三角网格曲面上的特征阵列
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摘要
针对三角网格曲面上复杂特征阵列式设计重用困难问题,提出一种两步法特征阵列重用策略。基于曲面空间向量平移理论,确定特征阵列位置,以角度和测地距离两个参数构建各阵列实例之间的关联;提出一种基于对偶图的曲面局部参数化方法,使参数化结果不受顶点法矢评估方法的影响,对噪声和锐边特征不敏感。在此基础上,采用微分坐标网格变形技术实现阵列实例的形状控制,使其适配曲面局部形状变化。给出了环形旋转阵列、沿曲线阵列以及方向阵列的具体算法实现。试验结果表明,所介绍方法鲁棒、有效,可用于复杂特征的阵列式实时交互设计。
Aiming at the difficult problem of design reuse of complex pattern feature on triangular mesh, a two-step strategy of reuse feature is proposed. Based on the theory of surface space vector translation, the position of the pattern feature is determined, and the correlation between the pattern instances is constructed by the two parameters of angle and geodesic distance. A localized parametric method based on the dual mesh is proposed, which makes the parametric result not affected by the method of evaluation vertex normal vector, which is insensitive to the noise and sharp features. On this basis, the shape control of the pattern instances is realized by Laplacian mesh deformation method, so that it fits the local surface shape. Finally, these specific algorithms to achieve patterns of circular rotation, along the curve and the directions are given in this paper. The experimental results show that the proposed method is robust and effective, and can be used in real-time interactive design of complex pattern features.
Aiming at the difficult problem of design reuse of complex pattern feature on triangular mesh, a two-step strategy of reuse feature is proposed. Based on the theory of surface space vector translation, the position of the pattern feature is determined, and the correlation between the pattern instances is constructed by the two parameters of angle and geodesic distance. A localized parametric method based on the dual mesh is proposed, which makes the parametric result not affected by the method of evaluation vertex normal vector, which is insensitive to the noise and sharp features. On this basis, the shape control of the pattern instances is realized by Laplacian mesh deformation method, so that it fits the local surface shape. Finally, these specific algorithms to achieve patterns of circular rotation, along the curve and the directions are given in this paper. The experimental results show that the proposed method is robust and effective, and can be used in real-time interactive design of complex pattern features.
引文
[1]KANAI T,SUZUKI H,KIMURA F.Three-dimensional geometric metamorphosis based on harmonic maps[J].Visual Computer,1998,14(4):166-176.
[2]万华根,金小刚,刘刚,等.基于变分隐式曲面的网格融合[J].软件学报,2005,16(11):2000-2007.WAN Huagen,JIN Xiaogang,LIU Gang,et al.Mesh fusion based on variational implicit Surfaces[J].Journal of Software,2005,16(11):2000-2007.
[3]SCHMIDT R.Part-based representation and editing of 3d surface models[D].Toronto:University of Toronto,2010.
[4]钱归平,童若锋.实时网格编辑的扩展中值坐标方法[J].计算机辅助设计与图形学学报,2012,24(10):1312-1318.QIAN Guiping,TONG Ruofeng.Real time mesh editing using extended mean value coordinates[J].Journal of Computer Aided Design&Computer Graphics,2012,24(10):1312-1318.
[5]TAKAYAMA K,SCHMIDT R,SINGH K,et al.Geo Brush:Interactive mesh geometry cloning[J].Computer Graphics Forum,2011,30(2):613-622.
[6]黄锦池,刘斌.网格曲面上自由形状特征设计重用[J].机械工程学报,2015,51(19):164-173.HUANG Jinchi,LIU Bin.Design and reuse of freeform features on mesh surface[J].Journal of Mechanical Engineering,2015,51(19):164-173.
[7]ZHOU K,HUANG X,WANG X,et al.Mesh quilting for geometric texture synthesis[J].ACM Transactions on Graphics(TOG),2006,25(3):690-697.
[8]ZHOU S,LASRAM A,LEFEBVRE S.By-example synthesis of curvilinear structured patterns[J].Computer Graphics Forum,2013,32(2pt3):355-360.
[9]LANDRENEAU E,SCHAEFER S.Scales and scale-like structures[J].Computer Graphics Forum,2010,29(5):1653-1660.
[10]GROOT E,WYVILL B,BARTHE L,et al.Implicit decals:Interactive editing of repetitive patterns on surfaces[J].Computer Graphics Forum,2014,33(1):141-151.
[11]刘斌,韩林,林俊义,等.网格曲面上测地B样条曲线交互操作与重用[J].机械工程学报,2012,48(9):170-177.LIU Bin,HAN Lin,LIN Junyi,et al.Interactive manipulation and reuse of geodesic B-spline curves on mesh surface[J].Journal of Mechanical Engineering,2012,48(9):170-177.
[12]SCHMIDT R,GRIMM C,WYVILL B.Interactive decal compositing with discrete exponential maps[J].ACMTransactions on Graphics,2006,25(3):605-613.
[13]MELV?R E L,REIMERS M.Geodesic polar coordinates on polygonal meshes[J].Computer Graphics Forum,2012,31(8):2423-2435.
[14]SCHMIDT R.Stroke parameterization[J].Computer Graphics Forum,2013,32(2pt2):255-263.
[15]CAMPEN M,HEISTERMANN M,KOBBELT L.Practical anisotropic geodesy[J].Computer Graphics Forum,2013,32(5):63-71.
[16]MITCHELL J S B,MOUNT D M,PAPADIMITRIOU CH.The discrete geodesic problem[J].Siam Journal on Computing,1987,16(4):647-668.
[17]ZHU F,LIU B.Computing the minimum distance between a point and a curve on mesh[J].Journal of Computational Methods in Sciences and Engineering,2015,15(1):13-22.
[18]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):136-142.LIU Bin,HUANG Changbiao,LIN Junyi,et al.Interpolation of geodesic B-spline curves on manifold triangulation[J].Journal of Mechanical Engineering,2011,47(19):136-142.
[2]万华根,金小刚,刘刚,等.基于变分隐式曲面的网格融合[J].软件学报,2005,16(11):2000-2007.WAN Huagen,JIN Xiaogang,LIU Gang,et al.Mesh fusion based on variational implicit Surfaces[J].Journal of Software,2005,16(11):2000-2007.
[3]SCHMIDT R.Part-based representation and editing of 3d surface models[D].Toronto:University of Toronto,2010.
[4]钱归平,童若锋.实时网格编辑的扩展中值坐标方法[J].计算机辅助设计与图形学学报,2012,24(10):1312-1318.QIAN Guiping,TONG Ruofeng.Real time mesh editing using extended mean value coordinates[J].Journal of Computer Aided Design&Computer Graphics,2012,24(10):1312-1318.
[5]TAKAYAMA K,SCHMIDT R,SINGH K,et al.Geo Brush:Interactive mesh geometry cloning[J].Computer Graphics Forum,2011,30(2):613-622.
[6]黄锦池,刘斌.网格曲面上自由形状特征设计重用[J].机械工程学报,2015,51(19):164-173.HUANG Jinchi,LIU Bin.Design and reuse of freeform features on mesh surface[J].Journal of Mechanical Engineering,2015,51(19):164-173.
[7]ZHOU K,HUANG X,WANG X,et al.Mesh quilting for geometric texture synthesis[J].ACM Transactions on Graphics(TOG),2006,25(3):690-697.
[8]ZHOU S,LASRAM A,LEFEBVRE S.By-example synthesis of curvilinear structured patterns[J].Computer Graphics Forum,2013,32(2pt3):355-360.
[9]LANDRENEAU E,SCHAEFER S.Scales and scale-like structures[J].Computer Graphics Forum,2010,29(5):1653-1660.
[10]GROOT E,WYVILL B,BARTHE L,et al.Implicit decals:Interactive editing of repetitive patterns on surfaces[J].Computer Graphics Forum,2014,33(1):141-151.
[11]刘斌,韩林,林俊义,等.网格曲面上测地B样条曲线交互操作与重用[J].机械工程学报,2012,48(9):170-177.LIU Bin,HAN Lin,LIN Junyi,et al.Interactive manipulation and reuse of geodesic B-spline curves on mesh surface[J].Journal of Mechanical Engineering,2012,48(9):170-177.
[12]SCHMIDT R,GRIMM C,WYVILL B.Interactive decal compositing with discrete exponential maps[J].ACMTransactions on Graphics,2006,25(3):605-613.
[13]MELV?R E L,REIMERS M.Geodesic polar coordinates on polygonal meshes[J].Computer Graphics Forum,2012,31(8):2423-2435.
[14]SCHMIDT R.Stroke parameterization[J].Computer Graphics Forum,2013,32(2pt2):255-263.
[15]CAMPEN M,HEISTERMANN M,KOBBELT L.Practical anisotropic geodesy[J].Computer Graphics Forum,2013,32(5):63-71.
[16]MITCHELL J S B,MOUNT D M,PAPADIMITRIOU CH.The discrete geodesic problem[J].Siam Journal on Computing,1987,16(4):647-668.
[17]ZHU F,LIU B.Computing the minimum distance between a point and a curve on mesh[J].Journal of Computational Methods in Sciences and Engineering,2015,15(1):13-22.
[18]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):136-142.LIU Bin,HUANG Changbiao,LIN Junyi,et al.Interpolation of geodesic B-spline curves on manifold triangulation[J].Journal of Mechanical Engineering,2011,47(19):136-142.