PHP: Hypertext Preprocessor (original) (raw)

imagesetstyle

(PHP 4 >= 4.0.6, PHP 5, PHP 7, PHP 8)

imagesetstyle — Set the style for line drawing

Description

Return Values

Returns [true](reserved.constants.php#constant.true) on success or [false](reserved.constants.php#constant.false) on failure.

Examples

Following example script draws a dashed line from upper left to lower right corner of the canvas:

Example #1 imagesetstyle() example

<?php header("Content-type: image/jpeg"); <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>i</mi><mi>m</mi><mo>=</mo><mi>i</mi><mi>m</mi><mi>a</mi><mi>g</mi><mi>e</mi><mi>c</mi><mi>r</mi><mi>e</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>t</mi><mi>r</mi><mi>u</mi><mi>e</mi><mi>c</mi><mi>o</mi><mi>l</mi><mi>o</mi><mi>r</mi><mo stretchy="false">(</mo><mn>100</mn><mo separator="true">,</mo><mn>100</mn><mo stretchy="false">)</mo><mo separator="true">;</mo><mo>&lt;</mo><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mi>c</mi><mi>l</mi><mi>a</mi><mi>s</mi><mi>s</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>k</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>x</mi><mi mathvariant="normal">&quot;</mi><mo>&gt;</mo><mo>&lt;</mo><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mi>c</mi><mi>l</mi><mi>a</mi><mi>s</mi><mi>s</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>k</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>x</mi><mo>−</mo><mi>m</mi><mi>a</mi><mi>t</mi><mi>h</mi><mi>m</mi><mi>l</mi><mi mathvariant="normal">&quot;</mi><mo>&gt;</mo><mo>&lt;</mo><mi>m</mi><mi>a</mi><mi>t</mi><mi>h</mi><mi>x</mi><mi>m</mi><mi>l</mi><mi>n</mi><mi>s</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>h</mi><mi>t</mi><mi>t</mi><mi>p</mi><mo>:</mo><mi mathvariant="normal">/</mi><mi mathvariant="normal">/</mi><mi>w</mi><mi>w</mi><mi>w</mi><mi mathvariant="normal">.</mi><mi>w</mi><mn>3.</mn><mi>o</mi><mi>r</mi><mi>g</mi><mi mathvariant="normal">/</mi><mn>1998</mn><mi mathvariant="normal">/</mi><mi>M</mi><mi>a</mi><mi>t</mi><mi>h</mi><mi mathvariant="normal">/</mi><mi>M</mi><mi>a</mi><mi>t</mi><mi>h</mi><mi>M</mi><mi>L</mi><mi mathvariant="normal">&quot;</mi><mo>&gt;</mo><mo>&lt;</mo><mi>s</mi><mi>e</mi><mi>m</mi><mi>a</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>c</mi><mi>s</mi><mo>&gt;</mo><mo>&lt;</mo><mi>m</mi><mi>r</mi><mi>o</mi><mi>w</mi><mo>&gt;</mo><mo>&lt;</mo><mi>m</mi><mi>i</mi><mo>&gt;</mo><mi>w</mi><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>m</mi><mi>i</mi><mo>&gt;</mo><mo>&lt;</mo><mi>m</mi><mi>o</mi><mo>&gt;</mo><mo>=</mo><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>m</mi><mi>o</mi><mo>&gt;</mo><mo>&lt;</mo><mi>m</mi><mi>i</mi><mo>&gt;</mo><mi>i</mi><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>m</mi><mi>i</mi><mo>&gt;</mo><mo>&lt;</mo><mi>m</mi><mi>i</mi><mo>&gt;</mo><mi>m</mi><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>m</mi><mi>i</mi><mo>&gt;</mo><mo>&lt;</mo><mi>m</mi><mi>i</mi><mo>&gt;</mo><mi>a</mi><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>m</mi><mi>i</mi><mo>&gt;</mo><mo>&lt;</mo><mi>m</mi><mi>i</mi><mo>&gt;</mo><mi>g</mi><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>m</mi><mi>i</mi><mo>&gt;</mo><mo>&lt;</mo><mi>m</mi><mi>i</mi><mo>&gt;</mo><mi>e</mi><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>m</mi><mi>i</mi><mo>&gt;</mo><mo>&lt;</mo><mi>m</mi><mi>i</mi><mo>&gt;</mo><mi>c</mi><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>m</mi><mi>i</mi><mo>&gt;</mo><mo>&lt;</mo><mi>m</mi><mi>i</mi><mo>&gt;</mo><mi>o</mi><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>m</mi><mi>i</mi><mo>&gt;</mo><mo>&lt;</mo><mi>m</mi><mi>i</mi><mo>&gt;</mo><mi>l</mi><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>m</mi><mi>i</mi><mo>&gt;</mo><mo>&lt;</mo><mi>m</mi><mi>i</mi><mo>&gt;</mo><mi>o</mi><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>m</mi><mi>i</mi><mo>&gt;</mo><mo>&lt;</mo><mi>m</mi><mi>i</mi><mo>&gt;</mo><mi>r</mi><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>m</mi><mi>i</mi><mo>&gt;</mo><mo>&lt;</mo><mi>m</mi><mi>i</mi><mo>&gt;</mo><mi>a</mi><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>m</mi><mi>i</mi><mo>&gt;</mo><mo>&lt;</mo><mi>m</mi><mi>i</mi><mo>&gt;</mo><mi>l</mi><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>m</mi><mi>i</mi><mo>&gt;</mo><mo>&lt;</mo><mi>m</mi><mi>i</mi><mo>&gt;</mo><mi>l</mi><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>m</mi><mi>i</mi><mo>&gt;</mo><mo>&lt;</mo><mi>m</mi><mi>i</mi><mo>&gt;</mo><mi>o</mi><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>m</mi><mi>i</mi><mo>&gt;</mo><mo>&lt;</mo><mi>m</mi><mi>i</mi><mo>&gt;</mo><mi>c</mi><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>m</mi><mi>i</mi><mo>&gt;</mo><mo>&lt;</mo><mi>m</mi><mi>i</mi><mo>&gt;</mo><mi>a</mi><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>m</mi><mi>i</mi><mo>&gt;</mo><mo>&lt;</mo><mi>m</mi><mi>i</mi><mo>&gt;</mo><mi>t</mi><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>m</mi><mi>i</mi><mo>&gt;</mo><mo>&lt;</mo><mi>m</mi><mi>i</mi><mo>&gt;</mo><mi>e</mi><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>m</mi><mi>i</mi><mo>&gt;</mo><mo>&lt;</mo><mi>m</mi><mi>o</mi><mi>s</mi><mi>t</mi><mi>r</mi><mi>e</mi><mi>t</mi><mi>c</mi><mi>h</mi><mi>y</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>f</mi><mi>a</mi><mi>l</mi><mi>s</mi><mi>e</mi><mi mathvariant="normal">&quot;</mi><mo>&gt;</mo><mo stretchy="false">(</mo><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>m</mi><mi>o</mi><mo>&gt;</mo><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>m</mi><mi>r</mi><mi>o</mi><mi>w</mi><mo>&gt;</mo><mo>&lt;</mo><mi>a</mi><mi>n</mi><mi>n</mi><mi>o</mi><mi>t</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>e</mi><mi>n</mi><mi>c</mi><mi>o</mi><mi>d</mi><mi>i</mi><mi>n</mi><mi>g</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>a</mi><mi>p</mi><mi>p</mi><mi>l</mi><mi>i</mi><mi>c</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi mathvariant="normal">/</mi><mi>x</mi><mo>−</mo><mi>t</mi><mi>e</mi><mi>x</mi><mi mathvariant="normal">&quot;</mi><mo>&gt;</mo><mi>w</mi><mo>=</mo><mi>i</mi><mi>m</mi><mi>a</mi><mi>g</mi><mi>e</mi><mi>c</mi><mi>o</mi><mi>l</mi><mi>o</mi><mi>r</mi><mi>a</mi><mi>l</mi><mi>l</mi><mi>o</mi><mi>c</mi><mi>a</mi><mi>t</mi><mi>e</mi><mo stretchy="false">(</mo><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>a</mi><mi>n</mi><mi>n</mi><mi>o</mi><mi>t</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mo>&gt;</mo><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>s</mi><mi>e</mi><mi>m</mi><mi>a</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>c</mi><mi>s</mi><mo>&gt;</mo><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>m</mi><mi>a</mi><mi>t</mi><mi>h</mi><mo>&gt;</mo><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mo>&gt;</mo><mo>&lt;</mo><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mi>c</mi><mi>l</mi><mi>a</mi><mi>s</mi><mi>s</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>k</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>x</mi><mo>−</mo><mi>h</mi><mi>t</mi><mi>m</mi><mi>l</mi><mi mathvariant="normal">&quot;</mi><mi>a</mi><mi>r</mi><mi>i</mi><mi>a</mi><mo>−</mo><mi>h</mi><mi>i</mi><mi>d</mi><mi>d</mi><mi>e</mi><mi>n</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>t</mi><mi>r</mi><mi>u</mi><mi>e</mi><mi mathvariant="normal">&quot;</mi><mo>&gt;</mo><mo>&lt;</mo><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mi>c</mi><mi>l</mi><mi>a</mi><mi>s</mi><mi>s</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>b</mi><mi>a</mi><mi>s</mi><mi>e</mi><mi mathvariant="normal">&quot;</mi><mo>&gt;</mo><mo>&lt;</mo><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mi>c</mi><mi>l</mi><mi>a</mi><mi>s</mi><mi>s</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>s</mi><mi>t</mi><mi>r</mi><mi>u</mi><mi>t</mi><mi mathvariant="normal">&quot;</mi><mi>s</mi><mi>t</mi><mi>y</mi><mi>l</mi><mi>e</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>h</mi><mi>e</mi><mi>i</mi><mi>g</mi><mi>h</mi><mi>t</mi><mo>:</mo><mn>0.4306</mn><mi>e</mi><mi>m</mi><mo separator="true">;</mo><mi mathvariant="normal">&quot;</mi><mo>&gt;</mo><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mo>&gt;</mo><mo>&lt;</mo><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mi>c</mi><mi>l</mi><mi>a</mi><mi>s</mi><mi>s</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>m</mi><mi>o</mi><mi>r</mi><mi>d</mi><mi>m</mi><mi>a</mi><mi>t</mi><mi>h</mi><mi>n</mi><mi>o</mi><mi>r</mi><mi>m</mi><mi>a</mi><mi>l</mi><mi mathvariant="normal">&quot;</mi><mi>s</mi><mi>t</mi><mi>y</mi><mi>l</mi><mi>e</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>m</mi><mi>a</mi><mi>r</mi><mi>g</mi><mi>i</mi><mi>n</mi><mo>−</mo><mi>r</mi><mi>i</mi><mi>g</mi><mi>h</mi><mi>t</mi><mo>:</mo><mn>0.02691</mn><mi>e</mi><mi>m</mi><mo separator="true">;</mo><mi mathvariant="normal">&quot;</mi><mo>&gt;</mo><mi>w</mi><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mo>&gt;</mo><mo>&lt;</mo><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mi>c</mi><mi>l</mi><mi>a</mi><mi>s</mi><mi>s</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>m</mi><mi>s</mi><mi>p</mi><mi>a</mi><mi>c</mi><mi>e</mi><mi mathvariant="normal">&quot;</mi><mi>s</mi><mi>t</mi><mi>y</mi><mi>l</mi><mi>e</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>m</mi><mi>a</mi><mi>r</mi><mi>g</mi><mi>i</mi><mi>n</mi><mo>−</mo><mi>r</mi><mi>i</mi><mi>g</mi><mi>h</mi><mi>t</mi><mo>:</mo><mn>0.2778</mn><mi>e</mi><mi>m</mi><mo separator="true">;</mo><mi mathvariant="normal">&quot;</mi><mo>&gt;</mo><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mo>&gt;</mo><mo>&lt;</mo><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mi>c</mi><mi>l</mi><mi>a</mi><mi>s</mi><mi>s</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>m</mi><mi>r</mi><mi>e</mi><mi>l</mi><mi mathvariant="normal">&quot;</mi><mo>&gt;</mo><mo>=</mo><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mo>&gt;</mo><mo>&lt;</mo><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mi>c</mi><mi>l</mi><mi>a</mi><mi>s</mi><mi>s</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>m</mi><mi>s</mi><mi>p</mi><mi>a</mi><mi>c</mi><mi>e</mi><mi mathvariant="normal">&quot;</mi><mi>s</mi><mi>t</mi><mi>y</mi><mi>l</mi><mi>e</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>m</mi><mi>a</mi><mi>r</mi><mi>g</mi><mi>i</mi><mi>n</mi><mo>−</mo><mi>r</mi><mi>i</mi><mi>g</mi><mi>h</mi><mi>t</mi><mo>:</mo><mn>0.2778</mn><mi>e</mi><mi>m</mi><mo separator="true">;</mo><mi mathvariant="normal">&quot;</mi><mo>&gt;</mo><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mo>&gt;</mo><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mo>&gt;</mo><mo>&lt;</mo><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mi>c</mi><mi>l</mi><mi>a</mi><mi>s</mi><mi>s</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>b</mi><mi>a</mi><mi>s</mi><mi>e</mi><mi mathvariant="normal">&quot;</mi><mo>&gt;</mo><mo>&lt;</mo><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mi>c</mi><mi>l</mi><mi>a</mi><mi>s</mi><mi>s</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>s</mi><mi>t</mi><mi>r</mi><mi>u</mi><mi>t</mi><mi mathvariant="normal">&quot;</mi><mi>s</mi><mi>t</mi><mi>y</mi><mi>l</mi><mi>e</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>h</mi><mi>e</mi><mi>i</mi><mi>g</mi><mi>h</mi><mi>t</mi><mo>:</mo><mn>1</mn><mi>e</mi><mi>m</mi><mo separator="true">;</mo><mi>v</mi><mi>e</mi><mi>r</mi><mi>t</mi><mi>i</mi><mi>c</mi><mi>a</mi><mi>l</mi><mo>−</mo><mi>a</mi><mi>l</mi><mi>i</mi><mi>g</mi><mi>n</mi><mo>:</mo><mo>−</mo><mn>0.25</mn><mi>e</mi><mi>m</mi><mo separator="true">;</mo><mi mathvariant="normal">&quot;</mi><mo>&gt;</mo><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mo>&gt;</mo><mo>&lt;</mo><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mi>c</mi><mi>l</mi><mi>a</mi><mi>s</mi><mi>s</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>m</mi><mi>o</mi><mi>r</mi><mi>d</mi><mi>m</mi><mi>a</mi><mi>t</mi><mi>h</mi><mi>n</mi><mi>o</mi><mi>r</mi><mi>m</mi><mi>a</mi><mi>l</mi><mi mathvariant="normal">&quot;</mi><mo>&gt;</mo><mi>i</mi><mi>m</mi><mi>a</mi><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mo>&gt;</mo><mo>&lt;</mo><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mi>c</mi><mi>l</mi><mi>a</mi><mi>s</mi><mi>s</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>m</mi><mi>o</mi><mi>r</mi><mi>d</mi><mi>m</mi><mi>a</mi><mi>t</mi><mi>h</mi><mi>n</mi><mi>o</mi><mi>r</mi><mi>m</mi><mi>a</mi><mi>l</mi><mi mathvariant="normal">&quot;</mi><mi>s</mi><mi>t</mi><mi>y</mi><mi>l</mi><mi>e</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>m</mi><mi>a</mi><mi>r</mi><mi>g</mi><mi>i</mi><mi>n</mi><mo>−</mo><mi>r</mi><mi>i</mi><mi>g</mi><mi>h</mi><mi>t</mi><mo>:</mo><mn>0.03588</mn><mi>e</mi><mi>m</mi><mo separator="true">;</mo><mi mathvariant="normal">&quot;</mi><mo>&gt;</mo><mi>g</mi><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mo>&gt;</mo><mo>&lt;</mo><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mi>c</mi><mi>l</mi><mi>a</mi><mi>s</mi><mi>s</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>m</mi><mi>o</mi><mi>r</mi><mi>d</mi><mi>m</mi><mi>a</mi><mi>t</mi><mi>h</mi><mi>n</mi><mi>o</mi><mi>r</mi><mi>m</mi><mi>a</mi><mi>l</mi><mi mathvariant="normal">&quot;</mi><mo>&gt;</mo><mi>e</mi><mi>c</mi><mi>o</mi><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mo>&gt;</mo><mo>&lt;</mo><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mi>c</mi><mi>l</mi><mi>a</mi><mi>s</mi><mi>s</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>m</mi><mi>o</mi><mi>r</mi><mi>d</mi><mi>m</mi><mi>a</mi><mi>t</mi><mi>h</mi><mi>n</mi><mi>o</mi><mi>r</mi><mi>m</mi><mi>a</mi><mi>l</mi><mi mathvariant="normal">&quot;</mi><mi>s</mi><mi>t</mi><mi>y</mi><mi>l</mi><mi>e</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>m</mi><mi>a</mi><mi>r</mi><mi>g</mi><mi>i</mi><mi>n</mi><mo>−</mo><mi>r</mi><mi>i</mi><mi>g</mi><mi>h</mi><mi>t</mi><mo>:</mo><mn>0.01968</mn><mi>e</mi><mi>m</mi><mo separator="true">;</mo><mi mathvariant="normal">&quot;</mi><mo>&gt;</mo><mi>l</mi><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mo>&gt;</mo><mo>&lt;</mo><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mi>c</mi><mi>l</mi><mi>a</mi><mi>s</mi><mi>s</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>m</mi><mi>o</mi><mi>r</mi><mi>d</mi><mi>m</mi><mi>a</mi><mi>t</mi><mi>h</mi><mi>n</mi><mi>o</mi><mi>r</mi><mi>m</mi><mi>a</mi><mi>l</mi><mi mathvariant="normal">&quot;</mi><mi>s</mi><mi>t</mi><mi>y</mi><mi>l</mi><mi>e</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>m</mi><mi>a</mi><mi>r</mi><mi>g</mi><mi>i</mi><mi>n</mi><mo>−</mo><mi>r</mi><mi>i</mi><mi>g</mi><mi>h</mi><mi>t</mi><mo>:</mo><mn>0.02778</mn><mi>e</mi><mi>m</mi><mo separator="true">;</mo><mi mathvariant="normal">&quot;</mi><mo>&gt;</mo><mi>o</mi><mi>r</mi><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mo>&gt;</mo><mo>&lt;</mo><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mi>c</mi><mi>l</mi><mi>a</mi><mi>s</mi><mi>s</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>m</mi><mi>o</mi><mi>r</mi><mi>d</mi><mi>m</mi><mi>a</mi><mi>t</mi><mi>h</mi><mi>n</mi><mi>o</mi><mi>r</mi><mi>m</mi><mi>a</mi><mi>l</mi><mi mathvariant="normal">&quot;</mi><mo>&gt;</mo><mi>a</mi><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mo>&gt;</mo><mo>&lt;</mo><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mi>c</mi><mi>l</mi><mi>a</mi><mi>s</mi><mi>s</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>m</mi><mi>o</mi><mi>r</mi><mi>d</mi><mi>m</mi><mi>a</mi><mi>t</mi><mi>h</mi><mi>n</mi><mi>o</mi><mi>r</mi><mi>m</mi><mi>a</mi><mi>l</mi><mi mathvariant="normal">&quot;</mi><mi>s</mi><mi>t</mi><mi>y</mi><mi>l</mi><mi>e</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>m</mi><mi>a</mi><mi>r</mi><mi>g</mi><mi>i</mi><mi>n</mi><mo>−</mo><mi>r</mi><mi>i</mi><mi>g</mi><mi>h</mi><mi>t</mi><mo>:</mo><mn>0.01968</mn><mi>e</mi><mi>m</mi><mo separator="true">;</mo><mi mathvariant="normal">&quot;</mi><mo>&gt;</mo><mi>l</mi><mi>l</mi><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mo>&gt;</mo><mo>&lt;</mo><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mi>c</mi><mi>l</mi><mi>a</mi><mi>s</mi><mi>s</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>m</mi><mi>o</mi><mi>r</mi><mi>d</mi><mi>m</mi><mi>a</mi><mi>t</mi><mi>h</mi><mi>n</mi><mi>o</mi><mi>r</mi><mi>m</mi><mi>a</mi><mi>l</mi><mi mathvariant="normal">&quot;</mi><mo>&gt;</mo><mi>o</mi><mi>c</mi><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mo>&gt;</mo><mo>&lt;</mo><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mi>c</mi><mi>l</mi><mi>a</mi><mi>s</mi><mi>s</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>m</mi><mi>o</mi><mi>r</mi><mi>d</mi><mi>m</mi><mi>a</mi><mi>t</mi><mi>h</mi><mi>n</mi><mi>o</mi><mi>r</mi><mi>m</mi><mi>a</mi><mi>l</mi><mi mathvariant="normal">&quot;</mi><mo>&gt;</mo><mi>a</mi><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mo>&gt;</mo><mo>&lt;</mo><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mi>c</mi><mi>l</mi><mi>a</mi><mi>s</mi><mi>s</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>m</mi><mi>o</mi><mi>r</mi><mi>d</mi><mi>m</mi><mi>a</mi><mi>t</mi><mi>h</mi><mi>n</mi><mi>o</mi><mi>r</mi><mi>m</mi><mi>a</mi><mi>l</mi><mi mathvariant="normal">&quot;</mi><mo>&gt;</mo><mi>t</mi><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mo>&gt;</mo><mo>&lt;</mo><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mi>c</mi><mi>l</mi><mi>a</mi><mi>s</mi><mi>s</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>m</mi><mi>o</mi><mi>r</mi><mi>d</mi><mi>m</mi><mi>a</mi><mi>t</mi><mi>h</mi><mi>n</mi><mi>o</mi><mi>r</mi><mi>m</mi><mi>a</mi><mi>l</mi><mi mathvariant="normal">&quot;</mi><mo>&gt;</mo><mi>e</mi><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mo>&gt;</mo><mo>&lt;</mo><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mi>c</mi><mi>l</mi><mi>a</mi><mi>s</mi><mi>s</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>m</mi><mi>o</mi><mi>p</mi><mi>e</mi><mi>n</mi><mi mathvariant="normal">&quot;</mi><mo>&gt;</mo><mo stretchy="false">(</mo><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mo>&gt;</mo><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mo>&gt;</mo><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mo>&gt;</mo><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mo>&gt;</mo><mi>i</mi><mi>m</mi><mo separator="true">,</mo><mn>255</mn><mo separator="true">,</mo><mn>255</mn><mo separator="true">,</mo><mn>255</mn><mo stretchy="false">)</mo><mo separator="true">;</mo><mo>&lt;</mo><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mi>c</mi><mi>l</mi><mi>a</mi><mi>s</mi><mi>s</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>k</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>x</mi><mi mathvariant="normal">&quot;</mi><mo>&gt;</mo><mo>&lt;</mo><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mi>c</mi><mi>l</mi><mi>a</mi><mi>s</mi><mi>s</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>k</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>x</mi><mo>−</mo><mi>m</mi><mi>a</mi><mi>t</mi><mi>h</mi><mi>m</mi><mi>l</mi><mi mathvariant="normal">&quot;</mi><mo>&gt;</mo><mo>&lt;</mo><mi>m</mi><mi>a</mi><mi>t</mi><mi>h</mi><mi>x</mi><mi>m</mi><mi>l</mi><mi>n</mi><mi>s</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>h</mi><mi>t</mi><mi>t</mi><mi>p</mi><mo>:</mo><mi mathvariant="normal">/</mi><mi mathvariant="normal">/</mi><mi>w</mi><mi>w</mi><mi>w</mi><mi mathvariant="normal">.</mi><mi>w</mi><mn>3.</mn><mi>o</mi><mi>r</mi><mi>g</mi><mi mathvariant="normal">/</mi><mn>1998</mn><mi mathvariant="normal">/</mi><mi>M</mi><mi>a</mi><mi>t</mi><mi>h</mi><mi mathvariant="normal">/</mi><mi>M</mi><mi>a</mi><mi>t</mi><mi>h</mi><mi>M</mi><mi>L</mi><mi mathvariant="normal">&quot;</mi><mo>&gt;</mo><mo>&lt;</mo><mi>s</mi><mi>e</mi><mi>m</mi><mi>a</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>c</mi><mi>s</mi><mo>&gt;</mo><mo>&lt;</mo><mi>m</mi><mi>r</mi><mi>o</mi><mi>w</mi><mo>&gt;</mo><mo>&lt;</mo><mi>m</mi><mi>i</mi><mo>&gt;</mo><mi>r</mi><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>m</mi><mi>i</mi><mo>&gt;</mo><mo>&lt;</mo><mi>m</mi><mi>i</mi><mo>&gt;</mo><mi>e</mi><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>m</mi><mi>i</mi><mo>&gt;</mo><mo>&lt;</mo><mi>m</mi><mi>i</mi><mo>&gt;</mo><mi>d</mi><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>m</mi><mi>i</mi><mo>&gt;</mo><mo>&lt;</mo><mi>m</mi><mi>o</mi><mo>&gt;</mo><mo>=</mo><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>m</mi><mi>o</mi><mo>&gt;</mo><mo>&lt;</mo><mi>m</mi><mi>i</mi><mo>&gt;</mo><mi>i</mi><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>m</mi><mi>i</mi><mo>&gt;</mo><mo>&lt;</mo><mi>m</mi><mi>i</mi><mo>&gt;</mo><mi>m</mi><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>m</mi><mi>i</mi><mo>&gt;</mo><mo>&lt;</mo><mi>m</mi><mi>i</mi><mo>&gt;</mo><mi>a</mi><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>m</mi><mi>i</mi><mo>&gt;</mo><mo>&lt;</mo><mi>m</mi><mi>i</mi><mo>&gt;</mo><mi>g</mi><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>m</mi><mi>i</mi><mo>&gt;</mo><mo>&lt;</mo><mi>m</mi><mi>i</mi><mo>&gt;</mo><mi>e</mi><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>m</mi><mi>i</mi><mo>&gt;</mo><mo>&lt;</mo><mi>m</mi><mi>i</mi><mo>&gt;</mo><mi>c</mi><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>m</mi><mi>i</mi><mo>&gt;</mo><mo>&lt;</mo><mi>m</mi><mi>i</mi><mo>&gt;</mo><mi>o</mi><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>m</mi><mi>i</mi><mo>&gt;</mo><mo>&lt;</mo><mi>m</mi><mi>i</mi><mo>&gt;</mo><mi>l</mi><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>m</mi><mi>i</mi><mo>&gt;</mo><mo>&lt;</mo><mi>m</mi><mi>i</mi><mo>&gt;</mo><mi>o</mi><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>m</mi><mi>i</mi><mo>&gt;</mo><mo>&lt;</mo><mi>m</mi><mi>i</mi><mo>&gt;</mo><mi>r</mi><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>m</mi><mi>i</mi><mo>&gt;</mo><mo>&lt;</mo><mi>m</mi><mi>i</mi><mo>&gt;</mo><mi>a</mi><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>m</mi><mi>i</mi><mo>&gt;</mo><mo>&lt;</mo><mi>m</mi><mi>i</mi><mo>&gt;</mo><mi>l</mi><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>m</mi><mi>i</mi><mo>&gt;</mo><mo>&lt;</mo><mi>m</mi><mi>i</mi><mo>&gt;</mo><mi>l</mi><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>m</mi><mi>i</mi><mo>&gt;</mo><mo>&lt;</mo><mi>m</mi><mi>i</mi><mo>&gt;</mo><mi>o</mi><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>m</mi><mi>i</mi><mo>&gt;</mo><mo>&lt;</mo><mi>m</mi><mi>i</mi><mo>&gt;</mo><mi>c</mi><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>m</mi><mi>i</mi><mo>&gt;</mo><mo>&lt;</mo><mi>m</mi><mi>i</mi><mo>&gt;</mo><mi>a</mi><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>m</mi><mi>i</mi><mo>&gt;</mo><mo>&lt;</mo><mi>m</mi><mi>i</mi><mo>&gt;</mo><mi>t</mi><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>m</mi><mi>i</mi><mo>&gt;</mo><mo>&lt;</mo><mi>m</mi><mi>i</mi><mo>&gt;</mo><mi>e</mi><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>m</mi><mi>i</mi><mo>&gt;</mo><mo>&lt;</mo><mi>m</mi><mi>o</mi><mi>s</mi><mi>t</mi><mi>r</mi><mi>e</mi><mi>t</mi><mi>c</mi><mi>h</mi><mi>y</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>f</mi><mi>a</mi><mi>l</mi><mi>s</mi><mi>e</mi><mi mathvariant="normal">&quot;</mi><mo>&gt;</mo><mo stretchy="false">(</mo><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>m</mi><mi>o</mi><mo>&gt;</mo><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>m</mi><mi>r</mi><mi>o</mi><mi>w</mi><mo>&gt;</mo><mo>&lt;</mo><mi>a</mi><mi>n</mi><mi>n</mi><mi>o</mi><mi>t</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>e</mi><mi>n</mi><mi>c</mi><mi>o</mi><mi>d</mi><mi>i</mi><mi>n</mi><mi>g</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>a</mi><mi>p</mi><mi>p</mi><mi>l</mi><mi>i</mi><mi>c</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi mathvariant="normal">/</mi><mi>x</mi><mo>−</mo><mi>t</mi><mi>e</mi><mi>x</mi><mi mathvariant="normal">&quot;</mi><mo>&gt;</mo><mi>r</mi><mi>e</mi><mi>d</mi><mo>=</mo><mi>i</mi><mi>m</mi><mi>a</mi><mi>g</mi><mi>e</mi><mi>c</mi><mi>o</mi><mi>l</mi><mi>o</mi><mi>r</mi><mi>a</mi><mi>l</mi><mi>l</mi><mi>o</mi><mi>c</mi><mi>a</mi><mi>t</mi><mi>e</mi><mo stretchy="false">(</mo><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>a</mi><mi>n</mi><mi>n</mi><mi>o</mi><mi>t</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mo>&gt;</mo><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>s</mi><mi>e</mi><mi>m</mi><mi>a</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>c</mi><mi>s</mi><mo>&gt;</mo><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>m</mi><mi>a</mi><mi>t</mi><mi>h</mi><mo>&gt;</mo><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mo>&gt;</mo><mo>&lt;</mo><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mi>c</mi><mi>l</mi><mi>a</mi><mi>s</mi><mi>s</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>k</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>x</mi><mo>−</mo><mi>h</mi><mi>t</mi><mi>m</mi><mi>l</mi><mi mathvariant="normal">&quot;</mi><mi>a</mi><mi>r</mi><mi>i</mi><mi>a</mi><mo>−</mo><mi>h</mi><mi>i</mi><mi>d</mi><mi>d</mi><mi>e</mi><mi>n</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>t</mi><mi>r</mi><mi>u</mi><mi>e</mi><mi mathvariant="normal">&quot;</mi><mo>&gt;</mo><mo>&lt;</mo><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mi>c</mi><mi>l</mi><mi>a</mi><mi>s</mi><mi>s</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>b</mi><mi>a</mi><mi>s</mi><mi>e</mi><mi mathvariant="normal">&quot;</mi><mo>&gt;</mo><mo>&lt;</mo><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mi>c</mi><mi>l</mi><mi>a</mi><mi>s</mi><mi>s</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>s</mi><mi>t</mi><mi>r</mi><mi>u</mi><mi>t</mi><mi mathvariant="normal">&quot;</mi><mi>s</mi><mi>t</mi><mi>y</mi><mi>l</mi><mi>e</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>h</mi><mi>e</mi><mi>i</mi><mi>g</mi><mi>h</mi><mi>t</mi><mo>:</mo><mn>0.6944</mn><mi>e</mi><mi>m</mi><mo separator="true">;</mo><mi mathvariant="normal">&quot;</mi><mo>&gt;</mo><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mo>&gt;</mo><mo>&lt;</mo><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mi>c</mi><mi>l</mi><mi>a</mi><mi>s</mi><mi>s</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>m</mi><mi>o</mi><mi>r</mi><mi>d</mi><mi>m</mi><mi>a</mi><mi>t</mi><mi>h</mi><mi>n</mi><mi>o</mi><mi>r</mi><mi>m</mi><mi>a</mi><mi>l</mi><mi mathvariant="normal">&quot;</mi><mo>&gt;</mo><mi>r</mi><mi>e</mi><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mo>&gt;</mo><mo>&lt;</mo><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mi>c</mi><mi>l</mi><mi>a</mi><mi>s</mi><mi>s</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>m</mi><mi>o</mi><mi>r</mi><mi>d</mi><mi>m</mi><mi>a</mi><mi>t</mi><mi>h</mi><mi>n</mi><mi>o</mi><mi>r</mi><mi>m</mi><mi>a</mi><mi>l</mi><mi mathvariant="normal">&quot;</mi><mo>&gt;</mo><mi>d</mi><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mo>&gt;</mo><mo>&lt;</mo><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mi>c</mi><mi>l</mi><mi>a</mi><mi>s</mi><mi>s</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>m</mi><mi>s</mi><mi>p</mi><mi>a</mi><mi>c</mi><mi>e</mi><mi mathvariant="normal">&quot;</mi><mi>s</mi><mi>t</mi><mi>y</mi><mi>l</mi><mi>e</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>m</mi><mi>a</mi><mi>r</mi><mi>g</mi><mi>i</mi><mi>n</mi><mo>−</mo><mi>r</mi><mi>i</mi><mi>g</mi><mi>h</mi><mi>t</mi><mo>:</mo><mn>0.2778</mn><mi>e</mi><mi>m</mi><mo separator="true">;</mo><mi mathvariant="normal">&quot;</mi><mo>&gt;</mo><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mo>&gt;</mo><mo>&lt;</mo><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mi>c</mi><mi>l</mi><mi>a</mi><mi>s</mi><mi>s</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>m</mi><mi>r</mi><mi>e</mi><mi>l</mi><mi mathvariant="normal">&quot;</mi><mo>&gt;</mo><mo>=</mo><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mo>&gt;</mo><mo>&lt;</mo><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mi>c</mi><mi>l</mi><mi>a</mi><mi>s</mi><mi>s</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>m</mi><mi>s</mi><mi>p</mi><mi>a</mi><mi>c</mi><mi>e</mi><mi mathvariant="normal">&quot;</mi><mi>s</mi><mi>t</mi><mi>y</mi><mi>l</mi><mi>e</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>m</mi><mi>a</mi><mi>r</mi><mi>g</mi><mi>i</mi><mi>n</mi><mo>−</mo><mi>r</mi><mi>i</mi><mi>g</mi><mi>h</mi><mi>t</mi><mo>:</mo><mn>0.2778</mn><mi>e</mi><mi>m</mi><mo separator="true">;</mo><mi mathvariant="normal">&quot;</mi><mo>&gt;</mo><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mo>&gt;</mo><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mo>&gt;</mo><mo>&lt;</mo><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mi>c</mi><mi>l</mi><mi>a</mi><mi>s</mi><mi>s</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>b</mi><mi>a</mi><mi>s</mi><mi>e</mi><mi mathvariant="normal">&quot;</mi><mo>&gt;</mo><mo>&lt;</mo><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mi>c</mi><mi>l</mi><mi>a</mi><mi>s</mi><mi>s</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>s</mi><mi>t</mi><mi>r</mi><mi>u</mi><mi>t</mi><mi mathvariant="normal">&quot;</mi><mi>s</mi><mi>t</mi><mi>y</mi><mi>l</mi><mi>e</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>h</mi><mi>e</mi><mi>i</mi><mi>g</mi><mi>h</mi><mi>t</mi><mo>:</mo><mn>1</mn><mi>e</mi><mi>m</mi><mo separator="true">;</mo><mi>v</mi><mi>e</mi><mi>r</mi><mi>t</mi><mi>i</mi><mi>c</mi><mi>a</mi><mi>l</mi><mo>−</mo><mi>a</mi><mi>l</mi><mi>i</mi><mi>g</mi><mi>n</mi><mo>:</mo><mo>−</mo><mn>0.25</mn><mi>e</mi><mi>m</mi><mo separator="true">;</mo><mi mathvariant="normal">&quot;</mi><mo>&gt;</mo><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mo>&gt;</mo><mo>&lt;</mo><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mi>c</mi><mi>l</mi><mi>a</mi><mi>s</mi><mi>s</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>m</mi><mi>o</mi><mi>r</mi><mi>d</mi><mi>m</mi><mi>a</mi><mi>t</mi><mi>h</mi><mi>n</mi><mi>o</mi><mi>r</mi><mi>m</mi><mi>a</mi><mi>l</mi><mi mathvariant="normal">&quot;</mi><mo>&gt;</mo><mi>i</mi><mi>m</mi><mi>a</mi><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mo>&gt;</mo><mo>&lt;</mo><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mi>c</mi><mi>l</mi><mi>a</mi><mi>s</mi><mi>s</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>m</mi><mi>o</mi><mi>r</mi><mi>d</mi><mi>m</mi><mi>a</mi><mi>t</mi><mi>h</mi><mi>n</mi><mi>o</mi><mi>r</mi><mi>m</mi><mi>a</mi><mi>l</mi><mi mathvariant="normal">&quot;</mi><mi>s</mi><mi>t</mi><mi>y</mi><mi>l</mi><mi>e</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>m</mi><mi>a</mi><mi>r</mi><mi>g</mi><mi>i</mi><mi>n</mi><mo>−</mo><mi>r</mi><mi>i</mi><mi>g</mi><mi>h</mi><mi>t</mi><mo>:</mo><mn>0.03588</mn><mi>e</mi><mi>m</mi><mo separator="true">;</mo><mi mathvariant="normal">&quot;</mi><mo>&gt;</mo><mi>g</mi><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mo>&gt;</mo><mo>&lt;</mo><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mi>c</mi><mi>l</mi><mi>a</mi><mi>s</mi><mi>s</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>m</mi><mi>o</mi><mi>r</mi><mi>d</mi><mi>m</mi><mi>a</mi><mi>t</mi><mi>h</mi><mi>n</mi><mi>o</mi><mi>r</mi><mi>m</mi><mi>a</mi><mi>l</mi><mi mathvariant="normal">&quot;</mi><mo>&gt;</mo><mi>e</mi><mi>c</mi><mi>o</mi><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mo>&gt;</mo><mo>&lt;</mo><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mi>c</mi><mi>l</mi><mi>a</mi><mi>s</mi><mi>s</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>m</mi><mi>o</mi><mi>r</mi><mi>d</mi><mi>m</mi><mi>a</mi><mi>t</mi><mi>h</mi><mi>n</mi><mi>o</mi><mi>r</mi><mi>m</mi><mi>a</mi><mi>l</mi><mi mathvariant="normal">&quot;</mi><mi>s</mi><mi>t</mi><mi>y</mi><mi>l</mi><mi>e</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>m</mi><mi>a</mi><mi>r</mi><mi>g</mi><mi>i</mi><mi>n</mi><mo>−</mo><mi>r</mi><mi>i</mi><mi>g</mi><mi>h</mi><mi>t</mi><mo>:</mo><mn>0.01968</mn><mi>e</mi><mi>m</mi><mo separator="true">;</mo><mi mathvariant="normal">&quot;</mi><mo>&gt;</mo><mi>l</mi><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mo>&gt;</mo><mo>&lt;</mo><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mi>c</mi><mi>l</mi><mi>a</mi><mi>s</mi><mi>s</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>m</mi><mi>o</mi><mi>r</mi><mi>d</mi><mi>m</mi><mi>a</mi><mi>t</mi><mi>h</mi><mi>n</mi><mi>o</mi><mi>r</mi><mi>m</mi><mi>a</mi><mi>l</mi><mi mathvariant="normal">&quot;</mi><mi>s</mi><mi>t</mi><mi>y</mi><mi>l</mi><mi>e</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>m</mi><mi>a</mi><mi>r</mi><mi>g</mi><mi>i</mi><mi>n</mi><mo>−</mo><mi>r</mi><mi>i</mi><mi>g</mi><mi>h</mi><mi>t</mi><mo>:</mo><mn>0.02778</mn><mi>e</mi><mi>m</mi><mo separator="true">;</mo><mi mathvariant="normal">&quot;</mi><mo>&gt;</mo><mi>o</mi><mi>r</mi><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mo>&gt;</mo><mo>&lt;</mo><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mi>c</mi><mi>l</mi><mi>a</mi><mi>s</mi><mi>s</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>m</mi><mi>o</mi><mi>r</mi><mi>d</mi><mi>m</mi><mi>a</mi><mi>t</mi><mi>h</mi><mi>n</mi><mi>o</mi><mi>r</mi><mi>m</mi><mi>a</mi><mi>l</mi><mi mathvariant="normal">&quot;</mi><mo>&gt;</mo><mi>a</mi><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mo>&gt;</mo><mo>&lt;</mo><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mi>c</mi><mi>l</mi><mi>a</mi><mi>s</mi><mi>s</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>m</mi><mi>o</mi><mi>r</mi><mi>d</mi><mi>m</mi><mi>a</mi><mi>t</mi><mi>h</mi><mi>n</mi><mi>o</mi><mi>r</mi><mi>m</mi><mi>a</mi><mi>l</mi><mi mathvariant="normal">&quot;</mi><mi>s</mi><mi>t</mi><mi>y</mi><mi>l</mi><mi>e</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>m</mi><mi>a</mi><mi>r</mi><mi>g</mi><mi>i</mi><mi>n</mi><mo>−</mo><mi>r</mi><mi>i</mi><mi>g</mi><mi>h</mi><mi>t</mi><mo>:</mo><mn>0.01968</mn><mi>e</mi><mi>m</mi><mo separator="true">;</mo><mi mathvariant="normal">&quot;</mi><mo>&gt;</mo><mi>l</mi><mi>l</mi><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mo>&gt;</mo><mo>&lt;</mo><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mi>c</mi><mi>l</mi><mi>a</mi><mi>s</mi><mi>s</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>m</mi><mi>o</mi><mi>r</mi><mi>d</mi><mi>m</mi><mi>a</mi><mi>t</mi><mi>h</mi><mi>n</mi><mi>o</mi><mi>r</mi><mi>m</mi><mi>a</mi><mi>l</mi><mi mathvariant="normal">&quot;</mi><mo>&gt;</mo><mi>o</mi><mi>c</mi><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mo>&gt;</mo><mo>&lt;</mo><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mi>c</mi><mi>l</mi><mi>a</mi><mi>s</mi><mi>s</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>m</mi><mi>o</mi><mi>r</mi><mi>d</mi><mi>m</mi><mi>a</mi><mi>t</mi><mi>h</mi><mi>n</mi><mi>o</mi><mi>r</mi><mi>m</mi><mi>a</mi><mi>l</mi><mi mathvariant="normal">&quot;</mi><mo>&gt;</mo><mi>a</mi><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mo>&gt;</mo><mo>&lt;</mo><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mi>c</mi><mi>l</mi><mi>a</mi><mi>s</mi><mi>s</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>m</mi><mi>o</mi><mi>r</mi><mi>d</mi><mi>m</mi><mi>a</mi><mi>t</mi><mi>h</mi><mi>n</mi><mi>o</mi><mi>r</mi><mi>m</mi><mi>a</mi><mi>l</mi><mi mathvariant="normal">&quot;</mi><mo>&gt;</mo><mi>t</mi><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mo>&gt;</mo><mo>&lt;</mo><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mi>c</mi><mi>l</mi><mi>a</mi><mi>s</mi><mi>s</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>m</mi><mi>o</mi><mi>r</mi><mi>d</mi><mi>m</mi><mi>a</mi><mi>t</mi><mi>h</mi><mi>n</mi><mi>o</mi><mi>r</mi><mi>m</mi><mi>a</mi><mi>l</mi><mi mathvariant="normal">&quot;</mi><mo>&gt;</mo><mi>e</mi><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mo>&gt;</mo><mo>&lt;</mo><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mi>c</mi><mi>l</mi><mi>a</mi><mi>s</mi><mi>s</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>m</mi><mi>o</mi><mi>p</mi><mi>e</mi><mi>n</mi><mi mathvariant="normal">&quot;</mi><mo>&gt;</mo><mo stretchy="false">(</mo><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mo>&gt;</mo><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mo>&gt;</mo><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mo>&gt;</mo><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mo>&gt;</mo><mi>i</mi><mi>m</mi><mo separator="true">,</mo><mn>255</mn><mo separator="true">,</mo><mn>0</mn><mo separator="true">,</mo><mn>0</mn><mo stretchy="false">)</mo><mo separator="true">;</mo><mi mathvariant="normal">/</mi><mo>∗</mo><mi>D</mi><mi>r</mi><mi>a</mi><mi>w</mi><mi>a</mi><mi>d</mi><mi>a</mi><mi>s</mi><mi>h</mi><mi>e</mi><mi>d</mi><mi>l</mi><mi>i</mi><mi>n</mi><mi>e</mi><mo separator="true">,</mo><mn>5</mn><mi>r</mi><mi>e</mi><mi>d</mi><mi>p</mi><mi>i</mi><mi>x</mi><mi>e</mi><mi>l</mi><mi>s</mi><mo separator="true">,</mo><mn>5</mn><mi>w</mi><mi>h</mi><mi>i</mi><mi>t</mi><mi>e</mi><mi>p</mi><mi>i</mi><mi>x</mi><mi>e</mi><mi>l</mi><mi>s</mi><mo>∗</mo><mi mathvariant="normal">/</mi><mo>&lt;</mo><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mi>c</mi><mi>l</mi><mi>a</mi><mi>s</mi><mi>s</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>k</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>x</mi><mi mathvariant="normal">&quot;</mi><mo>&gt;</mo><mo>&lt;</mo><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mi>c</mi><mi>l</mi><mi>a</mi><mi>s</mi><mi>s</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>k</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>x</mi><mo>−</mo><mi>m</mi><mi>a</mi><mi>t</mi><mi>h</mi><mi>m</mi><mi>l</mi><mi mathvariant="normal">&quot;</mi><mo>&gt;</mo><mo>&lt;</mo><mi>m</mi><mi>a</mi><mi>t</mi><mi>h</mi><mi>x</mi><mi>m</mi><mi>l</mi><mi>n</mi><mi>s</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>h</mi><mi>t</mi><mi>t</mi><mi>p</mi><mo>:</mo><mi mathvariant="normal">/</mi><mi mathvariant="normal">/</mi><mi>w</mi><mi>w</mi><mi>w</mi><mi mathvariant="normal">.</mi><mi>w</mi><mn>3.</mn><mi>o</mi><mi>r</mi><mi>g</mi><mi mathvariant="normal">/</mi><mn>1998</mn><mi mathvariant="normal">/</mi><mi>M</mi><mi>a</mi><mi>t</mi><mi>h</mi><mi mathvariant="normal">/</mi><mi>M</mi><mi>a</mi><mi>t</mi><mi>h</mi><mi>M</mi><mi>L</mi><mi mathvariant="normal">&quot;</mi><mo>&gt;</mo><mo>&lt;</mo><mi>s</mi><mi>e</mi><mi>m</mi><mi>a</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>c</mi><mi>s</mi><mo>&gt;</mo><mo>&lt;</mo><mi>m</mi><mi>r</mi><mi>o</mi><mi>w</mi><mo>&gt;</mo><mo>&lt;</mo><mi>m</mi><mi>i</mi><mo>&gt;</mo><mi>s</mi><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>m</mi><mi>i</mi><mo>&gt;</mo><mo>&lt;</mo><mi>m</mi><mi>i</mi><mo>&gt;</mo><mi>t</mi><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>m</mi><mi>i</mi><mo>&gt;</mo><mo>&lt;</mo><mi>m</mi><mi>i</mi><mo>&gt;</mo><mi>y</mi><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>m</mi><mi>i</mi><mo>&gt;</mo><mo>&lt;</mo><mi>m</mi><mi>i</mi><mo>&gt;</mo><mi>l</mi><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>m</mi><mi>i</mi><mo>&gt;</mo><mo>&lt;</mo><mi>m</mi><mi>i</mi><mo>&gt;</mo><mi>e</mi><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>m</mi><mi>i</mi><mo>&gt;</mo><mo>&lt;</mo><mi>m</mi><mi>o</mi><mo>&gt;</mo><mo>=</mo><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>m</mi><mi>o</mi><mo>&gt;</mo><mo>&lt;</mo><mi>m</mi><mi>i</mi><mo>&gt;</mo><mi>a</mi><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>m</mi><mi>i</mi><mo>&gt;</mo><mo>&lt;</mo><mi>m</mi><mi>i</mi><mo>&gt;</mo><mi>r</mi><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>m</mi><mi>i</mi><mo>&gt;</mo><mo>&lt;</mo><mi>m</mi><mi>i</mi><mo>&gt;</mo><mi>r</mi><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>m</mi><mi>i</mi><mo>&gt;</mo><mo>&lt;</mo><mi>m</mi><mi>i</mi><mo>&gt;</mo><mi>a</mi><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>m</mi><mi>i</mi><mo>&gt;</mo><mo>&lt;</mo><mi>m</mi><mi>i</mi><mo>&gt;</mo><mi>y</mi><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>m</mi><mi>i</mi><mo>&gt;</mo><mo>&lt;</mo><mi>m</mi><mi>o</mi><mi>s</mi><mi>t</mi><mi>r</mi><mi>e</mi><mi>t</mi><mi>c</mi><mi>h</mi><mi>y</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>f</mi><mi>a</mi><mi>l</mi><mi>s</mi><mi>e</mi><mi mathvariant="normal">&quot;</mi><mo>&gt;</mo><mo stretchy="false">(</mo><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>m</mi><mi>o</mi><mo>&gt;</mo><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>m</mi><mi>r</mi><mi>o</mi><mi>w</mi><mo>&gt;</mo><mo>&lt;</mo><mi>a</mi><mi>n</mi><mi>n</mi><mi>o</mi><mi>t</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>e</mi><mi>n</mi><mi>c</mi><mi>o</mi><mi>d</mi><mi>i</mi><mi>n</mi><mi>g</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>a</mi><mi>p</mi><mi>p</mi><mi>l</mi><mi>i</mi><mi>c</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi mathvariant="normal">/</mi><mi>x</mi><mo>−</mo><mi>t</mi><mi>e</mi><mi>x</mi><mi mathvariant="normal">&quot;</mi><mo>&gt;</mo><mi>s</mi><mi>t</mi><mi>y</mi><mi>l</mi><mi>e</mi><mo>=</mo><mi>a</mi><mi>r</mi><mi>r</mi><mi>a</mi><mi>y</mi><mo stretchy="false">(</mo><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>a</mi><mi>n</mi><mi>n</mi><mi>o</mi><mi>t</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mo>&gt;</mo><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>s</mi><mi>e</mi><mi>m</mi><mi>a</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>c</mi><mi>s</mi><mo>&gt;</mo><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>m</mi><mi>a</mi><mi>t</mi><mi>h</mi><mo>&gt;</mo><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mo>&gt;</mo><mo>&lt;</mo><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mi>c</mi><mi>l</mi><mi>a</mi><mi>s</mi><mi>s</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>k</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>x</mi><mo>−</mo><mi>h</mi><mi>t</mi><mi>m</mi><mi>l</mi><mi mathvariant="normal">&quot;</mi><mi>a</mi><mi>r</mi><mi>i</mi><mi>a</mi><mo>−</mo><mi>h</mi><mi>i</mi><mi>d</mi><mi>d</mi><mi>e</mi><mi>n</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>t</mi><mi>r</mi><mi>u</mi><mi>e</mi><mi mathvariant="normal">&quot;</mi><mo>&gt;</mo><mo>&lt;</mo><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mi>c</mi><mi>l</mi><mi>a</mi><mi>s</mi><mi>s</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>b</mi><mi>a</mi><mi>s</mi><mi>e</mi><mi mathvariant="normal">&quot;</mi><mo>&gt;</mo><mo>&lt;</mo><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mi>c</mi><mi>l</mi><mi>a</mi><mi>s</mi><mi>s</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>s</mi><mi>t</mi><mi>r</mi><mi>u</mi><mi>t</mi><mi mathvariant="normal">&quot;</mi><mi>s</mi><mi>t</mi><mi>y</mi><mi>l</mi><mi>e</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>h</mi><mi>e</mi><mi>i</mi><mi>g</mi><mi>h</mi><mi>t</mi><mo>:</mo><mn>0.8889</mn><mi>e</mi><mi>m</mi><mo separator="true">;</mo><mi>v</mi><mi>e</mi><mi>r</mi><mi>t</mi><mi>i</mi><mi>c</mi><mi>a</mi><mi>l</mi><mo>−</mo><mi>a</mi><mi>l</mi><mi>i</mi><mi>g</mi><mi>n</mi><mo>:</mo><mo>−</mo><mn>0.1944</mn><mi>e</mi><mi>m</mi><mo separator="true">;</mo><mi mathvariant="normal">&quot;</mi><mo>&gt;</mo><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mo>&gt;</mo><mo>&lt;</mo><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mi>c</mi><mi>l</mi><mi>a</mi><mi>s</mi><mi>s</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>m</mi><mi>o</mi><mi>r</mi><mi>d</mi><mi>m</mi><mi>a</mi><mi>t</mi><mi>h</mi><mi>n</mi><mi>o</mi><mi>r</mi><mi>m</mi><mi>a</mi><mi>l</mi><mi mathvariant="normal">&quot;</mi><mo>&gt;</mo><mi>s</mi><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mo>&gt;</mo><mo>&lt;</mo><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mi>c</mi><mi>l</mi><mi>a</mi><mi>s</mi><mi>s</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>m</mi><mi>o</mi><mi>r</mi><mi>d</mi><mi>m</mi><mi>a</mi><mi>t</mi><mi>h</mi><mi>n</mi><mi>o</mi><mi>r</mi><mi>m</mi><mi>a</mi><mi>l</mi><mi mathvariant="normal">&quot;</mi><mo>&gt;</mo><mi>t</mi><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mo>&gt;</mo><mo>&lt;</mo><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mi>c</mi><mi>l</mi><mi>a</mi><mi>s</mi><mi>s</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>m</mi><mi>o</mi><mi>r</mi><mi>d</mi><mi>m</mi><mi>a</mi><mi>t</mi><mi>h</mi><mi>n</mi><mi>o</mi><mi>r</mi><mi>m</mi><mi>a</mi><mi>l</mi><mi mathvariant="normal">&quot;</mi><mi>s</mi><mi>t</mi><mi>y</mi><mi>l</mi><mi>e</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>m</mi><mi>a</mi><mi>r</mi><mi>g</mi><mi>i</mi><mi>n</mi><mo>−</mo><mi>r</mi><mi>i</mi><mi>g</mi><mi>h</mi><mi>t</mi><mo>:</mo><mn>0.03588</mn><mi>e</mi><mi>m</mi><mo separator="true">;</mo><mi mathvariant="normal">&quot;</mi><mo>&gt;</mo><mi>y</mi><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mo>&gt;</mo><mo>&lt;</mo><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mi>c</mi><mi>l</mi><mi>a</mi><mi>s</mi><mi>s</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>m</mi><mi>o</mi><mi>r</mi><mi>d</mi><mi>m</mi><mi>a</mi><mi>t</mi><mi>h</mi><mi>n</mi><mi>o</mi><mi>r</mi><mi>m</mi><mi>a</mi><mi>l</mi><mi mathvariant="normal">&quot;</mi><mi>s</mi><mi>t</mi><mi>y</mi><mi>l</mi><mi>e</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>m</mi><mi>a</mi><mi>r</mi><mi>g</mi><mi>i</mi><mi>n</mi><mo>−</mo><mi>r</mi><mi>i</mi><mi>g</mi><mi>h</mi><mi>t</mi><mo>:</mo><mn>0.01968</mn><mi>e</mi><mi>m</mi><mo separator="true">;</mo><mi mathvariant="normal">&quot;</mi><mo>&gt;</mo><mi>l</mi><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mo>&gt;</mo><mo>&lt;</mo><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mi>c</mi><mi>l</mi><mi>a</mi><mi>s</mi><mi>s</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>m</mi><mi>o</mi><mi>r</mi><mi>d</mi><mi>m</mi><mi>a</mi><mi>t</mi><mi>h</mi><mi>n</mi><mi>o</mi><mi>r</mi><mi>m</mi><mi>a</mi><mi>l</mi><mi mathvariant="normal">&quot;</mi><mo>&gt;</mo><mi>e</mi><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mo>&gt;</mo><mo>&lt;</mo><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mi>c</mi><mi>l</mi><mi>a</mi><mi>s</mi><mi>s</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>m</mi><mi>s</mi><mi>p</mi><mi>a</mi><mi>c</mi><mi>e</mi><mi mathvariant="normal">&quot;</mi><mi>s</mi><mi>t</mi><mi>y</mi><mi>l</mi><mi>e</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>m</mi><mi>a</mi><mi>r</mi><mi>g</mi><mi>i</mi><mi>n</mi><mo>−</mo><mi>r</mi><mi>i</mi><mi>g</mi><mi>h</mi><mi>t</mi><mo>:</mo><mn>0.2778</mn><mi>e</mi><mi>m</mi><mo separator="true">;</mo><mi mathvariant="normal">&quot;</mi><mo>&gt;</mo><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mo>&gt;</mo><mo>&lt;</mo><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mi>c</mi><mi>l</mi><mi>a</mi><mi>s</mi><mi>s</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>m</mi><mi>r</mi><mi>e</mi><mi>l</mi><mi mathvariant="normal">&quot;</mi><mo>&gt;</mo><mo>=</mo><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mo>&gt;</mo><mo>&lt;</mo><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mi>c</mi><mi>l</mi><mi>a</mi><mi>s</mi><mi>s</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>m</mi><mi>s</mi><mi>p</mi><mi>a</mi><mi>c</mi><mi>e</mi><mi mathvariant="normal">&quot;</mi><mi>s</mi><mi>t</mi><mi>y</mi><mi>l</mi><mi>e</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>m</mi><mi>a</mi><mi>r</mi><mi>g</mi><mi>i</mi><mi>n</mi><mo>−</mo><mi>r</mi><mi>i</mi><mi>g</mi><mi>h</mi><mi>t</mi><mo>:</mo><mn>0.2778</mn><mi>e</mi><mi>m</mi><mo separator="true">;</mo><mi mathvariant="normal">&quot;</mi><mo>&gt;</mo><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mo>&gt;</mo><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mo>&gt;</mo><mo>&lt;</mo><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mi>c</mi><mi>l</mi><mi>a</mi><mi>s</mi><mi>s</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>b</mi><mi>a</mi><mi>s</mi><mi>e</mi><mi mathvariant="normal">&quot;</mi><mo>&gt;</mo><mo>&lt;</mo><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mi>c</mi><mi>l</mi><mi>a</mi><mi>s</mi><mi>s</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>s</mi><mi>t</mi><mi>r</mi><mi>u</mi><mi>t</mi><mi mathvariant="normal">&quot;</mi><mi>s</mi><mi>t</mi><mi>y</mi><mi>l</mi><mi>e</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>h</mi><mi>e</mi><mi>i</mi><mi>g</mi><mi>h</mi><mi>t</mi><mo>:</mo><mn>1</mn><mi>e</mi><mi>m</mi><mo separator="true">;</mo><mi>v</mi><mi>e</mi><mi>r</mi><mi>t</mi><mi>i</mi><mi>c</mi><mi>a</mi><mi>l</mi><mo>−</mo><mi>a</mi><mi>l</mi><mi>i</mi><mi>g</mi><mi>n</mi><mo>:</mo><mo>−</mo><mn>0.25</mn><mi>e</mi><mi>m</mi><mo separator="true">;</mo><mi mathvariant="normal">&quot;</mi><mo>&gt;</mo><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mo>&gt;</mo><mo>&lt;</mo><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mi>c</mi><mi>l</mi><mi>a</mi><mi>s</mi><mi>s</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>m</mi><mi>o</mi><mi>r</mi><mi>d</mi><mi>m</mi><mi>a</mi><mi>t</mi><mi>h</mi><mi>n</mi><mi>o</mi><mi>r</mi><mi>m</mi><mi>a</mi><mi>l</mi><mi mathvariant="normal">&quot;</mi><mo>&gt;</mo><mi>a</mi><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mo>&gt;</mo><mo>&lt;</mo><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mi>c</mi><mi>l</mi><mi>a</mi><mi>s</mi><mi>s</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>m</mi><mi>o</mi><mi>r</mi><mi>d</mi><mi>m</mi><mi>a</mi><mi>t</mi><mi>h</mi><mi>n</mi><mi>o</mi><mi>r</mi><mi>m</mi><mi>a</mi><mi>l</mi><mi mathvariant="normal">&quot;</mi><mi>s</mi><mi>t</mi><mi>y</mi><mi>l</mi><mi>e</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>m</mi><mi>a</mi><mi>r</mi><mi>g</mi><mi>i</mi><mi>n</mi><mo>−</mo><mi>r</mi><mi>i</mi><mi>g</mi><mi>h</mi><mi>t</mi><mo>:</mo><mn>0.02778</mn><mi>e</mi><mi>m</mi><mo separator="true">;</mo><mi mathvariant="normal">&quot;</mi><mo>&gt;</mo><mi>r</mi><mi>r</mi><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mo>&gt;</mo><mo>&lt;</mo><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mi>c</mi><mi>l</mi><mi>a</mi><mi>s</mi><mi>s</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>m</mi><mi>o</mi><mi>r</mi><mi>d</mi><mi>m</mi><mi>a</mi><mi>t</mi><mi>h</mi><mi>n</mi><mi>o</mi><mi>r</mi><mi>m</mi><mi>a</mi><mi>l</mi><mi mathvariant="normal">&quot;</mi><mo>&gt;</mo><mi>a</mi><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mo>&gt;</mo><mo>&lt;</mo><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mi>c</mi><mi>l</mi><mi>a</mi><mi>s</mi><mi>s</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>m</mi><mi>o</mi><mi>r</mi><mi>d</mi><mi>m</mi><mi>a</mi><mi>t</mi><mi>h</mi><mi>n</mi><mi>o</mi><mi>r</mi><mi>m</mi><mi>a</mi><mi>l</mi><mi mathvariant="normal">&quot;</mi><mi>s</mi><mi>t</mi><mi>y</mi><mi>l</mi><mi>e</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>m</mi><mi>a</mi><mi>r</mi><mi>g</mi><mi>i</mi><mi>n</mi><mo>−</mo><mi>r</mi><mi>i</mi><mi>g</mi><mi>h</mi><mi>t</mi><mo>:</mo><mn>0.03588</mn><mi>e</mi><mi>m</mi><mo separator="true">;</mo><mi mathvariant="normal">&quot;</mi><mo>&gt;</mo><mi>y</mi><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mo>&gt;</mo><mo>&lt;</mo><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mi>c</mi><mi>l</mi><mi>a</mi><mi>s</mi><mi>s</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>m</mi><mi>o</mi><mi>p</mi><mi>e</mi><mi>n</mi><mi mathvariant="normal">&quot;</mi><mo>&gt;</mo><mo stretchy="false">(</mo><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mo>&gt;</mo><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mo>&gt;</mo><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mo>&gt;</mo><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mo>&gt;</mo><mi>r</mi><mi>e</mi><mi>d</mi><mo separator="true">,</mo></mrow><annotation encoding="application/x-tex">im = imagecreatetruecolor(100, 100); &lt;span class=&quot;katex&quot;&gt;&lt;span class=&quot;katex-mathml&quot;&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;semantics&gt;&lt;mrow&gt;&lt;mi&gt;w&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;mi&gt;m&lt;/mi&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;mi&gt;g&lt;/mi&gt;&lt;mi&gt;e&lt;/mi&gt;&lt;mi&gt;c&lt;/mi&gt;&lt;mi&gt;o&lt;/mi&gt;&lt;mi&gt;l&lt;/mi&gt;&lt;mi&gt;o&lt;/mi&gt;&lt;mi&gt;r&lt;/mi&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;mi&gt;l&lt;/mi&gt;&lt;mi&gt;l&lt;/mi&gt;&lt;mi&gt;o&lt;/mi&gt;&lt;mi&gt;c&lt;/mi&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;mi&gt;e&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;(&lt;/mo&gt;&lt;/mrow&gt;&lt;annotation encoding=&quot;application/x-tex&quot;&gt;w = imagecolorallocate(&lt;/annotation&gt;&lt;/semantics&gt;&lt;/math&gt;&lt;/span&gt;&lt;span class=&quot;katex-html&quot; aria-hidden=&quot;true&quot;&gt;&lt;span class=&quot;base&quot;&gt;&lt;span class=&quot;strut&quot; style=&quot;height:0.4306em;&quot;&gt;&lt;/span&gt;&lt;span class=&quot;mord mathnormal&quot; style=&quot;margin-right:0.02691em;&quot;&gt;w&lt;/span&gt;&lt;span class=&quot;mspace&quot; style=&quot;margin-right:0.2778em;&quot;&gt;&lt;/span&gt;&lt;span class=&quot;mrel&quot;&gt;=&lt;/span&gt;&lt;span class=&quot;mspace&quot; style=&quot;margin-right:0.2778em;&quot;&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class=&quot;base&quot;&gt;&lt;span class=&quot;strut&quot; style=&quot;height:1em;vertical-align:-0.25em;&quot;&gt;&lt;/span&gt;&lt;span class=&quot;mord mathnormal&quot;&gt;ima&lt;/span&gt;&lt;span class=&quot;mord mathnormal&quot; style=&quot;margin-right:0.03588em;&quot;&gt;g&lt;/span&gt;&lt;span class=&quot;mord mathnormal&quot;&gt;eco&lt;/span&gt;&lt;span class=&quot;mord mathnormal&quot; style=&quot;margin-right:0.01968em;&quot;&gt;l&lt;/span&gt;&lt;span class=&quot;mord mathnormal&quot; style=&quot;margin-right:0.02778em;&quot;&gt;or&lt;/span&gt;&lt;span class=&quot;mord mathnormal&quot;&gt;a&lt;/span&gt;&lt;span class=&quot;mord mathnormal&quot; style=&quot;margin-right:0.01968em;&quot;&gt;ll&lt;/span&gt;&lt;span class=&quot;mord mathnormal&quot;&gt;oc&lt;/span&gt;&lt;span class=&quot;mord mathnormal&quot;&gt;a&lt;/span&gt;&lt;span class=&quot;mord mathnormal&quot;&gt;t&lt;/span&gt;&lt;span class=&quot;mord mathnormal&quot;&gt;e&lt;/span&gt;&lt;span class=&quot;mopen&quot;&gt;(&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;im, 255, 255, 255); &lt;span class=&quot;katex&quot;&gt;&lt;span class=&quot;katex-mathml&quot;&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;semantics&gt;&lt;mrow&gt;&lt;mi&gt;r&lt;/mi&gt;&lt;mi&gt;e&lt;/mi&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;mi&gt;m&lt;/mi&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;mi&gt;g&lt;/mi&gt;&lt;mi&gt;e&lt;/mi&gt;&lt;mi&gt;c&lt;/mi&gt;&lt;mi&gt;o&lt;/mi&gt;&lt;mi&gt;l&lt;/mi&gt;&lt;mi&gt;o&lt;/mi&gt;&lt;mi&gt;r&lt;/mi&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;mi&gt;l&lt;/mi&gt;&lt;mi&gt;l&lt;/mi&gt;&lt;mi&gt;o&lt;/mi&gt;&lt;mi&gt;c&lt;/mi&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;mi&gt;e&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;(&lt;/mo&gt;&lt;/mrow&gt;&lt;annotation encoding=&quot;application/x-tex&quot;&gt;red = imagecolorallocate(&lt;/annotation&gt;&lt;/semantics&gt;&lt;/math&gt;&lt;/span&gt;&lt;span class=&quot;katex-html&quot; aria-hidden=&quot;true&quot;&gt;&lt;span class=&quot;base&quot;&gt;&lt;span class=&quot;strut&quot; style=&quot;height:0.6944em;&quot;&gt;&lt;/span&gt;&lt;span class=&quot;mord mathnormal&quot;&gt;re&lt;/span&gt;&lt;span class=&quot;mord mathnormal&quot;&gt;d&lt;/span&gt;&lt;span class=&quot;mspace&quot; style=&quot;margin-right:0.2778em;&quot;&gt;&lt;/span&gt;&lt;span class=&quot;mrel&quot;&gt;=&lt;/span&gt;&lt;span class=&quot;mspace&quot; style=&quot;margin-right:0.2778em;&quot;&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class=&quot;base&quot;&gt;&lt;span class=&quot;strut&quot; style=&quot;height:1em;vertical-align:-0.25em;&quot;&gt;&lt;/span&gt;&lt;span class=&quot;mord mathnormal&quot;&gt;ima&lt;/span&gt;&lt;span class=&quot;mord mathnormal&quot; style=&quot;margin-right:0.03588em;&quot;&gt;g&lt;/span&gt;&lt;span class=&quot;mord mathnormal&quot;&gt;eco&lt;/span&gt;&lt;span class=&quot;mord mathnormal&quot; style=&quot;margin-right:0.01968em;&quot;&gt;l&lt;/span&gt;&lt;span class=&quot;mord mathnormal&quot; style=&quot;margin-right:0.02778em;&quot;&gt;or&lt;/span&gt;&lt;span class=&quot;mord mathnormal&quot;&gt;a&lt;/span&gt;&lt;span class=&quot;mord mathnormal&quot; style=&quot;margin-right:0.01968em;&quot;&gt;ll&lt;/span&gt;&lt;span class=&quot;mord mathnormal&quot;&gt;oc&lt;/span&gt;&lt;span class=&quot;mord mathnormal&quot;&gt;a&lt;/span&gt;&lt;span class=&quot;mord mathnormal&quot;&gt;t&lt;/span&gt;&lt;span class=&quot;mord mathnormal&quot;&gt;e&lt;/span&gt;&lt;span class=&quot;mopen&quot;&gt;(&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;im, 255, 0, 0);/* Draw a dashed line, 5 red pixels, 5 white pixels */ &lt;span class=&quot;katex&quot;&gt;&lt;span class=&quot;katex-mathml&quot;&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;semantics&gt;&lt;mrow&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;mi&gt;l&lt;/mi&gt;&lt;mi&gt;e&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;mi&gt;r&lt;/mi&gt;&lt;mi&gt;r&lt;/mi&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;(&lt;/mo&gt;&lt;/mrow&gt;&lt;annotation encoding=&quot;application/x-tex&quot;&gt;style = array(&lt;/annotation&gt;&lt;/semantics&gt;&lt;/math&gt;&lt;/span&gt;&lt;span class=&quot;katex-html&quot; aria-hidden=&quot;true&quot;&gt;&lt;span class=&quot;base&quot;&gt;&lt;span class=&quot;strut&quot; style=&quot;height:0.8889em;vertical-align:-0.1944em;&quot;&gt;&lt;/span&gt;&lt;span class=&quot;mord mathnormal&quot;&gt;s&lt;/span&gt;&lt;span class=&quot;mord mathnormal&quot;&gt;t&lt;/span&gt;&lt;span class=&quot;mord mathnormal&quot; style=&quot;margin-right:0.03588em;&quot;&gt;y&lt;/span&gt;&lt;span class=&quot;mord mathnormal&quot; style=&quot;margin-right:0.01968em;&quot;&gt;l&lt;/span&gt;&lt;span class=&quot;mord mathnormal&quot;&gt;e&lt;/span&gt;&lt;span class=&quot;mspace&quot; style=&quot;margin-right:0.2778em;&quot;&gt;&lt;/span&gt;&lt;span class=&quot;mrel&quot;&gt;=&lt;/span&gt;&lt;span class=&quot;mspace&quot; style=&quot;margin-right:0.2778em;&quot;&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class=&quot;base&quot;&gt;&lt;span class=&quot;strut&quot; style=&quot;height:1em;vertical-align:-0.25em;&quot;&gt;&lt;/span&gt;&lt;span class=&quot;mord mathnormal&quot;&gt;a&lt;/span&gt;&lt;span class=&quot;mord mathnormal&quot; style=&quot;margin-right:0.02778em;&quot;&gt;rr&lt;/span&gt;&lt;span class=&quot;mord mathnormal&quot;&gt;a&lt;/span&gt;&lt;span class=&quot;mord mathnormal&quot; style=&quot;margin-right:0.03588em;&quot;&gt;y&lt;/span&gt;&lt;span class=&quot;mopen&quot;&gt;(&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;red, </annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6595em;"></span><span class="mord mathnormal">im</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord 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style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord">0.4306</span><span class="mord mathnormal">e</span><span class="mord mathnormal">m</span><span class="mpunct">;</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">&quot;</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">/</span><span class="mord mathnormal">s</span><span class="mord mathnormal">p</span><span class="mord mathnormal">an</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord mathnormal">s</span><span class="mord 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style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord mathnormal" style="margin-right:0.02778em;">r</span><span class="mord mathnormal">i</span><span class="mord mathnormal" style="margin-right:0.03588em;">g</span><span class="mord mathnormal">h</span><span class="mord mathnormal">t</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">:</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord">0.02691</span><span class="mord mathnormal">e</span><span class="mord mathnormal">m</span><span class="mpunct">;</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">&quot;</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" 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style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord mathnormal">s</span><span class="mord mathnormal">p</span><span class="mord mathnormal">an</span><span class="mord mathnormal">c</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord mathnormal">a</span><span class="mord mathnormal">ss</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.7335em;vertical-align:-0.0391em;"></span><span class="mord">&quot;</span><span class="mord mathnormal">ba</span><span class="mord mathnormal">se</span><span class="mord">&quot;</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" 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class="mord mathnormal">hn</span><span class="mord mathnormal" style="margin-right:0.02778em;">or</span><span class="mord mathnormal">ma</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord">&quot;</span><span class="mord mathnormal">s</span><span class="mord mathnormal">t</span><span class="mord mathnormal" style="margin-right:0.03588em;">y</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord mathnormal">e</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord">&quot;</span><span class="mord mathnormal">ma</span><span class="mord mathnormal" style="margin-right:0.02778em;">r</span><span class="mord mathnormal" style="margin-right:0.03588em;">g</span><span class="mord 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class="mord">&quot;</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.7335em;vertical-align:-0.1944em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">g</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">/</span><span class="mord mathnormal">s</span><span class="mord mathnormal">p</span><span class="mord mathnormal">an</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord mathnormal">s</span><span class="mord mathnormal">p</span><span class="mord mathnormal">an</span><span class="mord mathnormal">c</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord mathnormal">a</span><span class="mord mathnormal">ss</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.7335em;vertical-align:-0.0391em;"></span><span class="mord">&quot;</span><span class="mord mathnormal">m</span><span class="mord mathnormal" style="margin-right:0.02778em;">or</span><span class="mord mathnormal">d</span><span class="mord mathnormal">ma</span><span class="mord mathnormal">t</span><span class="mord mathnormal">hn</span><span class="mord mathnormal" style="margin-right:0.02778em;">or</span><span class="mord mathnormal">ma</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord">&quot;</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.5782em;vertical-align:-0.0391em;"></span><span class="mord mathnormal">eco</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">/</span><span class="mord mathnormal">s</span><span class="mord mathnormal">p</span><span class="mord mathnormal">an</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord mathnormal">s</span><span class="mord mathnormal">p</span><span class="mord mathnormal">an</span><span class="mord mathnormal">c</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord mathnormal">a</span><span class="mord mathnormal">ss</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord">&quot;</span><span class="mord mathnormal">m</span><span class="mord mathnormal" style="margin-right:0.02778em;">or</span><span class="mord mathnormal">d</span><span class="mord mathnormal">ma</span><span class="mord mathnormal">t</span><span class="mord mathnormal">hn</span><span class="mord mathnormal" style="margin-right:0.02778em;">or</span><span class="mord 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style="margin-right:0.2778em;"></span><span class="mrel">&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">/</span><span class="mord mathnormal">s</span><span class="mord mathnormal">p</span><span class="mord mathnormal">an</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord mathnormal">s</span><span class="mord mathnormal">p</span><span class="mord mathnormal">an</span><span class="mord mathnormal">c</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord mathnormal">a</span><span class="mord mathnormal">ss</span><span class="mspace" style="margin-right:0.2778em;"></span><span 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style="margin-right:0.2778em;"></span><span class="mrel">&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">/</span><span class="mord mathnormal">s</span><span class="mord mathnormal">p</span><span class="mord mathnormal">an</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord mathnormal">s</span><span class="mord mathnormal">p</span><span class="mord mathnormal">an</span><span class="mord mathnormal">c</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord mathnormal">a</span><span class="mord mathnormal">ss</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.7335em;vertical-align:-0.0391em;"></span><span class="mord">&quot;</span><span class="mord mathnormal">m</span><span class="mord mathnormal" style="margin-right:0.02778em;">or</span><span class="mord mathnormal">d</span><span class="mord mathnormal">ma</span><span class="mord mathnormal">t</span><span class="mord mathnormal">hn</span><span class="mord mathnormal" style="margin-right:0.02778em;">or</span><span class="mord mathnormal">ma</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord">&quot;</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.5782em;vertical-align:-0.0391em;"></span><span class="mord mathnormal">e</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">/</span><span class="mord mathnormal">s</span><span class="mord mathnormal">p</span><span class="mord mathnormal">an</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord mathnormal">s</span><span class="mord mathnormal">p</span><span class="mord mathnormal">an</span><span class="mord mathnormal">c</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord mathnormal">a</span><span class="mord mathnormal">ss</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord">&quot;</span><span class="mord mathnormal">m</span><span class="mord mathnormal">o</span><span class="mord mathnormal">p</span><span class="mord mathnormal">e</span><span class="mord mathnormal">n</span><span class="mord">&quot;</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mrel">&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">/</span><span class="mord mathnormal">s</span><span class="mord 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style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord">1</span><span class="mord mathnormal">e</span><span class="mord mathnormal">m</span><span class="mpunct">;</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">v</span><span class="mord mathnormal" style="margin-right:0.02778em;">er</span><span class="mord mathnormal">t</span><span class="mord mathnormal">i</span><span class="mord mathnormal">c</span><span class="mord mathnormal">a</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord mathnormal">a</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord 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style="margin-right:0.2778em;"></span><span class="mrel">&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">/</span><span class="mord mathnormal">s</span><span class="mord mathnormal">p</span><span class="mord mathnormal">an</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord mathnormal">s</span><span class="mord mathnormal">p</span><span class="mord mathnormal">an</span><span class="mord mathnormal">c</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord mathnormal">a</span><span class="mord mathnormal">ss</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.7335em;vertical-align:-0.0391em;"></span><span class="mord">&quot;</span><span class="mord mathnormal">m</span><span class="mord mathnormal" style="margin-right:0.02778em;">or</span><span class="mord mathnormal">d</span><span class="mord mathnormal">ma</span><span class="mord mathnormal">t</span><span class="mord mathnormal">hn</span><span class="mord mathnormal" style="margin-right:0.02778em;">or</span><span class="mord mathnormal">ma</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord">&quot;</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.5782em;vertical-align:-0.0391em;"></span><span class="mord mathnormal">a</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">/</span><span class="mord mathnormal">s</span><span class="mord mathnormal">p</span><span class="mord mathnormal">an</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord mathnormal">s</span><span class="mord mathnormal">p</span><span class="mord mathnormal">an</span><span class="mord mathnormal">c</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord mathnormal">a</span><span class="mord mathnormal">ss</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.7335em;vertical-align:-0.0391em;"></span><span class="mord">&quot;</span><span class="mord mathnormal">m</span><span class="mord mathnormal" style="margin-right:0.02778em;">or</span><span class="mord mathnormal">d</span><span class="mord mathnormal">ma</span><span class="mord mathnormal">t</span><span class="mord mathnormal">hn</span><span class="mord mathnormal" style="margin-right:0.02778em;">or</span><span class="mord mathnormal">ma</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord">&quot;</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6542em;vertical-align:-0.0391em;"></span><span class="mord mathnormal">t</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">/</span><span class="mord mathnormal">s</span><span class="mord mathnormal">p</span><span class="mord mathnormal">an</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord mathnormal">s</span><span class="mord mathnormal">p</span><span class="mord mathnormal">an</span><span class="mord mathnormal">c</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord mathnormal">a</span><span class="mord mathnormal">ss</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.7335em;vertical-align:-0.0391em;"></span><span class="mord">&quot;</span><span class="mord mathnormal">m</span><span class="mord mathnormal" style="margin-right:0.02778em;">or</span><span class="mord mathnormal">d</span><span class="mord mathnormal">ma</span><span class="mord mathnormal">t</span><span class="mord mathnormal">hn</span><span class="mord mathnormal" style="margin-right:0.02778em;">or</span><span class="mord mathnormal">ma</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord">&quot;</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.5782em;vertical-align:-0.0391em;"></span><span class="mord mathnormal">e</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">/</span><span class="mord mathnormal">s</span><span class="mord mathnormal">p</span><span class="mord mathnormal">an</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord mathnormal">s</span><span class="mord mathnormal">p</span><span class="mord mathnormal">an</span><span class="mord mathnormal">c</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord mathnormal">a</span><span class="mord mathnormal">ss</span><span class="mspace" style="margin-right:0.2778em;"></span><span 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style="height:1em;vertical-align:-0.25em;"></span><span class="mord">/</span><span class="mord mathnormal">ma</span><span class="mord mathnormal">t</span><span class="mord mathnormal">h</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">/</span><span class="mord mathnormal">s</span><span class="mord mathnormal">p</span><span class="mord mathnormal">an</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord mathnormal">s</span><span class="mord mathnormal">p</span><span class="mord mathnormal">an</span><span class="mord mathnormal">c</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord mathnormal">a</span><span class="mord mathnormal">ss</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.7778em;vertical-align:-0.0833em;"></span><span class="mord">&quot;</span><span class="mord mathnormal">ka</span><span class="mord mathnormal">t</span><span class="mord mathnormal">e</span><span class="mord mathnormal">x</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.7778em;vertical-align:-0.0833em;"></span><span class="mord mathnormal">h</span><span class="mord mathnormal">t</span><span class="mord mathnormal">m</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord">&quot;</span><span class="mord mathnormal">a</span><span class="mord mathnormal" style="margin-right:0.02778em;">r</span><span class="mord mathnormal">ia</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.6944em;"></span><span class="mord mathnormal">hi</span><span class="mord mathnormal">dd</span><span class="mord mathnormal">e</span><span class="mord mathnormal">n</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.7335em;vertical-align:-0.0391em;"></span><span class="mord">&quot;</span><span class="mord mathnormal">t</span><span class="mord mathnormal" style="margin-right:0.02778em;">r</span><span class="mord mathnormal">u</span><span class="mord mathnormal">e</span><span class="mord">&quot;</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord mathnormal">s</span><span class="mord mathnormal">p</span><span class="mord mathnormal">an</span><span class="mord mathnormal">c</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord mathnormal">a</span><span class="mord mathnormal">ss</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.7335em;vertical-align:-0.0391em;"></span><span class="mord">&quot;</span><span class="mord mathnormal">ba</span><span class="mord mathnormal">se</span><span class="mord">&quot;</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord mathnormal">s</span><span class="mord mathnormal">p</span><span class="mord mathnormal">an</span><span class="mord mathnormal">c</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord mathnormal">a</span><span class="mord mathnormal">ss</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord">&quot;</span><span class="mord mathnormal">s</span><span class="mord mathnormal">t</span><span class="mord mathnormal" style="margin-right:0.02778em;">r</span><span class="mord mathnormal">u</span><span class="mord mathnormal">t</span><span class="mord">&quot;</span><span class="mord mathnormal">s</span><span class="mord mathnormal">t</span><span class="mord mathnormal" style="margin-right:0.03588em;">y</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord mathnormal">e</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord">&quot;</span><span class="mord mathnormal">h</span><span class="mord mathnormal">e</span><span class="mord mathnormal">i</span><span class="mord mathnormal" style="margin-right:0.03588em;">g</span><span class="mord mathnormal">h</span><span class="mord mathnormal">t</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">:</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord">0.8889</span><span class="mord mathnormal">e</span><span class="mord mathnormal">m</span><span class="mpunct">;</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">v</span><span class="mord mathnormal" style="margin-right:0.02778em;">er</span><span class="mord mathnormal">t</span><span class="mord mathnormal">i</span><span class="mord mathnormal">c</span><span class="mord mathnormal">a</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord mathnormal">a</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord mathnormal">i</span><span class="mord mathnormal" style="margin-right:0.03588em;">g</span><span class="mord mathnormal">n</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">:</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord">−</span><span class="mord">0.1944</span><span class="mord mathnormal">e</span><span class="mord mathnormal">m</span><span class="mpunct">;</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">&quot;</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">/</span><span class="mord mathnormal">s</span><span class="mord mathnormal">p</span><span class="mord mathnormal">an</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord mathnormal">s</span><span class="mord mathnormal">p</span><span class="mord mathnormal">an</span><span class="mord mathnormal">c</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord mathnormal">a</span><span class="mord mathnormal">ss</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.7335em;vertical-align:-0.0391em;"></span><span class="mord">&quot;</span><span class="mord mathnormal">m</span><span class="mord mathnormal" style="margin-right:0.02778em;">or</span><span class="mord mathnormal">d</span><span class="mord mathnormal">ma</span><span class="mord mathnormal">t</span><span class="mord mathnormal">hn</span><span class="mord mathnormal" style="margin-right:0.02778em;">or</span><span class="mord mathnormal">ma</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord">&quot;</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.5782em;vertical-align:-0.0391em;"></span><span class="mord mathnormal">s</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">/</span><span class="mord mathnormal">s</span><span class="mord mathnormal">p</span><span class="mord mathnormal">an</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord mathnormal">s</span><span class="mord mathnormal">p</span><span class="mord mathnormal">an</span><span class="mord mathnormal">c</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord mathnormal">a</span><span class="mord mathnormal">ss</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.7335em;vertical-align:-0.0391em;"></span><span class="mord">&quot;</span><span class="mord mathnormal">m</span><span class="mord mathnormal" style="margin-right:0.02778em;">or</span><span class="mord mathnormal">d</span><span class="mord mathnormal">ma</span><span class="mord mathnormal">t</span><span class="mord mathnormal">hn</span><span class="mord mathnormal" style="margin-right:0.02778em;">or</span><span class="mord mathnormal">ma</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord">&quot;</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6542em;vertical-align:-0.0391em;"></span><span class="mord mathnormal">t</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">/</span><span class="mord mathnormal">s</span><span class="mord mathnormal">p</span><span class="mord mathnormal">an</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord mathnormal">s</span><span class="mord mathnormal">p</span><span class="mord mathnormal">an</span><span class="mord mathnormal">c</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord mathnormal">a</span><span class="mord mathnormal">ss</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord">&quot;</span><span class="mord mathnormal">m</span><span class="mord mathnormal" style="margin-right:0.02778em;">or</span><span class="mord mathnormal">d</span><span class="mord mathnormal">ma</span><span class="mord mathnormal">t</span><span class="mord mathnormal">hn</span><span class="mord mathnormal" style="margin-right:0.02778em;">or</span><span class="mord mathnormal">ma</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord">&quot;</span><span class="mord mathnormal">s</span><span class="mord mathnormal">t</span><span class="mord mathnormal" style="margin-right:0.03588em;">y</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord mathnormal">e</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord">&quot;</span><span class="mord mathnormal">ma</span><span class="mord mathnormal" style="margin-right:0.02778em;">r</span><span class="mord mathnormal" style="margin-right:0.03588em;">g</span><span class="mord mathnormal">in</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord mathnormal" style="margin-right:0.02778em;">r</span><span class="mord mathnormal">i</span><span class="mord mathnormal" style="margin-right:0.03588em;">g</span><span class="mord mathnormal">h</span><span class="mord mathnormal">t</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">:</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord">0.03588</span><span class="mord mathnormal">e</span><span class="mord mathnormal">m</span><span class="mpunct">;</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">&quot;</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.7335em;vertical-align:-0.1944em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">y</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">/</span><span class="mord mathnormal">s</span><span class="mord mathnormal">p</span><span class="mord mathnormal">an</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord mathnormal">s</span><span class="mord mathnormal">p</span><span class="mord mathnormal">an</span><span class="mord mathnormal">c</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord mathnormal">a</span><span class="mord mathnormal">ss</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord">&quot;</span><span class="mord mathnormal">m</span><span class="mord mathnormal" 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mathnormal" style="margin-right:0.02778em;">r</span><span class="mord mathnormal" style="margin-right:0.03588em;">g</span><span class="mord mathnormal">in</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord mathnormal" style="margin-right:0.02778em;">r</span><span class="mord mathnormal">i</span><span class="mord mathnormal" style="margin-right:0.03588em;">g</span><span class="mord mathnormal">h</span><span class="mord mathnormal">t</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">:</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord">0.01968</span><span class="mord mathnormal">e</span><span class="mord 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class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord">0.2778</span><span class="mord mathnormal">e</span><span class="mord mathnormal">m</span><span class="mpunct">;</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">&quot;</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">/</span><span class="mord mathnormal">s</span><span class="mord mathnormal">p</span><span class="mord mathnormal">an</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">/</span><span class="mord mathnormal">s</span><span class="mord mathnormal">p</span><span class="mord mathnormal">an</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord mathnormal">s</span><span class="mord mathnormal">p</span><span class="mord mathnormal">an</span><span class="mord mathnormal">c</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord mathnormal">a</span><span class="mord mathnormal">ss</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.7335em;vertical-align:-0.0391em;"></span><span class="mord">&quot;</span><span class="mord mathnormal">ba</span><span class="mord 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style="margin-right:0.02778em;">r</span><span class="mord mathnormal">u</span><span class="mord mathnormal">t</span><span class="mord">&quot;</span><span class="mord mathnormal">s</span><span class="mord mathnormal">t</span><span class="mord mathnormal" style="margin-right:0.03588em;">y</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord mathnormal">e</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord">&quot;</span><span class="mord mathnormal">h</span><span class="mord mathnormal">e</span><span class="mord mathnormal">i</span><span class="mord mathnormal" style="margin-right:0.03588em;">g</span><span class="mord mathnormal">h</span><span class="mord mathnormal">t</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">:</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord">1</span><span class="mord mathnormal">e</span><span class="mord mathnormal">m</span><span class="mpunct">;</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">v</span><span class="mord mathnormal" style="margin-right:0.02778em;">er</span><span class="mord mathnormal">t</span><span class="mord mathnormal">i</span><span class="mord mathnormal">c</span><span class="mord mathnormal">a</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord mathnormal">a</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord mathnormal">i</span><span class="mord mathnormal" style="margin-right:0.03588em;">g</span><span class="mord mathnormal">n</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">:</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord">−</span><span class="mord">0.25</span><span class="mord mathnormal">e</span><span class="mord mathnormal">m</span><span class="mpunct">;</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">&quot;</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">/</span><span class="mord mathnormal">s</span><span class="mord mathnormal">p</span><span class="mord mathnormal">an</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord mathnormal">s</span><span class="mord mathnormal">p</span><span class="mord mathnormal">an</span><span class="mord mathnormal">c</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord mathnormal">a</span><span class="mord mathnormal">ss</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.7335em;vertical-align:-0.0391em;"></span><span class="mord">&quot;</span><span class="mord mathnormal">m</span><span class="mord mathnormal" style="margin-right:0.02778em;">or</span><span class="mord mathnormal">d</span><span class="mord mathnormal">ma</span><span class="mord mathnormal">t</span><span class="mord mathnormal">hn</span><span class="mord mathnormal" style="margin-right:0.02778em;">or</span><span class="mord mathnormal">ma</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord">&quot;</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.5782em;vertical-align:-0.0391em;"></span><span class="mord mathnormal">a</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">/</span><span class="mord mathnormal">s</span><span class="mord mathnormal">p</span><span class="mord mathnormal">an</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord mathnormal">s</span><span class="mord mathnormal">p</span><span class="mord mathnormal">an</span><span class="mord mathnormal">c</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord mathnormal">a</span><span class="mord mathnormal">ss</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord">&quot;</span><span class="mord mathnormal">m</span><span class="mord mathnormal" style="margin-right:0.02778em;">or</span><span class="mord mathnormal">d</span><span class="mord mathnormal">ma</span><span class="mord mathnormal">t</span><span class="mord mathnormal">hn</span><span class="mord mathnormal" style="margin-right:0.02778em;">or</span><span class="mord mathnormal">ma</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord">&quot;</span><span class="mord mathnormal">s</span><span class="mord mathnormal">t</span><span class="mord mathnormal" style="margin-right:0.03588em;">y</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord mathnormal">e</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord">&quot;</span><span class="mord mathnormal">ma</span><span class="mord mathnormal" style="margin-right:0.02778em;">r</span><span class="mord mathnormal" style="margin-right:0.03588em;">g</span><span class="mord mathnormal">in</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord mathnormal" style="margin-right:0.02778em;">r</span><span class="mord mathnormal">i</span><span class="mord mathnormal" style="margin-right:0.03588em;">g</span><span class="mord mathnormal">h</span><span class="mord mathnormal">t</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">:</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord">0.02778</span><span class="mord mathnormal">e</span><span class="mord mathnormal">m</span><span class="mpunct">;</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">&quot;</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.5782em;vertical-align:-0.0391em;"></span><span class="mord mathnormal" style="margin-right:0.02778em;">rr</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">/</span><span class="mord mathnormal">s</span><span class="mord mathnormal">p</span><span class="mord mathnormal">an</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord mathnormal">s</span><span class="mord mathnormal">p</span><span class="mord mathnormal">an</span><span class="mord mathnormal">c</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord mathnormal">a</span><span class="mord mathnormal">ss</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.7335em;vertical-align:-0.0391em;"></span><span class="mord">&quot;</span><span class="mord mathnormal">m</span><span class="mord mathnormal" style="margin-right:0.02778em;">or</span><span class="mord mathnormal">d</span><span class="mord mathnormal">ma</span><span class="mord mathnormal">t</span><span class="mord mathnormal">hn</span><span class="mord mathnormal" style="margin-right:0.02778em;">or</span><span class="mord mathnormal">ma</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord">&quot;</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.5782em;vertical-align:-0.0391em;"></span><span class="mord mathnormal">a</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">/</span><span class="mord mathnormal">s</span><span class="mord mathnormal">p</span><span class="mord mathnormal">an</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord mathnormal">s</span><span class="mord mathnormal">p</span><span class="mord mathnormal">an</span><span class="mord mathnormal">c</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord mathnormal">a</span><span class="mord mathnormal">ss</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord">&quot;</span><span class="mord mathnormal">m</span><span class="mord mathnormal" style="margin-right:0.02778em;">or</span><span class="mord mathnormal">d</span><span class="mord mathnormal">ma</span><span class="mord mathnormal">t</span><span class="mord mathnormal">hn</span><span class="mord mathnormal" style="margin-right:0.02778em;">or</span><span class="mord mathnormal">ma</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord">&quot;</span><span class="mord mathnormal">s</span><span class="mord mathnormal">t</span><span class="mord mathnormal" style="margin-right:0.03588em;">y</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord mathnormal">e</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord">&quot;</span><span class="mord mathnormal">ma</span><span class="mord mathnormal" style="margin-right:0.02778em;">r</span><span class="mord mathnormal" style="margin-right:0.03588em;">g</span><span class="mord mathnormal">in</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord mathnormal" style="margin-right:0.02778em;">r</span><span class="mord mathnormal">i</span><span class="mord mathnormal" style="margin-right:0.03588em;">g</span><span class="mord mathnormal">h</span><span class="mord mathnormal">t</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">:</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord">0.03588</span><span class="mord mathnormal">e</span><span class="mord mathnormal">m</span><span class="mpunct">;</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">&quot;</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.7335em;vertical-align:-0.1944em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">y</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">/</span><span class="mord mathnormal">s</span><span class="mord mathnormal">p</span><span class="mord mathnormal">an</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord mathnormal">s</span><span class="mord mathnormal">p</span><span class="mord mathnormal">an</span><span class="mord mathnormal">c</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord mathnormal">a</span><span class="mord mathnormal">ss</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord">&quot;</span><span class="mord mathnormal">m</span><span class="mord mathnormal">o</span><span class="mord mathnormal">p</span><span class="mord mathnormal">e</span><span class="mord mathnormal">n</span><span class="mord">&quot;</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mrel">&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">/</span><span class="mord mathnormal">s</span><span class="mord mathnormal">p</span><span class="mord mathnormal">an</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">/</span><span class="mord mathnormal">s</span><span class="mord mathnormal">p</span><span class="mord mathnormal">an</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">/</span><span class="mord mathnormal">s</span><span class="mord mathnormal">p</span><span class="mord mathnormal">an</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">/</span><span class="mord mathnormal">s</span><span class="mord mathnormal">p</span><span class="mord mathnormal">an</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord mathnormal">re</span><span class="mord mathnormal">d</span><span class="mpunct">,</span></span></span></span>red, <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>r</mi><mi>e</mi><mi>d</mi><mo separator="true">,</mo></mrow><annotation encoding="application/x-tex">red, </annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord mathnormal">re</span><span class="mord mathnormal">d</span><span class="mpunct">,</span></span></span></span>red, <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>r</mi><mi>e</mi><mi>d</mi><mo separator="true">,</mo></mrow><annotation encoding="application/x-tex">red, </annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord mathnormal">re</span><span class="mord mathnormal">d</span><span class="mpunct">,</span></span></span></span>w, <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>w</mi><mo separator="true">,</mo></mrow><annotation encoding="application/x-tex">w, </annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.1944em;"></span><span class="mord mathnormal" style="margin-right:0.02691em;">w</span><span class="mpunct">,</span></span></span></span>w, <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>w</mi><mo separator="true">,</mo></mrow><annotation encoding="application/x-tex">w, </annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.1944em;"></span><span class="mord mathnormal" style="margin-right:0.02691em;">w</span><span class="mpunct">,</span></span></span></span>w); imagesetstyle($im, $style); imageline($im, 0, 0, 100, 100, IMG_COLOR_STYLED);/* Draw a line of happy faces using imagesetbrush() with imagesetstyle */ <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>s</mi><mi>t</mi><mi>y</mi><mi>l</mi><mi>e</mi><mo>=</mo><mi>a</mi><mi>r</mi><mi>r</mi><mi>a</mi><mi>y</mi><mo stretchy="false">(</mo></mrow><annotation encoding="application/x-tex">style = array(</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord mathnormal">s</span><span class="mord mathnormal">t</span><span class="mord mathnormal" style="margin-right:0.03588em;">y</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord mathnormal">e</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal">a</span><span class="mord mathnormal" style="margin-right:0.02778em;">rr</span><span class="mord mathnormal">a</span><span class="mord mathnormal" style="margin-right:0.03588em;">y</span><span class="mopen">(</span></span></span></span>w, <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>w</mi><mo separator="true">,</mo></mrow><annotation encoding="application/x-tex">w, </annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.1944em;"></span><span class="mord mathnormal" style="margin-right:0.02691em;">w</span><span class="mpunct">,</span></span></span></span>w, <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>w</mi><mo separator="true">,</mo></mrow><annotation encoding="application/x-tex">w, </annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.1944em;"></span><span class="mord mathnormal" style="margin-right:0.02691em;">w</span><span class="mpunct">,</span></span></span></span>w, <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>w</mi><mo separator="true">,</mo></mrow><annotation encoding="application/x-tex">w, </annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.1944em;"></span><span class="mord mathnormal" style="margin-right:0.02691em;">w</span><span class="mpunct">,</span></span></span></span>w, <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>w</mi><mo separator="true">,</mo></mrow><annotation encoding="application/x-tex">w, </annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.1944em;"></span><span class="mord mathnormal" style="margin-right:0.02691em;">w</span><span class="mpunct">,</span></span></span></span>w, <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>w</mi><mo separator="true">,</mo></mrow><annotation encoding="application/x-tex">w, </annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.1944em;"></span><span class="mord mathnormal" style="margin-right:0.02691em;">w</span><span class="mpunct">,</span></span></span></span>w, <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>w</mi><mo separator="true">,</mo></mrow><annotation encoding="application/x-tex">w, </annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.1944em;"></span><span class="mord mathnormal" style="margin-right:0.02691em;">w</span><span class="mpunct">,</span></span></span></span>red); imagesetstyle($im, <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>s</mi><mi>t</mi><mi>y</mi><mi>l</mi><mi>e</mi><mo stretchy="false">)</mo><mo separator="true">;</mo></mrow><annotation encoding="application/x-tex">style);</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal">s</span><span class="mord mathnormal">t</span><span class="mord mathnormal" style="margin-right:0.03588em;">y</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord mathnormal">e</span><span class="mclose">)</span><span class="mpunct">;</span></span></span></span>brush = imagecreatefrompng("http://www.libpng.org/pub/png/images/smile.happy.png"); <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>w</mi><mn>2</mn><mo>=</mo><mi>i</mi><mi>m</mi><mi>a</mi><mi>g</mi><mi>e</mi><mi>c</mi><mi>o</mi><mi>l</mi><mi>o</mi><mi>r</mi><mi>a</mi><mi>l</mi><mi>l</mi><mi>o</mi><mi>c</mi><mi>a</mi><mi>t</mi><mi>e</mi><mo stretchy="false">(</mo></mrow><annotation encoding="application/x-tex">w2 = imagecolorallocate(</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord mathnormal" style="margin-right:0.02691em;">w</span><span class="mord">2</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal">ima</span><span class="mord mathnormal" style="margin-right:0.03588em;">g</span><span class="mord mathnormal">eco</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord mathnormal" style="margin-right:0.02778em;">or</span><span class="mord mathnormal">a</span><span class="mord mathnormal" style="margin-right:0.01968em;">ll</span><span class="mord mathnormal">oc</span><span class="mord mathnormal">a</span><span class="mord mathnormal">t</span><span class="mord mathnormal">e</span><span class="mopen">(</span></span></span></span>brush, 255, 255, 255); imagecolortransparent($brush, $w2); imagesetbrush($im, $brush); imageline($im, 100, 0, 0, 100, IMG_COLOR_STYLEDBRUSHED);imagejpeg($im); ?>

The above example will output something similar to:

Found A Problem?

Michael_Todd_335 at yahoo dot com

17 years ago

Watch out! If you pass imagesetstyle() an empty array as the second argument, it will crash your server! I was messing with it just earlier and accidentally did so, and the page took a good minute to process, when my Apache server came up with the good ol' Windows 'Send Error Report' window.

dazbert

8 years ago

`To clarify, for lines where the thickness is greater than 1, the total length of the $style array needs to be an exact divisor of the length of the line.

This is because the pattern is repeated lengthways and wraps onto the second row of pixels, causing staggering to occur.

So if you have 5 red and 5 white pixels, and you want a line length of 55 pixels, either change the length to a multiple of 10, or change the dashes to, say, 6 red and 5 white.

`

Anonymous

12 years ago

`a shortcut for basic dashed lines, making it easy to adjust the lengths:

length2=10;<spanclass="katex"><spanclass="katex−mathml"><mathxmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>s</mi><mi>t</mi><mi>y</mi><mi>l</mi><mi>e</mi><mo>=</mo><mi>a</mi><mi>r</mi><mi>r</mi><mi>a</mi><msub><mi>y</mi><mi>m</mi></msub><mi>e</mi><mi>r</mi><mi>g</mi><mi>e</mi><mostretchy="false">(</mo><mi>a</mi><mi>r</mi><mi>r</mi><mi>a</mi><msub><mi>y</mi><mi>f</mi></msub><mi>i</mi><mi>l</mi><mi>l</mi><mostretchy="false">(</mo><mn>0</mn><moseparator="true">,</mo></mrow><annotationencoding="application/x−tex">style=arraymerge(arrayfill(0,</annotation></semantics></math></span><spanclass="katex−html"aria−hidden="true"><spanclass="base"><spanclass="strut"style="height:0.8889em;vertical−align:−0.1944em;"></span><spanclass="mordmathnormal">s</span><spanclass="mordmathnormal">t</span><spanclass="mordmathnormal"style="margin−right:0.03588em;">y</span><spanclass="mordmathnormal"style="margin−right:0.01968em;">l</span><spanclass="mordmathnormal">e</span><spanclass="mspace"style="margin−right:0.2778em;"></span><spanclass="mrel">=</span><spanclass="mspace"style="margin−right:0.2778em;"></span></span><spanclass="base"><spanclass="strut"style="height:1.0361em;vertical−align:−0.2861em;"></span><spanclass="mordmathnormal">a</span><spanclass="mordmathnormal"style="margin−right:0.02778em;">rr</span><spanclass="mordmathnormal">a</span><spanclass="mord"><spanclass="mordmathnormal"style="margin−right:0.03588em;">y</span><spanclass="msupsub"><spanclass="vlist−tvlist−t2"><spanclass="vlist−r"><spanclass="vlist"style="height:0.1514em;"><spanstyle="top:−2.55em;margin−left:−0.0359em;margin−right:0.05em;"><spanclass="pstrut"style="height:2.7em;"></span><spanclass="sizingreset−size6size3mtight"><spanclass="mordmathnormalmtight">m</span></span></span></span><spanclass="vlist−s">​</span></span><spanclass="vlist−r"><spanclass="vlist"style="height:0.15em;"><span></span></span></span></span></span></span><spanclass="mordmathnormal"style="margin−right:0.02778em;">er</span><spanclass="mordmathnormal"style="margin−right:0.03588em;">g</span><spanclass="mordmathnormal">e</span><spanclass="mopen">(</span><spanclass="mordmathnormal">a</span><spanclass="mordmathnormal"style="margin−right:0.02778em;">rr</span><spanclass="mordmathnormal">a</span><spanclass="mord"><spanclass="mordmathnormal"style="margin−right:0.03588em;">y</span><spanclass="msupsub"><spanclass="vlist−tvlist−t2"><spanclass="vlist−r"><spanclass="vlist"style="height:0.3361em;"><spanstyle="top:−2.55em;margin−left:−0.0359em;margin−right:0.05em;"><spanclass="pstrut"style="height:2.7em;"></span><spanclass="sizingreset−size6size3mtight"><spanclass="mordmathnormalmtight"style="margin−right:0.10764em;">f</span></span></span></span><spanclass="vlist−s">​</span></span><spanclass="vlist−r"><spanclass="vlist"style="height:0.2861em;"><span></span></span></span></span></span></span><spanclass="mordmathnormal">i</span><spanclass="mordmathnormal"style="margin−right:0.01968em;">ll</span><spanclass="mopen">(</span><spanclass="mord">0</span><spanclass="mpunct">,</span></span></span></span>length1,length2 = 10; <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>s</mi><mi>t</mi><mi>y</mi><mi>l</mi><mi>e</mi><mo>=</mo><mi>a</mi><mi>r</mi><mi>r</mi><mi>a</mi><msub><mi>y</mi><mi>m</mi></msub><mi>e</mi><mi>r</mi><mi>g</mi><mi>e</mi><mo stretchy="false">(</mo><mi>a</mi><mi>r</mi><mi>r</mi><mi>a</mi><msub><mi>y</mi><mi>f</mi></msub><mi>i</mi><mi>l</mi><mi>l</mi><mo stretchy="false">(</mo><mn>0</mn><mo separator="true">,</mo></mrow><annotation encoding="application/x-tex">style = array_merge(array_fill(0, </annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord mathnormal">s</span><span class="mord mathnormal">t</span><span class="mord mathnormal" style="margin-right:0.03588em;">y</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord mathnormal">e</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.0361em;vertical-align:-0.2861em;"></span><span class="mord mathnormal">a</span><span class="mord mathnormal" style="margin-right:0.02778em;">rr</span><span class="mord mathnormal">a</span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">y</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em;"><span style="top:-2.55em;margin-left:-0.0359em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">m</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mord mathnormal" style="margin-right:0.02778em;">er</span><span class="mord mathnormal" style="margin-right:0.03588em;">g</span><span class="mord mathnormal">e</span><span class="mopen">(</span><span class="mord mathnormal">a</span><span class="mord mathnormal" style="margin-right:0.02778em;">rr</span><span class="mord mathnormal">a</span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">y</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361em;"><span style="top:-2.55em;margin-left:-0.0359em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.10764em;">f</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2861em;"><span></span></span></span></span></span></span><span class="mord mathnormal">i</span><span class="mord mathnormal" style="margin-right:0.01968em;">ll</span><span class="mopen">(</span><span class="mord">0</span><span class="mpunct">,</span></span></span></span>length1, length2=10;<spanclass="katex"><spanclass="katexmathml"><mathxmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>s</mi><mi>t</mi><mi>y</mi><mi>l</mi><mi>e</mi><mo>=</mo><mi>a</mi><mi>r</mi><mi>r</mi><mi>a</mi><msub><mi>y</mi><mi>m</mi></msub><mi>e</mi><mi>r</mi><mi>g</mi><mi>e</mi><mostretchy="false">(</mo><mi>a</mi><mi>r</mi><mi>r</mi><mi>a</mi><msub><mi>y</mi><mi>f</mi></msub><mi>i</mi><mi>l</mi><mi>l</mi><mostretchy="false">(</mo><mn>0</mn><moseparator="true">,</mo></mrow><annotationencoding="application/xtex">style=arraymerge(arrayfill(0,</annotation></semantics></math></span><spanclass="katexhtml"ariahidden="true"><spanclass="base"><spanclass="strut"style="height:0.8889em;verticalalign:0.1944em;"></span><spanclass="mordmathnormal">s</span><spanclass="mordmathnormal">t</span><spanclass="mordmathnormal"style="marginright:0.03588em;">y</span><spanclass="mordmathnormal"style="marginright:0.01968em;">l</span><spanclass="mordmathnormal">e</span><spanclass="mspace"style="marginright:0.2778em;"></span><spanclass="mrel">=</span><spanclass="mspace"style="marginright:0.2778em;"></span></span><spanclass="base"><spanclass="strut"style="height:1.0361em;verticalalign:0.2861em;"></span><spanclass="mordmathnormal">a</span><spanclass="mordmathnormal"style="marginright:0.02778em;">rr</span><spanclass="mordmathnormal">a</span><spanclass="mord"><spanclass="mordmathnormal"style="marginright:0.03588em;">y</span><spanclass="msupsub"><spanclass="vlisttvlistt2"><spanclass="vlistr"><spanclass="vlist"style="height:0.1514em;"><spanstyle="top:2.55em;marginleft:0.0359em;marginright:0.05em;"><spanclass="pstrut"style="height:2.7em;"></span><spanclass="sizingresetsize6size3mtight"><spanclass="mordmathnormalmtight">m</span></span></span></span><spanclass="vlists"></span></span><spanclass="vlistr"><spanclass="vlist"style="height:0.15em;"><span></span></span></span></span></span></span><spanclass="mordmathnormal"style="marginright:0.02778em;">er</span><spanclass="mordmathnormal"style="marginright:0.03588em;">g</span><spanclass="mordmathnormal">e</span><spanclass="mopen">(</span><spanclass="mordmathnormal">a</span><spanclass="mordmathnormal"style="marginright:0.02778em;">rr</span><spanclass="mordmathnormal">a</span><spanclass="mord"><spanclass="mordmathnormal"style="marginright:0.03588em;">y</span><spanclass="msupsub"><spanclass="vlisttvlistt2"><spanclass="vlistr"><spanclass="vlist"style="height:0.3361em;"><spanstyle="top:2.55em;marginleft:0.0359em;marginright:0.05em;"><spanclass="pstrut"style="height:2.7em;"></span><spanclass="sizingresetsize6size3mtight"><spanclass="mordmathnormalmtight"style="marginright:0.10764em;">f</span></span></span></span><spanclass="vlists"></span></span><spanclass="vlistr"><spanclass="vlist"style="height:0.2861em;"><span></span></span></span></span></span></span><spanclass="mordmathnormal">i</span><spanclass="mordmathnormal"style="marginright:0.01968em;">ll</span><spanclass="mopen">(</span><spanclass="mord">0</span><spanclass="mpunct">,</span></span></span></span>length1,red), array_fill(0, length2,length2, length2,w)); imagesetstyle($im, $style);?>

`

Wander

17 years ago

`Function to make a line with random fading:

r=rand(0,5);r=rand(0,5);r=rand(0,5);g=rand(0,5);$b=rand(0,5); l=sqrt(((l=sqrt(((l=sqrt(((ex-$sx)*($ex-$sx))+(($ey-$sy)*($ey-$sy))); for($i=0;$i<$l;$i++){ a=array(255−((255/a = array(255-((255/a=array(255((255/l)*$i), 255,0,(255/$l)*$i/2,(255/$l)*$i,(255-((255/$l)*$i))/2); style[]=imagecolorallocate(style[]=imagecolorallocate(style[]=imagecolorallocate(img,$a[$r],$a[$g],$a[$b]); } imagesetstyle($img,$style); imageline($img,$sx,$sy,$ex,$ey,IMG_COLOR_STYLED); }fading_line($img,10,20,490,40); // image, start x, start y, end x, end y ?>

`

Cruz at FtUC dot net

19 years ago

`When lines drawn with imagesetstyle seem to produce a thin white line only, make sure antialiasing is disabled.

style=array(style = array(style=array(gridxcolor, $gridxcolor, IMG_COLOR_TRANSPARENT, IMG_COLOR_TRANSPARENT); imagesetstyle($im, $style); imageline($im, x,0,x, 0, x,0,x, $ymax+5, IMG_COLOR_STYLED); imageantialias($im, true); ?>

Setstyle and Antialias don't go together.

`

php at imperium dot be

14 years ago

`Be aware that styles are applied towards the width of the line instead of linear.
To convert a style to be used for thick lines you can use the function below:

,) --> is the style array for a thickness of 1 (see imagesetstyle()). is the new thickness to apply (see imagesetthickness()). is the style array suitable for the given thickness. */ function ImageStyleThicken($_1,$_2) { $a = array(); foreach ($_1 as $x) { i=i = i=_2; do a[]=a[] = a[]=x; while (--$i>0); } return $a; } ?>

`

zackbloom at gmail dot com

19 years ago

`Use this to set the style to any combination of pixels.
You can pass as many modifiers as you wish.
Use the format [num]r[red]g[green]b[blue].

For example: im=dashed(im=dashed(im=dashed(im,"4r255g0b0","2r0g255b0","5r0g0b255");
imageline($im, 0, 0, 600, 600, IMG_COLOR_STYLED);

function dashed($im){
$size = func_num_args();
for($i = 0; i<i < i<size; $i++){ arg=funcgetarg(arg = func_get_arg(arg=funcgetarg(i);
if(!is_resource($arg)){ r=substr(r=substr(r=substr(arg,strpos($arg,"r")+1,
strpos($arg,"g")-strpos($arg,"r")-1); g=substr(g=substr(g=substr(arg,strpos($arg,"g")+1,
strpos($arg,"b")-strpos($arg,"g")-1); b=substr(b=substr(b=substr(arg,strpos($arg,"b")+1,
strlen($arg)-strpos($arg,"b")); color=imagecolorallocate(color = imagecolorallocate(color=imagecolorallocate(im,$r,$g,$b); x=substr(x = substr(x=substr(arg,0,strpos($arg,"r")); vals[vals[vals[i] = array_fill(0,$x,$color);
}
}
for($k=0;$k<count($vals)+1;$k++)
if(array_key_exists($k,$vals)) prop=arraymerge(prop=array_merge(prop=arraymerge(prop,$vals[$k]);
imagesetstyle($im, $prop);
return $im;
}

`