曲面造型中一种快速的曲面跟踪求交算法

提出了一种新的曲面求交算法，采用精度好、效率高、计算稳定的迭代方法求得等参数网格线在曲面上的交点，并通过跟踪获得两曲面的交线。本算法由三个子算法组成，一个是求曲面上到固定点距离最近的点，一个是求参数网格线与曲面的交点，一个是求曲面与曲面的交点。为保证不遗漏交点，利用第一个算法对参数网格点进行分类，跟踪交点时利用第三个求下一个交点。与离散法求交相比，本算法具有计算稳定性、可靠性好，速度快，精度高的优点

A New Method of Questing for Intersections in Construction of Curved Surfaces

A new algorithm is presented to quest for intersection of curved surfaces. It adopts iteration method with high specision, efficiency, and calculation stability to obtain intersecting points between parmetric grid lines and the curved surfaces. Then, the intersect lines between two curved surfaces can be calculated by tracing such initiated points. This algorithm consists of three sub algorithms. The first one is used to seek for the colosest point in the curved surface to the fixed point. The second one is used to obtain intersecting points between the parametric grid lines and the curved surface. The third one is used to get intersecting points between curves each other. To ensure not to omit intersect points, the first one is used to classify points at parametric grid lines and the third one is used to seek for the next intersecting point when tracing the initiated intersect point. Compared with dispersing method, high calculation stability, reliability, and calculation velocity can be obtained with help of this algorithm.