Unbiased Sampling and Meshing of Isosurfaces

摘要

In this paper, we present a new technique to generate unbiased samples on isosurfaces. An isosurface, $F(x,y,z) = c$ , of a function, $F$ , is implicitly defined by trilinear interpolation of background grid points. The key idea of our approach is that of treating the isosurface within a grid cell as a graph (height) function in one of the three coordinate axis directions, restricted to where the slope is not too high, and integrating / sampling from each of these three. We use this unbiased sampling algorithm for applications in Monte Carlo integration, Poisson-disk sampling, and isosurface meshing.