Transitive mesh space of a progressive mesh (original) (raw)
Abstract
This paper investigates the set of all selectively refined meshes that can be obtained from a progressive mesh. We call the set the transitive mesh space of a progressive mesh and present a theoretical analysis of the space. We define selective edge collapse and vertex split transformations, which we use to traverse all selectively refined meshes in the transitive mesh space. We propose a complete selective refinement scheme for a progressive mesh based on the transformations and compare the scheme with previous selective refinement schemes in both theoretical and experimental ways. In our comparison, we show that the complete scheme always generates selectively refined meshes with smaller numbers of vertices and faces than previous schemes for a given refinement criterion. The concept of dual pieces of the vertices in the vertex hierarchy plays a central role in the analysis of the transitive mesh space and the design of selective edge collapse and vertex split transformations.
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References (29)
- P. S. Heckbert and M. Garland, "Survey of polygonal surface simplification algorithms," SIGGRAPH '97 Course Notes # 25, 1997.
- P. Cignoni, C. Montani, and R. Scopigno, "A comparison of mesh simplification algorithms," Computers & Graphics, vol. 22, no. 1, pp. 37-54, 1998.
- D. Luebke, "A developer's survey of polygonal simplification algorithms," IEEE Computer Graphics and Applications, vol. 21, no. 3, pp. 24-35, 2001.
- H. Hoppe, "Progressive meshes," ACM Computer Graphics (Proc. SIGGRAPH '96), pp. 99- 108, 1996.
- H. Hoppe, "View-dependent refinement of progressive meshes," ACM Computer Graphics (Proc. SIGGRAPH '97), pp. 189-198, 1997.
- L. Kobbelt, S. Campagna, J. Vorsatz, and H.-P. Seidel, "Interactive multi-resolution modeling on arbitrary meshes," ACM Computer Graphics (Proc. SIGGRAPH '98), pp. 105-114, 1998.
- I. Guskov, W. Sweldens, and P. Schröder, "Multiresolution signal processing for meshes," ACM Computer Graphics (Proc. SIGGRAPH '99), pp. 325-334, 1999.
- R. Pajarola and J. Rossignac, "Compressed progressive meshes," IEEE Trans. Visualization and Computer Graphics, vol. 6, no. 1, pp. 79-93, 2000.
- J. C. Xia and A. Varshney, "Dynamic view-dependent simplification for polygonal models," in Proc. IEEE Visualization '96, pp. 327-334, 1996.
- J. El-Sana and A. Varshney, "Generalized view-dependent simplification," Computer Graph- ics Forum (Proc. Eurographics'99), vol. 18, no. 3, pp. 83-94, 1999.
- J. Kim and S. Lee, "Truly selective refinement of progressive meshes," in Proc. Graphics Interface 2001, pp. 101-110, 2001.
- R. Pajarola, "Fastmesh: Efficient view-depenent meshing," in Proc. Pacific Graphics 2001, pp. 22-30, IEEE Computer Society Press, 2001.
- P. Lindstrom, D. Koller, W. Ribarsky, L. F. Hodges, N. Faust, and G. A. Turner, "Real- time, continuous level of detail rendering of height fields," ACM Computer Graphics (Proc. SIGGRAPH '96), pp. 109-118, 1996.
- H. Hoppe, "Smooth view-dependent level-of-detail control and its application to terrain ren- dering," in Proc. IEEE Visualization '98, pp. 35-42, 1998.
- J. Rossignac and P. Borrel, "Multi-resolution 3D approximations for rendering complex scenes," in Geometric Modeling in Computer Graphics (B. Falcidieno and T. L. Kunii, eds.), pp. 455-465, Springer-Verlag, 1993.
- W. J. Schroeder, J. A. Zarge, and W. E. Lorensen, "Decimation of triangle meshes," ACM Computer Graphics (Proc. SIGGRAPH '92), pp. 65-70, 1992.
- D. Luebke and C. Erikson, "View-dependent simplification of arbitrary polygonal environ- ment," ACM Computer Graphics (Proc. SIGGRAPH '97), pp. 199-208, 1997.
- D. Schmalstieg and G. Schaufler, "Smooth levels of detail," in Proc. IEEE VRAIS '97, pp. 12- 19, 1997.
- L. D. Floriani, P. Magillo, and E. Puppo, "Efficient implementation of multi-triangluation," in Proc. IEEE Visualization '98, pp. 18-23, 1998.
- H. Hoppe, T. DeRose, T. Dunchamp, J. McDonald, and W. Stuetzle, "Mesh optimization," Tech. Rep. TR 93-01-01, University of Washington, 1993.
- T. K. Dey, H. Edelsbrunner, S. Guha, and D. V. Nekhayev, "Topology preserving edge con- traction," Tech. Rep. rgi-tech-98-018, Raindrop Geomagic, 1998.
- A. J. Willmott, P. S. Heckbert, and M. Garland, "Face cluster radiosity," in Rendering Tech- niques '99 (Proc. 10th Eurographics Workshop on Rendering), pp. 293-304, 1999.
- M. Garland, A. Willmott, and P. S. Heckbert, "Hierarchical face clustering on polygonal surfaces," in Proc. 2001 ACM Symposium on Interactive 3D Graphics, pp. 49-58, 2001.
- C. C. Pinter, Set Theory. Addison-Wesley, 1971.
- T. H. Cormen, C. E. Leiserson, and R. L. Rivest, Introduction to Algorithms. MIT Press, 1990.
- M. Garland and P. S. Heckbert, "Surface simplification using quadric error metrics," ACM Computer Graphics (Proc. SIGGRAPH '97), pp. 209-216, 1997.
- L. A. Shirman and S. S. Abi-Ezzi, "The cone of normals technique for fast processing of curved patches," Computer Graphics Forum (Proc. Eurographics'93), vol. 12, no. 3, pp. 261- 272, 1993.
- T. Gieng, B. Hamann, K. I. Joy, G. L. Schussman, and I. J. Trotts, "Constructing hierar- chies for triangle meshes," IEEE Trans. Visualization and Computer Graphics, vol. 4, no. 2, pp. 145-161, 1998.
- I. Guskov and Z. J. Wood, "Topological noise removal," in Proc. Graphics Interface 2001, pp. 19-26, 2001.