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It is hard to extract skeletons using geometric models with limited information such as point models without topology and models with low resolution. This paper proposes a novel skeleton-extracting and animation approach for point models, which explores the differential properties of point models without triangulating the discrete points. First, this paper gives definitions of the attributes of surface and tangency, and then uses these attributes to iteratively contract the model to get the skeleton. At last the point models animation driven by the resulting skeleton is presented. Results show that our approach can get good skeletons even if the model is lacking connection information and in low resolution. Also, it can obtain good animation results and make the animation more convenient since the binding of skeleton points and skin is obtained.