Research On T-Splines Modeling Technology

Surface modeling has been the primary task in product design. Yet, the existing B-spline surface modeling technology increasingly becomes less insufficient to meet the practical demands from designers, such as in surface refining, surface matching, surface merging, and surface trimming.T-Splines can be applied to remedy these old problems in B-spline surface modeling, but also brings in some new modeling problems. By going deeper into the basics of T-Splines, this thesis proposes some new practical and handy approaches for surface modeling, improving the existing modeling approach for B-spline surface and T-Splines. The main content and achievements are presented as follows:Firstly, a local-uniform-refining approach based on full-row-column T-Splines is proposed for surface refinement, overcoming the negative effect on affine invariance of surface from the over-flexible T-Splines local refinements. By restricting the standard property of initial T-Mesh and choosing the proper local refining approach, a standard T-Splines could be always obtained by applying this refining approach, making the surface modeling more convenient.Secondly, a T-splines matching approach is proposed by matching boundary T-Meshes for surface matching, avoiding the bothersome knot-coordinate-system during surface hybrid matching and enabling the surface matching more convenient. To achieve the surface hybrid matching between neighboring B-splines surfaces with incompatible boundary conditions, another T-Splines matching approach based on local-row-refinement and combined-refinement is also proposed, obtaining a compact combined T-Splines. By introducing the standard unidirectional T-Mesh during local refinement, a handy-for-modeling standard T-Splines could be always obtained after surface hybrid matching.Thirdly, the combined-refinement is also applied to achieve the surface matching between two B-spline surfaces having incompatible vertical and horizonal boundary conditions, so that the deficiency of existing T-Splines merging approach used in merging adjacent B-spline surfaces along the whole boundary is solved, resulting in a more practical T-Splines merging approach. To solve the disability of merging two B-spline surfaces along hybrid boundary, a new merging approach based on multilateral T-Splines is proposed, enabling the merged surface to be more simply defined and easily altered.Finally, a new geometric trimming approach based on multilateral T-Splines is proposed forsurface trimming, amending the shortcomings of B-spline surface and T-Splines in geometrically trimming the isoparametric multilateral rectangular domain. This trimming approach is easy to implement by using only local refinements to isolate the trimming domain, producing a multilateral T-Splines without extraordinary points. To obtain a standard multilateral T-Splines after geometric trimming, the full-row-column refinement and combined-refinement are both chosen to isolate the trimming domain before geometrically trimming the surface.All of the above newly proposed modeling approaches not only contribute to the research on surface modeling theory in CAGD, but are also verified in car-body design. Some drawbacks of B-spline surface and T-Splines modeling during the car-body design have been solved in this thesis,thus the working efficiency of designers would be further improved by applying these new modeling tools.