基于约束优化的B样条曲线形状修改

B样条曲线广泛应用于计算机辅助几何设计(CAGD),并且与Bézier曲线等其它著名曲线相比,在形状设计方面有其更独特的性质。对曲线的设计和形状的修改是一个重要的课题,也是计算机图形学、CAD/CAM和数控技术领域最重要的研究主题之一。论文运用约束优化的方法,修改均匀B-样条的控制点,使B样条曲线通过调整的控制点,使修改前后曲线的距离范数达到最小,并给出相应的实例说明算法的有效性。

Shape Modification of B Spline Curves by Constrained Optimization

The B spline curve is one of the most commonly used parametric curves in CAGD and Computer Graphics.It has much better properties for shape design than some other curves.Developing more convenient techniques for designing and modifying B spline curve is an important problem,and is also an important research issue in CAD/CAM and NC Technology fields.The paper investigates the optimal shape modification of B spline curves by geometric constraints.The paper presents a new method constrained optimization based on changing the control points of the curves.By this method,the authors modify control points of the original B spline curves to satisfy the given constraints and modify the shape of the curves optimally.Practical examples are also given.