Research On Reconstruction Algorithm Of Non Tensor Product Algebra B Spline Surface

In the recent year,with the rapid development of science and technology,the data is increasing from a variety of the scientific computing,the engineering computing and the measurement.The required accuracy becomes more accurate,and the pending problems increasingly large scale.Therefore,the study on the surface reconstruction of large scale data increasingly become urgent to solve the problem.In this paper,the problem of surface reconstruction based on large scale scattered data is studied.Firstly,a fitting function is constructed to reconstruct the implicit surface.Secondly,by using the integral structure spline function method and the spline function space,we can construct the piecewise polynomial form of Box spline as the basis function of the fitting function.Then,by using the idea of the least square method,the Box spline function is introduced into the surface reconstruction,the control coefficient of the fitting function is solved well.Finally,the surface reconstruction is performed according to the fitting function,at the same time,the time complexity of the algorithm is analysis,and the effectiveness of the algorithm is verified by an example analysis.The specific research work is as follows:(1)We complete the construction of Box spline.As we can see,the method is based on ?-type partition to subdivide the spline function space.We can obtain the local branch of the Box spline by the integral method.(2)By constructing the non-tensor product algebra Box spline,we can reconstruct the implicit function.In the basis on tensor algebra B-spline surface algorithm,we can convert the multiplication of three one-dimensional B-spline to a Box spline basis function,it can greatly reduce the amount of computation;moreover,the three one-dimensional B-spline can't fit to the point,the Box-spline can fit in the same order.