Point-based representations are becoming increasingly common in computer graphics, especially for visualizing data sets where the number of points is large relative to the number of pixels involved in their display. When dealing with sparse point sets, however, many traditional rendering algorithms for point data perform poorly, either by generating blurry or non-occluding surface representations or by requiring extensive pre-processing to yield good results. In this paper we present a novel method for point-based surface visualization that we call Voronoi rasterization. Voronoi rasterization uses modem programmable graphics hardware to generate occluding surface representations from sparse, oriented point sets without preprocessing. In particular, Voronoi rasterization clips away overlapping flaps between neighboring splats and generates an approximation of the Voronoi diagram of the points under the surface's geodesic distance. To approximate smooth shading and texturing on top of this clipped surface, our method uses existing techniques to construct a smoothly blended screen-space attribute field that implicitly accounts for neighborhood relations between points.