基于新型Gregory三角面片的G^1连续曲面拼接

Research of G^1 smooth surface based on Gregory triangular patches

为有效解决构造光滑曲面的三角网格插值问题,将Gregory四边形面片的易控性嫁接到Bézier三角面片上,提出一种新型双三次Gregory三角面片的插值模型。因为公共边界处的G1连续仅取决于2个相邻三角面片的控制点或向量,而无其它连续性限制,所以,该方法可有效消除使用Gregory四边形面片时需分割三角域产生的扭曲现象。实验结果表明,使用该模型对给定的三角网格进行插值,总能生成G1连续的光滑曲面。

To solve the triangular mesh interpolation problem of constructing a smooth surface effectively, a novel bi-cubic Gregory triangular patch for interpolation model was presented by grafting the controllability of Gregory quadrilateral patch into Bfzier triangular patch. Because G1 continuity at the common boundary depends only on two adjacent triangular patches＇ control point or vector without other continuity restrictions, the method can effectively eliminate the distortions of spliting triangular domain which emerge when Gregory quadrilateral patch in used. Experimental results show that when the new bi-cubic Gregory triangular patch is used in triangular mesh interpolation, a G1 continuous smooth surface can always be generated.