Rational surfaces with linear normals and their convolutions with rational surfaces

Authors:
Maria Lucia Sampoli;Martin Peternell;Bert Jüttler
Affiliations:
Università di Siena, Dipartimento di Scienze Matematiche ed Informatiche, Italy;Technische Universität Wien, Inst. für Diskrete Mathematik und Geometrie, Austria;J. Kepler Universität Linz, Institut für Angewandte Geometrie, Austria
Venue:
Computer Aided Geometric Design
Year:
2006

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Abstract

It is shown that polynomial (or rational) parametric surfaces with a linear field of normal vectors are dual to graphs bivariate polynomials (or rational functions). We discuss the geometric properties of these surfaces. In particular, using the dual representation it is shown that the convolution with general rational surfaces yields again rational surfaces. Similar results hold in the case of curves.