摘要
Bézier曲面是 CAD/ CAM系统中的最常用的造型工具之一 ,因此在造型系统的发展过程中 ,对两相邻Bézier曲面近似合并算法进行研究是非常重要的。两相邻 Bézier曲面的近似合并就是 :在一定的误差允许范围内 ,用一片 k× l(k≥ m,l≥ n)次的 Bézier曲面去逼近相邻的两片 m× n次 Bézier曲面。但随着国际互联网越来越发展和跨国企业的大量建立 ,在产品设计中信息的交换越来越重要 ,且已能够实现。当前 ,产品模型数据的交换比以前更加频繁 ,但由于数据量特别巨大 ,因此如果在数据交换之前采用近似合并算法 ,则可减少几何数据。为了能较佳地进行 Bézier曲面近似合并 ,因此利用张量积 Bézier曲面细分后的矩阵表示 ,并根据所定义的原 Bézier曲面与合并Bézier曲面间的距离函数取最小值 ,给出了张量积 Bézier曲面近似合并的一种方法 ,以便得到合并 Bézier曲面控制顶点的显示表示式。该方法在合并过程中 ,由于考虑了原 Bézier曲面与合并 Bézier曲面在边界达到高阶连续的情形 ,因此利用该方法可直接完成两相邻 Bézier曲面的近似合并。
Bézier surface is one of the most commonly used modeling tools in CAD/CAM systems. During the development of a system, the research of approximate merging algorithms for a pair of adjacent Bézier surfaces is of great importance. Approximate merging of two adjacent Bézier surfaces is that two adjacent Bézier surfaces of degree m×n is approximated by one of degree k×l(k≥m,l≥n) within the admissible error bound. As exchanging information becomes more and more important in product design, the international network is more and more developed, and more and more enterprises have been vastly established, the exchanging of product model data is becoming far more frequent than ever. Before the exchanging of product model data, if approximate merging algorithms are used, then geometric data can be reduced. In this paper, an approximate merging method for tensor product Bézier surfaces is presented by using the matrix representation of subdivided Bézier surface and by minimizing the distance function defined between the original Bézier surfaces and the merged Bézier surface. The explicit representation for control points of the merged surface is obtained. Higher order of continuity along the boundaries of surfaces is considered in the merging process. The approximate merging for a pair of adjacent Bézier surfaces can be directly carried out by using the method of this paper.
出处
《中国图象图形学报（A辑）》
CSCD
北大核心
2004年第5期598-603,共6页
Journal of Image and Graphics
基金
国家自然科学基金资助项目(10171026)
