Romain Pascual

Karlsruhe Institute of Technology | KIT · Institute of Information Security and Dependability

This report presents a set-theoretic framework for the instantiation of rule schemes in the Jerboa platform, a tool for developing domain-specific geometric modelers. Jerboa enables the design of geometric modeling operations as graph transformation rules generalized to rule schemes for genericity over the topological content of the operations. Cur...

Los's theorem, also known as the fundamental result of ultraproducts, states that the ultraproduct over a family of structures for the same language satisfies a first-order formula if and only if the set of indices for which the structures satisfy the formula belongs to the underlying ultrafilter. The associated notion of satisfaction is the Tarski...

In a previous publication, we introduced an abstract logic via an abstract notion of quantifier. Drawing upon concepts from categorical logic, this abstract logic interprets formulas from context as subobjects in a specific category, e.g., Cartesian, regular, or coherent categories, Grothendieck, or elementary toposes. We proposed an entailment sys...

Strokes concerned more than 795,000 individuals annually in the United States as of 2021. Detecting thrombus (blood clot) is crucial for aiding surgeons in diagnosis, a process heavily reliant on 3D models reconstructed from medical imaging. While these models are very dense with information (many vertices, edges, faces in the mesh, and noise), ext...

In this thesis, we present a formalization of geometric modeling operations as rules from the theory of graph transformation.First, we investigate the construction of a dedicated rule-based language. We describe the combinatorial models of generalized and oriented maps as labeled graphs, subject to consistency conditions. This topological represent...

Labeled graphs are particularly well adapted to represent objects in the context of topology-based geometric modeling. Thus, graph transformation theory is used to implement modeling operations and check their consistency. This article defines a class of graph transformation rules dedicated to embedding computations. Objects are here defined as a p...

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 a compa...

Topology-based geometric modeling tackles the issue of representing objects with data structures that encode the topological subdivision of modeled objects in vertices, edges, faces, and volumes. Such subdivisions can be represented with graphs labeled by dimensions on arcs, while modeling operations used to edit the objects can be formalized as gr...