曲率线驱动的B样条曲面交互编辑
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摘要
为了使曲面的曲率线分布更加整齐,以用户绘制的曲线作为目标曲率线优化曲面的形状,提出一种曲率线驱动的交互式B样条曲面形状编辑方法.首先通过绘制生成用户期望的曲率线走向;然后以用户期望的曲率线走向作为曲面形状修改的目标;最后通过优化极小化目标函数实现对曲面形状的编辑.通过几个B样条曲面模型,展示了该方法的有效性.
An interactive approach is proposed for B-spline surface editing to improve the distribution of curvature lines on surface. In order to indicate a more regular distribution of curvature lines and to decrease the number of umbilical points, desired curvature lines are plotted on surface interactively. The plotted lines are used as target curvature lines in an optimization algorithm for surface modification, which becomes approximate curvature lines on surface after optimization. The effectiveness of the proposed method is demonstrated by several B-spline surface models.
An interactive approach is proposed for B-spline surface editing to improve the distribution of curvature lines on surface. In order to indicate a more regular distribution of curvature lines and to decrease the number of umbilical points, desired curvature lines are plotted on surface interactively. The plotted lines are used as target curvature lines in an optimization algorithm for surface modification, which becomes approximate curvature lines on surface after optimization. The effectiveness of the proposed method is demonstrated by several B-spline surface models.
引文
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[2]Bo P B,Liu Y,Tu C H,et al.Surface fitting with cyclide splines[J].Computer Aided Geometric Design,2016,43(C):2-15
[3]Mamoru H.Theory of curve and surface synthesis and their smooth fitting[J].Ipsj Magazine,1969,10(3):60-68
[4]Kjellander J A P.Smoothing of bicubic parametric surfaces[J].Computer-Aided Design,1983,15(5):288-293
[5]Farin G,Rein G,Sapidis N,et al.Fairing cubic B-spline curves[J].Computer Aided Geometric Design,1987,4(1/2):91-103
[6]Sapidis N,Farin G.Automatic fairing algorithm for B-spline curves[J].Computer-Aided Design,1990,22(2):121-129
[7]Lott N J,Pullin D I.Method for fairing B-spline surfaces[J].Computer-Aided Design,1988,20(10):597-604
[8]Rando T,Roulier J A.Designing faired parametric surfaces[J].Computer-Aided Design,1991,23(7):492-497
[9]Poliakoff J F.An improved algorithm for automatic fairing of non-uniform parametric cubic splines[J].Computer-Aided Design,1996,28(1):59-66
[10]Joshi P P.Minimizing curvature variation for aesthetic surface design[D].Berkeley:University of California at Berkeley,2008
[11]Beier K P,Chen Y F.Highlight-line algorithm for realtime surface-quality assessment[J].Computer-Aided Design,1994,26(4):268-277
[12]Chen Y F,Beier K P,Papageorgiou D.Direct highlight line modification on NURBS surfaces[J].Computer Aided Geometric Design,1997,14(6):583-601
[13]Zhang C M,Cheng F H.Removing local irregularities of NURBS surfaces by modifying highlight lines[J].Computer-Aided Design,1998,30(12):923-930
[14]Zhang C M,Zhang P F,Cheng FH.Fairing spline curves and surfaces by minimizing energy[J].Computer-Aided Design,2001,33(13):913-923
[15]Zhang Genquan,Zhang Caiming.Removing local unfairness of NURBS surfaces based on high light line model[J].Journal of Computer-Aided Design&Computer Graphics,2003,15(5):561-565(in Chinese)(张跟全,张彩明.基于高光线模型修改NURBS曲面不光顺性[J].计算机辅助设计与图形学学报,2003,15(5):561-565)
[16]Yong J H,Deng B L,Cheng F H,et al.Removing local irregularities of triangular meshes with highlight line models[J].Science in China Series F,2009,52(3):418-430
[17]Liu Y,Xu W W,Wang J,et al.General planar quadrilateral mesh design using conjugate direction field[J].ACM Transactions on Graphics,2011,30(6):Article No.140
[18]Pan H,Liu Y,Sheffer A,et al.Flow aligned surfacing of curve networks[J].ACM Transactions on Graphics,2015,34(4):Article No.127
[19]Nicholas M P,Takashi M.Shape interrogation for computer aided design and manufacturing[M].Beijing:China Machine Press,2005:20-30(in Chinese)(Nicholas M P,Takashi M.计算机辅助设计与制造中的外形分析[M].冯结青,叶修梓,译.北京:机械工业出版社,2005:20-30)
[20]Manfredo Perdigao do C.Differential geometry of curves and surfaces[M].Upper Saddle River:Prentice-Hall.Inc,1976:147-148