Mixing symbolic and numerical approaches for the surface‐to‐surface intersection problem

Abstract

This paper shows how the efficiency of the current methodologies applied to the surface-to-surface intersection problem can be improved by combining an algebraic/symbolic framework with efficient and robust numerical techniques. The algebraic/symbolic framework is used to translate the computation of resultants, subresultants, discriminants, etc. to one or several generalized eigenvalue problems and SVD computations. The framework requires only the values of the involved polynomials at some set of points, and it will guide the numerical computations, providing thus a certificate of the topological correctness of the output.