Blending implicit shapes using smooth unit step functions

Abstract

In constructive solid geometry (CSG), highly smooth and manageable blending operations are always desirable. In this paper, we propose two novel ways to blend implicitly defined geometric objects using smooth unit step func- tions. With the proposed techniques, not only is it direct to build an implicit blending operation with controllable blending range, but also the blending operation can be constructed to whatever level of smoothness. In addition, the mathematical descriptions of the techniques are quite simple and elegant.