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Beyond the Hausdorff Metric in Digital Topology
Two objects may be close in the Hausdorff metric, yet have very differen...
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SNEngine, a Scalefree Geometric Modelling Environment
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An Efficient Data Retrieval Parallel Reeb Graph Algorithm
The Reeb graph of a scalar function defined on a domain gives a topologi...
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Topological Sweep for MultiTarget Detection of Geostationary Space Objects
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A Topological Nomenclature for 3D Shape Analysis in Connectomics
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Rulebased transformations for geometric modelling
The context of this paper is the use of formal methods for topologybased geometric modelling. Topologybased geometric modelling deals with objects of various dimensions and shapes. Usually, objects are defined by a graphbased topological data structure and by an embedding that associates each topological element (vertex, edge, face, etc.) with relevant data as their geometric shape (position, curve, surface, etc.) or application dedicated data (e.g. molecule concentration level in a biological context). We propose to define topologybased geometric objects as labelled graphs. The arc labelling defines the topological structure of the object whose topological consistency is then ensured by labelling constraints. Nodes have as many labels as there are different data kinds in the embedding. Labelling constraints ensure then that the embedding is consistent with the topological structure. Thus, topologybased geometric objects constitute a particular subclass of a category of labelled graphs in which nodes have multiple labels.
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