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Interactive Visualization of Implicit Surfaces with Singularities
Author(s) -
Rösch Angela,
Ruhl Matthias,
Saupe Dietmar
Publication year - 1997
Publication title -
computer graphics forum
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.578
H-Index - 120
eISSN - 1467-8659
pISSN - 0167-7055
DOI - 10.1111/1467-8659.00196
Subject(s) - gravitational singularity , visualization , computer graphics , computer science , surface (topology) , bounded function , graphics , boundary (topology) , algebraic surface , cusp (singularity) , algebraic number , theoretical computer science , computer graphics (images) , mathematics , geometry , artificial intelligence , mathematical analysis
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.