Triangular Mesh Model Piecewise B-spline Surface Fitting Technology Research

In recent years, as the devices for measuring coordinates developing, themeasured data points of triangle mesh model of complicated parts can be acquiredeasily. As a result, it is profoundly urgent to develop the reverse engineeringtechnology for those data. Region segmentation based on triangle mesh model andreconstructions of B-spline surface patch are investigated deeply in this paper. Themain research contents and achievement are as follows:(1) Aiming at deleting the fault regarding the triangle data points directly measured, the triangle model, firstly, is pretreated; the abnormal triangles are wiped off in the non-manifold surface; the uneven edges are trimmed; furthermore, there is much improvement on the tracing project approach for building primary profiles, with the result of figuring out the non-concave problem in the course of path searching effectively.(2) Investigating the technology for building the four-side-region interactively in triangle mesh model and searching for the mesh info of these regions. On the one hand, with respect to the mesh model with single boundary, the method is proposed to build the boundary with lines and thin the relative tiles with edition; on the other hand, as for the complicated triangle mesh model, the approach is presented to generate the primary four-edge-tile based on the extension of small four-edge-tile and adjust these tiles, and finally the corresponding four-edge-tile is built for all models effectively and precisely. Furthermore, A method is presented for searching mesh vertex info within those four-edge-tile, resulting in approximating the B-spline surface for discrete mesh data points with the least square method effectively.(3) Fitting B-spline surface for discrete points data based on triangle mesh model. The patch surface is primarily fitted with the B-spline surface for the completed four-edge-tile based on approximating discrete points with the least square method, nevertheless, adding the smoothing term to guarantee the inter-smoothness of surface patch and the penalty function with boundary continuity to achieve the continuity of tangent vector between surface patches,resulting in attaining the smooth B-spline surface satisfying engineering needs effectively. These methods are validated by the mechanical and aeronautic instancesacquired by measuring real parts.