1. A method of mesh simplification, the method comprising: decimating, by a graphics-processing unit, a data set for an input mesh that describes a three dimensional object, the data set including data that is represented by a probabilistic octree on the graphics-processing unit, wherein decimating the data set for the input mesh includes: providing the data set for the input mesh in a first pass and a third pass of first, second, and third passes of multiple passes through the pipeline of the graphics-processing unit, wherein each mesh triangle in each pass through the pipeline is accessed once; generating the probabilistic octree, generating a quadric map, and computing a cluster for each vertex of the input mesh at the first pass of the multiple passes; computing, at the second pass of the multiple passes, an optimal vertex position of each cluster using the quadric map generated at the first pass and storing the optimal vertex position for use in the third pass; inputting the input mesh through the pipeline a second time and decimating the data set of the input mesh at the third pass of the multiple passes; and computing multiple levels of detail for the input mesh without repeating each of the multiple passes; and producing, at the graphics-processing unit, in response to decimating the data set for the input mesh, a simplified mesh that describes the three-dimensional object in less detail than the input mesh.