Reparameterization of curves and surfaces with respect to their convolution

Authors:
Miroslav Lávička;Bohumír Bastl;Zbyněk Šír
Affiliations:
Faculty of Applied Sciences, Department of Mathematics, University of West Bohemia, Plzeň, Czech Republic;Faculty of Applied Sciences, Department of Mathematics, University of West Bohemia, Plzeň, Czech Republic;Faculty of Applied Sciences, Department of Mathematics, University of West Bohemia, Plzeň, Czech Republic
Venue:
MMCS'08 Proceedings of the 7th international conference on Mathematical Methods for Curves and Surfaces
Year:
2008

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Abstract

Given two parametric planar curves or surfaces we find their new parameterizations (which we call coherent) permitting to compute their convolution by simply adding the points with the same parameter values. Several approaches based on rational reparameterization of one or both input objects or direct computation of new parameterizations are shown. Using the Gröbner basis theory we decide the simplest possible way for obtaining coherent parametrizations. We also show that coherent parameterizations exist whenever the convolution hypersurface is rational.