Building a 4D Cell Complex Topology Through the Extrusion Process

Abstract. This paper is a step forward towards a construction of 4D cell-complex models implemented using a topological data structure, dual half-edge. This allows for explicit representation of spatial relations among objects, such as adjacency relationship, coincidence or order of construction elements, e.g. vertices and edges. A method based on extrusion is proposed. An original 2D model is extruded to 3D, where adjacent cells sharing the same face are directly linked. Then extrusion to 4D is performed. In this case individual 4D cells sharing the same 3D cell are linked together. A model is kept valid at any stage of the construction process and links among cells are automatically provided by the construction operators. Implementation is based on the 4D data structure, which is used at each stage of construction, even in intermediate models of lower dimensionality.