Simplification,Displaying And Fitting By Subdivision Based On Point Cloud Data

Surface modeling method is one of the research emphases all the time,and what it focuses on is the denotation,design,display,and analysis of surface under the environment of computer graphics system.In this paper,firstly I introduce the functions and significances of data reduction in reverse engineering ,ayalyze and compare errors of these kind of reduction methods ,then I choose the"normal errors"as my reduction methods.At last I present the flowchart of this arithmetic and get good result.Subdivision is one method to denote surface,a branch of the research emphases of surface modeling. In recent years, subdivision surface becomes one of the hot topic in international CAD/CG areas. From the metaphase anaphase of 70's in the 20th century,with the development of subdivision theories and the expansion of application fields. Subdivision modeling method have been put into wider application in computer graphics,computer aided geometric design (CAGD),computer animation, and virtual reality(VR) etc. In fact subdivision is a method that recursively computers the new vertices, which are averaged with weight by old vertices in previous level, from the initial polyhedron named control mesh.The biggest advantage of subdivision method is that it can generate smooth surface from arbitrary initial mesh. Besides its local controllability, immutability of affine transformation etc like NURBS, the most outstanding advantage of subdivision surfaces is its arbitrary topology that just is the most difficulty of the development of NURBS. Moreover, subdivision surfaces can guaranteed continuity automatically and avoid concatenating. In this paper, describing the base theory, flow and data-structure of the reconstruction of subdivision surfaces and implementing the Loop subdivision scheme. We present the Edge—Vertex and the Vertex—Vertex as follows: Edge—Vertex:Let two Vertex of the internal edge be V0,V1, The two neighboring triangles is (v0 , v1,v2),(v0,v1,v3), so the Edge—Vertex: Vertex—Vertex:Let n neighboring Vertex of the Vertex be V0, V1,……,Vn-1, so the Vertex—Vertex:Subdivision surfaces have been put into wider application in computer animation, but subdivision surfaces have been put into little application in the Reverse Engineering. Hoppe and Suzuki [5,6] Have done a lot of research in the Reverse Engineering. Hoppe's approach about subdivision surface Reconstruction from point cloud is complex. It get control point of subdivision surface by solve a huge Nonlinear energy equation. So the reconstruction of subdivision surfaces spend as long as ten hours. Suzuki's approach is iteratively getting control point of subdivision surface. The approach doesn't spend too much time, but the approach can not reflect the detail characteristics of point cloud very well, so the approach is just applied to the surface which is topologically equivalent to ball.Then we have a approach to reconstruct subdivision surfaces from point cloud of arbitrary topology is proposed. At first we use the reduction method to reduce the point number of point cloud .Second, we cite Zhang Dinglin's approach to get Initial triangular mesh. At last we reconstruct surfaces which are piecewise smooth subdivision surfaces without trimming and sewing. The main idea is to utilize the local characteristic of Loop subdivision to adjust , optimize and adaptive subdivide control mesh to let the subdivision surface fit the data points . Examples demonstrated that the algorithm is efficient and robust , can effectively preserve the detail characteristics of data points. Experiments show that we can obtain the best result whenα=1.55,ε= 6×10?6.