B-spline Surface Hole Filling Based On Adjusting Control Points

Hole filling of three-dimensional model is an important subject in Computer Aided Geometric Design. Because the integrity of data is the most impartment requirement no matter what kind of operations is going to be done on the model. The researches on triangular mesh is much more than that on freeform surface now in the field of hole filling technology according to the information the author knows. However the importance of freeform surface hole filling technology is self-evident in Computer Aided Geometric Design. The author discovered that there are still some problems worth further researching and discussion in freeform surface hole filling while studying on the existing method. For example, how to split holes better, how to make the final hole with G1continuity and how to get the better effect for hole filling etc. Some B-spline surface hole filling work is done in this paper on the basis of previous researches, and the work mainly includes the following three aspects:Firstly, an algorithm to fill a B-spline surface hole basis on adjusting control points is presented by this paper. It uses control mesh of B-spline surface to express hole in freeform surface hole filling, and makes the hole G1continuous by adjusting the control points. The main idea of the algorithm is compute a central point and a center normal in condition of given a set of boundary curves and corresponding cross-boundary derivatives, then compute the inner curves to split the region into n quadrangular areas. After that each quadrangular surface is represented with B-spline surface. Finally, the algorithm adjusts the control points of B-spline surfaces to make both the border and the interior of the hole achieve G1continuity.Secondly, this paper gives several different hole filling examples basis on the algorithm above, and analyze the hole filling algorithm from graphical effects and numerical results respectively. Graphical experimental results show that, this algorithm can get good visual effects of hole filling; while numerical experimental results show that, the algorithm can meet the demand of G1continuous hole filling, interpolating the boundary curves and boundary cross-boundary derivatives.Thirdly, basis on the algorithm above, this paper introduces shape parameter in freeform surface hole filling, and presents an algorithm to fill a B-spline surface hole with shape adjustment. The main idea of the algorithm is to modify the hole shape by adjusting the shape parameters. It includes center point position adjustment, hole concavity and convexity adjustment and hole smoothness adjustment. The algorithm in this paper is simple and effective to make the hole G1continuous by adjusting the b-spline control points. It not only increases freedom degrees of hole filling, but also compatible with the industrial CAD/CAM software system that B-spline surfaces are used. This offers the possibility of further theoretical research and application development. Modifying the hole shape by adjusting the shape parameters increases the flexibility of the hole filling. It also can be used in the process of designing hole when the constraints of parameters are relaxed.