Boundary Controlled Iterated Function Systems

International audienceBoundary Controlled Iterated Function Systems is a new layer of control over traditional (linear) IFS, allowing creation of a wide variety of shapes. In this work, we demonstrate how subdivision schemes may be generated by means of Boundary Controlled Iterated Function Systems, as well as how we may go beyond the traditional subdivision schemes to create free-form fractal shapes. BC-IFS is a powerful tool allowing creation of an object with a prescribed topology (e.g. surface patch) independent of its geometrical texture. We also show how to impose constraints on the IFS transformations to guarantee the production of smooth shapes. Objects modeled through Computer Aided Geometric Design (CAGD) systems are often inspired by standard machining processes. However, other types of objects, such as objects with a porous structure or with a rough surface, may be interesting to create: porous structures can be used for their lighter weight while maintaining satisfactory mechanical properties, rough surfaces can be used for acoustic absorption. Fractal geometry is a relatively new branch of mathematics that studies complex objects of non-integer dimensions. Because of their specific physica