Curves and surfaces represented by polynomial support functions

Authors:
Zbynk ír;Jens Gravesen;Bert Jüttler
Affiliations:
Faculty of Mathematics and Physics, Charles University, Prague, Czech Republic;Technical University of Denmark, Department of Mathematics, Kgs. Lyngby, Denmark;Johannes Kepler University Linz, Institute of Applied Geometry, Austria
Venue:
Theoretical Computer Science
Year:
2008

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Abstract

This paper studies shapes (curves and surfaces) which can be described by (piecewise) polynomial support functions. The class of these shapes is closed under convolutions, offsetting, rotations and translations. We give a geometric discussion of these shapes and present methods for the approximation of general curves and surfaces by them. Based on the rich theory of spherical spline functions, this leads to computational techniques for rational curves and surfaces with rational offsets, which can deal with shapes without inflections/parabolic points.