用优化凸包法作B—Spline曲线的求交运算

本文在分析B-Spline曲线所具有的几何特性的基础上,提出了用优化凸包方法,作B-Spline曲线的求交运算,内容包括B-Spline曲线与直线求交、B-Spline曲线与圆弧求交及B-Spline曲线与B-Spline曲线求交。 本算法主要从工程应用的实用性出发,首先将B-Spline曲线作离散处理,然后为了提高求交速度,依据其理论,对B样条曲线的凸包多边形进行了优化处理,使得凸包多边形的包括范围大为减小,在判断该优化凸包是否与直线、圆弧或另一样条曲线段的优化凸包相交的前提下,作求交运算。求交精度随B-Spline曲线离散精度的提高而提高。

Find B-spline's intersections with optimization convex hull

This paper, based on the analysis of B-spline curve geometric features, presents a method for finding B-spline curve intersections in the way of using optimization convex hull. It in eludes the contents of a B-spline curve as well as a B-spline curve intersecting another B-spline curve.in order to make caculating faster, we disper B-spline curve from the point of the view of practice in engineering at first, treat the B-spline convex hull in an optimization way by its nature, lessen the area of the convex hull greatly. Thus, it makes theefficiency higher in finding B-spline curve intersections by detecting the relatives of the optimization hull with a straight line, a circle or another curve segment' s convex hull. The precision of caculation is based on B-spline curve' s dispersing precision. This way may be extended to the area of finding B-spline curve surface' s intersections.