Isotopic Approximation of Implicit Curves and Surfaces

Plantinga, Simon; Vegter, Gert

Isotopic Approximation of Implicit Curves and Surfaces

Files

251-260.pdf (2.14 MB)

Date

2004

Authors

Plantinga, Simon
Vegter, Gert

Publisher

The Eurographics Association

Abstract

Implicit surfaces are defined as the zero set of a function F : R<sup>3</sup>-> R. Although several algorithms exist for generating piecewise linear approximations, most of them are based on a user-defined stepsize or bounds to indicate the precision, and therefore cannot guarantee topological correctness. Interval arithmetic provides a mechanism to determine global properties of the implicit function. In this paper we present an algorithm that uses these properties to generate a piecewise linear approximation of implicit curves and surfaces, that is isotopic to the curve or surface itself. The algorithm is simple and fast, and is among the first to guarantee isotopy for implicit surface meshing.

        @inproceedings{10.2312:SGP/SGP04/251-260
,
booktitle = {Symposium on Geometry Processing
},
editor = {Roberto Scopigno and Denis Zorin
},
title = {{Isotopic Approximation of Implicit Curves and Surfaces
}},
author = {Plantinga, Simon and 
Vegter, Gert
},
year = {2004
},
publisher = {The Eurographics Association
},
ISSN = {1727-8384
},
ISBN = {3-905673-13-4
},
DOI = {10.2312/SGP/SGP04/251-260
}
}