Degenerate parametric curves

Authors:
Thomas W. Sederberg
Affiliations:
Department of Civil Engineering, Brigham Young University, Provo, UT 84602, U.S.A.
Venue:
Computer Aided Geometric Design
Year:
1984

Citing 3
Cited 4

On Euclid's Algorithm and the Computation of Polynomial Greatest Common Divisors

Journal of the ACM (JACM)
Computational Geometry for Design and Manufacture

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On square-free decomposition algorithms

SYMSAC '76 Proceedings of the third ACM symposium on Symbolic and algebraic computation

Curves with rational chord-length parametrization

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Complex rational Bézier curves

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Letter to the editor: On the conditions for the coincidence of two cubic Bézier curves

Journal of Computational and Applied Mathematics

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Abstract

This paper discusses two degenerate cases of polynomial parametric curves for which the degrees of the defining polynomials can be reduced without altering the curve. The first case is the improperly parametrized curve for which each point on the curve corresponds to several parameter values. The second case, which can only occur for rational polynomial parametric curves, exists when the defining polynomials all have a common factor. This paper describes how to detect and correct each type of degeneracy. Examples are given which demonstrate that seemingly innocuous Bezier curves may suffer from either of these degeneracies.