Implicit Formulations of Rough Surfaces

Proc. Implicit Surfaces, 1995, pp. 33-44.

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 overcoming current challenges in natural modeling, including grafting a stem onto the base of a fractal leaf and continuously interpolating geometric bark across branching points in a tree.

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