Duality in Data Structures and Euler Operators of Solid Modelers

A dual data structure and dual Euler operators for the boundary representation of solid models is presented. This new dual edge based data structure is called the Quarteredge data structure. Then a data structure with complete duality between faces and vertices is derived. This data structure allows multiple loops of Quarteredges to belong to a single vertex. Euler operators based on the Quartereedge and this dual data structure makes it possible to use the same program for a pair of two dual Euler operations. Duality in data structures and programs contribute to the robustness and efficiency in both the implementation and the execution of solid modeling programs. These concepts can be extended easily to non-manifold solid models.