International Journal of Shape Modeling c  World Scientific Publishing Company MESH-BASED PARAMETRIZED L-SYSTEMS AND GENERALIZED SUBDIVISION FOR GENERATING COMPLEX GEOMETRY ROBERT F. TOBLER STEFAN MAIERHOFER VRVis Research Center Vienna, Austria * and ALEXANDER WILKIE Institute of Computer Graphics and Algorithms Vienna University of Technology, Austria † We propose two mechanisms that can be used to generate complex geometry: gener- alized subdivision and mesh-based parametrized L-Systems. Instead of using standard subdivision, which uses the same subdivision rule at each level of the subdivision pro- cess, in order to converge to a limit surface, we employ a generalized approach, that allows different subdivision rules at each level. By limiting the variations at each level, it is possible to ensure convergence. Mesh-based parametrized L-Systems represent an extension to L-systems which associates symbols to the faces in a mesh. Thereby com- plex geometry can be introduced into an existing mesh by using procedural substitution rules. Combining both these mechanisms, a wide variety of complex models can be easily generated from very compact representations. Keywords : meshes, procedural modelling, fractals, subdivision surfaces. 1. Introduction Complex objects which exhibit different features at different resolution levels are difficult to model and render with conventional, manual modeling techniques. In order to facilitate such tasks it is necessary to resort to procedural modeling. Cur- rently three different developments concentrate on different aspects of procedural generation of models: • Subdivision surfaces: a sequence of subdivision steps applied to a base mesh generates a series of meshes that converges to a limit surface. The objective of this development is to generate smooth models with G 1 or — even better — G 2 continuity. • Fractal surfaces: certain natural phenomena like terrains or wrinkled tissues can be nicely described by recursively adding random displacements to the * Donau-City-Str. 1/3, A-1220 Vienna, Austria. † Favoritenstr. 9/5, A-1040 Vienna, Austria. 1