三角域Bézier曲面片GC~2拼接的几何条件

本文利用Ｂｅｒｎｓｔｅｉｎ基函数的线性无关性，引入重心坐标的概念，给出了两个三角域Ｂｅａｉｅｒ曲面片拼接达到ＧＣ２３光滑的一种几何构造，具有直观的几何解释，文中给出的定理条件对构造一个三角城Ｂｅｚｉｅｒ曲面使其与另一个三角域Ｂｅｚｉｅｒ曲面达到ＧＣ２光滑拼接，是行之有效的．

Geometric Condition for GC~2 Continuity between Adjacent Triangular Bezier Surface Patches

Different from a large amount of Dprevious mathematical results on curvature continuity GCZ between adjacent B6zier patches6,7],in this paper the authors present a geometric construction theorem forGCd continvity between triangular B6zicr patches that is much more convenient for engineers to apply.The authors'proper geometric construction theorem is derived mainly through making use of theInearly independent property of Bernstein basic functions and through the introduction of the concept ofoarycentric coordinates.It is very important to point out that the geometric construction theorem allows us to see clearly andcastly that GC2 continuity between adjacent triangular B6zier patches depends only on two row Det pointSon the two sides of the common boundary curve.When GCZ continuity is satisfied,the net points of onetriangular B6zier patch can be linearly expressed in terms of the net points of the adjacent trangular B6zierpatch.