Inferring topological operations on G-maps formalism: application to iterated function systems

Romain Pascual (1) , Hakim Belhaouari (2, 3) , Agnès Arnould (2, 3) , Pascale Le Gall (1)

1 MICS - Mathématiques et Informatique pour la Complexité et les Systèmes
2 Université de Poitiers - Faculté de Sciences fondamentales et appliquées
3 XLIM-ASALI - Synthèse et analyse d'images

The design of correct topological modeling operations is known to be a time-consuming and challenging task. However, these operations are intuitively understood via simple drawings of a representative object before and after modification. We propose to infer topological modeling operations from an application example. Our algorithm exploits the compact and expressive graph-based language used in the Jerboa platform. In this framework, topological modeling operations on generalized maps are represented as rules from the theory of graph transformations. Most of the time, operations are generic up to a topological cell (vertex, face, volume). Thus, the rules are annotated with variables indicating which kind of cells is involved. Our main idea is to infer a Jerboa rule by folding a graph representing the object before and after modification. We fold this graph according to the cell parametrization of the operation under design. We illustrate our approach with some examples of iterated function systems.

Mots clés: Topology-based geometric modeling; Iterated function systems; Operation inference; Inference from examples; Topological operation; Computational topology

Domaines: Synthèse d'image et réalité virtuelle [cs.GR]

Romain Pascual, Hakim Belhaouari, Agnès Arnould, Pascale Le Gall. Inferring topological operations on G-maps formalism: application to iterated function systems. 2021. ⟨hal-03491856v1⟩