Abstract: This paper proposes a new method for curve metamorphosis，where the in-between curves are constructed by using unstructed meshes.The key idea is to implicitly represent the curve as the level set of a higher dimensional function，and solve the morphing equations on unstructed meshes using finite volume methods.This approach thereby eliminates the round-off errors taken by the interpolation in a Cartesian coordinate system.Experimental result is presented to demonstrate the effectiveness of this method.

摘要： 采用基于非结构网格的水平集方法对曲线变形问题进行了数值模拟。通过度量函数最优化过程得到曲线变形的驱动方程，驱动方程中增加曲线曲率项对度量函数进行优化，空间上采用有限体积法求解水平集方程，时间上采用Runge-kutta显式方法，时间、空间均达到2阶精度。实验结果得到了高质量的过渡曲线，显示复杂几何拓扑形变可以理想地实现。