Algorithms Research About CAD Data Repair

In practical engineering, analysis using CAD data is more and more popular. In a general way, a complicated real-world geometry is composed of thousands of patches, which are usually described in terms of piecewise polynomial B-spline patches. Complicated CAD models often have errors, such as surface cracks, intersecting surface, surface with holes and surface overlaps and so on. These errors are usually introduced in solid models due to imprecise calculation, model transformation, and designer's fault, programming bugs. In addition, complicated models often contain errors due to inconsistent model modifications of various designers working on the same model or without the same standard. Such errors often hamper further processing, for example, finite element analysis, rapid prototyping and generation of mesh and so on. This paper go deep into researching CAD data repair from theory analysis to programming. In the third section of this paper, I present and realize a new algorithm about looking up CAD errors in a geometry. At first searching adjacent surfaces of every surface using box intersection algorithm and adjacent surfaces of every edge. And then implement boundary matching operation in order to look up entirely matching surfaces. In during of boundary matching, I present algorithms about discretizing curve and calculating minimum distance from a point in space to curve. As two surfaces are not entirely matching surfaces, we need implement intersection judging about those. In order to look up intersection curve between two surfaces, I adopt curve track algorithm. If the relation between two surfaces is not confirmed through above process, we need implement overlap judging operation. The key of overlap judging algorithm is finding projection points of discrete points on the appointed surface. The paper adopt Newton-Raphson method to settle it. At last, the paper implement gap judging algorithm on residuary surfaces. The key of gap judging algorithm is to stretch two adjacent surfaces, and then transform gap problem into overlap or intersection problem. Almost all surfaces that need to be repaired are not entirety distorted. So newly-built surfaces should approximate original surfaces. In the fourth section of this paper, I present and realize a new method for the repair of CAD data. The main idea of this method is based on constructing an initial surface approximant, which is projected onto the given geometry thereby defining a new B-spline surface. At last, the new B-spline surface replaces original surface. The main steps of the method is as follows: (i) Selecting or creating four surface boundary curves. (ii) Constructing a bilinear blend Coons patch from four curves. (iii) Discretizing Coons patch, the resulting 3D points are marked as Pi , j(u , v) , and construct an "upper"offset point and a "lower"offset point of every point Pi , j(u , v) . (iv) Constructing 3D bounding box containing Coons patch and offset points. (v) Clipping original surface against 3D bounding box. (vi) Projecting a set of points Pi , j(u , v) on Coons patch onto original surface after being clipped, which Pi , j(u , v) do not include discrete points on boundary curves. (vii) Constructing a B-spline surface interpolating projection points and Pi , j(u , v) on boundary curves. (viii) Estimating the error between surface approximant and original surface. If error is not within the precision extension, user need restart from (i). The difficulty of the repair method origins in projection course. In the...