Based On A Collection Of Graph Rotation System Operation

In the field of computer graphic solid modeling, set operations are very important tools. Because traditional 2-manifold through set operations is not closed, it can't guarantee the 2-manifold property of the resulting polyhedron on which some operations can't be continued such as subdivision.The theory of graph rotation system topologically represents the graph embedding. Graph rotation system only has two kinds of operations: edge insertion and edge deletion, which both of them can guarantee the 2-manifold property. To be added the isolated vertex creation and isolated vertex deletion, it is now complete and sound. We have known that every rotation system of a graph gives a unique oriented 2-manifold, which is constructible. Therefore, the existence of bijective correspondence between graph embedding and graph rotation enables us to replace graph operations with the operations of graph rotation system, which can guarantee the 2-manifold property of the graph embedding.In this paper we extend the data structure and data operations of the Doubly Linked Face List (for short DLFL) which is based on the theory of computer graph rotation system and we use DLFL as the data structure of our graph modeling system, and the extended structure can represent the non-manifold. Based on new structure we completed the set operations using the theory of vertex neighborhood classifier, which is completed and sound, that is which can guarantee the 2-manifold property of the resulting polyhedron. At the same time, we give the union operation a parameter, by which we can choose that whether the resulting polyhedron is connected. Using the vertex, edge, face glue algorithm of two polyhedrons, we can make the result of union operation to become a connectedpolyhedron and guarantee its topological consistency.Based on the theory of graph rotation system, we built a graph modeling system by using Visual C++ and OpenGL. The system can guarantee the 2-manifold property and have plenty topological transformation and have good user interaction, and most exciting is that the system can build artful graph easily.