Abstract: This paper presents a novel approach for appearance and geometry completion over point-sampled geometry. Based on the result of surface clustering and a given texture sample, we define a global texture energy function on the point set surface for direct texture synthesis. The color texture completion is performed by minimizing a constrained global energy using the existing surface texture on the surface as the input texture sample. We convert the problem of context-based geometry completion into a task of texture completion on the surface. The geometric detail is then peeled and converted into a piece of signed gray-scale texture on the base surface of the point set surface. We fill the holes on the base surface by smoothed extrapolation and the geometric details over these patches are reconstructed by a process of gray-scale texture completion. Experiments show that our method is flexible, efficient and easy to implement. It provides a practical texture synthesis and geometry completion tool for 3D point set surfaces.