Solid Modeling Study Based On Graph Rotation System

In the field of computer graphics, Solid modeling is very important. But traditional 2-manifold is not closed in many operations, such as set operations. 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 operations of Dubly Linked Face List(for short DLFL) which is based on the theory of computer graph rotation system and can reduce the complexity of time. Based on the data 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. Based on the 2-manifold set operation and the basic operation of graph rotation system we build a basic kernel of operation set, through the expansion of this operation can be improved into a complete modeling approach.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.