双三次参数曲面求交的一种新方法

A New Method for Fast Finding the Intersection of wo Bicubic Parametric Surfaces

针对工程上广泛应用的双三次Ｂｅｚｉｅｒ，Ｂ样条曲面，提出一种新的曲面求交方法．这种方法基于曲面控制网格的“子”分方法，只要控制网格足够逼近曲面，便可用控制网格的小平面代替曲面本身，从而快速求出两张双三次参数曲面的交线．

A new method for fast finding the intersection of two bicubic parametric sulfaces in theform of Bezier and B-spline is proposed.It is an improvement on three existing ones.Thismethod is based on the“subdivision”of control polygons of the surfaces. If two control poly-gons are sufficiently approximate to the surfaces,the latter can be replaced by the tinyplanes of the control polygons and the curve of intersection can be quickly found by a seriesof intersections of triangles and lines defined in a particular way.This method is stable andof good convergence rate and high efficiency.It has been successfully used in the investiga-tion on VISC for a 3-D computer electromagnetic radiation field and some other investiga-tions.