Computing Birational Polynomial Surface Parametrizations without Base Points

TL;DR

This paper introduces an algorithm to convert birational surface parametrizations into polynomial forms without base points, under certain conditions, simplifying their use in computational geometry.

Contribution

It provides a novel method for reparametrizing birational surfaces into polynomial parametrizations without base points, assuming a transversality condition.

Findings

Successfully reparametrizes surfaces without base points

Operates under a transversality condition

Enhances computational geometry techniques

Abstract

In this paper, we present an algorithm for reparametrizing birational surface parametrizations into birational polynomial surface parametrizations without base points, if they exist. For this purpose, we impose a transversality condition to the base points of the input parametrization.