Graph rewriting for topology-based geometric modeling

Presentation for done at the Christmas event of the MICS laboratory.

Abstract : The work I will present lies at the interface of computer graphics (how to represent objects within a computer) and graph rewriting (how to create a new graph out of an already existing one). Graph transformation generalizes rewriting (such as string rewriting) to non-linear structures, namely graphs. In this approach, transformations are rule-based, and rules comprise a left-hand side (what we want to delete) and a right-hand side (what we want to add) expressed as graphs. Combinatorial maps represent (quasi-)manifolds through their subdivision into topological cells (vertices, edges, faces, volumes). The graph-based definition of combinatorial maps enables the formalization of modeling operations as graph rewriting rules. I will explain how this rule-based approach allowed the creation of Jerboa. This editor generates dedicated geometric modeling kernels (software for visualizing and manipulating nD objects).