Research On The Surface Refinement Method Of T-spline

With the continuous development of free-form surface modeling technology,B-spline is widely used in engineering design.To overcome the limitation of tensor product for B-spline in local subdivision,T-spline surface is introduced.It can reduce redundant control points via single-level local subdivision and perform watertight splicing.T-spline surface has played an important role in free-form surface modeling technology.Since not all T-splines meet the unit divisibility and linear independence,a further study is performed to propose a new method of free-form surface modeling for T-spline,which improved the performance of local refinement of T-splines.A standard local refinement algorithm based on the uniform mesh T-spline surface is proposed.First,the bounding box method is used to obtain a uniform T-spline surface,and then the standard control points are inserted to realize the local subdivision in T-spline surface.The progressive insertion of form is adopted to achieve the affine invariability of T-spline surface,which the full line(or full column)uniform control point is inserted via the grid with local features,and then the local column(local row)uniform control point is inserted.Finally,the conversion matrix of the blending function is used to quantitatively verify the unit divisibility,and the Bézier operator extraction is used to verify the linear independence.The feasibility of the algorithm is proved by experiment.Compared with the B-spline surface,a large number of redundant control points are reduced by the proposed algorithm.Compared with the existing T-spline surface which is suitable for analysis,the complexity of arbitrary control point insertion is simplified.The experiment proves that the standard T-spline surface meets the demand for linear independence.A semi-standard local refinement algorithm based on the uniform mesh T-spline surface is proposed.The local subdivision of arbitrary features and nested subdivision can be realized by the uniform mesh T-spline surface.To meet the demand for local feature subdivision of surface,the overdetermined equations are established by the extra coefficient determination method and solved via the neural network algorithm,which ensure the affine invariance of the T-spline surface.Further,the conversion matrix of the blending function is used to quantitatively verify the unit divisibility,and the Bézier operator extraction is used to verify the linear independence.The feasibility of the algorithm is proved by an example.Compared with the existing T-spline which is suitable for analysis,the redundant control points are reduced via the proposed algorithm.The example proves that the semi-standard T-spline surface meets the demand for linear independence.Application analysis for T-spline surface is achieved.An analysis program for T-spline surface is established based on MATLAB.Several sub-modules for standard T-spline and semi-standard T-spline surfaces are created.These sub-modules which contain importing relevant initial condition information,related data operations,and storage module are established in the module.The T-spline surface analysis can be realized via the operation of man-machine interactive.