Approximate algebraic methods for curves and surfaces and their applications

Authors:
Bert Jüttler;Pavel Chalmovianský;Mohamed Shalaby;Elmar Wurm
Affiliations:
Johannes Kepler University, Linz, Austria;Johannes Kepler University, Linz, Austria;Johannes Kepler University, Linz, Austria;Johannes Kepler University, Linz, Austria
Venue:
Proceedings of the 21st spring conference on Computer graphics
Year:
2005

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Abstract

We report on approximate techniques for conversion between the implicit and the parametric representation of curves and surfaces, i.e., implicitization and parameterization. It is shown that these techniques are able to handle general free-form surfaces, and they can therefore be used to exploit the duality of implicit and parametric representations. In addition, we discuss several applications of these techniques, such as detection of self-intersections, ray-tracing, footpoint computation and parameterization of scattered data for parametric curve or surface fitting.