<title>Robust techniques for curve and surface intersections</title>

Abstract

The problems of computing the intersection of curves and surfaces are fundamental to computer graphics and geometric and solid modeling. Earlier algorithms were based either on subdivision methods or algebraic techniques. They are generally restricted to simple intersections. It has been generally regarded that algebraic approach is impractical due to numerical problems on higher degree curves and surfaces (beyond cubics). In our earlier work we have applied Elimination theory and reduced the problem of intersections of curves and surfaces to matrix computations. These include Gauss elimination, matrix inversion, singular value decomposition, eigenvalues and eigenvectors etc. In this paper, we present robust algorithms based on techniques from linear algebra and numerical analysis for computing the zero dimensional intersections of curves and surface. These include intersection of parametric and algebraic curves and curve-surface intersections. In particular, we present a robust algorithm for computer higher order intersections.