CAD Data Repair Basing On The Surface With Defect

The technology of CAGD has been mature during thirty years' development. B-spline has replaces all kinds of curves that is popular in the world. Most of the commercial CAD softwares are based on B-spline。B-spline is successful as a kind of descriptive way, but as the constructive way, many people are not satisfied with the traditional method of B-spline. For example, the traditional method isn't convenient for the designer. Especially, the designers expend more energy on the artistic construction of the appliance, but the result of construction isn't perfect. So searching the new constructive method based on B-spline of finishing the complicated geometry's design is becoming the focus. Many new methods appeared on this kind of background such as N-side, morpbing, energy, the method of energy is more noticeable in many new technology.Typically, a complicated real-world geometry is defined in terms of thousand of patches, usually piecewise polynomial (or even rational) B-spline patches. We describe an algorithm of repairing polyhedral CAD models that have errors. Errors like cracks, degeneracies, duplication, holes and overlaps are usually introduced in solid models due to imprecise arithmetic, modle transformations, and designer's fault, programming bugs. Complicated models often contain errors due to inconsistent model modifications of various designers working on the same model without necessarily enforcing consistency checks and enforcement. Such errors often hamper further processing like finite element analysis, rapid prototyping and generation of mesh.In this paper, I present a new method about CAD data repairing. First, judging the topological structure of the surfaces, viz, searching adjacent surfaces of every surface. Verify the connectivity along all the edges of each patch and visualize the errors (discontinuities) in the model, viz, judging the crack and overlap between the surfaces. When there is the crack between two neighbor patches, we compute the midpoints of the resulting closest point pairs in the crack and interpolate the midpoints by an interpolating cubic B-spline. Then the new B-spline replace the neighbor boundary curves, so each approximating surface patch is constructed by specifying four boundary curves(original three boundary curves, new B-spline curve), computing a coons patch interpolating the four curves and convert the coons surface to B-spline surface. The purpose of this step is that solving the problem of energy method with external conditions in the same parameter region. Selecting some controlling points on the new B-spline surface and compute the normal vector of these points. Getting the line by the point and its normal vector and computing the intersection points of these lines in the new B-spline. Getting the distance of intersection points and controlling points and searching the pair points with the long distance. Taking this point in the original surface as external energy constraints, calculate the internal energy and external energy of the surface and get the function of energy; calculate the new controlling points with the optimization approach. New controlling points generate the B-spline surface with the minimal energy. By the adjusting the conditions of coons surface, the continuous surface will be generated. A simple example is given to prove the algorithms feasible.Curve fairing methods mainly consist of revising selected points and global optimization. Kjellanders algorithm is one of the most common methods in revision of selected points. We present a local energy optimization approach .In the case of uniformly parameterized cubic splines, LEO improves Kjellander's algorithm and gets better fairing effect. In the paper, the common method of selecting points is introduced at first, then a local energy optimization approach based on the Kjellander's algorithm is presented, the main steps is that, searching the bad point in the curve, selecting some adjacent points around the bad point, the number of the points is ,,the new par...