Graph transformations and application to geometric modeling

Groupe de travail toposique at Centre Lagrange (Huawei).

Abstract: Graph transformations provide a tool to formalize and study the rule-based evolution of systems modeled as graphs with applications across software engineering, meta-modeling, chemistry or computer graphics. However, this variety of application domains also means different (application-based) concepts of graphs, for which the constructions need to be re-specified. In this context, as usual in computer science, category theory provides an abstraction layer to reason more systematically and generically about these transformations of graphs. In the meantime, the induced abstraction should still allow for efficient implementations. After detailing the underlying theory, I will highlight some benefits of formalizing topology-based geometric modelling operations (think algorithms that describe the modifications of geometric objects in computer graphics) as graph transformations.