等边折线的离散曲率表示及应用

Discrete curvature representation of equilateral polylines and its application in morphing

给出平面等边折线的离散曲率表示方法。引入离散曲率的一种计算公式,通过求解方程组,使顶点处的离散曲率和折线的边长分别等于给定的离散曲率值和边长值,可重构出平面等边折线,并得到等边折线顶点坐标的解析表达式。可以证明,若忽略刚体运动变换,则重构出的平面等边折线唯一确定。所给表示方法可应用于计算机动画中的变形(Morphing)问题。

A discrete curvature representation method of planar equilateral polyline is given. A formula for calculating discrete curvature is introduced. By solving an equation set, in which the discrete curvatures at the vertices and the edge length of the polyline are equal to the given values respectively, the planar equilateral polyline can be reconstructed, and the analytic expression of the vertex coordinates of the equilateral polyline are acquired. It can be proved that the reconstructed planar equilateral polyline is uniquely determined if the rigid body motion transformation is ignored. The proposed representation method can be applied to “Morphing” in computer animation.