Filling N-Sided Patch with a Trimmed Parametric Surface : N-Sided Surface Construction for Car Body Design

Abstract

In this paper, an algorithm of filling N-sided patch with a trimmed bipolynomial parametric surface is proposed. First, a virtual boundary is used and the N-sided curves are treated as some discrete points. Then using a algorithm of fitting arbitrary scattered points to parametric surface, a smoothly large piece of surface can be generated to approximate the N-sided curves within a given tolerance. In the end, the N-sided surface is produced by trim operation. Using this algorithm, the shape of the initial produced surface can be modified in an interactive way by pulling some points or curves on it. In order to approximate G¹ continuity with adjacent surfaces, Levenberg-Marquardt optimal method is used for final refinement. Several examples are given out to show the effectiveness of the proposed algorithm.