Research On Surface Reconstruction In Reverse Engineering

With the rapid development of computer science and modern manufacturing technology, more and more attention has been paid to the studies on the reverse engineering, which now is a research focus. In the reverse engineering, CAD model can be reconstructed by the numerical information of the object, which can make full use of the advanced manufacturing and management technology such as CAD/CAM. Besides, due to the ability of duplicating object in short time, the technology can sharpen the productivity, the product quality and enterprises's market competition strength, and increase economic efficiency.The reverse engineering consists of data acquirement, data pre-processing and surface reconstruction. Data acquirement can obtain the coordinates of the discrete points by the fixed measuring equipment and methods. Data pre-processing includes the transformation of data format, data splicing, data smoothing and data cracking. The process decides whether the following CAD model reconstruction process is convenient, and whether the reconstruction model meets the application need. The goal of surface reconstruction is to seek some mathematics description form, which satisfies the given precision, effectively describes the shape of physical surface, and carries on the analysis, the computation, the revision and the rendering of the surface itself in this foundation.Surface reconstruction is the most important and difficult problem in the reverse engineering, but there still are key and difficult questions to wait for the solution and consummation. To large-scale data set, the surface reconstruction speed is slow; the reconstruction quality is not high and it needs massive human-computer interaction operations, and so on. In this paper, complex surface reconstruction technologies in the reverse engineering are studied, and new algorithms for quadrilateral mesh reconstruction as well as mesh subdivision and mesh parameterization are put forward, which provide the basis for the reconstruction of different surface types. The main contributions are as follows:(1) The shortest path algorithm for the curve reconstruction of scattered points is presented. It improves the quality of the reconstruction curve, and provides the effective rechnology for the screw reconstruction.The curve reconstruction is the base of the surface reconstruction, but now the present solutions can't ensure the quality of reconstruction curve especially for the multiply connected scattered points. The shortest path approximation algorithm builds a weighted graph from the given set of scattered points using the distribution of these data points. By computing the shortest path in the weighted graph, the problem of curve reconstruction from scattered data points is transformed into that of curve reconstruction from a set of ordered data points.The potential function reflects the relationship between the scattered points, so the shortest path of the point set based on the potential function can keep the whole shape well. Besides, Delaunay triangulation and the deletion of some edges help identify the topology of the scattered point set. The proposed method can reconstruct curves from data set with arbitrary topology, such as simply connected, multiple connected and closed scattered points, keep the shape characteristic of point set well, especially in the segments with high curvature, and provide effective methods and technologies for the screw reconstrucion.(2) To reduce the face number of reconstruction meshes, a new method for quadrilateral mesh reconstruction is proposed.The reconstruction meshes of scattered point set are based on triangular meshes mainly, which makes the number of the meshes too large and can't operate them in real time. The process of the quadrilateral mesh reconstruction proposed in this paper is as follows: Firstly, the least bounding box of scattered points is split into several cubic voxels, and the scattered points of every cubic voxel are simplified into one point. Secondly, each simplified point is connected with other simplified ones associated with its neighboring voxels, and then polygonal meshes are formed. Finally, the polygonal meshes are subdivided into quadrilateral meshes. The quadrilateral meshes with different precision can be obtained by adjusting the size of the cubic voxel. Compared with the triangular meshes, the proposed method reduces the number of the meshes, and makes it easier to reconstruct the surface, so it is suitable for the surface reconstruction of large-scale data set.(3) A new ternary stationary subdivision scheme for quadrilateral mesh is put forward, which provides new way to increase the subdivision efficiency.Subdivision technology is able to realize the trimming of any topological meshes, and the subdivision surface is an important expression form of reconstruction surfaces. There are many subdivision technologies on quadrilateral meshes, but most of them try to reduce the increasing speed of face number. This is extremely essential to the net transmission, but does not suit to construct the reconstruction surface.For regular and irregular quadrilateral meshes, different subdivision schemes are adopted respectively. The face number of the refined mesh is about nine times the face number of the coarse mesh every refinement. The limit surface of regular mesh is C~2 and the limit surface of irregular mesh is C~1. The characteristic of the ternary subdivision scheme is fast convergence speed, and is suitable for the reconstruction subdivision surface of large-scale data set.(4) To construct the parameterization form of reconstruction surface, a new algorithm for the planar parameterization of quadrilateral meshes is presented.To construct the parametric surface, the first step is to parameterize the quadrilateral meshes, but the present methods are almost used to parameterize the triangular meshes, so the parameterization technique for non-closed quadrilateral meshes based on mesh simplification is proposed. In the parameterization process, the global optimal parametric coordinates are attained by deleting interior vertices with low Gaussian curvature while preserving the whole shape as much as possible; then a local coordinate frame is chosen to adjust the positions of the deleted vertices through the weighted discrete mapping and minimize the local distortion; finally the parameterization meshes are optimized to avoid the overlapping.The weighted mapping is adopted to parameterize the vertices with low Gaussian curvature, which minimizes both the local and global distortion of the parameterization meshes. Different parameterization results can be obtained by adjusting the weight values in the energy function, thus it is very suitable for computer graphics applications that require parameterization with low geometric distortion. Besides, the solution of large equation set can be avoided and the computation efficiency can be increased using the algorithm for the planar parameterization of quadrilateral meshes, so it provides the basis for the reconstruction of parameterization surfaces for quadrilateral meshes.