Automatic parameterization of rational curves and surfaces III: Algebraic plane curves
β Scribed by Shreeram S. Abhyankar; Chanderjit L. Bajaj
- Book ID
- 107919414
- Publisher
- Elsevier Science
- Year
- 1988
- Tongue
- English
- Weight
- 924 KB
- Volume
- 5
- Category
- Article
- ISSN
- 0167-8396
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
An efficient way of drawing parametric curves and surfaces is to approximate the curve or surface by a sequence of straight-line segments or a mesh of polygons, respectively. In such an approximation, many small line segments or polygons are needed in regions of high curvature, and fewer and larger
Given the implicit equation for degree two curves (conics) and degree two surfaces (conicoids), algorithms are described here, which obtain their corresponding rational parametric equations (a polynomial divided by another). These rational parameterizaUons are considered over the fields of rationals
A Igorithms that can obtain rational and special parametric equations for degree three algebraic curves (cubics) and degree three algebraic surfaces (cubicoids), given their implicit equations are described. These algorithms have been implemented on a VAX8600 using VAXIMA.