Surface Reconstruction | --.----.2000 | GFX |
by Hin Jang
[ -- incomplete first draft -- ]
[1] Forsey, D., and D. Wong, Multiresolution Surface Reconstruction For Hierarchical B-splines, Department of Computer Science, University of British Columbia, 1995[2] Hoppe, H., T. DeRose, T. Duchamp, M. Halstead, H. Jin, J. McDonald, J. Schweitzer, and W. Stuetzle, "Piecewise Smooth Surface Reconstruction," Computer Graphics, SIGGRAPH 1994 Proceedings, 28(4):295-302
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Mesh Optimisation | --.----.2000 | GFX |
by Hin Jang
[ -- incomplete first draft -- ]
Mesh optimisation is means by which that a given set of data points X, distributed in three dimensions, and an initial triangular mesh M can be represented by a mesh M' such that M' maintains the same topological type as M but with a fewer number of vertices. The solution to the mesh optimisation problem is to minimize an energy function [4]. This function represents the goal to find a tight geometric fit to the original mesh with a compact representation (i.e., a smaller number of vertices). Hoppe et al have developed an algorithm that can also be applied to surface reconstruction and mesh simplification.
A mesh is a piecewise linear surface consisting of triangles connected together along their edges. The simplical complex K of a triangle is
vertices: {1}, {2}, {3} edges: {1, 2}, {2, 3}, {1, 3} faces: {1, 2, 3}
[1] Brown, P.J.C., A Fast Algorithm for Selective Refinement of Terrain Meshes, TR-417, Computer Laboratory, University of Cambridge, UK, February 1997[2] Brown, P.J.C., and C.T. Faigle A Robust Efficient Algorithm for Point Location in Triangulations, Computer Laboratory, University of Cambridge, UK, February 27, 1997
[3] Chow, M.M., "Optimised Geometry Compression for Real-time Rendering," 1997 IEEE Visualisation Conference
[4] Hoppe, H., T. DeRose, T. Duchamp, J. McDonald, and W. Stuetzle, "Mesh Optimisation," Computer Graphics, SIGGRAPH 1993 Proceedings, 27(4):19-26
[5] Hoppe, H., "Progressive Meshes," Computer Graphics, SIGGRAPH 1996 Proceedings, 30(4):99-108
[6] Mavriplis, D.J., Adaptive Meshing Techniques for Viscous Flow Calculations on Mixed Element Unstructured Meshes, NASA CR-201675 ICASE Report No. 97-20, May 1997