隐式曲面／参数曲面的求交算法

AN ALGORITHM FOR INTERSECTING IMPLICIT SURFACES WITH PARAMETRIC SURFACES

本文介绍了一种实用有效的隐式曲面／参数曲面求交算法。算法主要分为两部分：特征初始点（边界点，转折点和奇异点）的求取和单调段的踉踪。解双变量多项式方程（组）求解特征初始点。跟踪在三维空间进行，易于控制跟踪步长和离散交点对交线的逼近精度。算法不离散参数曲面，不漏交。

This paper presents a robust algorithm for the computation of the intersection of an implicit surface and a parametric surface. Analytic representation of intersection as a plane algebraic curve is obtained, and then numerical techniques are used to compute characteristic initial points (border points, turning points and singular points).Monotonic intersection segments are traced in three-dimensional space. So it is easy to tackle with the step and the tolerance. The algorithm has been proved to be reliable, efficient and accurate.