Ensuring semantic spatial constraints in virtual environments using UML/OCL

Spatial objects and relationships between them, compose a spatial model that is the backbone of virtual environments (VEs). However, due to the natural complexity of both spatial objects and spatial information, the modeling of such spatial relationships is still a difficult task. This paper presents a novel approach for representing semantic spatial relations in VEs using the Unified Modeling Language (UML) and the Object Constraint Language (OCL). Our approach first uses the UML class model as a conceptual model for VEs. We then propose a spatial extension of OCL named VRX-OCL as a high-level and flexible language to cover multidimensional, manifold, and reference frame-dependent spatial constraints. We mainly focus on two important classes of spatial relations, namely, topological and projective relations that allow nonmetric representation of space. The applicability of our approach is demonstrated in the Virtual Physics Laboratory, a VE for learning physics. Based on the constraints satisfaction, the system is able to visualize abstract spatial information and thus provides educational assistance to the learners.

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