Continuation Methods for Approximating Isovalued Complex Surfaces

Abstract

Basically there are two different approaches for rendering isovalued surfaces in 3D space: projection methods and surface reconstruction. We are discussing two algorithms of the second kind. Both use continuation methods for efficiently scanning an isovalued surface. A simplicial pivoting algorithm by Ralf Widmann which continues earlier work of E. L. Allgower et al., is compared to an approach which is based on subdividing space into cubes. The algorithms determine all simplices or cubes intersecting the surface and then generate an oriented polygonal approximation. For demonstration and comparison we use several fractal and some smooth surfaces. These surfaces are implicitely defined by a function, but it is also possible to apply both methods to 3D volume data.