Birational Reparametrizations of Surfaces
Jorge Caravantes, Sonia P\'erez-D\'iaz, J. Rafael Sendra
TL;DR
This paper introduces algorithms to find birational parameterizations of surfaces from unirational ones, improving efficiency under certain conditions by reducing solution space dimensions.
Contribution
It presents a general algorithm for birational reparametrization of surfaces without relying on existing parameterization algorithms, and a faster method for specific cases.
Findings
A general algorithm for birational reparametrization of surfaces.
A faster algorithm when the surface has a birational parametrization with empty base locus.
The degree of the solution can be pre-determined in certain cases.
Abstract
Given a unirational parameterization of a surface, we present a general algorithm to determine a birational parameterization without using parameterization algorithms. Additionally, if the surface is assumed to have a birational parametrization with empty base locus, and the input parametrization is transversal, the degree of the solution is determined in advance and the dimension of the space of solutions is reduced. As a consequence, for these cases, we present a second faster algorithm.
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Taxonomy
TopicsManufacturing Process and Optimization · 3D Shape Modeling and Analysis · Advanced Numerical Analysis Techniques