样条曲线的参数化变形方法

提出一种曲线在几何约束下发生整体变形，且约束能够被精确满足的计算曲线变形的方法，该方法被称为参数化变形，位移曲线被定义为变形后曲线的表达式与变形前曲线的表达式之差所表示的曲线，对传统能量法进行改进，提出对位移曲线的能量在线性约束下求最小的方法，得到了精确的变形计算公式，以此公式为基础，提出在非线性约束情况下曲线变形的计算方法，文中提出的参数化变形的计算方法可用于二维参数化设计模型中。

Deformation Calculation of Curve under Constraints

A new approach is proposed in the paper on the B-spline curve deformation controlled by global geometric constraints. When a CAD software environment is involved, curve deformation has to accurately meet some geometric constraints often associated with the functional requirements. Here the deformation method is called parametric deformation technique, and the expression of the deformed curve apart from that of initial curve represents a curve called displacement curve. By minimizing the energy of displacement curve under linear constraints, the deformation formula is obtained, and the formula is used as a foundation in calculating the deformation under non-linear constraints. The method proposed in this paper can be used in a 2D parametric design system.