复合三角Bezier曲面/平面的过渡和裁剪

The blending and Trimming berween Composite Triangular Beaier Surface and Plane

由初始交点出发，利用拓朴关系跟踪计算复合三角 Beaier 曲面与平面的交线。对一系列交点进行点对应修正、曲面片间边界点计算、交线两端交点的跟踪、截面线构造、截面线离散，构造出与基曲面达到G′连续、结构相似的过渡曲面。将交点作为型值点插入复合曲面的型值点集中、对三角网格局域三角化、以交线边界分离、重新构造拓朴关系生成两张新曲面，实现裁剪的目的。测试显示，上述方法简单可靠。

Started form initial intersection points, the intersection curves between the composite triangular Bezier surface and plane can be marched continuously with its topology. A series of measured points can be derived from the intersection points, by refining point correspondences, calculation border point between patch and plane, tracing intersection curve ends, constructing and scattering cross sections. After that, a blending surface that is G′continuous with base surface can be constructed. The blending surface has the same topology as base surface. Inserting intersection points into surface as measured points, retriangulationg meshes locally and detaching along intersection curve, the original surface can be trimmed into two composite triangular Bezier surfaces. Experiments show that the method is sample.