GReTA seminar #18: "Combinatorial maps: transformations and application to geometric modeling"
Channel: GReTA Seminar
Date: 2021-09-24

Speaker:

Romain Pascual (MICS laboratory, CentraleSupélec, University Paris-Saclay, France)


Abstract:

In the first part of the talk, I will present generalized maps that represent quasi-manifolds through their subdivision into topological cells (vertices,edges, faces, volumes). We defined generalized maps as constrained labeled graphs. Arc labels encode topological relations of the subparts modeled object while node labels describe the geometric data used to represent the object. Modeling operations are designed regardless of the object's underlying topology. Therefore, we generalize DPO rules with a functorial approach to encode semi-global relabeling with a product operation. Rules and their extensions (called rule schemes) are considered valid if any application to a well-formed graph results in an equally well-formed graph. We provide set-theoric conditions on rules and rule schemes to ensure the preservation of the model consistency. In the second part of the talk, I will present how this approach allows the design of geometric modelers (software used to create and edit geometric objects) in Jerboa. The set-theoric conditions can be checked via graph traversal in Jerboa's rule editor to ensure that the code derived from the rule will never break the model. The generated code can be used as an add-on in other software or Jerboa's generic viewer. 


About the GReTA seminars:

The GReTA – Graph TRansformation Theory and Applications virtual seminar series aims to serve as a platform for the international graph rewriting community, to promote recent developments and trends in the field, and to permit a regular networking and interaction between members of this community. Seminars are held twice a month in the form of Zoom sessions (some of which will be live-streamed to YouTube). Please refer to http://www.irif.fr/~greta for further details (including information on how to register for participating in the Zoom meetings).