基于复合三角Bezier曲面／平面的交线构造过渡曲面

由初始交点出发，利用三角Bezier曲面片间的拓扑关系，采用连续跟踪的算法计算复合三角Bezier曲面与平面的交线；对所得的交线通过点对应修正、曲面片间边界点计算、交线两端交点的跟踪、截面线的构造、截面线离散，得到一系列的型值点，从而可构造出与基曲面达到G′连续、结构的过渡曲线面。测试显示，该方法简单可靠，能满足反求工程CAD建模的要求，在曲面造型和加工领域具有广泛的应用潜力。

A Blending Method Based on the Intersection of Composite Triangular Bezier Surface and Plane

Starting from initial intersection points, using the topology among triangular Bezier patches, the intersection curves between composite triangular Bezier surface and plane can be traced continuously. Having obtained the intersection curves, a series of measured points can be derived by refning point correspondences, calculating border point between two patches, tracing end points of intersection curve, constructing and discrete cross sections. Then a blend surface that is G'continuous with base surface can be constructed. The blend surface has the same topology as base surface. Experiments show that the method is simple, robust, and applicable to CAD modeling in reverse engineering. It is believed that the method will be widely used in surface modeling and manufacturing in automotive and aviation industries.