Application of the stochastic sampling method to various implicit surfaces

Abstract

Recently, we proposed the stochastic sampling method (SSM) to numerically generate sample points on implicit surfaces quickly and uniformly. In this paper, we apply the SSM to various complicated implicit surfaces to demonstrate its usefulness. Namely, we demonstrate that the SSM works well for surfaces with much ruggedness and/or many holes, blobbies, and open surfaces. We also show that the SSM enables effective techniques for quick rendering and visualizing outlines of implicit surfaces. Many other new information/hints, which are useful in applying the SSM to complicated surfaces effectively and easily, are also presented.