Implicit representation of inscribed volumes

We present an implicit approach for constructing smooth 3-D inscribed volumes intended for modeling porous structures, such as volcanic rocks, foam, radiolarians, and Swiss cheese. Positive inscribed volumes can model natural pebbles, and negative volumes can model porous structures. We introduce two techniques for blending and creating interconnections between these inscribed volumes to adapt our approach to both regular and irregular. We begin with a set of convex polytopes such as 3-D Voronoi diagram cells and compute inscribed volumes bounded by the cells. The cells can be irregular in shape, scale, and topology, and this irregularity transfers to the inscribed volumes, producing natural-looking spongy structures. Describing the inscribed volumes with implicit functions gives us the freedom to exploit volumetric surface combinations and deformation operations effortlessly.