基于约束优化的有理Bezier曲线形状修改

摘要

point or strained the new ：This paper investigates the optimal shape modification of rational Bezier curves by geometric constraints such as single multi-target points constraints or added end point/tangent constraint The method is presented in this paper by con- optimization based on changing the control points of the curves. Explicit formulae are derived to compute positions of control points of the modified curve. Practical examples are also given.%研究了基于某种约束条件的有理Bezier曲线的形状修改，约束条件为曲线通过某个单点或多个点，或在端点处满足某种切矢条件。方法是修改控制点。目的是使得修改前后的曲线的控制点的改变量最小。给出了具体控制点的扰动的计算公式，且给出了具体实例。