为了获得光滑自然的点模型渐变效果，基于球面参数化，提出了一种鲁棒的渐变算法。该算法首先对源和目标模型进行球面参数化，使得参数化后的模型嵌入到单位球面上；然后在球面上自适应地对齐模型间的相应特征点，并将球面映射到矩形参数域上，基于该域建立模型间各采样点的对应关系；接着在渐变过程中，采用拉普拉斯算子计算出中间点模型的几何位置，以保持模型的细节；最后利用移动最小二乘曲面进行动态上采样，以消除中间模型的裂缝。实验结果表明，该算法具有良好匹配的采样点对应和光滑的渐变过程。

Morphing of point-sampled geometry is one important research area in the field of computer animations. Based on spherical parameterization, we put forward a robust morphing of point-sampled geometry. Source and target models represented by point-sampled geometry are first parameterized onto a sphere, respectively. After aligning the corresponding features of two models on their spheres, two spheres are projected onto a common rectangle-parameter domain and the correspondence between sample points on the two models is built using this rectangle domain. In order to preserve the geometric details of point set surfaces, the absolute geometry of the in-between models is computed by means of Laplacian operator and is dynamically up-sampled using a moving least square method so as to eliminate the cracks. Experiment results demonstrate that our algorithm can preserve the geometric details very well and produce a smooth transition sequence.