Polyhedral Partitioning of Space for Digital Modelling of Topology and Geometry

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Topological and geometrical description of objects is a fundamental requirement in science and technology. Scientific foundations for digital solutions, which satisfy this demand adequately, are a world-wide topic of research. The known problems relate to two basic scientific issues: the accuracy and the complexity of the digital models.Experience shows that digital mapping of large and complex originals to sufficiently realistic computer models is associated with unavoidable errors due to the storage and processing characteristics of digital devices. It is therefore essential to structure the models and to perform the mapping such that the errors can be observed and controlled. The methods employed must not only be correct and sufficiently accurate, they must also be efficient and robust. It is proposed to address this basic scientific problem by space partitioning for polyhedral objects with cell structure, whose outer and inner boundaries are composed of flat surfaces with straight edges.Topological computer models can be used to study neighborhood that varies with time. Such neighborhood is of importance in many areas of technology, for example in evacuation control. Advanced methods exist which create two-dimensional models by digital mapping of objects with polygonal structure. Comparable methods of digital mapping do not yet exist for three-dimensional models of objects with polyhedral structure. The available three-dimensional concepts are not readily applied in technology, where the abstract and the intuitive approach are used simultaneously. Preliminary research has revealed that significant improvements can probably be achieved through additional research. It is proposed to investigate a novel digital model structure for polyhedral objects, which is based on extensions of conventional characteristics of nodes, edges, faces and cells, and which requires only two structural relations to map the originals: oriented plane polygons and dihedral cycles of faces at the edges of the object. This reduces the complexity of the models significantly. The work program for the project describes an interface model, which is designed for simple construction and use, and a core model, whose data structure and methods are optimized for efficient and reliable handling of the topology and the geometry of the space partitioning. The mapping between interface and core model is automatic such that the user need not be familiar with the core model. The theory, data structure and methods for the novel approach will be developed, implemented, tested, documented, verified and validated. The work program and data handling are planned such that the joint project can readily be performed simultaneously at Berlin and at Moscow. The results are widely applicable in engineering practice. Significant added value is expected to result from the international cooperation, particularly in the areas of academic development and of building information modelling.