留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

三角网格曲面上测地B样条曲线偏置

容振乾 刘斌

容振乾, 刘斌. 三角网格曲面上测地B样条曲线偏置[J]. 机械科学与技术, 2014, 33(8): 1177-1182. doi: 10.13433/j.cnki.1003-8728.2014.0813
引用本文: 容振乾, 刘斌. 三角网格曲面上测地B样条曲线偏置[J]. 机械科学与技术, 2014, 33(8): 1177-1182. doi: 10.13433/j.cnki.1003-8728.2014.0813
Rong Zhenqian, Liu Bin. Offset of Geodesic B-spline Curves on Triangulation Surface[J]. Mechanical Science and Technology for Aerospace Engineering, 2014, 33(8): 1177-1182. doi: 10.13433/j.cnki.1003-8728.2014.0813
Citation: Rong Zhenqian, Liu Bin. Offset of Geodesic B-spline Curves on Triangulation Surface[J]. Mechanical Science and Technology for Aerospace Engineering, 2014, 33(8): 1177-1182. doi: 10.13433/j.cnki.1003-8728.2014.0813

三角网格曲面上测地B样条曲线偏置

doi: 10.13433/j.cnki.1003-8728.2014.0813
基金项目: 

国家自然科学金项目(51175191)

国家科技支撑计划项目(2012BAF12B15)

福建省自然科学基金项目(2011J01314)资助

详细信息
    作者简介:

    容振乾(1987-),硕士研究生,研究方向为数字化设计,641441071@qq.com;刘斌(联系人),教授,博士,mold-bin@hqu.edu.cn

    容振乾(1987-),硕士研究生,研究方向为数字化设计,641441071@qq.com;刘斌(联系人),教授,博士,mold-bin@hqu.edu.cn

Offset of Geodesic B-spline Curves on Triangulation Surface

  • 摘要: 针对曲面上曲线偏置方法存在的不足,提出一种流形网格曲面上测地B样条曲线偏置方法。该方法将流形网格曲面上曲线偏置的问题转换为平面曲线偏置的问题。对于给定的流形网格曲面上测地B样条曲线,将测地B样条曲线所在的区域用离散指数映射的方法进行局部参数化;利用基于控制顶点偏移的方法,将参数域上的曲线进行偏置;利用参数匹配的方法将偏置后的曲线映射到流形网格曲面上,完成曲面上曲线的偏置。针对平面偏置曲线出现的自交,提出了一种新的检测与去除自交的方法,能够有效地去除自交。试验结果表明:该方法不仅健壮、有效,能够满足交互设计要求,而且偏置曲线的表达式与源曲线具有相同形式。
  • [1] Bukchin J,DAR-EI E M,Rubinovitz J. Mixed modelassembly line design in a make-to-order environment[J]. Computer and Industrial Engineering,2002,41(4):405-421
    [2] Patrikalakis N M,Bardis L. Offsets of curves on rationalb-spline surfaces[M]. Engineering with Computers,1989,5(1):39-46
    [3] Hatna A,Grieve R J,Broomhead P. Offsetting 3Dcontours on parametric surfaces[C]// The InternationalJournal of Advanced Manufacturing Technology,2000,16(3):189-95
    [4] Piegl L A,Tiller W. Computing offsets of NURBS curvesand surfaces[J]. Computer-Aided Design,1999,31(2):147-56
    [5] 余正生,杨章通. 球面上等距线的构造[J]. 系统仿真学报,2008,20(17):4630-4632,4642Yu Z S,Yang Z T. Offset of curves on spherical surfaces[J]. Journal of System Simulation,2008,20(17):4630-4632,4642 (in Chinese)
    [6] Holla V D,Shastry K G,Prakash B G. Offset of curveson tessellated surfaces[J]. Computer-Aided Design,2003,35(12):1099-108
    [7] 陈正鸣,刘景,王志坚. 一个三角网格上曲线的等距线计算方法[J]. 计算机集成制造系统,2008,14(1):124-131Chen Z M,Liu J,Wang Z J. Offset algorithm for curveson triangle meshes [J]. Computer IntegratedManufacturing Systems,2008,14 (1 ): 124-131 (in Chinese)
    [8] 舒莲卿,余正生,杜辉. 基于网格的球面上等距线的构造方法[J]. 计算机仿真,2010,27(7):321-325Shu L Q,Yu Z S,Du H. Mesh based offset algorithmfor curves on spherical surfaces [J]. ComputerSimulation,2010,27(7):321-325 (in Chinese)
    [9] Bommes D,Kobbelt L. Accurate computation of geodesicdistance fields for polygonal curves on triangle meshes[C]//Proc. Work-shop on Vision,Modeling,and Visualization,November,2007,(7/9):151-60
    [10] Xin S Q,Ying X,He Y. Efficiently computing geodesicoffsets on triangle meshes by the extended Xin-Wangalgorithm[J]. Computer-Aided Design,2011,43(11) :1468-1476
    [11] Hofer M,Pottmann H. Energy-minimizing splines inmanifolds[J]. ACM Transactions on Graphics,2004,23(3):284-293
    [12] Pottmann H,Hofer M. A variational approach to splinecurves on surfaces[J]. Computer Aided GeometricDesign,2005,22(7):693-709
    [13] Rodrigues R C,Leite F S,Jakubiak J. A new geometricalgorithm to generate smooth interpolating curves onRiemannian manifolds[J]. LMS Journal of Computationand Mathematics,2005,(8):251-266
    [14] Park F,Cqravani B. Bézier curves on riemannianmanifolds and lie groups with kinematicapplications [J]. ASME Journal of MechanicalDesign,1995,117:36-40
    [15] Martínez D,Carvalho P C,Velho L. Modeling ontriangula-tions with geodesic curves[J]. The VisualComputer,2008,24(12):1025-1037
    [16] 朱文明,邓建松,陈发来. 应用保角映射构造流形上的细分曲线[J]. 计算机辅助设计与图形学学报,2007,19(1):48-53Zhu W M,Deng J S,Chen F L. Constructing subdivisioncurves on manifolds using conformal mapping [J].Journal of Computer-Aided Design & ComputerGraphics,2007,19(1):48-53 (in Chinese)
    [17] 刘斌,黄常标,林俊义,等. 流形网格曲面上测地 B 样条插值[J]. 机械工程学报,2011,47(19):136-142Liu B,Huang C B,Lin J Y,et al. Interpolation ofgeodesic B-spline curves on manifold triangulation[J].Journal of Mechanical Engineering,2011,47(19):136-142 (in Chinese)
    [18] Schmidt R,Grimm C,Wyvill B. Interactive decalcompositing with discrete exponential maps[J]. ACMTransactions on Graphics,2006,25(3):605-613
    [19] 刘利刚,王国瑾. 基于控制顶点偏移的等距曲线最优逼近[J]. 软件学报,2002,13(3):398-403Liu L G,Wang G J. Optimal approximation to curveoffset based on shifting control points[J]. Journal ofSoftware,2002,13(3):398-403 (in Chinese)
  • 加载中
计量
  • 文章访问数:  213
  • HTML全文浏览量:  49
  • PDF下载量:  11
  • 被引次数: 0
出版历程
  • 收稿日期:  2012-11-19

目录

    /

    返回文章
    返回