Techniques For CAD Surface Modeling Based On Mesh

With the rapid development of computer science and data acquisition techniques,Reverse Engineering has become one of the import techniques for product design and manufacture.Reconstructing surface from scanned data and obtaining the final CAD model of existing physical object is an essential task of Reverse Engineering.This dissertation introduces several different RE modeling strategies and focuses on reconsructing CAD surfaces from mesh data. It mainly studies the following key topics: reconstruction of regular sweeping surfaces(include extruded surface and rotational surface) and free-from surfaces from mesh model after segmentation, construction of smooth B-spline surfaces over a quad-partitioned mesh model, generation of NURBS surfaces over quadrilateral mesh based on subdivision. The main contributions are as follows:(1)An algorithm to extract compound extruded and rotational surfaces is proposed.The extruding direction is extracted by using Gaussian Sphere, and the rotational axis is extracted based on the Plücker coordinates of line. A method is provided to get a reasonal profile of extruded or rotational surface by using the section profile and projection profile together in order to get a full profile and keep the sharp features of the profile. Then use Hough transform to detect all the possible line segments in the profile , use persudo-random circle detection algorithm to get all the possible circular arcs in the profile. Then delete false line segments and false circular arcs by using region merging method and local geometrical parameter estimation. Using curves' geometrical parameters, add possible geometrical constraints into the curves.Then using geometrical constraint fitting formula, re-fit all line segments and circular arcs. Finally fit the left points in profile by B-spline curves according to possible constraints.This algorithm is much robust with noise than the traditional methods which do recognition after segmentation, and can effectively and rationally recognize circular arcs and line segments in the profile, and can well reconstruct the nature definitions. (2) A rapid B-spline surface fitting algorithm is developed by generating regularized grid points from scattered vertex points of the mesh.First, a rectangular parameter region is obtained on the least square plane and planar regularized grid points are constructed. Then most of the planar grid points are mapped back onto the mesh model and the spacial regularized grid points are obtained, where some points in the grid are missed. The neighbor information of the spacial grid points is used to evaluate the positions of the four corner points. Then a radial basis function surface is constructed and used to fill the missing points. Finally, a smooth B-Spline surface is fitted to these spacial regularized grid points. For a mesh with holes, the presented algorithm automatically fills the hole regions by using radial basis function surface and captures the original shape well. The experimental data shows that the presented algorithm is fast, accurate and robust. The reconstructed surface has good smoothness and extensionality. It can be well applied to reconstruct B-Spline surface from mesh model after segmentation.(3) For a mesh model with quad-partition, an algorithm of constructing G~1/C~2 continuous bi-cubic B-spline surfaces is developed. First, a curve network is constructed over the quad-partitioned model. Then for each quadrilateral patch, a bi-cubic B-spline surface is fitted from four boundary curves and internal data points. After obtaining G°continuous surface patches network, a method of modifying the cross-boundary derivatives is proposed to make two adjacent surfaces to be C~2 continuous along regular edges or approximately G~1 continuous along irregular edges. The presented algorithm well solves the compatible problem around the corner. It is also simple, efficient and practical, and has no restriction on the topology structure of the quadrilateral network.The reconstructed surfaces not only have good continuity but also capture the geometric details of the model and can satisfy the engineering requirements.(4) Based on Catmull-Clark subdivision, an algorithm for generating smoothly connected NURBS patches that interpolate the mesh vertices over a quadrilateral mesh is proposed. The input quadrilateral mesh is took as the initial control mesh of Catmull-Clark subdivision, and the subdivision limit surface is converted into Bézier patches. For each facet of the quadrilateral mesh, a Bézier surface is obtained. The Bézier patches are G~1 continuous along boundaries connecting to extraordinary pointsand C~2 continuous everywhere else. A recursive method to expand the initial control mesh is proposed based on the deviation analysis, so the final surfaces generated from the expanded mesh interpolate the vertices of the input quadrilateral mesh.The presented algorithm is effective and the constructed surfaces have good smoothness and continuity . For a triangular mesh, we can construct an approximate quadrilateral mesh first, then reconstruct smooth NURBS surface from the quadrilateral mesh. The algorithm implements the conversion from Catmull-Clark subdivision surface to NURBS surface, and solves the shrinking problem of Catmull-Clark subdivision, and enlarge the application fields of subdivision surface.