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Simple and Efficient Polygonization of Implicit Surfaces
"... 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 ..."
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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.
Adaptive polygonization made simple
 In Proceedings of SIBGRAPI '95
, 1995
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Piecewise Descriptions of Implicit Surfaces and Solids
, 1994
"... This thesis presents a complete framework for the description of implicit surfaces and solids. We propose piecewise representations that are based on decomposition models and constructed using methods adapted to the geometry of objects. These models are general, in the sense that they can represent ..."
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This thesis presents a complete framework for the description of implicit surfaces and solids. We propose piecewise representations that are based on decomposition models and constructed using methods adapted to the geometry of objects. These models are general, in the sense that they can represent arbitrary shapes, and support variable precision, permitting approximations at any desirable resolution. The contribution of our work consists of: (i) an original characterization of the implicit description of shapes, (ii) a new method for generating a smooth implicit function corresponding to a solid object, and (iii) two new piecewise representation schemes based on a multiscale decomposition of the implicit function and on an adapted simplicial decomposition of the domain of the implicit function. We characterize the implicit model through an analysis of the implicit function. We show that the skeleton of a shape and the tubular neighborhood of its boundary are dual structures that relate an object with the space in which it is embedded. We develop a method that allows the generation of smooth implicit functions from