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Detecting symmetries of rational plane and space curves

Abstract

This paper addresses the problem of determining the symmetries of a plane or space curve defined by a rational parametrization. We provide effective methods to compute the involution and rotation symmetries for the planar case. As for space curves, our method finds the involutions in all cases, and all the rotation symmetries in the particular case of Pythagorean-hodograph curves. Our algorithms solve these problems without converting to implicit form. Instead, we make use of a relationship between two proper parametrizations of the same curve, which leads to algorithms that involve only univariate polynomials. These algorithms have been implemented and tested in the Sage system.

Category

Academic article

Client

  • Research Council of Norway (RCN) / 222335

Language

English

Author(s)

Affiliation

  • University of Alcalá
  • University of Oslo
  • SINTEF Digital / Mathematics and Cybernetics

Year

2014

Published in

Computer Aided Geometric Design

ISSN

0167-8396

Publisher

Elsevier

Volume

31

Issue

3-4

Page(s)

199 - 209

View this publication at Cristin