Euler operators and navigation of multi-shell building models

Abstract

This work presents the Dual Half Edge (DHE) structure and the associated construction methods for 3D models. Three different concepts are developed and described with particular reference to the Euler operators. All of them allow for simultaneous maintenance of both the primal and dual graphs. They can be used to build cell complexes in 2D or 3D. They are general, and different cell shapes such as building interiors are possible. All cells are topologically connected and may be navigated directly with pointers. Our ideas may be used when maintenance of the dual structure is desired, for example for path planning, and the efficiency of computation or dynamic change of the structure is essential.