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Isotopic meshing of implicit surfaces

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Abstract

Implicit surfaces are given as the zero set of a function F:ℝ3→ℝ. Although several algorithms exist for generating piecewise linear approximations, most of these 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.

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Authors and Affiliations

  1. University of Groningen, Groningen, The Netherlands

    Simon Plantinga & Gert Vegter

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  1. Simon Plantinga
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  2. Gert Vegter
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Correspondence to Simon Plantinga.

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Plantinga, S., Vegter, G. Isotopic meshing of implicit surfaces. Visual Comput 23, 45–58 (2007). https://doi.org/10.1007/s00371-006-0083-6

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  • DOI: https://doi.org/10.1007/s00371-006-0083-6

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