A note on the rational parameterization of algebraic curves inMathematica ®

Michal Bizzarri, Miroslav Lávička
2009 Journal of Interdisciplinary Mathematics  
The choice of an appropriate representation of geometric objects (explicit, parametric, or implicit one) is a fundamental issue for the development of efficient algorithms. Whereas for example Computer Graphics seem to use all the above mentioned representations, CAD focuses on a few of them -mainly on the parametric one. Among all parameterizations, the most important ones are those that can be described with the help of polynomials or rational functions since these descriptions can be easily
more » ... ncluded into standard CAD systems and then used in technical applications. The main aim of the paper is to describe an efficient algorithm which can be used for finding rational parameterizations of special classes of algebraic curves. Some advantages and disadvantages of the presented method will be discussed and the implementation in M athematica will be presented.
doi:10.1080/09720502.2009.10700627 fatcat:niei7enxlzdf5lxwq6wxj6buzq