网格曲面上自由形状特征交互式阵列设计
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摘要
为了提高设计效率、便于后续布局设计优化,提出一种流形网格曲面上自由形状特征可参数驱动的阵列重用设计方法,引入场向参数化方法获得网格曲面上的等值分布线,再由两组不同角度的等值分布线的交点确定特征的阵列位置;以阵列位置点的法矢和方向矢量构建局部坐标标架,用以确定阵列特征的朝向,并交互式确定各特征大小;最后采用基于旋转不变量的拉普拉斯网格变形方法,使得各阵列特征和目标曲面自然过渡,实现自由形状特征的有序多重复制。将位置阵列和特征变形分开处理,使得阵列特征的变形不依赖于场向参数化,仅与其所在的局部区域有关而与曲面整体无关,既保证了各特征和目标网格的融合效果,也为实施并行计算、降低时间成本提供了条件。试验结果表明,所介绍方法可行、有效,能满足自由形状特征在曲面上的阵列式交互设计要求。
Aiming at improving the efficiency of freeform features design on mesh and optimizing subsequent layout design more easily,aparameter-driven pattern design method for freeform features on surface was proposed.The field-aligned parameterization method was introduced to determine the location of the features by intersecting two iso-lines on mesh with different angles,and the local coordinate frame for each feature was established through the normal and the vector of pattern location to determine its orientation.Moreover,the size of each feature could be determined interactively.The features were deformed to match the target mesh by Laplacian deformation based on linear rotation-invariant coordinates,which made the features and target mesh connect smoothly and naturally,and achieved the orderly multiple replication of freeform features.By handling the feature pattern and deformation separately,it was not only easy to ensure the result of mixing features with target mesh,but also reduce the cost of time to make parallel computation possible.The experimental results showed that our method was robust,effective,and could meet the requirements of interactive pattern design of freeform features on surface.
Aiming at improving the efficiency of freeform features design on mesh and optimizing subsequent layout design more easily,aparameter-driven pattern design method for freeform features on surface was proposed.The field-aligned parameterization method was introduced to determine the location of the features by intersecting two iso-lines on mesh with different angles,and the local coordinate frame for each feature was established through the normal and the vector of pattern location to determine its orientation.Moreover,the size of each feature could be determined interactively.The features were deformed to match the target mesh by Laplacian deformation based on linear rotation-invariant coordinates,which made the features and target mesh connect smoothly and naturally,and achieved the orderly multiple replication of freeform features.By handling the feature pattern and deformation separately,it was not only easy to ensure the result of mixing features with target mesh,but also reduce the cost of time to make parallel computation possible.The experimental results showed that our method was robust,effective,and could meet the requirements of interactive pattern design of freeform features on surface.
引文
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[3]DUMAS J,LU A,LEFEBVRE S,et al.By-example synthesis of structurally sound patterns[J].ACM Transactions on Graphics,2015,34(4):1-12.
[4]BHAT P,INGRAM S,TURK G.Geometric texture synthesis by example[C]//Proceedings of the 2004 Eurographics Symposium on Geometry Processing.New York,N.Y.,USA:ACM,2004:43-46.
[5]ZHOU K,HUANG X,WANG X,et al.Mesh quilting for geometric texture synthesis[J].ACM Transactions on Graphics,2006,25(3):690-697.
[6]SUZUKI R,YEH T,YATANI K,et al.Autocomplete textures for 3Dprinting[EB/OL].[2018-05-20].https://arxiv.org/pdf/1703.05700.pdf.
[7]KONAKOVIC M,CRANE K,DENG B,et al.Beyond developable:computational design and fabrication with auxetic materials[J].ACM Transactions on Graphics,2016,35(4):89.DOI:10.1145/2897824.25944.
[8]ANDRADE D F,SHIMADA K.Automatic generation of a pattern of geometric features for industrial design[J].Journal of Mechanical Design,2013,135(11):115001.DOI:10.1115/1.4025371.
[9]ANDRADE D,VYAS V,SHIMADA K.Automatic generation of anisotropic patterns of geometric features for industrial design[J].Journal of Mechanical Design,2016,138(2):021403.DOI:1115/1.4032092.
[10]SCHUMACHER C,THOMASZEWSKI B,GROSS M.Stenciling:designing structurally-sound surfaces with decorative patterns[J].Computer Graphics Forum,2016,35(5):101-110.
[11]LANDRENEAU E,SCHAEFER S.Scales and scale-like structures[J].Computer Graphics Forum,2010,29(5):1653-1660.
[12]KNOPPEL F,CRANE K,PINKALL U,et al.Stripe patterns on surfaces[J].ACM Transactions on Graphics,2015,34(4):39.DOI:10.1145/27670000.
[13]HUANG Jinchi,LIU Bin,et al.Design and reuse of freeform features on mesh surface[J].Journal of Mechanical Engineering,2015,51(19):164-173(in Chinese).[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.]
[14]KNOPPEL F,CRANE K,PINKALL U,et al.Globally optimal direction fields[J].ACM Transactions on Graphics,2013,32(4):1-10.
[15]CHEN Y,DAVIS T,HAGER W,et al.Algorithm 887:CHOLMOD,supernodal sparse cholesky factorization and update/downdate[J].ACM Transactions on Mathematical Software,2009,35(3):22.DOI:10.1145/1391989.1391995.