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Polygonization of Implicit Surfaces (1988)

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by Jules Bloomenthal
Citations:323 - 3 self
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BibTeX

@MISC{Bloomenthal88polygonizationof,
    author = {Jules Bloomenthal},
    title = {Polygonization of Implicit Surfaces},
    year = {1988}
}

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Abstract

This paper discusses a numerical technique that approximates an implicit surface with a polygonal representation. The implicit function is adaptively sampled as it is surrounded by a spatial partitioning. The partitioning is represented by an octree, which may either converge to the surface or track it. A piecewise polygonal representation is derived from the octree.

Citations

363 The Quadtree and Related Hierarchical Data Structures - Samet - 1984
330 A generalization of algebraic surface drawing - Blinn - 1982
255 B.: Data structures for soft objects - Wyvill, McPheeters, et al. - 1986
235 Stochastic sampling in computer graphics - Cook - 1986
179 Regular polytopes - Coxeter - 1973
152 Numerical methods - Dahlquist, Bjorek - 1974
73 Modeling the mighty maple - BLOOMENTHAL - 1985
71 Representation and Description of Curved Objects - Agin - 1972
69 Accurate triangulations of deformed, intersecting surfaces - Herzen, Barr - 1987
65 Solid modeling: a historical summary and contemporary assessment - Requicha, Voelcker - 1982
51 The theory, design, implementation and evaluation of a three-dimensional surface detection algorithm. Computer Graphics and Image Processing, 15:1–24 - Artzy, Frieder, et al. - 1981
40 Numerical Grid Generation. Foundations and Applications - Thompson, Warsi, et al. - 1985
31 Simplicial and continuation methods for approximating fixed points and solutions to systems of equations - Allgower, Georg - 1980
30 An algorithm for piecewise linear approximation of implicitly defined two-dimensional surfaces - Allgower, Gnutzmann - 1987
17 The potential method for blending surfaces and corners - Hoffmann, Hopcroft - 1987
12 Cylindrical algebraic decomposition I - Arnon, Collins, et al. - 1984
9 Geometric Modeling Using Octree Encoding, Comput - Meagher - 1982
5 A survey of ray-surface intersection algorithms - Hanrahan - 1989
4 Automatic contour map - COTTAFAVA, MOLI - 1969
2 Contour Tracing by - Dobkin, Levy, et al. - 1988
1 Personal Communication regarding a 1983, unpublished report on the contouring of analytic functions - Hunter - 1987
1 Algebraic geometry for computer-aided geometric design - PARC, CSL-87-2 - 1987
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