一种对称非均匀细分曲面算法

摘要

为了得到能更好应用于CAD系统的细分曲面造型方法,提出一种基于B-样条的对称非均匀细分算法,其中的思想和均匀Lane-Riesenfeld节点插入算法相似。基于B-样条的节点插入算法,以Blossoming为工具,计算出细分后的新控制顶点。细分后得到的极限曲面由张量积样条曲面组成,在奇异点达到2C连续。与传统的细分曲面算法相比,该细分曲面算法具有良好的局部支撑性,大大降低了算法的复杂度,而且该算法是对称的,不用考虑定向问题。%In order to get a subdivision algorithm which was more compatible with NURBS,presented a non-uniform subdivision algorithm which share similar properties with Lane-Riesenfeld refine and smooth construction.The algorithm was based on knot insertion algorithm of B-splines and was expressed in terms of blossoming.After subdivision,get a limit surface consisting of tensor-product splines and was 2 C at extraordinary points.Compared with the conventional subdivision surfaces algorithm,ours was locally supported that largely reduced the complexity of algorithm,and the algorithm is symmetric,avoiding the problem of direction-orientation.