منابع مشابه
Symbolic Parametrization of Curves
If algebraic varieties like curves or surfaces are to be manipulated by computers, it is essential to be able to represent these geometric objects in an appropriate way. For some applications an implicit representation by algebraic equations is desirable, whereas for others an explicit or parametric representation is more suitable. Therefore, transformation algorithms from one representation to...
متن کاملOn Symbolic Parametrization of Algebraic Curves
In this paper we give an overview of the symbolic computation of rational parametrizations for algebraic curves. Parametrization of algebraic curves has been a topic in algebraic geometry for a long time and there are basically two approaches to the problem. The first approach is a geometric one, whereby a parametrization is determined from the intersection points of the given curve with a cert...
متن کاملReal Parametrization of Algebraic Curves
There are various algorithms known for deciding the parametrizability (rationality) of a plane algebraic curve, and if the curve is rational, actually computing a parametrization. Optimality criteria such as low degrees in the parametrization or low degree field extensions are met by some parametrization algorithms. In this paper we investigate real curves. Given a parametrizable plane curve ov...
متن کاملSparse Parametrization of Plane Curves
We present a new method for the rational parametrization of plane algebraic curves. The algorithm exploits the shape of the Newton polygon of the defining implicit equation and is based on methods of toric geometry.
متن کاملRadical parametrization of algebraic curves and surfaces
Parametrization of algebraic curves and surfaces is a fundamental topic in CAGD (intersections; offsets and conchoids; etc.) There are many results on rational parametrization, in particular in the curve case, but the class of such objects is relatively small. If we allow root extraction, the class of parametrizable objetcs is greatly enlarged (for example, elliptic curves can be parametrized w...
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ژورنال
عنوان ژورنال: Journal of Symbolic Computation
سال: 1991
ISSN: 0747-7171
DOI: 10.1016/s0747-7171(08)80144-7