Boundary Controlled Iterated Function Systems

Dmitry Sokolov (1, 2) , Gilles Gouaty (2) , Christian Gentil (2) , Anton Mishkinis (2)

1 ALICE - Geometry and Lighting
2 Le2i - Laboratoire Electronique, Informatique et Image [UMR6306]

Boundary 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 physical

Mots clés: subdivision surfaces; fractals; Iterated Function System; B-splines

Domaines: Géométrie algorithmique [cs.CG]

Dmitry Sokolov, Gilles Gouaty, Christian Gentil, Anton Mishkinis. Boundary Controlled Iterated Function Systems. Curves and Surfaces, Springer, 2015, Lecture Notes in Computer Science - 8th International Conference, Paris, France, June 12-18, 2014, Revised Selected Papers, 978-3-319-22803-7. ⟨10.1007/978-3-319-22804-4_29⟩. ⟨hal-01244612⟩