Efficient Surface Reconstruction using Generalized Coulomb Potentials
IEEE Transactions on Visualization and Computer Graphics
Exact geometric-topological analysis of algebraic surfaces
Proceedings of the twenty-fourth annual symposium on Computational geometry
From Segmented Images to Good Quality Meshes Using Delaunay Refinement
Emerging Trends in Visual Computing
An efficient algorithm for the stratification and triangulation of an algebraic surface
Computational Geometry: Theory and Applications
Ambient Isotopic Meshing for Implicit Algebraic Surfaces with Singularities
CASC '09 Proceedings of the 11th International Workshop on Computer Algebra in Scientific Computing
Certified computation of planar morse-smale complexes
Proceedings of the twenty-eighth annual symposium on Computational geometry
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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.