# An approach for inferring geometric expressions in topology-based modeling

FM&AI working group at LMF (Université Paris-Saclay).

**Abstract:** Designing geometric modelling operations means implementing them using a programming language. This task can be simplified using a high-level description of these operations. Nevertheless, the difficulty of implementation remains, contrasting with the apparent simplicity of their description via an example. We propose a method for inferring operations from a representative example in topology-based geometric modelling. This domain represents nD objects by their decomposition into topological cells (vertices, edges, faces, volumes, etc.) extended with geometric information. Topology is specified by combinatorial structures represented as graphs such that an operation can be formalised as a graph transformation rule. Here, we complete our topological folding algorithm (which allows retrieving a generic topological operation from an example) with an approach for deducing geometric expressions. We exploit two main ideas: topological abstractions of geometric computations to ensure the genericity of the retrieved expression and a formalisation of the expression to be retrieved as a constraint satisfaction problem.