NURBS曲面片的混合与填充

Blending and Filling of NURBS Patches

摘要: 本文提出用轮廓删除法对NURBS曲面片进行细分的曲面混合及N边洞填充的方法。该方法先根据非均匀Catmull-Clark细分原理进行曲面混合，构造插值于角点的非均匀Catmull-Clark细分曲面法，再运用轮廓删除法在细分迭代的过程中去除控制网格边界轮廓，然后进行N边洞的填充以生成一张整体光滑的连续曲面。该方法在保证混合曲面与基曲面片在边界处C2连续时，能使N边洞填充曲面具有较好的光顺性。实例结果表明，该方法简化了具体的计算机实现过程，拓宽了细分曲面应用范围，解决了细分曲面与经典样条拼接的不相容问题，且使生成的曲面兼顾了二者的优点，具有较好的填充效果。

Abstract: This paper presents a method for subdividing the NURBS surface patches blending and N-sided hole filling by contour deletion method. First, surface blended according to the principle of non- uniform Catmull-Clark subdivision surface, and the non-uniform Catmull-Clark subdivision method which builds the surface interpolating corner vertices and boundary curves was constructed. Then the contour deletion method was used to remove the control mesh boundary contour in the process of segmentation iteration. Last, N-sided hole filling was used to generate an integral smooth continuous surface. The method not only can guarantee the blending surface and the base surface patches C2 continuity at the boundary, but also can make the N-sided hole filling surface have better smoothness. Results show that, this method simplifies the specific computer realization process, broads the scope of application of subdivision surfaces, and solves the problem of incompatibility between subdivision surface and classic spline splicing; the resulting surface has both advantages with better filling effect.