Research On Related Technologies Of Reconstruction And Process Of Surface Triangle Mesh

Triangular mesh surface model is a common representation for 3D object, and it plays a very important role in various fields of mechanical engineering such as reverse design, rapid prototyping, 3D printing, finite element analysis, virtual simulation. Therefore triangular surface mesh reconstruction and processing technology have been a significant topic of mechanical engineering for decades.The research of this paper is to deal with the technologies of triangular surface mesh reconstruction and processing. In research of reverse engineering based on ICT(Industrial Computed Tomography), corresponding from a stack of planar contours is the key step of surface mesh reconstruction, but it would become a difficult issue when the contours or topology of the object are complex. When the reconstructed triangular surface mesh has been obtained, certain appropriate processing(such as feature region extraction, developable region extraction and mesh parameterization) is necessary to be done sometimes to meet the requirement of subsequent various applications. In the extraction of feature regions from surface mesh, as for a surface mesh model of mechanical part whose surface geometry transits drastically and where concave and convex features are equally important when modeling, it should be dealt with specially. In the existed related methods of extracting developable regions from surface mesh, continuous developable surface couldn’t be identified and developable types can’t be classified on the extracted regions. One important objective of all the involved research of the surface mesh parameterization has been always to reduce the metric distortion. The existing methods of mesh parameterization are not perfect which cannot meet the requirements of related research and application.To solve the above problems,this paper focuses on corresponding vectorized contours in model reconstruction, extracting feature regions from surface mesh model, extracting developable surface regions and classifying them, and mesh parameterization. The main contents and achievements are listed as follows:(1) Given the regularity of industrial parts and similarity of contours between adjacent layers, we presented a shape-based corresponding method specialized in ICT-based reverse engineering based on vectorized contours. Firstly the primitives between adjacent layers are corresponded with each other by utilizing the characteristics of primitives, and then based on the corresponded primitives, the contours of interlayer are corresponded with each other in two cases: pair-wise and branch by utilizing rules of proximity and exhaustive search. The method makes full use of shape information and is able to deal with industrial parts with complex structure.(2) Referring to the original approach which is based on the minima rule(MR) in cognitive science, we created the revised minima rule(RMR) and presented the improved approach in the paper based on RMR. Using the logarithmic function in terms of the minimum curvatures which are normalized by the standard deviation on the vertices of the mesh, we determined the solution formulas for the feature vertices according to RMR. Because in the developed formulas only a small range of the threshold parameters was to be selected from, an iterative process has been implemented to realize automatic selection of thresholds. Finally according to the obtained feature vertices, the feature edges and facets were achieved by growing neighbors. The improved approach has overcome the inherent shortcomings of the original approach, realized full automation without setting parameters, and could achieve more accurate results compared with the latest conventional approaches.(3) Against disadvantages of conventional methods, a novel method was presented in the paper to extract and classify developable surface mesh. Firstly, Gaussian curvature was utilized to extract the developable regions. Then, fitted ruled surface for the divided developable layer regions and judging the fitted equation if developable or not was performed according to the developable condition in differential geometry. Finally it was determined and grown for each layer region that which developable type it belongs to by use of the attributes of generators on each developable type. The result mesh patches contains continuous cylindrical ones or conical ones and tangent surface mesh which could not be obtained by conventional methods; furthermore, it is favorable to the later mesh processing that the developable type of each result patches by our method are accurate.(4) Likewise to further reduce area and angle distortion simultaneously, a novel method of boundary-free mesh parameterization is presented in the paper. Firstly, we carried out the initial boundary-fixed conformal parameterization from 3D surface mesh patch to the plane. Then on basis of the initial parameterized results, we executed the developed iteration of the boundary-free quasi-harmonic parameterization, where the tensor fields are updated on each iterative step and the principal curvature directions are utilized to construct the iterative terminating criterion. The solution of the novel method only involves a series of linear systems which are convenient to calculate. Lower metric distortion and considerable efficiency in our parameterization method has been demonstrated in experiments.The research achievements above have been integrated into a software system developed by our research group. The results on the software system have demonstrated the effectiveness of these methods.