Construction Of Adaptive Subdivision Surfaces Based On Triangular Domain

Subdivision surface technique has many advantages which traditional parametric surface and implicit surface modeling don't have,so it is widely used in computer aided geometric design and computer animation modeling.However,a problem is existed in it: When we subdivide the model iteratively,each iteration is global subdivision,so the number of mesh would increase exponentially,which is too difficult to deal with other operation.However,in practice,it is not necessary to subdivide the whole model to obtain a smooth surface,which is only to be subdivided in a region with an uneven or higher curvature.As for the problem of subdivision on smooth area,this paper proposed an adaptive subdivision algorithm based on dihedral angle threshold and dihedral cycle using local information which can control grids.The algorithm can avoid the relatively smooth part where would be subdivided again,compared with normal subdivision,our method greatly reduces the amount of data,and improve the processing speed,what's more,it achieves the purpose to subdivide the model.The main contents of this paper are as follows:(1)A comprehensive elaboration about basic theory and method of subdivision is given in this paper.And we compared the several properties of subdivision curve algorithm,Doo-Sabin subdivision algorithm,Catmull-Clark subdivision algorithm,butterfly subdivision mode and?3 subdivision mode,etc.(2)The existed adaptive algorithms are compared and their advantages and disadvantages are analyzed.According to the Loop subdivision mode,we realized adaptive subdivision scheme based on threshold dihedral angle.The new subdivision rules are constructed,and the experimental results show that the method can control the excessive growth of the number of subdivision surfaces while guaranteeing the quality of the surface.(3)Our program was performed under Ubuntu 16.04 64 bit Operation System using technology of OpenGL,CGAL and GLUT.And we used the half data structure which can quickly search the grid information and the off model file which is easy to read and write,so the adaptive Loop subdivision surface modeling algorithm is realized.At the same time,the algorithm can realize the rotation,scaling and other operations.We select dragon,tetrahedron and rabbit model to validate the Global Subdivision and adaptive subdivision.The results show that,for different models,the reduction rate of patches is from 9.4%-82.0%,which saves a lot of computer resources.