Set Manipulations of Fractal Objects Using Matrices of IFS

1 I n t r o d u c t i o n The aim of geometric modeling is to model forms by manipulating or combining well-known shapes such as circles and boxes. In order to be convenient such a model should allow easy control and manipulation of the final shape. When dealing with fractal geometric modeling, the control on ffactal figures is not so easily achieved as with classical smooth ones. The difficulty comes from the fact that fractal shapes are usually generated with iterative or recursive procedures. In order to have a better control on the shape, we wish to develop a fractal modeler. Such a modeler should be constituted of a set of basic shapes, a set of unary operations (shape modifications) and a set of binary operations (shape combinations). Our work focuses on set operations based on the IFS model. This approach has been inspired by constructive solid geometry (CSG). This technique is classical in geometric modeling. It permits to build complex objects using set operations (union, intersection, ...). In fractal modeling such operations are possible using IFS matrices which are a way to generate a wide class of fractat shapes, not necessarily self-similar. These matrices can be combined using certain operations to yield complex fractal shapes in a constructive way.