| 摘要: |
| 目前有两种常用的Bézier曲面片，分别称为三角和四边Bézier曲面片，它们分别用不同的基函数表示.本文通过移位算子和函数复合的方法，得到了两个关于这两种Bézier曲面片的结果.一个是四边Bézier曲面片与一次三角Bézier函数的复合，另一个是三角Bézier曲面片与双线性四边Bézier函数的复合.在每一种情况中，复合所得到的Bézier曲面片的控制顶点是原来Bézier曲面片的控制顶点的线性组合.移位算子的应用使得相应的推导过程变得简洁和直观.这两个结果的应用包括：两种Bézier面片间的转化 |
| 关键词: 四边Bézier曲面片,三边Bézier曲面片,函数复合,计算机辅助几何设计,de'Casteljau算法. |
| DOI： |
| 分类号: |
| 基金项目:This research is supported by the National Natural Science Foundation of China. |
|
| Functional Compositions via Shifting Operators for Bézier Patches and Their Applications |
|
FENG Jie-qing,PENG Qun-sheng
|
| Abstract: |
| There are two kinds of Bézier patches which are represented by different base functions, namely the triangular Bézier patch and the rectangular Bézier patch. In this paper, two results about these patches are obtained by employing functional compositions via shifting operators. One is the composition of a rectangular Bézier patch with a triangular Bézier function of degree 1, the other is the composition of a triangular Bézier patch with a rectangular Bézier function of degree 1×1. The control points of the resultant patch in either case are the linear convex combinations of the control points of the original patch. With the shifting operators, the respective procedure becomes concise and intuitive. The potential applications of the two results include conversions between two kinds of Bézier patches, exact representation of a trimmed surface, natural extension of original patches, etc. |
| Key words: Rectangular Bézier patch, triangular Bézier patch, functional composition, computer aided geometric design, de, Casteljau algorithm. |
