Topological Representation of a 4D Cell Complex and Its Dual-Feasibility Study

Representations of an object in different granularity using the Level of Detail concept are usually separated without links between corresponding components. Extension of a 3D model to the fourth dimension opens new possibilities for spatial analysis. Integration of scale using additional spatial dimension can help in scale-dependent analysis and preserving consistency, especially in case of model updates. In this paper, an extended version of the dual half-edge structure for topological representation of 4D cell complexes is proposed. This feasibility study shows implementation of the Poincaré duality theorem in practice. Thanks to that, the data structure remains simple, where only two atomic elements are used in a construction process i.e. nodes and edges. This solution lays the groundwork for future research, where topological links in the fourth dimension will be used to connect consecutive object representations of different granularity.