Translational Research, Based On Graph Rotation System Of Non-manifold Surface

Polygon surfaces are used to describe the geometry model in three-dimensional geometric modeling. Non-manifold surfaces, which are produced in most modeling, do not have European space properties. But they have topological surfaces with more complex topological properties and description. However, most graphics algorithms and operating applying in polygon surfaces require manifold. For example, subdivision, simplification, smooth, compression, these operation algorithms also require polygon surfaces of initial grid structures are effective and robust manifold surfaces. It is too complicated to redesign and modify graphics algorithms to make it be applicable for non-manifold surfaces and it's difficult to make true. In this paper, non-manifold surfaces were transferred into manifold surfaces with the similar geometric appearance and topological relationship so as to be applicable for most graphics algorithms. Since the conversion of non-manifold surfaces include the conversion of non-manifold points and non-manifold edges, conversion of non-manifold edges were investigated as an importance. Since original conversion algorithm of non-manifold edges have some limitations, such as generation again of non-manifold structures couldn't avoided in, exterior of original object would be changed and so on. A new conversion algorithm of cutting-construction management, based on graph rotation system, was proposed to treat non-manifold edges. In this case, production of new non-manifold edges could be inhibited and the manifold structures with connected topological structure and similar outward would exist to meet the requirements of graphic modeling.Mesh adta structure-double link face list DLFL based on faces were proposed in our work to discribe the non-manifold faces correctly. The pointer assays of mstedgenode edges extended not only can inherit abundant topology information contained by original data structure, but also can discibe and display non-manifold edges. Non-manifold edges and points could be searched and marked based on this data structure. For the non-manifold points search algorithm, vertexes were first optimized and then searched which greatly reduces the time complexity.The conversion of non-manifold surfaces can be divided into non-manifold edges and non-manifold points conversion. The endpoints of non-manifold edges are non-manifold points. We first conduct the conversion of non-manifold edge.The present conversion and repair algorithms of non-manifold edges primarily emphasize on the conversion and the elimination of non-manifold edge in simplification. While the appearance and connectivity of three-dimensional mode were not considered and new non-manifold surfaces would be produced in the transformation process.A method of holing-piping was proposed by investigating cutting-stitching. In this method, the operation of holing-piping was conducted between adjacent structures which share the same non-manifold edges so that each structure which have common non-manifold edges could connect with others. In this case, non-manifold surfaces were conversed into manifold surfaces with similar apparent structure and non-manifold edges would not be produced.The present non-manifold point conversion algorithms almostly produce only one topological separated manifold structure. In order to avoid problems of piping numbers and angles, an idea of the operation of holing-piping was conducted between adjacent structures which share the same non-manifold edges was proposed based on piping operation. The results showed that manifold topology described unicom was obtained and non-manifold surfaces would not be produced.Finally, we used the Doo-Sabin algorithm to subdivide the grid surface after conversion, and the results revealed that the surface has been transformed into manifold with similar appearance structure.