On computing the intersection of B-splines (extended abstract)

Abstract

We consider the problem of computing a piecewise linear approximation to the intersection of a pair of tensor product B-spline surfaces in 3-space. The problem is rather central in solid modeling. We present a fast and robust divide-and-conquer algorithm for the problem, that is a generalization of the bisection algorithm for computing the roots of non-linear equations. The algorithm is guaranteed to solve a “nearby” problem, and our analysis proves that its expected run-time is linear in the worst-case size of the output. To our knowledge, this is the first such analysis, resulting in the first provably efficient algorithm for the problem.