Automatic Detection of Topological Changes in Geometric Modeling Operations

Abstract

Advanced geometric modelers require the detection of topological changes caused by modeling operations such as edge creation, face splitting or volume merging... Such a detection can be dynamically performed by comparing all topological cells (vertices, edges, faces, volumes) before and after each modification, which can be very time consuming. Then, for some events generated in a systematic way, it can also be performed statically before applying each operation, but it entails several hurdles due to the lack of formalization of such events: while some events may seem obvious, others may not appear intuitively or systematically, and this work of defining events needs to be done again for each newly developed operation. In this paper, we propose to formalize the static detection of events and to automate this process based on automatic analysis of operations. To achieve this, we leverage on the formalism of graph transformation rules to describe geometric operations, and on the topological model of G-maps that enables homogeneous modeling of manifold geometric objects in any dimension. The syntactic analysis of rules enables the detection of all events that can be detected statically and also specifies the cells on which events that can only be detected dynamically could occur. With this approach, any new operation can be developed faster within the modeler, ensuring a complete, accurate and automatic event detection.