Barycentric combinations based subdivision shaders

We present a new representation of uniform subdivision surfaces based on Iterated Functions Systems formalism. Main advantages of this new representation are the formalization of topological subdivision, multiscale representation of limit surface, separation of iterative space where the attractor is computed once for all and modeling space where the attractor is projected many times. An important consequence of this approach is that all uniform subdivision schemes are handled in the same way whatever there are primal or dual, approximating or interpolating. Subdivision surfaces are no longer viewed as a set of rules but as a list of barycentric combinations to apply on neighborhoods of the coarse mesh. These combinations are representative subsets of the attractor which is deduced from a Controlled Iterated Functions System automaton. From this new point of view we present in this paper a straightforward implementation to directly compute a tessellation of the subdivision surface from a control mesh. This implementation takes full advantage of Graphics Processing Units high capability of computation and Tessellation Stage of OpenGL/GLSL rendering pipeline to generate on the fly a tessellation of the limit surface with a chosen Level of Details