A parallel B-spline surface fitting algorithm

Abstract

A parallel fitting algorithm using uniform bicubic B-spline surfaces is presented. This algorithm is based on the observation that a tensor product spline surface fitting problem can be split into two spline curve fitting problems, and each of these problems can be carried out in parallel by cyclic reduction. Using this approach, the control points of a uniform bicubic B-spline surface that interpolates a grid of m x n points can be found in O (log m + log n ) time on mn processors. Furthermore, since smaller systems of equations are solved in the algorithm, the accumulated error resulting from this approach is smaller than that of the traditional algorithms.