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Abstract: Many algorithms for reducing the number of triangles in a surface model have been proposed, but to date there has been little theoretical analysis of the approximations they produce. Previously we described an algorithm that simplifies polygonal models using a quadric error metric. This method is fast and produces high quality approximations in practice. Here we provide some theory to explain why the algorithm works as well as it does. Using methods from differential geometry and approximation... (Update)
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BibTeX entry: (Update)
P. Heckbert and M. Garland, "Optimal Triangulation and Quadric-Based Surface Simplification," submitted for publication. http://citeseer.ist.psu.edu/heckbert99optimal.html More
@article{ heckbert99optimal,
author = "Paul S. Heckbert and Michael Garland",
title = "Optimal triangulation and quadric-based surface simplification",
journal = "Computational Geometry",
volume = "14",
number = "1-3",
pages = "49-65",
year = "1999",
url = "citeseer.ist.psu.edu/heckbert99optimal.html" }
Citations (may not include all citations):430 Progressive meshes - Hoppe - 1996
298 Surface simplification using quadric error metrics - Garland, Heckbert - 1997
131 Simplification envelopes - Cohen, Varshney et al. - 1996
99 Full-range approximation of triangulated polyhedra (context) - Ronfard, Rossignac - 1996
72 Unsolved Problems in Geometry (context) - Croft, Falconer et al. - 1991
67 Simplifying surfaces with color and texture using quadric er.. - Garland, Heckbert - 1998
38 Geometry and the Imagination (context) - Hilbert, Cohn-Vossen - 1952
35 Invariant surface characteristics for 3D object recognition .. (context) - Besl, Jain - 1986
26 Quadric-based polygonal surface simplification - Garland - 1999
26 On optimal interpolation triangle incidences (context) - D'Azevedo, Simpson - 1989
25 Long and thin triangles can be good for linear interpolation (context) - Rippa - 1992
24 A pliant method for anisotropic mesh generation - Bossen, Heckbert - 1996
20 Anisotropic mesh transformations and optimal error control - Simpson - 1994
15 Adaptive remeshing for three-dimensional compressible flow c.. (context) - Peraire, Peir - 1992
11 Introduction to Differential Geometry and Riemannian Geometr.. (context) - Kreyszig - 1968
10 An efficient algorithm for terrain simplifications - Agarwal, Desikan - 1997
10 Piecewise linear best L 2 approximation on triangulations (context) - Nadler - 1986
3 Optimal triangular mesh generation by coordinate transformat.. (context) - D'Azevedo - 1991
2 Surface simplification inside a tolerance volume (context) - Guziec - 2044
2 Unit surface mesh simplification (context) - Frey, Borouchaki - 1997
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