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Proceedings Paper

Polynomial parametrizations for rational curves
Author(s): Dinesh Manocha; John F. Canny
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Paper Abstract

Rational curves and splines are one of the building blocks of computer graphics and geometric modeling. Although a rational curve is more flexible than its polynomial counterpart, many properties of polynomial curves are not applicable to it. For this reason it is very useful to know if a curve presented as a rational space curve has a polynomial parametrization. In this paper, we present an algorithm to decide if a polynomial parametrization exists, and to compute the parametrization. In algebraic geometry it is known that a rational algebraic curve is polynomially parametrizable if it has one place at infinity. This criterion has been used in earlier methods to test polynomial parametrizability of space curves. These methods project the curve into the plane and test parametrizability there. But this gives only a sufficient condition for the original curve. In this paper we give a simple condition which is both necessary and sufficient for polynomial parametrizability. The calculation of the polynomial parametrization is simple, and involves only a rational reparametrization of the curve.

Paper Details

Date Published: 1 August 1990
PDF: 12 pages
Proc. SPIE 1251, Curves and Surfaces in Computer Vision and Graphics, (1 August 1990); doi: 10.1117/12.19743
Show Author Affiliations
Dinesh Manocha, Univ. of California/Berkeley (United States)
John F. Canny, Univ. of California/Berkeley (United States)

Published in SPIE Proceedings Vol. 1251:
Curves and Surfaces in Computer Vision and Graphics
Leonard A. Ferrari; Rui J. P. de Figueiredo, Editor(s)

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