p Fq(v)5 b Ft(\))48 b Fu(wher)-6 b(e)49 b(the)f(sites)g Fq(u)h Fu(and)f Fq(v)53 b Fu(ar)-6 b(e)-303 2989 y(c)n(hosen)31 b(fr)-7 b(om)32 b(among)e(all)h(sites)h(of)f Fq(D)t Fu(.)45 b(F)-16 b(or)32 b(e)n(very)h(site)f Fq(w)k Fu(of)31 b Fq(D)t Fu(,)i Fq(d)p Ft(\()p Fq(q)5 b(;)25 b(w)t Ft(\))42 b Fk(\025)-303 3185 y Ft(min)p Fk(f)p Fq(\015)118 3056 y Fi(p)p 271 3056 V 271 3185 a Fq(\015)359 3142 y Fj(2)462 3185 y Ft(+)35 b(1)o Fq(m;)26 b Ft(b)t(dr)1131 3202 y Fj(min)1341 3185 y Ft(\()p Fq(\015)9 b Ft(\))p Fq(=)p Ft(\()p Fq(\015)1774 3122 y Fj(4)1877 3185 y Ft(+)35 b Fq(\015)2119 3122 y Fj(2)2188 3185 y Ft(\))p Fk(g)p Fu(.)48 b(Thus,)38 b(the)f(insertion)f(of)-303 3360 y Fq(q)42 b Fu(into)36 b Fq(D)41 b Fu(cr)-6 b(eates)39 b(no)d(inter)m(-site)g(distance)h(shorter)g(than)f(that.)-150 3675 y Fv(P)8 b Fg(R)s(O)g(O)g(F)m Fv(.)57 b(The)41 b(violator)d Fq(q)45 b Fv(does)40 b(not)f(encroach)i(upon)e(an)n(y)g(subse)n(gment) -303 3849 y(\(otherwise)46 b(it)g(w)o(ould)f(not)i(be)g(inserted\).)75 b(If)47 b Fq(q)52 b Fv(is)47 b(a)h(wedge)f(violator)-6 b(,)48 b(the)-303 4024 y(result)d(follo)l(ws)g(from)h(Lemmas)i(19)e (and)h(16.)73 b(If)46 b Fq(q)52 b Fv(is)46 b(a)h(violator)d(by)i(mis-) -303 4198 y(tak)o(en)53 b(identity)-10 b(,)57 b(the)c(result)h(follo)l (ws)e(from)i(Lemmas)i(20)d(and)h(16.)97 b(Oth-)-303 4372 y(erwise,)57 b Fq(q)i Fv(dualizes)52 b(to)h(a)h(poorly)d(shaped)i (triangle)f Fq(t)74 b Ft(=)f Fk(4)p Fq(v)3095 4389 y Fj(1)3163 4372 y Fq(v)3238 4389 y Fj(2)3307 4372 y Fq(v)3382 4389 y Fj(3)3451 4372 y Fv(.)94 b(If)-303 4547 y Fq(d)-223 4564 y Fp(v)-161 4585 y Fa(i)-101 4547 y Ft(\()p Fq(v)34 4564 y Fp(j)99 4547 y Ft(\))48 b Fk(\025)g Ft(b)t(dr)q(\()p Fq(v)744 4564 y Fp(i)796 4547 y Fq(;)26 b(\015)9 b Ft(\))40 b Fv(for)f(an)n(y)h Fq(i;)25 b(j)56 b Fk(2)49 b(f)p Ft(1)p Fq(;)25 b Ft(2)p Fq(;)g Ft(3)p Fk(g)p Fv(,)41 b(then)e(by)h(Lemma)i (14,)-303 4721 y Fq(d)p Ft(\()p Fq(q)5 b(;)24 b(w)t Ft(\))62 b Fk(\025)h Ft(b)t(dr)631 4738 y Fj(min)841 4721 y Ft(\()p Fq(\015)9 b Ft(\))p Fq(=)p Ft(\()p Fq(\015)1274 4658 y Fj(3)1384 4721 y Ft(+)43 b Fq(\015)9 b Ft(\))47 b Fv(as)h(claimed.)78 b(Hence,)51 b(assume)e(that)-303 4895 y Fq(d)-223 4912 y Fp(v)-161 4933 y Fa(i)-101 4895 y Ft(\()p Fq(v)34 4912 y Fp(j)99 4895 y Ft(\))66 b Fq(<)g Ft(b)t(dr)q(\()p Fq(v)780 4912 y Fp(i)832 4895 y Fq(;)25 b(\015)9 b Ft(\))50 b Fv(for)e(e)l(v)n(ery)i Fq(i;)25 b(j)74 b Fk(2)67 b(f)p Ft(1)p Fq(;)25 b Ft(2)p Fq(;)g Ft(3)p Fk(g)p Fv(.)83 b(By)49 b(Lemma)i(18,)-303 5092 y Fq(d)-223 5109 y Fp(w)-124 5092 y Ft(\()p Fq(q)5 b Ft(\))42 b Fk(\025)h Fq(\015)362 5028 y Fj(2)431 4962 y Fi(p)p 585 4962 V 130 x Fq(\015)673 5049 y Fj(2)776 5092 y Ft(+)35 b(1)p Fq(m)p Fv(.)47 b(The)37 b(result)g(follo)l(ws)f(from)h(Lemma)h(16.)207 b Fh(\004)-133 5407 y Fv(L)8 b Fg(E)g(M)g(M)g(A)85 b Fv(22.)75 b Fu(Let)55 b Fq(s)g Fu(be)h(a)f(se)-6 b(gment)55 b(with)f(endpoints)g Fq(a)i Fu(and)f Fq(b)g Fu(in)g(a)-303 5581 y(PSLG)47 b Fq(X)12 b Fu(.)78 b(Let)48 b Fq(z)54 b Fu(be)48 b(the)f (\223midpoint\224)f(of)h Fq(s)p Fu(,)j(de\002ned)d(so)h(that)e Fq(d)3227 5598 y Fp(a)3302 5581 y Ft(\()p Fq(z)6 b Ft(\))63 b(=)-303 5756 y Fq(d)-223 5774 y Fp(b)-161 5756 y Ft(\()p Fq(z)6 b Ft(\))p Fu(.)83 b(Let)49 b Fq(D)k Fu(be)c(a)g(V)-17 b(or)-7 b(onoi)49 b(dia)o(gr)n(am)d(whose)j(sites)g(include)f(the)h (sites)-303 5930 y(in)38 b Fq(X)52 b Fu(\(including)36 b Fq(a)k Fu(and)f Fq(b)p Fu(\).)53 b(Let)40 b Fq(q)k Fu(be)c(a)f(point)f(suc)n(h)h(that)f Ft(V)-13 b(or\()p Fq(q)5 b Ft(\))39 b Fu(would)-303 6104 y(contain)31 b Fq(z)40 b Fu(if)32 b Fq(q)38 b Fu(wer)-6 b(e)34 b(inserted)e(into)g Fq(D)37 b Fu(\(thus)32 b Fq(q)38 b Fu(would)31 b(encr)-7 b(oac)n(h)33 b(upon)f Fq(s)p Fu(\).)-154 6279 y(Suppose)48 b Fq(\034)17 b Ft(\()p Fq(a;)25 b(q)5 b Ft(\))64 b Fk(\024)g Fq(\015)58 b Fu(and)48 b Fq(\034)17 b Ft(\()p Fq(b;)24 b(q)5 b Ft(\))64 b Fk(\024)h Fq(\015)57 b Fu(for)48 b(some)h Fq(\015)73 b Fk(\025)64 b Ft(1)p Fu(.)81 b(Then)-303 6475 y Fq(d)-223 6492 y Fp(a)-148 6475 y Ft(\()p Fq(z)6 b Ft(\))43 b(=)g Fq(d)334 6493 y Fp(b)396 6475 y Ft(\()p Fq(z)6 b Ft(\))43 b Fk(\025)g Ft(min)p Fk(f)p Fq(d)1211 6492 y Fp(a)1286 6475 y Ft(\()p Fq(q)5 b Ft(\))p Fq(;)25 b(d)1628 6493 y Fp(b)1691 6475 y Ft(\()p Fq(q)5 b Ft(\))p Fk(g)p Fq(=)p Ft(\()p Fq(\015)2187 6345 y Fi(p)p 2339 6345 V 2339 6475 a Fq(\015)2427 6432 y Fj(2)2530 6475 y Ft(+)35 b(1)o(\))p Fu(.)-150 6790 y Fv(P)8 b Fg(R)s(O)g(O)g(F)m Fv(.)93 b(Consider)51 b(a)i(line)e Fq(l)j Fv(through)d Fq(z)59 b Fv(that)51 b(is)h(perpendicular)f(to)g Fq(s)-303 6965 y Fv(from)42 b Fq(q)5 b Fv(')-8 b(s)43 b(point)e(of)i(vie)l(w)-10 b(.)63 b(Speci\002cally)-10 b(,)45 b Fq(l)g Fv(is)e(composed)g(of)g (the)f(points)g Fq(p)-303 7139 y Fv(that)g(satisfy)h Fq(d)478 7156 y Fp(q)546 7139 y Ft(\()p Fq(b;)25 b(z)6 b Ft(\))877 7075 y Fj(2)986 7139 y Ft(+)39 b Fq(d)1224 7156 y Fp(q)1292 7139 y Ft(\()p Fq(z)6 b(;)26 b(p)p Ft(\))1635 7075 y Fj(2)1759 7139 y Ft(=)54 b Fq(d)2012 7156 y Fp(q)2081 7139 y Ft(\()p Fq(b;)25 b(p)p Ft(\))2412 7075 y Fj(2)2524 7139 y Fv(\(Pythagoras')42 b(La)n(w\).)-303 7313 y(Suppose)c(without)f (loss)i(of)f(generality)g(that)g Fq(q)45 b Fv(lies)38 b(on)h(the)g(same)h(side)f(of)f Fq(l)-303 7488 y Fv(as)46 b Fq(b)p Fv(,)i(or)e Fq(q)51 b Fv(lies)46 b(on)f Fq(l)r Fv(.)73 b(Then)46 b Fq(d)1349 7505 y Fp(q)1417 7488 y Ft(\()p Fq(b;)25 b(z)6 b Ft(\))1748 7424 y Fj(2)1859 7488 y Ft(+)41 b Fq(d)2099 7505 y Fp(q)2167 7488 y Ft(\()p Fq(z)6 b Ft(\))2364 7424 y Fj(2)2493 7488 y Fk(\025)59 b Fq(d)2751 7505 y Fp(q)2820 7488 y Ft(\()p Fq(b)p Ft(\))3006 7424 y Fj(2)3074 7488 y Fv(.)73 b(Because)-303 7662 y Fq(\034)17 b Ft(\()p Fq(b;)24 b(q)5 b Ft(\))43 b Fk(\024)g Fq(\015)9 b Fv(,)37 b(it)g(follo)l(ws)f(that)g Fq(\015)1428 7598 y Fj(2)1497 7662 y Fq(d)1577 7680 y Fp(b)1640 7662 y Ft(\()p Fq(z)6 b Ft(\))1837 7598 y Fj(2)1940 7662 y Ft(+)35 b Fq(d)2174 7679 y Fp(q)2242 7662 y Ft(\()p Fq(z)6 b Ft(\))2439 7598 y Fj(2)2551 7662 y Fk(\025)44 b Fq(d)2794 7680 y Fp(b)2856 7662 y Ft(\()p Fq(q)5 b Ft(\))3050 7598 y Fj(2)3119 7662 y Fq(=\015)3284 7598 y Fj(2)3352 7662 y Fv(.)-154 7836 y Ft(V)-13 b(or\()p Fq(q)5 b Ft(\))47 b Fv(w)o(ould)f(contain)g Fq(z)54 b Fv(if)47 b Fq(q)52 b Fv(were)c(inserted)f(into)e Fq(D)t Fv(,)51 b(so)c Fq(d)3235 7853 y Fp(q)3303 7836 y Ft(\()p Fq(z)6 b Ft(\))62 b Fk(\024)-303 8011 y Fq(d)-223 8029 y Fp(b)-161 8011 y Ft(\()p Fq(z)6 b Ft(\))p Fv(.)74 b(Therefore,)49 b Ft(\()p Fq(\015)970 7947 y Fj(2)1080 8011 y Ft(+)42 b(1\))p Fq(d)1458 8029 y Fp(b)1520 8011 y Ft(\()p Fq(z)6 b Ft(\))1717 7947 y Fj(2)1846 8011 y Fk(\025)61 b Fq(d)2106 8029 y Fp(b)2168 8011 y Ft(\()p Fq(q)5 b Ft(\))2362 7947 y Fj(2)2431 8011 y Fq(=\015)2596 7947 y Fj(2)2664 8011 y Fv(,)49 b(from)d(which)g(the) -303 8185 y(result)36 b(follo)l(ws.)3013 b Fh(\004)-133 8500 y Fv(L)8 b Fg(E)g(M)g(M)g(A)85 b Fv(23.)75 b Fu(Let)42 b Fq(z)49 b Fu(be)42 b(a)g(site)g(inserted)g(on)g(a)g(se)-6 b(gment)42 b Fq(s)f Fu(because)i(a)-303 8675 y(violator)c Fq(q)47 b Fu(\(not)40 b(inserted\))h(encr)-7 b(oac)n(hes)42 b(upon)f Fq(s)p Fu(.)58 b(Let)42 b Fq(D)j Fu(be)d(the)f(V)-17 b(or)-7 b(onoi)-303 8849 y(dia)o(gr)n(am)43 b(just)h(befor)-6 b(e)46 b Fq(z)52 b Fu(is)45 b(inserted.)71 b(Let)45 b Fq(m)59 b Ft(=)f(min)2649 8867 y Fp(u)p Fs(6)p Fj(=)p Fp(v)2916 8849 y Fq(d)2996 8866 y Fp(u)3077 8849 y Ft(\()p Fq(v)5 b Ft(\))45 b Fu(wher)-6 b(e)-303 9023 y(the)65 b(sites)h Fq(u)g Fu(and)f Fq(v)71 b Fu(ar)-6 b(e)67 b(c)n(hosen)e(fr)-7 b(om)66 b(among)f(all)f(sites)i(of)f Fq(D)t Fu(.)133 b(De-)-303 9198 y(\002ne)68 b Fq(\015)78 b Fu(as)68 b(in)g(Theor)-6 b(em)69 b(11.)140 b(F)-16 b(or)69 b(e)n(very)h(site)e Fq(w)73 b Fu(of)68 b Fq(D)t Fu(,)77 b Fq(d)p Ft(\()p Fq(z)6 b(;)25 b(w)t Ft(\))102 b Fk(\025)-303 9394 y Ft(min)p Fk(f)p Fq(m;)25 b Ft(b)t(dr)468 9411 y Fj(min)678 9394 y Ft(\()p Fq(\015)9 b Ft(\))p Fq(=)p Ft(\(\()p Fq(\015)1171 9330 y Fj(5)1273 9394 y Ft(+)35 b Fq(\015)1515 9330 y Fj(3)1584 9394 y Ft(\))1644 9264 y Fi(p)p 1797 9264 V 1797 9394 a Fq(\015)1885 9351 y Fj(2)1988 9394 y Ft(+)g(1\))p Fk(g)p Fu(.)-150 9709 y Fv(P)8 b Fg(R)s(O)g(O)g(F)m Fv(.)46 b(The)30 b(se)n(gment)g Fq(s)g Fv(intersects)f(only)g(tw)o(o)f(V)-19 b(oronoi)28 b(cells,)k(namely)-303 9883 y Ft(V)-13 b(or\()p Fq(a)p Ft(\))48 b Fv(and)g Ft(V)-13 b(or\()p Fq(b)p Ft(\))48 b Fv(where)g Fq(a)h Fv(and)f Fq(b)g Fv(are)h(the)f(endpoints)e(of)i Fq(s)p Fv(.)79 b(Other)m(-)-303 10058 y(wise,)62 b(the)57 b(algorithm)e(w)o(ould)g(ha)m(v)n(e)i(split)f Fq(s)h Fv(before)g(trying)e(to)h(insert)g Fq(q)5 b Fv(.)-303 10232 y(There)45 b(are)g(tw)o(o)f(cases)i(to)e(consider)-8 b(.)69 b(In)44 b(Case)i(A,)f Fq(z)52 b Fv(lies)44 b(on)g(the)h(V)-19 b(oronoi)-303 10406 y(curv)n(e)33 b Ft(V)-13 b(or\()p Fq(a)p Ft(\))20 b Fk(\\)g Ft(V)-13 b(or)q(\()p Fq(b)p Ft(\))p Fv(.)44 b(In)33 b(Case)i(B,)e Fq(z)41 b Fv(lies)33 b(in)g(just)g(one)g(V)-19 b(oronoi)31 b(cell\227)-303 10581 y(without)j(loss)j(of)g(generality)-10 b(,)36 b(say)h Ft(V)-13 b(or)q(\()p Fq(b)p Ft(\))p Fv(\227because)37 b(if)g Fq(q)42 b Fv(were)37 b(inserted,)-303 10755 y Ft(V)-13 b(or\()p Fq(q)5 b Ft(\))37 b Fv(w)o(ould)e(not)h(intersect)h Fq(s)d Fk(\\)g Ft(V)-13 b(or)q(\()p Fq(a)p Ft(\))p Fv(.)4230 -137 y(If)43 b Fq(d)4453 -120 y Fp(q)4522 -137 y Ft(\()p Fq(b)p Ft(\))55 b Fk(\025)h Ft(b)t(dr)q(\()p Fq(q)5 b(;)25 b(\015)9 b Ft(\))p Fv(,)46 b(the)e(result)f(follo)l(ws)g(by)h(Lemma)h (15.)67 b(Hence,)4080 37 y(assume)59 b Fq(\034)17 b Ft(\()p Fq(q)5 b(;)25 b(b)p Ft(\))81 b Fk(\024)h Fq(\015)9 b Fv(.)108 b(Similarly)-10 b(,)62 b(in)57 b(Case)h(A)g(the)g(result)f (follo)l(ws)f(if)4080 211 y Fq(d)4160 228 y Fp(q)4229 211 y Ft(\()p Fq(a)p Ft(\))42 b Fk(\025)h Ft(b)t(dr)q(\()p Fq(q)5 b(;)25 b(\015)9 b Ft(\))p Fv(,)37 b(so)h(assume)g(in)f(that)f (case)j(that)d Fq(\034)17 b Ft(\()p Fq(q)5 b(;)25 b(a)p Ft(\))43 b Fk(\024)g Fq(\015)9 b Fv(.)4230 386 y(Let)55 b Fq(v)4559 403 y Fj(1)4628 386 y Fq(;)25 b(:)h(:)f(:)g(;)g(v)5044 404 y Fp(k)5176 386 y Fv(be)55 b(the)h(sites)f(whose)g(V)-19 b(oronoi)54 b(cells)h(contain)g Fq(q)5 b Fv(.)101 b(In)4080 560 y(Case)31 b(A,)g(by)e(Lemma)j(22,)g Fq(d)5542 578 y Fp(b)5604 560 y Ft(\()p Fq(z)6 b Ft(\))43 b Fk(\025)g Ft(min)p Fk(f)p Fq(d)6419 577 y Fp(a)6494 560 y Ft(\()p Fq(q)5 b Ft(\))p Fq(;)25 b(d)6836 578 y Fp(b)6898 560 y Ft(\()p Fq(q)5 b Ft(\))p Fk(g)p Fq(=)p Ft(\()p Fq(\015)7394 431 y Fi(p)p 7547 431 V 7547 560 a Fq(\015)7635 517 y Fj(2)7738 560 y Ft(+)34 b(1\))p Fv(.)4080 734 y(Because)43 b Fq(q)k Fv(lies)42 b(in)f Ft(V)-13 b(or\()p Fq(v)5518 751 y Fp(i)5570 734 y Ft(\))42 b Fv(for)f(each)i Fq(i)51 b Fk(2)g Ft([1)p Fq(;)25 b(k)t Ft(])42 b Fv(and)g Fq(z)49 b Fv(lies)41 b(in)g Ft(V)-13 b(or)q(\()p Fq(b)p Ft(\))p Fv(,)4080 909 y(for)28 b(an)n(y)g(site)g Fq(w)k Fv(of)c Fq(D)k Fv(we)d(ha)m(v)n(e)f Fq(d)5803 926 y Fp(w)5903 909 y Ft(\()p Fq(z)6 b Ft(\))43 b Fk(\025)g Fq(d)6385 927 y Fp(b)6447 909 y Ft(\()p Fq(z)6 b Ft(\))44 b Fk(\025)f Ft(min)p Fk(f)p Fq(d)7263 926 y Fp(a)7338 909 y Ft(\()p Fq(q)5 b Ft(\))p Fq(;)24 b(d)7679 927 y Fp(b)7742 909 y Ft(\()p Fq(q)5 b Ft(\))p Fk(g)p Fq(=)4080 1105 y Ft(\()p Fq(\015)4228 975 y Fi(p)p 4381 975 V 4381 1105 a Fq(\015)4469 1062 y Fj(2)4573 1105 y Ft(+)34 b(1\))42 b Fk(\025)h Fq(d)5147 1122 y Fp(v)5209 1143 y Fa(i)5270 1105 y Ft(\()p Fq(q)5 b Ft(\))p Fq(=)p Ft(\()p Fq(\015)5689 975 y Fi(p)p 5842 975 V 5842 1105 a Fq(\015)5930 1062 y Fj(2)6033 1105 y Ft(+)34 b(1\))p Fv(.)4230 1279 y(A)62 b(similar)g(result)f (holds)g(in)h(Case)h(B.)g(Let)f Fq(D)6778 1296 y Fp(q)6909 1279 y Fv(be)h(the)f(V)-19 b(oronoi)60 b(di-)4080 1454 y(agram)d(formed)f(by)g(inserting)f Fq(q)61 b Fv(into)55 b Fq(D)61 b Fv(\(e)l(v)n(en)56 b(though)f(the)h(algorithm)4080 1628 y(does)45 b(not)f(insert)f Fq(q)5 b Fv(\).)69 b(In)44 b Fq(D)5537 1645 y Fp(q)5606 1628 y Fv(,)j(there)d(are)i(one)e(or)g(tw) o(o)g(intersection)f(points)4080 1802 y Fq(s)34 b Fk(\\)h Ft(V)-13 b(or)q(\()p Fq(b)p Ft(\))34 b Fk(\\)h Ft(V)-13 b(or\()p Fq(q)5 b Ft(\))p Fv(,)38 b(and)g Fq(z)45 b Fv(is)37 b(the)h(one)g(furthest)f(from)g Fq(b)p Fv(.)49 b(Although)35 b Fq(z)4080 1977 y Fv(lies)44 b(in)g Ft(V)-13 b(or\()p Fq(b)p Ft(\))44 b Fv(in)g Fq(D)5250 1994 y Fp(q)5318 1977 y Fv(,)j(either)d Fq(z)51 b Fv(is)44 b(not)g(visible)f(from)h Fq(b)g Fv(within)e Ft(V)-13 b(or)q(\()p Fq(b)p Ft(\))p Fv(,)4080 2151 y(or)51 b Fq(z)57 b Fv(lies)51 b(where)g Ft(V)-13 b(or\()p Fq(q)5 b Ft(\))50 b Fv(tangentially)f(intersects)h Fq(s)h Fv(at)f(a)i(single)e(point.)4080 2325 y(By)41 b(Lemma)h(3,)g Fq(z)48 b Fv(lies)41 b(outside)f Ft(w)l(edge\()p Fq(b;)25 b(q)5 b Ft(\))41 b Fv(on)f Fq(q)5 b Fv(')-8 b(s)41 b(side)g(of)f(the)h(wedge.)4080 2521 y(From)50 b(Lemma)h(5)e(we)h(ha)m(v)n(e)g Fq(d)5715 2538 y Fp(q)5783 2521 y Ft(\()p Fq(z)6 b Ft(\))67 b Fk(\025)f Fq(d)6312 2538 y Fp(q)6381 2521 y Ft(\()p Fq(b)p Ft(\))p Fq(=)6644 2392 y Fi(p)p 6796 2392 V 6796 2521 a Fq(\015)6884 2478 y Fj(2)6988 2521 y Fk(\000)34 b Ft(1)p Fv(.)84 b(In)49 b Fq(D)t Fv(,)k Fq(q)i Fv(lies)4080 2696 y(in)43 b Ft(V)-13 b(or)q(\()p Fq(v)4615 2713 y Fp(i)4667 2696 y Ft(\))43 b Fv(for)g(each)i Fq(i)54 b Fk(2)h Ft([1)p Fq(;)25 b(k)t Ft(])p Fv(,)46 b(and)e(in)f Fq(D)6515 2713 y Fp(q)6583 2696 y Fv(,)j Fq(z)k Fv(lies)44 b(in)f Ft(V)-13 b(or\()p Fq(q)5 b Ft(\))p Fv(,)45 b(so)f(for)4080 2892 y(an)n(y)49 b(site)g Fq(w)54 b Fv(of)49 b Fq(D)54 b Fv(we)c(ha)m(v)n(e)f Fq(d)5749 2909 y Fp(w)5849 2892 y Ft(\()p Fq(z)6 b Ft(\))66 b Fk(\025)g Fq(d)6377 2909 y Fp(q)6446 2892 y Ft(\()p Fq(z)6 b Ft(\))66 b Fk(\025)g Fq(d)6974 2909 y Fp(q)7043 2892 y Ft(\()p Fq(b)p Ft(\))p Fq(=)7306 2762 y Fi(p)p 7458 2762 V 7458 2892 a Fq(\015)7546 2849 y Fj(2)7649 2892 y Fk(\000)35 b Ft(1)66 b Fk(\025)4080 3094 y Fq(d)4160 3112 y Fp(b)4223 3094 y Ft(\()p Fq(q)5 b Ft(\))p Fq(=)p Ft(\()p Fq(\015)4642 2964 y Fi(p)p 4794 2964 V 4794 3094 a Fq(\015)4882 3051 y Fj(2)4985 3094 y Fk(\000)35 b Ft(1\))42 b Fk(\025)h Fq(d)5560 3111 y Fp(v)5622 3132 y Fa(i)5683 3094 y Ft(\()p Fq(q)5 b Ft(\))p Fq(=)p Ft(\()p Fq(\015)6102 2964 y Fi(p)p 6254 2964 V 6254 3094 a Fq(\015)6342 3051 y Fj(2)6445 3094 y Fk(\000)35 b Ft(1\))p Fv(.)4230 3296 y(In)52 b(either)h(Case)h(A)f(or)f(B,)i Fq(d)5754 3313 y Fp(w)5853 3296 y Ft(\()p Fq(z)6 b Ft(\))73 b Fk(\025)h Fq(d)6396 3313 y Fp(v)6458 3334 y Fa(i)6518 3296 y Ft(\()p Fq(q)5 b Ft(\))p Fq(=)p Ft(\()p Fq(\015)6937 3167 y Fi(p)p 7090 3167 V 7090 3296 a Fq(\015)7178 3253 y Fj(2)7281 3296 y Ft(+)35 b(1)o(\))53 b Fv(for)g(an)n(y)4080 3471 y(site)41 b Fq(w)k Fv(of)c Fq(D)k Fv(and)c(an)n(y)g Fq(i)49 b Fk(2)i Ft([1)p Fq(;)24 b(k)t Ft(])p Fv(.)59 b(Suppose)40 b(that)h Fq(d)6892 3488 y Fp(v)6954 3509 y Fa(i)7014 3471 y Ft(\()p Fq(q)5 b Ft(\))50 b Fk(\025)g Ft(b)t(dr)q(\()p Fq(v)7797 3488 y Fp(i)7849 3471 y Fq(;)26 b(\015)9 b Ft(\))4080 3667 y Fv(for)41 b(some)i Fq(i)51 b Fk(2)h Ft([1)p Fq(;)25 b(k)t Ft(])p Fv(.)60 b(Then)43 b Fq(d)5754 3684 y Fp(w)5853 3667 y Ft(\()p Fq(z)6 b Ft(\))52 b Fk(\025)g Ft(b)t(dr)q(\()p Fq(v)6643 3684 y Fp(i)6695 3667 y Fq(;)25 b(\015)9 b Ft(\))p Fq(=)p Ft(\()p Fq(\015)7136 3537 y Fi(p)p 7289 3537 V 7289 3667 a Fq(\015)7377 3624 y Fj(2)7480 3667 y Ft(+)35 b(1)o(\))42 b Fv(and,)4080 3869 y(by)g(Lemma)h(16,)g Fq(d)5080 3886 y Fp(z)5151 3869 y Ft(\()p Fq(w)t Ft(\))51 b Fk(\025)h Ft(b)t(dr)5842 3886 y Fj(min)6052 3869 y Ft(\()p Fq(\015)9 b Ft(\))p Fq(=)p Ft(\()p Fq(\015)6485 3806 y Fj(2)6553 3740 y Fi(p)p 6707 3740 V 129 x Fq(\015)6795 3826 y Fj(2)6898 3869 y Ft(+)34 b(1\))42 b Fv(for)f(an)n(y)h(site)f Fq(w)4080 4043 y Fv(of)c Fq(D)t Fv(,)h(so)f(the)g(result)f(follo)l(ws.) 4230 4218 y(If)47 b(the)h(supposition)d(is)j(not)f(true)h(for)f(an)n(y) h Fq(i)63 b Fk(2)g Ft([1)p Fq(;)25 b(k)t Ft(])p Fv(,)51 b(then)c Fq(d)7566 4235 y Fp(v)7628 4256 y Fa(i)7689 4218 y Ft(\()p Fq(q)5 b Ft(\))63 b Fq(<)4080 4392 y Ft(b)t(dr)q(\()p Fq(v)4450 4409 y Fp(i)4502 4392 y Fq(;)25 b(\015)9 b Ft(\))38 b Fv(and)g(thus)f Fq(\034)17 b Ft(\()p Fq(v)5517 4409 y Fp(i)5568 4392 y Fq(;)26 b(q)5 b Ft(\))43 b Fk(\024)h Fq(\015)j Fv(for)37 b(e)l(v)n(ery)h Fq(i)43 b Fk(2)h Ft([1)p Fq(;)25 b(k)t Ft(])p Fv(.)49 b(This)37 b(implies)4080 4566 y(that)g Fq(\034)17 b Ft(\()p Fq(v)4562 4583 y Fp(i)4613 4566 y Fq(;)26 b(v)4757 4583 y Fp(j)4821 4566 y Ft(\))43 b Fk(\024)g Fq(\015)5174 4503 y Fj(2)5280 4566 y Fv(for)37 b(an)n(y)g Fq(i;)25 b(j)51 b Fk(2)43 b Ft([1)p Fq(;)24 b(k)t Ft(])p Fv(.)4230 4741 y(Suppose)65 b(that)g(there)g(are)h(tw)o(o) e(sites)i Fq(v)6399 4758 y Fp(i)6517 4741 y Fv(and)f Fq(v)6873 4758 y Fp(j)7003 4741 y Fv(for)g(which)g Fq(i;)25 b(j)105 b Fk(2)4080 4915 y Ft([1)p Fq(;)25 b(k)t Ft(])75 b Fv(and)f Fq(d)4840 4932 y Fp(v)4902 4953 y Fa(i)4963 4915 y Ft(\()p Fq(v)5098 4932 y Fp(j)5162 4915 y Ft(\))114 b Fk(\025)g Ft(b)t(dr)q(\()p Fq(v)5939 4932 y Fp(i)5991 4915 y Fq(;)25 b(\015)9 b Ft(\))p Fv(.)158 b(By)74 b(the)h(triangle)e (inequality)-10 b(,)4080 5090 y Fq(d)4160 5107 y Fp(v)4222 5128 y Fa(i)4283 5090 y Ft(\()p Fq(v)4418 5107 y Fp(j)4482 5090 y Ft(\))68 b Fk(\024)h Fq(d)4878 5107 y Fp(v)4940 5128 y Fa(i)5001 5090 y Ft(\()p Fq(q)5 b Ft(\))43 b(+)i Fq(d)5482 5107 y Fp(v)5544 5128 y Fa(i)5605 5090 y Ft(\()p Fq(q)5 b(;)25 b(v)5882 5107 y Fp(j)5946 5090 y Ft(\))68 b Fk(\024)h Fq(d)6342 5107 y Fp(v)6404 5128 y Fa(i)6465 5090 y Ft(\()p Fq(q)5 b Ft(\))43 b(+)i Fq(\015)6954 5026 y Fj(2)7023 5090 y Fq(d)7103 5107 y Fp(v)7165 5128 y Fa(j)7235 5090 y Ft(\()p Fq(q)5 b Ft(\))68 b(=)h(\()p Fq(\015)7833 5026 y Fj(2)7946 5090 y Ft(+)4080 5302 y(1\))p Fq(d)4297 5319 y Fp(v)4359 5340 y Fa(i)4419 5302 y Ft(\()p Fq(q)5 b Ft(\))65 b Fk(\024)h Ft(\()p Fq(\015)5011 5238 y Fj(3)5123 5302 y Ft(+)44 b Fq(\015)9 b Ft(\))5434 5173 y Fi(p)p 5587 5173 V 5587 5302 a Fq(\015)5675 5259 y Fj(2)5778 5302 y Ft(+)35 b(1)p Fq(d)6089 5319 y Fp(w)6188 5302 y Ft(\()p Fq(z)6 b Ft(\))50 b Fv(for)f(an)n(y)g(site)g Fq(w)k Fv(of)c Fq(D)t Fv(.)82 b(Thus)4080 5504 y Fq(d)4160 5521 y Fp(w)4260 5504 y Ft(\()p Fq(z)6 b Ft(\))92 b Fk(\025)g Ft(b)t(dr)q(\()p Fq(v)5130 5521 y Fp(i)5182 5504 y Fq(;)25 b(\015)9 b Ft(\))p Fq(=)p Ft(\(\()p Fq(\015)5683 5441 y Fj(3)5805 5504 y Ft(+)54 b Fq(\015)9 b Ft(\))6126 5375 y Fi(p)p 6279 5375 V 6279 5504 a Fq(\015)6367 5461 y Fj(2)6470 5504 y Ft(+)35 b(1\))63 b Fv(and,)69 b(by)63 b(Lemma)h(16,)4080 5706 y Fq(d)4160 5723 y Fp(z)4231 5706 y Ft(\()p Fq(w)t Ft(\))83 b Fk(\025)g Ft(b)t(dr)4985 5723 y Fj(min)5195 5706 y Ft(\()p Fq(\015)9 b Ft(\))p Fq(=)p Ft(\(\()p Fq(\015)5688 5643 y Fj(4)5806 5706 y Ft(+)51 b Fq(\015)6064 5643 y Fj(2)6133 5706 y Ft(\))6193 5577 y Fi(p)p 6346 5577 V 6346 5706 a Fq(\015)6434 5664 y Fj(2)6538 5706 y Ft(+)34 b(1\))58 b Fv(for)g(each)h(site)f Fq(w)t Fv(,)64 b(so)4080 5881 y(the)37 b(result)g(follo)l(ws.)4230 6055 y(If)59 b(the)g(supposition)e(is)i(not)g(true,)65 b(then)59 b Fq(d)6522 6072 y Fp(v)6584 6093 y Fa(i)6645 6055 y Ft(\()p Fq(v)6780 6072 y Fp(j)6844 6055 y Ft(\))85 b Fq(<)g Ft(b)t(dr)q(\()p Fq(v)7563 6072 y Fp(i)7615 6055 y Fq(;)26 b(\015)9 b Ft(\))59 b Fv(for)4080 6230 y(e)l(v)n(ery)37 b(pair)g(of)g(sites)g Fq(v)5253 6247 y Fp(i)5343 6230 y Fv(and)g Fq(v)5671 6247 y Fp(j)5773 6230 y Fv(whose)g(V)-19 b(oronoi)35 b(cells)i(contain)g Fq(q)5 b Fv(.)46 b(One)38 b(of)4080 6404 y(the)f(preconditions)e(for)i (Lemma)i(18)d(is)h(thus)g(satis\002ed.)4230 6578 y(Depending)46 b(on)h(what)g(type)g(of)g(violator)e Fq(q)53 b Fv(is,)d(Lemma)f(18,)h (19,)g(or)d(20)4080 6769 y(applies,)57 b(sho)l(wing)51 b(that)h Fq(d)5510 6786 y Fp(w)5610 6769 y Ft(\()p Fq(q)5 b Ft(\))72 b Fk(\025)g Ft(min)p Fk(f)p Fq(\015)6488 6706 y Fj(2)6557 6640 y Fi(p)p 6711 6640 V 129 x Fq(\015)6799 6726 y Fj(2)6902 6769 y Ft(+)34 b(1)p Fq(m;)26 b Ft(b)t(dr)7571 6786 y Fj(min)7781 6769 y Ft(\()p Fq(\015)9 b Ft(\))p Fq(=)4080 6944 y Ft(\()p Fq(\015)4228 6880 y Fj(3)4333 6944 y Ft(+)37 b Fq(\015)9 b Ft(\))p Fk(g)39 b Fv(for)g(e)l(v)n(ery)h (site)f Fq(w)44 b Fv(of)c Fq(D)t Fv(.)54 b(It)39 b(follo)l(ws)g(that)g Fq(d)7081 6961 y Fp(w)7180 6944 y Ft(\()p Fq(z)6 b Ft(\))48 b Fk(\025)g Fq(d)7672 6961 y Fp(v)7734 6982 y Fa(i)7795 6944 y Ft(\()p Fq(q)5 b Ft(\))p Fq(=)4080 7140 y Ft(\()p Fq(\015)4228 7010 y Fi(p)p 4381 7010 V 4381 7140 a Fq(\015)4469 7097 y Fj(2)4573 7140 y Ft(+)34 b(1\))132 b Fk(\025)h Ft(min)p Fk(f)p Fq(\015)9 b(m;)25 b Ft(b)t(dr)6106 7157 y Fj(min)6317 7140 y Ft(\()p Fq(\015)9 b Ft(\))p Fq(=)p Ft(\(\()p Fq(\015)6810 7076 y Fj(4)6947 7140 y Ft(+)71 b Fq(\015)7225 7076 y Fj(2)7294 7140 y Ft(\))7354 7010 y Fi(p)p 7507 7010 V 7507 7140 a Fq(\015)7595 7097 y Fj(2)7698 7140 y Ft(+)35 b(1\))p Fk(g)4080 7314 y Fv(and,)65 b(by)58 b(Lemma)i(16,)k Fq(d)5452 7331 y Fp(z)5523 7314 y Ft(\()p Fq(w)t Ft(\))83 b Fk(\025)h Ft(min)p Fk(f)p Fq(m;)26 b Ft(b)t(dr)6815 7331 y Fj(min)7025 7314 y Ft(\()p Fq(\015)9 b Ft(\))p Fq(=)p Ft(\(\()p Fq(\015)7518 7251 y Fj(5)7636 7314 y Ft(+)51 b Fq(\015)7894 7251 y Fj(3)7963 7314 y Ft(\))p Fk(\001)4080 7381 y Fi(p)p 4234 7381 V 129 x Fq(\015)4322 7467 y Fj(2)4425 7510 y Ft(+)35 b(1)o(\))p Fk(g)i Fv(for)g(each)h(site)f Fq(w)k Fv(of)c Fq(D)k Fv(as)d(claimed.) 1196 b Fh(\004)4234 7914 y Fv(P)8 b Fg(R)s(O)g(O)g(F)51 b(O)8 b(F)53 b Fv(T)8 b Fg(H)g(E)g(O)g(R)g(E)g(M)50 b Fv(1)8 b(1)g(.)72 b(The)46 b(anisotropic)e(V)-19 b(oronoi)43 b(diagram)i(of)4080 8089 y(the)35 b(sites)h(in)f Fq(X)47 b Fv(has)36 b(no)f(inter)m(-site)f(distance)h(less)h(than)f Ft(lfs)7138 8106 y Fj(min)7348 8089 y Fv(,)h(by)f(the)h(def-)4080 8263 y(inition)43 b(of)i Ft(lfs)4836 8280 y Fj(min)5046 8263 y Fv(.)71 b(By)44 b(Lemmas)j(17,)g(21,)g(and)e(23,)i(e)l(v)n(ery)f (inter)m(-site)d(dis-)4080 8437 y(tance)38 b(created)f(by)g(an)n(y)g (site)g(the)g(algorithm)e(inserts)i(is)g(at)g(least)g(as)h(great)f(as) 4080 8628 y(either)43 b Ft(lfs)4614 8645 y Fj(min)4824 8628 y Fq(=\015)9 b Fv(,)45 b Ft(b)t(dr)5306 8645 y Fj(min)5516 8628 y Ft(\()p Fq(\015)9 b Ft(\))p Fq(=)p Ft(\(\()p Fq(\015)6009 8565 y Fj(5)6115 8628 y Ft(+)39 b Fq(\015)6361 8565 y Fj(3)6430 8628 y Ft(\))6490 8499 y Fi(p)p 6644 8499 V 129 x Fq(\015)6732 8586 y Fj(2)6835 8628 y Ft(+)34 b(1\))p Fv(,)45 b(or)e(the)f(shortest)4080 8803 y(inter)m(-site)36 b(distance)h(e)n(xisting)e(prior)h(to)h(the)g(site)g(insertion.)4230 8977 y(By)d(induction)f(on)i(the)g(sequence)i(of)d(site)h(insertions,)g (for)f(an)n(y)h(tw)o(o)g(sites)4080 9152 y Fq(v)k Fv(and)34 b Fq(w)39 b Fv(that)33 b(are)h(e)l(v)n(er)h(inserted)e(by)h(the)f(V)-19 b(oronoi)32 b(re\002nement)j(algorithm,)4080 9343 y Fq(d)p Ft(\()p Fq(v)5 b(;)25 b(w)t Ft(\))42 b Fk(\025)h Fq(\026)g Ft(=)g(min)p Fk(f)p Ft(lfs)5527 9360 y Fj(min)5737 9343 y Fq(=\015)9 b(;)25 b Ft(b)t(dr)6205 9360 y Fj(min)6415 9343 y Ft(\()p Fq(\015)9 b Ft(\))p Fq(=)p Ft(\(\()p Fq(\015)6908 9279 y Fj(5)6978 9343 y Ft(+)r Fq(\015)7187 9279 y Fj(3)7256 9343 y Ft(\))7316 9213 y Fi(p)p 7470 9213 V 130 x Fq(\015)7558 9300 y Fj(2)7661 9343 y Ft(+)35 b(1)o(\))p Fk(g)p Fv(.)4230 9517 y(Let)e Fq(\025)4552 9534 y Fj(max)4818 9517 y Fv(be)h(an)g(upper) e(bound)h(on)g(the)g(lar)m(gest)g(eigen)-6 b(v)l(alue)33 b(of)g Fq(M)50 b Fv(o)n(v)n(er)4080 9691 y(the)39 b(domain)f Ft(\012)p Fv(.)52 b(F)n(or)39 b(an)n(y)g(tw)o(o)e(sites)i Fq(v)44 b Fv(and)39 b Fq(w)t Fv(,)h Fq(\026)46 b Fk(\024)h Fq(d)7003 9708 y Fp(v)7076 9691 y Ft(\()p Fq(w)t Ft(\))f(=)h Fk(k)p Fq(F)7697 9708 y Fp(v)7771 9691 y Ft(\()p Fq(v)40 b Fk(\000)4080 9883 y Fq(w)t Ft(\))p Fk(k)4331 9900 y Fj(2)4443 9883 y Fk(\024)j(k)p Fq(F)4780 9900 y Fp(v)4854 9883 y Fk(k)4931 9900 y Fj(2)5000 9883 y Fk(k)p Fq(v)25 b Fk(\000)20 b Fq(w)t Fk(k)5507 9900 y Fj(2)5619 9883 y Ft(=)44 b(\(max)6127 9900 y Fp(x)6231 9883 y Fq(x)6318 9820 y Fp(T)6415 9883 y Fq(M)6563 9900 y Fp(v)6637 9883 y Fq(x=x)6888 9820 y Fp(T)6986 9883 y Fq(x)p Ft(\))7133 9820 y Fj(1)p Fp(=)p Fj(2)7326 9883 y Fk(k)p Fq(v)25 b Fk(\000)20 b Fq(w)t Fk(k)7833 9900 y Fj(2)7946 9883 y Fk(\024)4080 9939 y(p)p 4208 9939 323 7 v 119 x Fq(\025)4298 10075 y Fj(max)4579 10058 y Fk(k)p Fq(v)47 b Fk(\000)c Fq(w)t Fk(k)5131 10075 y Fj(2)5200 10058 y Fv(.)80 b(Therefore,)52 b(measured)d(in)e(ph)o(ysical)h(space,)53 b Fk(k)p Fq(v)47 b Fk(\000)4080 10232 y Fq(w)t Fk(k)4271 10249 y Fj(2)4400 10232 y Fk(\025)59 b Fq(\026=)4748 10113 y Fk(p)p 4876 10113 V 119 x Fq(\025)4966 10249 y Fj(max)5198 10232 y Fv(.)73 b(Imagine)46 b(that)f(a)h(disk)g(of)f(radius)g Fq(\026=)p Ft(\(2)7410 10113 y Fk(p)p 7537 10113 V 7537 10232 a Fq(\025)7627 10249 y Fj(max)7860 10232 y Ft(\))h Fv(is)4080 10406 y(centered)e(at)f(each)h(site.)65 b(The)44 b(interiors)d(of)i(these)h(disks)e(do)h(not)g(intersect.)4080 10581 y(Only)h(a)h(\002nite)f(number)g(of)g(such)h(nono)n(v)n (erlapping)c(disks)j(can)h(be)g(pack)o(ed)4080 10755 y(so)37 b(their)g(centers)g(lie)g(in)g Ft(\012)p Fv(,)g(therefore)g (the)g(algorithm)e(terminates.)323 b Fh(\004)p eop %%Page: 10 10 10 9 bop -303 -137 a Fw(11.)198 b(Conclusions)-154 79 y Fv(There)57 b(are)h(se)l(v)n(eral)f(clear)g(directions)e(for)h(impro) n(v)n(ement)f(and)h(e)n(xten-)-303 253 y(sion)41 b(of)h(our)f(results.) 61 b(W)-12 b(e)43 b(suspect)f(it)f(is)h(straightforw)o(ard)d(\(albeit)i (messy\))-303 427 y(to)52 b(pro)n(v)n(e)g(that)g(our)h(V)-19 b(oronoi)51 b(re\002nement)i(algorithm)e(generates)j Fu(gr)n(aded)-303 602 y Fv(meshes)47 b(in)f(which)g(edge)h(lengths)e (are)i(dictated)f(primarily)e(by)i(local)g(fea-)-303 776 y(tures\227the)37 b(mesh)h(is)f(not)f(re\002ned)h(to)g(v)n(ery)g (small)g(triangles)f(in)h(one)g(re)n(gion)-303 950 y(because)42 b(of)e(v)n(ery)g(small)h(features)g(f)o(ar)f(a)n(w)o(ay)-10 b(.)58 b(Ruppert)39 b([13])h(pro)n(v)n(es)g(such)-303 1125 y(a)33 b(result)e(for)h(isotropic)f(meshing.)45 b(Ho)l(we)l(v)n(er)-6 b(,)34 b(the)e(anisotropic)f(grading)g(re-)-303 1299 y(sult)37 b(w)o(ould)g(be)h(weak)o(er)h(than)f(Ruppert')-8 b(s)37 b(isotropic)f(result)i(because)h(a)g(site)-303 1473 y(whose)i(metric)g(tensor)f(is)h(small)g(sees)i(f)o(ara)n(w)o(ay)d (elements)h(as)h(being)f(close)-303 1648 y(by)-10 b(,)47 b(and)d(therefore)g(its)h(in\003uence)f(on)h(them)g(is)f(less)h (attenuated.)69 b(Speci\002-)-303 1822 y(cally)-10 b(,)36 b(a)g(site)f(with)g(a)h(small)g(metric)f(tensor)g(has)h(a)g(wide)g (paraboloid)d(which)-303 1996 y(can)45 b(create)g(orphans)f(at)g(a)i (great)e(distance,)i(thereby)e(causing)h(re\002nement)-303 2171 y(in)c(distant)f(locations)h(to)g(remo)n(v)n(e)g(the)h(orphans.)59 b(These)43 b(ef)l(fects)f(might)f(be)-303 2345 y(mitig)o(ated)50 b(by)h(simply)g(remo)n(ving)f(the)i(orphans)e(without)g(inserting)f(ne) l(w)-303 2519 y(sites)j(\(e)n(xploiting)d(the)j(\003e)n(xibility)e(of)i (loose)g(V)-19 b(oronoi)50 b(diagrams\),)56 b(or)c(by)-303 2694 y(resizing)36 b(the)h(metric)g(tensors)g(\(and)g(paraboloids\))e (of)i(problem)g(sites.)-154 2868 y(Our)45 b(V)-19 b(oronoi)44 b(re\002nement)j(algorithm,)f(lik)o(e)f(Ruppert')-8 b(s)44 b(Delaunay)i(re-)-303 3042 y(\002nement)58 b(algorithm,)63 b(reco)n(v)n(ers)c(se)n(gments)f(of)h(the)f(PSLG)h(by)g(splitting)-303 3217 y(them.)50 b(There)39 b(are)h(man)n(y)e(adv)l(antages)h(to)f (using)f(a)i(constrained)f(Delaunay)-303 3391 y(triangulation)k (\(CDT\))i(instead.)70 b(But)44 b(can)i(CDTs)f(be)g(made)h (anisotropic?)-303 3565 y(Seidel)31 b([14])h(proposes)f(the)h Fu(e)m(xtended)g(V)-17 b(or)-7 b(onoi)32 b(dia)o(gr)n(am)p Fv(,)g(which)f(dualizes)-303 3740 y(the)50 b(\(isotropic\))f(CDT)i(by)g (e)n(xtending)e(the)i(plane)g(so)g(that)f(each)i(se)n(gment)-303 3914 y(serv)n(es)38 b(as)g(a)h(g)o(ate)l(w)o(ay)f(to)f(another)g (\223sheet\224)i(of)e(paper)-6 b(,)39 b(inhabited)d(by)h(some)-303 4089 y(of)49 b(the)g(f)o(aces)h(of)f(the)g(V)-19 b(oronoi)47 b(diagram.)83 b(As)49 b(a)h(natural)f(generalization,)-303 4263 y(we)43 b(suggest)f(e)n(xtended)g(anisotropic)e(V)-19 b(oronoi)41 b(diagrams,)j(which)e(dualize)-303 4437 y(to)j(constrained) f(triangulations)f(under)i(the)g(same)i(conditions)c(for)i(which)-303 4612 y(anisotropic)35 b(V)-19 b(oronoi)35 b(diagrams)i(dualize)g(to)g (triangulations.)-154 4786 y(F)n(or)j(practical)h(mesh)h(generation,)f (it)f(is)h(attracti)l(v)n(e)f(to)g(maintain)g(the)h(re-)-303 4960 y(stricted)e(V)-19 b(oronoi)38 b(diagram)i Fq(D)t Fk(j)1400 4977 y Fj(\012)1535 4960 y Fv(rather)g(than)g Fq(D)k Fv(because)e(the)e(rest)g(of)g Fq(D)-303 5135 y Fv(is)31 b(not)h(needed.)45 b(W)-12 b(e)32 b(could)g(also)g (rede\002ne)g(loose)g(site)g(insertion)e(so)i(that)f(the)-303 5309 y(depth-\002rst)40 b(search)i(stops)f(at)h(the)g(boundary)e(of)h Ft(\012)p Fv(,)j(b)m(ut)c(the)i(diagram)f(cre-)-303 5483 y(ated)35 b(this)g(w)o(ay)g(is)g(not)f(necessarily)i Fq(L)p Fk(j)1725 5500 y Fj(\012)1819 5483 y Fv(.)46 b(It)35 b(is)g(an)h(open)f(problem)f(whether)-303 5658 y(an)e(analog)g(of)f (Lemma)j(20)e(holds)f(for)g(this)h(weak)o(er)g(site)g(insertion)e (method.)-303 5832 y(More)h(generally)-10 b(,)32 b(if)f(loose)f (insertion)g(and)h(e)n(xtended)f(anisotropic)g(V)-19 b(oronoi)-303 6006 y(diagrams)35 b(can)g(be)h(made)g(to)e(w)o(ork)g (together)-6 b(,)35 b(the)f(combination)g(might)g(en-)-303 6181 y(jo)o(y)h(the)i(speed)h(of)f(loose)g(insertion)e(and)i(the)g (bene\002ts)h(of)e(CDTs.)-154 6355 y(In)45 b(three)f(dimensions)g(or)h (more,)i(we)e(cannot)g(pro)n(v)n(e)f(that)g(our)g(V)-19 b(oronoi)-303 6529 y(re\002nement)40 b(algorithm)f(creates)i(a)g (triangulation)c(with)i(no)h(geometrically)-303 6704 y(in)-6 b(v)n(erted)48 b(elements,)54 b(for)49 b(the)g(same)j(reason)e (that)f(it)g(is)g(dif)l(\002cult)g(to)g(pro)n(v)n(e)-303 6878 y(that)35 b(isotropic)f(three-dimensional)g(mesh)j(generation)e (algorithms)f(create)-303 7052 y(no)50 b(sli)l(v)n(er)g(tetrahedra.)87 b(Delaunay)51 b(re\002nement)g(algorithms)e(for)h(tetrahe-)-303 7227 y(dral)56 b(mesh)i(generation)e(are)i(ne)l(v)n(ertheless)f(ef)l (fecti)l(v)n(e)g(in)f(practice)i(at)f(re-)-303 7401 y(mo)n(ving)51 b(sli)l(v)n(ers)h([17],)k(and)c(we)h(belie)l(v)n(e)f(the)h(same)h(is)e (true)g(of)g(three-di-)-303 7575 y(mensional)36 b(V)-19 b(oronoi)35 b(re\002nement)j(in)f(the)g(anisotropic)e(case.)-303 8005 y Fw(12.)198 b(Refer)l(ences)-229 8248 y Fv([1])74 b(P)n(ankaj)37 b(K.)h(Ag)o(arw)o(al,)f(Boris)f(Arono)n(v)-10 b(,)36 b(and)h(Micha)h(Sharir)-8 b(.)20 8422 y Fu(Computing)35 b(Lower)i(En)-6 b(velopes)38 b(in)e(Four)i(Dimensions)e(with)20 8597 y(Applications)p Fv(.)g(Proceedings)g(of)h(the)g(T)-10 b(enth)37 b(Annual)f(Symposium)20 8771 y(on)g(Computational)e(Geometry) -10 b(,)36 b(pages)h(348\226358.)e(Association)f(for)20 8945 y(Computing)h(Machinery)-10 b(,)38 b(1994.)-229 9136 y([2])74 b(P)n(ankaj)37 b(K.)h(Ag)o(arw)o(al,)f(Otfried)f(Schw)o (arzk)o(opf,)g(and)h(Micha)g(Sharir)-8 b(.)20 9311 y Fu(Overlay)38 b(of)f(Lower)g(En)-6 b(velopes)38 b(and)e(its)h (Applications)p Fv(.)e(T)-10 b(echnical)20 9485 y(Report)36 b(CS-1994-18,)g(Department)h(of)f(Computer)h(Science,)h(Duk)o(e)20 9659 y(Uni)l(v)n(ersity)-10 b(,)36 b(1994.)-229 9850 y([3])74 b(Thomas)38 b(Apel.)f Fu(Anisotr)-7 b(opic)36 b(Finite)h(Elements:)46 b(Local)37 b(Estimates)20 10025 y(and)g(Applications)p Fv(.)e(B.)j(G.)f(T)-10 b(eubner)37 b(V)-17 b(erlag,)38 b(Stuttg)o(art,)d(1999.)-229 10216 y([4])74 b(Franz)38 b(Aurenhammer)f(and)h(Herbert)e(Edelsbrunner)-8 b(.)37 b Fu(An)g(Optimal)20 10390 y(Algorithm)f(for)h(Constructing)d (the)j(Weighted)g(Vor)-7 b(onoi)37 b(Dia)o(gr)n(am)p Fv(.)20 10564 y(P)n(attern)g(Recognition)e Fr(17)p Fv(:251\226257,)g (1984.)-229 10755 y([5])74 b(Frank)37 b(J.)h(Bossen)f(and)g(P)n(aul)g (S.)h(Heckbert.)f Fu(A)h(Pliant)e(Method)h(for)4404 -137 y(Anisotr)-7 b(opic)36 b(Mesh)i(Gener)n(ation)p Fv(.)e(Fifth)g (International)f(Meshing)4404 37 y(Roundtable,)h(pages)h(63\22674,)g (October)f(1996.)4155 228 y([6])74 b(Adrian)36 b(Bo)l(wyer)-8 b(.)37 b Fu(Computing)e(Diric)n(hlet)g(Tessellations)p Fv(.)4404 402 y(Computer)h(Journal)g Fr(24)p Fv(\(2\):162\226166,)e (1981.)4155 593 y([7])74 b(P)n(aul-Louis)36 b(Geor)m(ge)h(and)h(Houman) f(Borouchaki.)f Fu(Delaunay)4404 768 y(Triangulation)e(and)i(Meshing:) 46 b(Application)35 b(to)h(Finite)h(Elements)p Fv(.)4404 942 y(Herm)4752 941 y(\036)4744 942 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b(Dia)o(gr)n(ams)e(for)i(Riemannian)f (Manifolds)p Fv(.)4404 3084 y(Proceedings)h(of)g(the)g(Sixteenth)e (Annual)i(Symposium)f(on)4404 3258 y(Computational)f(Geometry)i(\(Hong) f(K)-5 b(ong\),)36 b(pages)i(341\226349.)4404 3433 y(Association)e(for) g(Computing)f(Machinery)-10 b(,)38 b(June)f(2000.)4080 3624 y([11])74 b(Xiang-Y)-15 b(ang)36 b(Li,)i(Shang-Hua)e(T)-10 b(eng,)38 b(and)f(Alper)7113 3591 y(\250)7084 3624 y(Ung)7354 3623 y(\250)7342 3624 y(or)-8 b(.)37 b Fu(Biting)4404 3798 y(Ellipses)g(to)f(Gener)n(ate)h(Anisotr)-7 b(opic)36 b(Mesh)p Fv(.)j(Eighth)d(International)4404 3972 y(Meshing)g (Roundtable)g(\(Lak)o(e)h(T)-12 b(ahoe,)38 b(California\),)e(pages)4404 4147 y(97\226108,)g(October)h(1999.)4080 4338 y([12])74 b(Shmuel)37 b(Rippa.)g Fu(Long)f(and)h(Thin)f(Triangles)h(Can)f(Be)i (Good)e(for)4404 4512 y(Linear)h(Interpolation)p Fv(.)d(SIAM)j(Journal) g(on)f(Numerical)h(Analysis)4404 4686 y Fr(29)p Fv(\(1\):257\226270,)d (February)j(1992.)4080 4877 y([13])74 b(Jim)37 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