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  Simple and Efficient Polygonization of Implicit Surfaces (1996) [26 citations — 3 self]

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by Luiz Velho
Journal of Graphics Tools
http://www.visgraf.impa.br/RefBib/Data/PS_PDF/luizvelho96a/jgt96.ps.gz
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Abstract:

This paper describes a simple and efficient polygonization algorithm that gives a practical way to construct adapted piecewise linear representations of implicit surfaces. The method starts with a coarse uniform polygonal approximation of the surface and subdivides each polygon recursively according to local curvature. In that way, the inherent complexity of the problem is tamed by separating structuring from sampling and reducing part of the full three dimensional search to two dimensions. 1

Citations

1350 Marching Cubes: A high resolution 3D surface construction algorithm – Lorensen, Cline - 1987
517 Decimation of Triangle Meshes – Schroeder, Zarge, et al. - 1992
293 Introduction to implicit sur-faces – Bloomenthal, editor - 1997
285 A Generalization Of Algebraic Surface Drawing – Blinn - 1982
243 Data structures for soft objects – Wyvill, McPheeters - 1986
189 Representations for rigid solids: Theory methods, and systems – Requicha - 1980
115 Regular Polytopes – Coxeter - 1973
72 Collision detection by four-dimensional intersection testing – Cameron - 1990
39 Adaptive Polygonalization of Implicitly Defined Surfaces – Hall, Warren - 1990
37 An algorithm for piecewise linear approximation of an implicitly defined manifold – Allgower, Gnutzmann - 1987
28 Physically-Based Methods for Polygonization of Implicit Surfaces – Figueiredo, Gomes, et al. - 1992
19 Adaptive polygonization of implicit surfaces using simplicial decomposition and boundary constraints – Velho - 1990
11 Practical uses for implicit surfaces in animation – Beier - 1993
11 Computational morphology of curves – Figueiredo, Gomes - 1994
4 The algebraic properties of homogeneous second order surfaces – Blinn - 1984
4 A functional view of proteins – Olson, Goodsell - 1991
4 casting as a method for solid modeling – Ray - 1982
3 Using implicit surfaces to blend arbitrary solid models – Rockwood, Owen - 1987
2 Graphics Gems IV, volume 4, chapter An Implicit Surface Polygonizer – Bloomenthal - 1994
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