外载荷的B样条曲线变形

运用能量优化的思想，提出一种B样条曲线变形的新方法，可用于B样条曲线的变形。首先将B样条曲线段类比为有限单元法中线单元，并将作用在B样条曲线段的外载荷等效成线单元的端点力，分别建立B样条曲线内部能量、外载荷能量函数方程；外载荷的改变将引起B样条曲线能量的变化，通过求解一个使曲线能量的变化量为最小的优化问题，得到变形后的B样条曲线。运用该方法实现了B样条曲线的局部、整体等变形操作。

Shape modification of B-spline curve via external loads

Based on the idea of energy optimization, a new method for shape modification of the B-spine curve is proposed. First, using an analogy between the B-spline curve and the curve element of finite element method, and making the external load acting on the curve be equivalent to the end force into the element, the internal energy functional equation of the B-spline curve and the energy functional equation of the load are constructed respectively. The energy change of the B-spline curve with the change of the load, a new curve is generated by solving an optimization problem of the change of the energy. Using this approach, the local or total modification of the curve can be accomplished.