关键词: 曲面求交, 跟踪法, 微分方程, 法向共线点

Abstract:  Intersection of parametric surfaces is one of the key technologies in the field of computer aided geometric design (CAGD). In this paper, an improved tracing algorithm based on differential equation is proposed to solve the problem in traditional tracing algorithm of missing intersection line and difficulty to trace at normal collinear points. Firstly, the algorithm chooses the boundary points and the inflection points as the starting points of the tracing, so it solves the problem of missing intersection line. Then the tracing formula based on the differential form is used to calculate the successor intersection, which solves the problem of processing tracing at normal collinear points. Finally, the Newton iteration is used to get the exact intersection. The algorithm not only correctly traces each branch of the intersection line, but also is easy to deal with the tracing at normal collinear points. Without missing the key points, the algorithm solves the problem that the traditional tracing method is not continuous at the normal collinear points. Compared with the traditional tracing method, its robustness and stability are stronger characterized with higher precision and slightly faster convergence, and it is suitable for solving any parametric surface intersection problem.

Key words:  surface intersection, tracing method, differential equation, normal collinear points