快速计算平面与高精度细分曲面交线的方法

Efficient algorithm for computing intersection curve between plane and subdivision surface

为解决平面与高精度细分曲面求交效率低和稳定性差的问题,根据细分曲面网格拓扑结构特性,提出平面与Catmull-Clark细分曲面求交的高效方法。基于细分曲面的分片表示,将平面与复杂细分曲面模型的求交问题转化为平面与形状简单的细分曲面面片的求交问题。分析了平面与细分曲面交线的特点,将交线的交点分为起始交点、后续交点和终止交点三种基本类型。根据细分曲面面片网格拓扑结构特性,提出细分曲面面片多级分割技术。在此基础上,结合包围盒干涉检测技术,判断平面与细分曲面面片的相交性并计算起始交点。针对细分曲面面片规则的拓扑结构,计算后续交点和判定终止交点。根据细分曲面面片之间的拓扑关系,将获得的若干无序交线段排序合并为完整的有序交线。通过实例进行了算法测试,测试结果表明该算法具有较高的性能。

To solve the problems of inefficiency and poor stability in computing intersection curve between plane and subdivision surface, an high efficient method for plane and CatmulbClark subdivision surface intersection was presented according to mesh topological characteristics of subdivision surface. Based on piecewise representation of subdivision surface, the problem of computing intersection curve between plane and complex subdivision surface was transformed into the problem of computing intersection curve between plane and subdivision surface patch. From analysis of intersection points between plane and subdivision surface patch, the intersection points were divided into three basic types., initial intersection point, following intersection point and terminal intersection point. The multisegmentation technology for subdivision surface patch was presented on the basis of topological characteristics of subdivision surface patch. By applying multi-segmentation in combination with the bounding box interference detecting technique, subdivision surface patches non-intersecting the plane was determined and the initial intersection point could be obtained. According to the topological relationship between subdivision surface patches, all the unordered curve segments were merged orderly together into an intersection curve.The high performance of proposed al gorithm was verified through the practical cases.