We introduce the point-and-edge model for edge-preserving modeling and rendering. Besides a set of surface points, the point-and-edge model also includes edge points representing the sharp edges in the model. The surface points and the sharp edges are relatively independent of each other. We present a feedback algorithm to simplify the point-and-edge model with bounded error based on an edge-preserving clustering method. An efficient constrained splatting method is used to preserve the sharp edges in the rendering, regardless of the surface point density.