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. Developingmore convenient techniques for designing and modifying Bézier curve and surfaces are an important problem. This paper investigates the optimal shapemodification ofBézier surfaces by geometric constraints. A constrained optimizationmethod based on changing the control points of the surfaces is presented in this paper. Ahich modifys control points of the originalBézier surfaces to satisfy the given constraints andmodify the shape of the surfaces optimally. Practical examples are also given. The results indicate thatLagrange multipliermethod is an effective way to solve the problem of shape ofBézier surfaces.