Topological classification of the intersection curves of two quadrics using a set of discriminants

Abstract

Computing the intersection curves of two quadrics (QSIC) is a fundamental problem in computer aided design system, where the topology analysis of the QSIC is an essential task to realize the robust computation. In this paper, a new method is proposed to classify the topology of the QSIC in three dimensional projective space by using a set of discriminants associated with the two quadrics. The new topology classification method presents explicit representations and can be applied even when the coefficients of the two quadrics contain symbols. Some examples are provided to illustrate the usage of the new classification method.