Consistent geometric modeling operations

Formal Methods research seminar at KIT (Karlsruhe).

Abstract: Geometric modeling operations describe modifications of 3D shapes (or, more generally, nD objects). Their design and implementation are error-prone, partially due to the complex data structures used to describe objects. We represent geometric objects as embedded generalized maps, seen as typed attributed graphs subject to constraints. Therefore, we can formalize modeling operations as graph transformations to obtain a rule-based language. We investigate the conception of consistent modeling operations in this language. Here, consistency means that modifying a well-formed object should result in a well-formed object. We ensure the preservation of topological and geometric constraints via conditions statically checked on the rules.