基于C-B 样条的三角形和四边形曲面生成

文章给出了基于C-B 样条的由网格数据产生三角形和四边形曲面片的方 法，C-B 样条是由基底函数{sin t, cos t, t, 1}导出的一种新型样条曲线，它可以克服现在正在 使用的B 样条和有理B 样条为了满足数据网格的拓扑结构而增加多余的控制点，求导求积 分复杂繁琐，阶数过高，从而讨论其连续拼接时增加了困难等缺点，如何将它推广成曲面就 成为一个重要问题。作者利用边-顶点方法构造插值算子，再将这些算子进行凸性组合，将 C-B 样条曲线推广成三角形曲面片和四边形曲面片，它可以用于CAD 的逆向工程中散乱数 据的曲面重构。

Triangular and quadrilateral surface construction using C-B spline

This paper provides a different solution to represent basic smooth elements like triangular and quadrilateral surface patches from mesh using C-B spline curves. C-B spline curves are developed by the basis {sin t, cos t, t, 1}, and it overcomes some shortcomings of the B-spline and non-uniform rational B-splines (NURBS) model, for example, they have to increase unnecessary control point in order to satisfy the data grid topology, their derivative and integral are complex and tedious, their degrees are too high, and it is difficult to discuss their continuous conditions. How to develop C-B spline curves into surface becomes an important problem. In this paper, the interpolation operators are constructed by using side-vertex method and a convex combination of these operators is achieved. The C-B spline curves are developed into triangular and quadrilateral surface patches which can be used in reverse engineering of CAD.