Research On Surface Reconstruction Method Of Binary Quadratic Polynomial Spline In Type-2 Triangulation

In the field of computation geometry,the use of surface fitting scattered data points is a hot issue for CG and CAGD.The traditional bivariate spline surface reconstruction algorithm based on uniform type-2 triangulation exists shortcomings of the slow speed and the poor accuracy.Aiming at these problems above,a new bivariate spline surface reconstruction method based on uniform type-2 triangulation is developed successfully in this thesis.The convolution type control coefficients are offered through the data points in the type-2 triangulated mesh,the distance between the original sample points and the corresponding sample points on the surface is obtained by iterative method.Then according to the distance,control coefficient is adjusted until the difference is less than the appropriate threshold before and after the maximum distance between the original sample points and the corresponding sample points on the surface,so the optimum control coefficient is determined.Then using blocks as basic calculation units and eliminating repeated calculation at the boundary by the down-rounding method will reduce computation times.At the same time,the data points required are reduced from five to four for each block,so the overall need for data points is reduced by 50 percent.At last the time complexity of the method and convergence are analyzed.The method not only reduces the number of data points required,but also effectively improves the speed and quality of surface reconstruction.The results showed that the method is better than traditional bivariate spline surface reconstruction algorithm based on uniform type-2 triangulation.