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To increase the efficiency of surface reconstruction, the surface-reconstruction step was performed following an object-simplification step. However, point simplification often destroys the point distribution and increases the difficulty of surface reconstruction. To reconstruct a low-resolution point-cloud model, this study presents a novel shape-sensitive point sampling approach for modifying a sampling region adaptively. The proposed method extends the projection-based reconstruction method proposed by Gopi. Therefore, our method inherits the high performance of the other method. Generally, a surface reconstruction method only works when the point distribution in a point-cloud model is dense, but the point distribution on feature surfaces is often nonuniform. To overcome this limitation, we adopt the discrete shape operator (DSO) to quantify model features and determine sampling regions to reconstruct surfaces. Experimental results show the DSO efficiently extracts features of a 3D model, and the sampling regions determined by the DSO provide sufficient reconstruction information, thereby avoiding generation of undesired holes.