基于约束优化的Bézier曲面形状修改  

Shape Modification of Bézier Surfaces by Contrained Optimization

作　　者：夏飞海[1] 吴庆标[1] 

机构地区：[1]浙江大学数学系科学与工程计算研究所,杭州310028

出　　处：《中国图象图形学报》2006年第2期265-268,共4页Journal of Image and Graphics

基　　金：浙江省自然科学基金项目(101027)

摘　　要：Bézier曲线和曲面广泛应用于CAGD(计算机辅助几何设计)和计算机图形学,对Bézier曲线或者曲面的设计和形状修改是一个重要的问题。研究了基于几何约束的Bézier曲面优化问题,对单点和多点约束的问题,提出了一种通过修改控制点的约束优化方法。用这种方法,通过修改原Bézier曲面的控制点来修改曲面的形状并满足给定的约束条件,同时给出了数值实例,其结果表明,用拉格朗日方法能有效地解决Bézier曲面的形状修改问题。Bézier curve and surfaces are one kind of the most commonly used parametric curves in CAGD and computer graphics. Developing more convenient techniques for designing and modifying Bézier curve and surfaces are an important problem. This paper investigates the optimal shape modification of Bvzier surfaces by geometric constraints. A constrained optimization method based on changing the control points of the surfaces is presented in this paper. Ahich modifys control points of the original Bézier Surfaces to satisfy the given constraints and modify the shape of the surfaces optimally. Practical examples are also given. The results indicate that Lagrange multiplier method is an effective way to solve the problem of shape of Bézier surfaces.

关 键 词：BÉZIER曲面 约束优化 形状修改 控制点 

分 类 号：TP391.72[自动化与计算机技术—计算机应用技术]