Research On The Algorithms Of Triangular Mesh & System Realization

In current 3D modeling research area, generating solid model by triangular mesh is becoming more and more important. According to three basic algorithms: model rendering, model modification and model simplification in mesh operations, new and efficiency algorithms are presented. Topological mapping is introduced into backface culling, region search is introduced into mesh trimming, vector angle is introduced into mesh simplification.Angle comparison of two vectors in three dimensional space is converted to that of two projected vectors in two dimensional plane, then to two mapped points in one dimensional projection line. We partition the normal space by symmetrically subdividing the surface of a unit sphere. For each polygon, we can determine the cells it located according to the position of its mapping coordinates. In each cell, we compute all normals' topological mapping coordinates on the bounding plane.By one specified point on the model surface, boundaries of the selected patch in form as closed cutting line loops are automatically found out, and all the vertexes and faces in the patch are also confirmed. According to this information about the selected patch, new mesh is generated.We address a method for 3D triangular mesh simplification with vector average angle. The vector is made by the vertex and all the vertexes around it. And the average angle is calculated by the vector and all neighbor triangles' center of gravity. We decide the area is flat or not by the vertex's average angle, if the area is flat, the vertex will be deleted and the polygon will be re-triangulated.All the researches are integrated in 3D garment design system.