Implicit Representations of Rough Surfaces

Implicit surface techniques provide useful tools for modeling and rendering smooth surfaces. Deriving implicit formulations for fractal representations extends the scope of implicit surface techniques to rough surfaces. Linear fractals modeled by recurrent iterated function systems may be defined implicitly using either geometric distance or escape time. Random fractals modeled using Perlin's noise function are already defined implicitly when described as “hypertexture.” Deriving new implicit formulae is only the first step. Unlike their smooth counterparts, rough implicit surfaces require special rendering techniques that do not rely on continuous differentiation of the defining function. Preliminary experiments applying blending operations to rough surfaces have succeeded in an initial attempt to overcome current challenges in natural modeling. The grafting of a stem onto the base of a linear fractal leaf continuously blends smooth detail into rough detail. The blend of two textured cylinders interpolates geometric bark across branching points in a tree.