Shape morphing, as the efficient means to enhance the visual effects, is widely used in computer animation. In this paper, we propose a novel approach to perform shape morphing for point set surface based on vertex deformation gradient. The basic idea of our approach is to interpolate the vertex deformation gradients of the input point set surfaces with polar factorization, and the in-between point set surface is reconstructed with a quadratic energy optimization by minimizing the difference between the interpolated and the actual deformation gradient. Due to the differential property of the deformation gradient and polar factorization, this optimization can avoid the shrinkage and wrinkles problem in the linear interpolation method. The vertex deformation gradient is defined on each point of the point set surface, a closed form solution of which is also presented from the view of quadratic energy optimization. Several examples are presented to demonstrate the effectiveness of our proposed method.
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