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Abstract: We discuss the problem of adaptive polygonization of regular surfaces of the euclidean 3D space, and present e#ective 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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1.8: A Unified Approach for Hierarchical Adaptive Tesselation .. - Velho, de Figueiredo.. (2000) (Correct)
0.6: Sampling implicit objects with physically-based particle.. - de Figueiredo, Gomes (1996) (Correct)
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1.2: 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/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/velho97methodology.html" }
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83 Polygonization of implicit surfaces - Bloomenthal - 1988
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29 erential Geometry of Curves and Surfaces (context) - Carmo - 1976
24 Computer Graphics (context) - Perlin, Ho et al. - 1989
22 Interval methods in computer graphics (context) - Su, Fackerell - 1991
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17 An adaptive subdivision algorithm for crack prevention in th.. (context) - Forsey, Klassen - 1990
17 A fast algorithm for rendering parametric surfaces (context) - Clark - 1988
15 Adaptive polygonization of implicitly defined surfaces (context) - Hall, Warren - 1990
14 Adaptive polygonization of implicit surfaces using simplicia.. (context) - Velho - 1990
12 Accurate triangulations of deformed (context) - Von Herzen, Barr - 1987
9 Interval arithmetic and recursive subdivision for implicit f.. (context) - Du - 1992
8 Adaptive subdivision algorithms for a set of Bezier triangle.. (context) - Filip - 1986
7 Computational techniques for processing parametric surfaces (context) - Koparkar, Mudur - 1984
7 Tessellation of NURB surfaces (context) - Peterson - 1994
7 Approximate conversion of parametric to implicit surfaces - Velho, Gomes - 1995
7 Curvature-dependent parametrization of curves and surfaces (context) - Kosters - 1991
6 Implicit Objects in Computer Graphics (context) - Gomes, Velho - 1993
6 Linear approximation of curves with bounded curvature and a .. (context) - Crampin, Guifo et al. - 1985
5 A recursive technique for rendering parametric curves (context) - Chandler - 1990
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5 A generalized scan line algorithm for the computer display o.. (context) - Lane, Carpenter - 1979
4 Adaptive polygonization made simple - Velho - 1995
4 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
3 Explicating implicit surfaces (context) - Wyvill - 1994
3 Adaptive sampling of parametric curves (context) - de Figueiredo - 1995
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2 Interactive modeling of soft objects (context) - Velho - 1990
1 University of Minnesota (context) - at, Center
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