Invited speakers

Professor Rimvydas Krasauskas, Department of Mathematics and Informatics. Vilnius University, Lithuania.

Rational Canal surfaces. A canal surface with the rational spine curve and rational radius is known to be rational. We study all such parametrizations with a rational Gaussian image and present an algorithm that generates Bezier patches of minimal degree on such canal surfaces with given boundary curves. Applications include exact NURBS representations of several fixed or variable radius rolling ball blends between two natural quadrics in an arbitrary given position.

Professor Josef Schicho, Johann Radon Institute for Computational and Applied Mathematics (RICAM) Austrian Academy of Sciences (ÖAW)

Sparse parametrization of algebraic curves and surfaces. (Based on joint work with Tobias Beck) There are well-known algorithms for deciding rationality and computing rational parametrizations (if exist) for implicit curves in the projective plane, and for implicit surfaces in projective 3-space. In some examples, the equation has specific structure one can exploit in order to reduce the computational costs. The stepping stone in this new technique is (once more) the Newton polygon/polehedron of the implicit equation.

Professor Falai Chen, Department of Mathematics, University of Science and Technology of China Hefei

Mu-basis of rational curves and surfaces: Theory and Applications. In this talk, I will review the theory and algorithms for the mu-bases of rational curves and surfaces-- a newly developed algebraic tool to handle rational curves and surfaces. Then I will talk about some applications of the mu-basis theory, such as implicitzation, reparameterization and computing singular points/locus of rational curves/surfaces.

Published August 31, 2005