Optimized Sub‐Sampling of Point Sets for Surface Splatting

Abstract Using surface splats as a rendering primitive has gained increasing attention recently due to its potential for high‐performance and high‐quality rendering of complex geometric models. However, as with any other rendering primitive, the processing costs are still proportional to the number of primitives that we use to represent a given object. This is why complexity reduction for point‐sampled geometry is as important as it is, e.g., for triangle meshes. In this paper we present a new sub‐sampling technique for dense point clouds which is specifically adjusted to the particular geometric properties of circular or elliptical surface splats. A global optimization scheme computes an approximately minimal set of splats that covers the entire surface while staying below a globally prescribed maximum error tolerance ε . Since our algorithm converts pure point sample data into surface splats with normal vectors and spatial extent, it can also be considered as a surface reconstruction technique which generates a hole‐free piecewise linear C −1 continuous approximation of the input data. Here we can exploit the higher flexibility of surface splats compared to triangle meshes. Compared to previous work in this area we are able to obtain significantly lower splat numbers for a given error tolerance.