Polynomial parametrizations for rational curves

Dinesh Manocha; John F. Canny

doi:10.1117/12.19743

1 August 1990 Polynomial parametrizations for rational curves

Dinesh Manocha, John F. Canny

Proceedings Volume 1251, Curves and Surfaces in Computer Vision and Graphics; (1990) https://doi.org/10.1117/12.19743
Event: Electronic Imaging: Advanced Devices and Systems, 1990, Santa Clara, CA, United States

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.

Citation Download Citation

Dinesh Manocha and John F. Canny "Polynomial parametrizations for rational curves", Proc. SPIE 1251, Curves and Surfaces in Computer Vision and Graphics, (1 August 1990); https://doi.org/10.1117/12.19743

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