Intelligent Optimization Of T-spline Knot Vector For Surface Fitting

With the appearance of computer and the rapid development of modern industry, such as aviation, ship building, mold manufacturing and so on, the problem that how to represent, analyze and apply the shape information of products by the computer has becoming a hot research spot. The core problem is to seek a method that not only can conform to the computer processing but also meet the shape representation and design requirements. In the process of surface modeling technology development, many problems including the representation of curves and surfaces, shape control and connection, local modification and application range have been effectively solved with the development of parametric curve surface. However, for some complex models and application fields of high precision, the accuracy of products, computation efficiency and contour smoothing still need to be greatly improved. The main research content in this paper is showed in below:(1).On the basis of the classical B-spline parametric surface fitting, the Gaussian mixture model is used to optimize knot vectors in the direction of the two parameters in order to obtain a reconstructed surface which has a high accuracy. In the process of optimization, the priority work is to parameterize the point cloud of single patch. Then, the Gaussian mixture model is used to optimize the knot vectors. Finally, the least squares method is adopted to realize the B-spline surface reconstruction. Compared with the traditional genetic algorithms, the method proposed in this paper can ensure species diversity, enhance the ability of searching the global optimal individual and improve the precision of the approximate surface.(2). Gaussian mixture model is used to optimize knot vector of T- spline. The specific implementation process is showed in below. Firstly, the input data points are interpolated with spline curves. According to certain rules, the control curves can be obtained through linear combination of interpolation curves. Finally, the control curves are used to fit the T-spline surface. Since the knot vector of each section curve is different, knot vector compatibility can make a sharp increase on control points. In order to avoid the above situation, we can firstly reduce the number of knot vectors by approaching to control curve. Then, GMM algorithm is used to make a clustering analysis and new population can be generated by the probability model. Finally, Continuous iteration is performed to obtain the optimized knot vector. Compared with B-spline surface reconstruction, this algorithm greatly reduces the number of redundancy control points and improves the precision of detail approximation.(3). Surface stitching. Complex surface model fitting needs to shard the initial point cloud. In this paper, we firstly make a fitting on single patch. Since the T-spline has a unique advantage in blending surface, so T-spline is selected as the fitting tool in this paper. In the process of stitching, boundary can obtain continuous through merging control points. The appropriate control points will be inserted into the intersection of several surfaces. In this paper, we use particle swarm optimization algorithm to find the position of global optimal control point by following the current best particle and finally realize the local refinement of angular point. This algorithm is simple and easily realized. The algorithm also has high search efficiency. In addition, the surfaces that do not achieve the approximation precision surface need to be subdivided again in order to obtain high quality of the reconstructed surface. Experimental results show that the algorithm proposed in this paper has an ideal effect on improving the precision of the reconstructed surface, reducing the number of redundant control points and the smoothness of subdivision surface stitching.