基于微分几何的隐式曲面交线跟踪方法

摘要

Surface intersection is a fundamental problem in CAD applications. Instead of using Newton method to locate points on the curve for the marching method, a new method with dimidiate structure is proposed to trace implicit surface intersection in this paper. The starting and termination points are selected by solving constrained optimization problems. The tracing of intersection curve relies on differential geometry of the intersecting sur-faces. The curvature of intersection curve determines the adaptive step. A generalized tracing method is also pre-sented. Numerical examples show the effectiveness of both methods.%曲面求交是许多CAD应用的基本问题，针对目前在曲面交线跟踪方法中使用最广泛的行进方法要对估计点利用牛顿法进行校正的问题，提出一种二分方式的隐式曲面交线的跟踪方法。该方法通过求解约束优化问题选取起止点，根据相交曲面的微分几何结构跟踪2个隐式曲面的交线，在跟踪过程中使用由曲面交线的曲率确定的自适应步长，并给出此跟踪方法的一个拓展方法。最后通过数值算例验证文中方法的有效性。