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Abstract: We discuss the problem of adaptive polygonization of regular surfaces of the euclidean 3D space, and present effective algorithms for computing optimal polygonizations of surfaces described in parametric or implicit form. Keywords: Surface approximation, polygonization, parametric surfaces, implicit surfaces, geometric modeling. 1 Introduction The polygonization of surfaces is a classical problem in computer graphics and geometric modeling that has many practical applications. The problem... (Update)
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...ray tracing [18] especially for objects with high algebraic degree. Other solutions are based on enumeration algorithms [3, 6, 7, 11, 12, 22, 30, 31], marching squares cubes triangles [1, 14, 27] particle systems [10, 17] or stochastic differential equations [25] These...
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1.1: Adaptive Polygonal Approximation of Parametric Surfaces.. - Velho, al. (Correct)
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BibTeX entry: (Update)
L. Velho, L. H. de Figueiredo and J. Gomes, A methodology for piecewise linear approximation of surfaces. Journal of the Brazilian Computer Society, 3(3), 1997, pp. 30--42. http://citeseer.nj.nec.com/article/velho97methodology.html More
@article{ velho97methodology,
author = "Luiz Velho and Luiz Henrique {de Figueiredo} and Jonas Gomes",
title = "A methodology for piecewise linear approximation of surfaces",
journal = "Journal of the Brazilian Computer Society",
volume = "3",
number = "3",
pages = "30--42",
year = "1997",
url = "citeseer.nj.nec.com/article/velho97methodology.html" }
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141 A generalization of algebraic surface drawing (context) - Blinn - 1982
83 Polygonization of implicit surfaces - Bloomenthal - 1988
66 Interval analysis for computer graphics - Snyder - 1992
57 Regular Polytopes (context) - Coxeter - 1963
52 Interval arithmetic and recursive subdivision for implicit f.. (context) - Duff - 1992
51 Computer Methods for the Range of Functions (context) - Ratschek, Rokne - 1984
51 A theoretical development for the computer generation and di.. (context) - Lane, Riesenfeld - 1980
48 An algorithm for piecewise linear approximation of an implic.. (context) - Allgower, Schmidt - 1985
45 An iterative procedure for the polygonal approximation of pl.. (context) - Ramer - 1972
43 An implicit surface polygonizer - Bloomenthal - 1994
36 Introduction to Piecewise Linear Topology (context) - Rourke, Sanderson - 1982
27 Accurate triangulations of deformed (context) - Von Herzen, Barr - 1987
25 Modeling with cubic A-Patches - Bajaj, Chen et al. - 1995
23 Computer Graphics (context) - Perlin, Hoffert - 1989
22 Interval methods in computer graphics (context) - Suffern, Fackerell - 1991
18 Interval methods for processing geometric objects (context) - Mudur, Koparkar - 1984
17 A fast algorithm for rendering parametric surfaces (context) - Clark - 1988
17 An adaptive subdivision algorithm for crack prevention in th.. (context) - Forsey, Klassen - 1990
15 Adaptive polygonization of implicitly defined surfaces (context) - Hall, Warren - 1990
14 Adaptive polygonization of implicit surfaces using simplicia.. (context) - Velho - 1990
11 Adaptive enumeration of implicit surfaces with affine arithm.. (context) - de Figueiredo, Stolfi - 1996
7 Approximate conversion of parametric to implicit surfaces - Velho, Gomes - 1996
7 Computational techniques for processing parametric surfaces (context) - Koparkar, Mudur - 1984
7 Adaptive subdivision algorithms for a set of B'ezier triangl.. (context) - Filip - 1986
7 Curvature-dependent parametrization of curves and surfaces (context) - Kosters - 1991
7 Tessellation of NURB surfaces (context) - Peterson - 1994
6 Linear approximation of curves with bounded curvature and a .. (context) - Crampin, Guifo et al. - 1985
6 Implicit Objects in Computer Graphics (context) - Gomes, Velho - 1993
5 A recursive technique for rendering parametric curves (context) - Chandler - 1990
5 Efficient adaptive subdivision of B'ezier surfaces (context) - Clay, Moreton - 1988
5 A generalized scan line algorithm for the computer display o.. (context) - Lane, Carpenter - 1979
5 An integrity filter for recursive subdivision meshes (context) - Tamminen, Jansen - 1985
5 Sampling implicit objects with physically-based particle sys.. - de Figueiredo, Gomes - 1996
4 Optimal adaptive polygonal approximation of parametric surfa.. - Velho, de Figueiredo - 1996
4 personal communication (context) - Beier - 1990
4 Adaptive polygonization made simple - Velho - 1995
3 Adaptive sampling of parametric curves - de Figueiredo - 1995
3 Explicating implicit surfaces (context) - Wyvill - 1994
2 Interactive modeling of soft objects (context) - Velho - 1990
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