基于权因子变动和约束优化的NURBS曲线形状修改

摘要

A new method for shape modification of non-uniform rational B-splines (NURBS) curves is presented, which is based on constrained optimization by means of altering the corresponding weights of their control points. Using this method, the original NURBS curve is modified to satisfy the specified geometric constraints, including single point and multi-point constraints. With the introduction of free parameters, the shapes of modified NURBS curves can be further controlled by users without destroying geometric constraints and seem more naturally. Since explicit formulae are derived to compute new weights of the modified curve, the method is simple and easy to program. Practical examples show that the method is applicable for computer aided design (CAD) system.%提出了一种通过约束优化改变控制顶点相应的权因子, 进行NURBS曲线形状修改的新方法. 运用该方法可使得修改后的NURBS曲线满足给定的几何约束, 如单点约束和多点约束. 同时引入了一些自由参数,可以在不破坏几何约束的条件下能进一步改变NURBS曲线的形状,而且能使修改后的曲线形状更自然.由于推导出了明确的公式来计算修改后曲线新的权因子, 因而该方法简单且易于编写程序. 实例表明该方法适用于CAD软件系统.