  The context of this paper is the use of formal methods for topology-based
geometric modelling. Topology-based geometric modelling deals with objects of
various dimensions and shapes. Usually, objects are defined by a graph-based
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
topology-based 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,
topology-based geometric objects constitute a particular subclass of a category
of labelled graphs in which nodes have multiple labels.
