Interactive Visualization of Implicit Surfaces with Singularities

Angela Rösch, Matthias Ruhl, and Dietmar Saupe

Eurographics Computer Graphics Forum
Vol. 16, no. 5, pp. 295-306, December 1997

A preliminary version appeared in:
Eurographics/SIGGRAPH Workshop on Implicit Surfaces (IMPLICIT SURFACES '96)
Eindhoven, October 1996

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This paper presents work on two methods for interactive visualization of implicit surfaces: physically-based sampling using particle systems and polygonization followed by physically-based mesh improvement which explicitly makes use of the surface-defining equation. While most previous work applied to bounded manifolds without singularities and without boundary (topological spheres) we broaden the scope of the methods to include surfaces with such features, in particular cusp points and surface self-intersections. These aspects are not (yet) essential for computer graphics modelling with implicit surfaces but they naturally occur in simulations of interest in mathematical visualization. In this paper we use the Kummer family of algebraic surfaces as an example.

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