基于Poisson方程的曲线形状渐变方法

以定义在分段线性曲线上的离散Poisson方程为理论基础,提出了一种同时适用于平面和空间曲线形状渐变的方法.通过在源曲线和目标曲线上定义局部标架,给出了一种非线性梯度场插值算法,使得源曲线的梯度场逐步过渡到目标曲线的梯度场,所得到的中间梯度场与用户指定的关键节点路径一起输入离散Poisson方程求解得到渐变序列 .该方法不直接插值顶点坐标,而是将源曲线与目标曲线视为定义在公共定义域上的标量场,并在梯度域进行梯度场操纵.对中间帧曲线周长以及平面曲线所包围的内部面积变化的统计表明:该算法尽可能地保持了几何形状的刚性,在中间帧求解的稳定性方面该算法优于同类其他方法.

Poisson-Based Curve Blending

In this paper,we introduce a novel blending approach for both 2D and 3D curves with the discrete Poisson equation defined on piecewise linear curves as the theoretical foundation.Based on defining local frames on source and target curves,a non-linear gradient field interpolation algorithm is proposed.With user-specified boundary conditions,the in-between curves are reconstructed implicitly from the interpolated gradient fields.By viewing the source curve and the target one as scalar fields defined on the common domain,our algorithm has the distinctive feature that it generates blending sequences via manipulating gradient fields instead of interpolating node coordinates.Statistics of the perimeter and the interior area(for 2D curves)show our method keeps the in-between curves as rigid as possible.Compared with competing methods,our method is more stable.