Mixed-aspect fractal surfaces

In order to provide accurate tools to model original surfaces in a Computer Aided Geometric Design context, we develop a formalism based on iterated function systems. This model enables us to represent both smooth and fractal free-form curves and surfaces. But, because of the self-similarity property underlying the iterated function systems, curves and surfaces can only have homogeneous roughness. The aim of our work was to elaborate a method to build parametric shapes (curves, surfaces, …) with a non-uniform local aspect: every point is assigned a “geometric texture” that evolves continuously from a smooth to a rough aspect. The principle is to blend shapes with uniform aspects to define a shape with a variable aspect. A blending function controls the influence of each initial shape. An illustrated application is then built, joining surfaces characterized by different kinds of roughness.

► We elaborate a model to build parametric shapes with a non-uniform local aspect.
► The local aspect can evolve continuously from a smooth to a rough aspect.
► We blend shapes with uniform aspects to define a shape with a variable aspect.
► A blending function controls the influence of each initial shape.
► We show how to build a surface with different imposed rough curves as boundaries.