尺度自动感知的几何体变形技术

Zheng LIU; Wei-ming WANG; Xiu-ping LIU; Li-gang LIU

doi:10.1631/jzus.C1400122

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尺度自动感知的几何体变形技术

数字娱乐、艺术与智能CAD专题 | Updated：2022-05-19

- 尺度自动感知的几何体变形技术
- Scale-aware shape manipulation
- 信息与电子工程前沿（英文） 2014年15卷第9期页码：764-775
- Affiliations：
  
  1.School of Mathematical Sciences, University of Science and Technology of China, Hefei 230026, China
  2.School of Mathematical Sciences, Dalian University of Technology, Dalian 116023, China
- Author bio：
  
  [ "Zheng LIU E-mail:Liu.Zheng.jojo@gmail.com" ]
- Funds：
  
  Project supported by the National Natural Science Foundation of China (No.61222206) and the One Hundred Talent Project of the Chinese Academy of Sciences, China
- DOI：10.1631/jzus.C1400122
  中图分类号： TP391.41
- 收稿：2014-04-01，
  
  修回：2014-;8-19，
  
  纸质出版：2014-09
- Accepted：
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尺度自动感知的几何体变形技术[J]. 信息与电子工程前沿（英文）, 2014,15(9):764-775.

Zheng LIU, Wei-ming WANG, Xiu-ping LIU, et al. Scale-aware shape manipulation[J]. Frontiers of Information Technology & Electronic Engineering, 2014, 15(9): 764-775.
尺度自动感知的几何体变形技术[J]. 信息与电子工程前沿（英文）, 2014,15(9):764-775. DOI： 10.1631/jzus.C1400122.

Zheng LIU, Wei-ming WANG, Xiu-ping LIU, et al. Scale-aware shape manipulation[J]. Frontiers of Information Technology & Electronic Engineering, 2014, 15(9): 764-775. DOI： 10.1631/jzus.C1400122.

摘要

研究目的

针对三角形网格的大尺度形变，提出一种基于尺度不变量的变形技术。

研究方法

针对三角形网格中基于顶点--领域的局部微分坐标，提出一套尺度不变的几何量（图1）。基于这套几何不变量，给出尺度自适应的几何体变形能量（方程6）。该复杂方程难以直接求解；为有效求解，利用分离变量原理，设计了一个两步迭代算法（算法1）。将此算法获得的几何变形结果与多种知名的几何变形算法进行比较（图9~11）。最后展示了一系列利用我们的算法进行网格变形的结果（图12~14）。

重要结论

针对三角形网格微分坐标中的尺度不变量，提出了一种新颖的基于尺度不变度量的网格变形技术，使得几何体在大尺度形变过程中能够有效保持几何细节不变。

Abstract

A novel representation of a triangular mesh surface using a set of scale-invariant measures is proposed. The measures consist of angles of the triangles (triangle angles) and dihedral angles along the edges (edge angles) which are scale and rigidity independent. The vertex coordinates for a mesh give its scale-invariant measures

unique up to scale

rotation

and translation. Based on the representation of mesh using scale-invariant measures

a two-step iterative deformation algorithm is proposed

which can arbitrarily edit the mesh through simple handles interaction. The algorithm can explicitly preserve the local geometric details as much as possible in different scales even under severe editing operations including rotation

scaling

and shearing. The efficiency and robustness of the proposed algorithm are demonstrated by examples.

关键词

Keywords

references

O.K.C. Au , , , C.L. Tai , , , L.G. Liu , , , 等 . . Dual Laplacian editing for meshes . . IEEE Trans. Visual. Comput. Graph. , , 2006 . . 12 ( ( 3 ): ): 386 - - 395 . . DOI: 10.1109/TVCG.2006.47 http://doi.org/10.1109/TVCG.2006.47 . .

Y.F. Bao , , , X.H. Guo , , , H. Qin . . Physically based morphing of point-sampled surfaces . . Comput. Anim. Virt. Worlds , , 2005 . . 16 ( ( 3-4 ): ): 509 - - 518 . . DOI: 10.1002/cav.100 http://doi.org/10.1002/cav.100 . .

M. Botsch , , , L. Kobbelt . . An intuitive framework for real-time freeform modeling . . ACM Trans. Graph. , , 2004 . . 23 ( ( 3 ): ): 630 - - 634 . . DOI: 10.1145/1015706.1015772 http://doi.org/10.1145/1015706.1015772 . .

M. Botsch , , , O. Sorkine . . On linear variational surface deformation methods . . IEEE Trans. Visual. Comput. Graph. , , 2008 . . 14 ( ( 1 ): ): 213 - - 230 . . DOI: 10.1109/TVCG.2007.1054 http://doi.org/10.1109/TVCG.2007.1054 . .

M. Botsch , , , M. Pauly , , , M.H. Gross , , , 等 . . PriMo: coupled prisms for intuitive surface modeling . . Proc. Symp. on Geometry Processing , , 2006 . . p.11 - - 20 . . . .

I. Chao , , , U. Pinkall , , , P. Sanan , , , 等 . . A simple geometric model for elastic deformations . . ACM Trans. Graph. , , 2010 . . 29 ( ( 4 ): ): 38:6 DOI: 10.1145/1778765.1778775 http://doi.org/10.1145/1778765.1778775 . .

R.J. Chen , , , O. Weber , , , D. Keren , , , 等 . . Planar shape interpolation with bounded distortion . . ACM Trans. Graph. , , 2013 . . 32 ( ( 4 ): ): Article 108 DOI: 10.1145/2461912.2461983 http://doi.org/10.1145/2461912.2461983 . .

K. Crane , , , U. Pinkall , , , P. Schröber . . Spin transformations of discrete surfaces . . ACM Trans. Graph. , , 2011 . . 30 ( ( 4 ): ): Article 104 DOI: 10.1145/2010324.1964999 http://doi.org/10.1145/2010324.1964999 . .

S. Fröhlich , , , M. Botsch . . Example-driven deformations based on discrete shells . . Comput. Graph. Forum , , 2011 . . 30 ( ( 8 ): ): 2246 - - 2257 . . DOI: 10.1111/j.1467-8659.2011.01974.x http://doi.org/10.1111/j.1467-8659.2011.01974.x . .

J. Gain , , , D. Bechmann . . A survey of spatial deformation from a user-centered perspective . . ACM Trans. Graph. , , 2008 . . 27 ( ( 4 ): ): Article 107 DOI: 10.1145/1409625.1409629 http://doi.org/10.1145/1409625.1409629 . .

L. Gao , , , G.X. Zhang , , , Y.K. Lai . . Lp shape deformation . . Sci. China Inform. Sci. , , 2012 . . 55 ( ( 5 ): ): 983 - - 993 . . DOI: 10.1007/s11432-012-4574-y http://doi.org/10.1007/s11432-012-4574-y . .

E. Grinspun , , , A.N. Hirani , , , M. Desbrun , , , 等 . . Discrete shells . . Proc. ACM SIGGRAPH/Eurographics Symp. on Computer Animation , , 2003 . . p.62 - - 67 . . . .

S.M. Hu , , , C.F. Li , , , H. Zhang . . Actual morphing: a physics-based approach to blending . . Proc. 9th ACM Symp. on Solid Modeling and Applications , , 2004 . . p.309 - - 314 . . . .

T. Igarashi , , , T. Moscovich , , , J.F. Hughes . . As-rigidas-possible shape manipulation . . ACM Trans. Graph. , , 2005 . . 24 ( ( 3 ): ): 1134 - - 1141 . . DOI: 10.1145/1073204.1073323 http://doi.org/10.1145/1073204.1073323 . .

A. Jacobson , , , I. Baran , , , J. Popović , , , 等 . . Bounded biharmonic weights for real-time deformation . . ACM Trans. Graph. , , 2011 . . 30 ( ( 4 ): ): Article 78 DOI: 10.1145/2010324.1964973 http://doi.org/10.1145/2010324.1964973 . .

S. Kircher , , , M. Garland . . Free-form motion processing . . ACM Trans. Graph. , , 2008 . . 27 ( ( 2 ): ): Article 12 DOI: 10.1145/1356682.1356685 http://doi.org/10.1145/1356682.1356685 . .

L. Kobbelt , , , S. Campagna , , , J. Vorsatz , , , 等 . . Interactive multi-resolution modeling on arbitrary meshes . . Proc. 25th Annual Conf. on Computer Graphics and Interactive Techniques , , 1998 . . p.105 - - 114 . . DOI: 10.1145/280814.280831 http://doi.org/10.1145/280814.280831 . .

Z. Levi , , , D. Levin . . Shape deformation via interior RBF . . IEEE Trans. Visual. Comput. Graph. , , 2014 . . 20 ( ( 7 ): ): 1062 - - 1075 . . DOI: 10.1109/TVCG.2013.255 http://doi.org/10.1109/TVCG.2013.255 . .

Y. Lipman . . Bounded distortion mapping spaces for triangular meshes . . ACM Trans. Graph. , , 2012 . . 31 ( ( 4 ): ): Article 108 DOI: 10.1145/2185520.2185604 http://doi.org/10.1145/2185520.2185604 . .

Y. Lipman , , , O. Sorkine , , , D. Levin , , , 等 . . Linear rotation-invariant coordinates for meshes . . ACM Trans. Graph. , , 2005 . . 24 ( ( 3 ): ): 479 - - 487 . . DOI: 10.1145/1073204.1073217 http://doi.org/10.1145/1073204.1073217 . .

Y. Lipman , , , D. Levin , , , D. Cohen-Or . . Green coordinates . . ACM Trans. Graph. , , 2008 . . 27 ( ( 3 ): ): Article 78 DOI: 10.1145/1360612.1360677 http://doi.org/10.1145/1360612.1360677 . .

T. Milliron , , , R.J. Jensen , , , R. Barzel , , , 等 . . A framework for geometric warps and deformations . . ACM Trans. Graph. , , 2002 . . 21 ( ( 1 ): ): 20 - - 51 . . DOI: 10.1145/504789.504791 http://doi.org/10.1145/504789.504791 . .

N. Paries , , , P. Degener , , , R. Klein . . Simple and efficient mesh editing with consistent local frames . . Proc. 15th Pacific Conf. on Computer Graphics and Applications , , 2007 . . p.461 - - 464 . . DOI: 10.1109/PG.2007.43 http://doi.org/10.1109/PG.2007.43 . .

A. Sheffer , , , V. Kraevoy . . Pyramid coordinates for morphing and deformation . . Proc. 2nd Int. Symp. on 3D Data Processing, Visualization and Transmission , , 2004 . . p.68 - - 75 . . DOI: 10.1109/3DPVT.2004.99 http://doi.org/10.1109/3DPVT.2004.99 . .

O. Sorkine , , , M. Alexa . . As-rigid-as-possible surface modeling . . Symp. on Geometry Processing , , 2007 . . p.109 - - 116 . . . .

O. Sorkine , , , D. Cohen-Or , , , Y. Lipman , , , 等 . . Laplacian surface editing . . Proc. Eurographics/ACM SIGGRAPH Symp. on Geometry Processing , , 2004 . . p.175 - - 184 . . DOI: 10.1145/1057432.1057456 http://doi.org/10.1145/1057432.1057456 . .

Y. Wang , , , B. Liu , , , Y. Tong . . Linear surface reconstruction from discrete fundamental forms on triangle meshes . . Comput. Graph. Forum , , 2012 . . 31 ( ( 8 ): ): 2277 - - 2287 . . DOI: 10.1111/j.1467-8659.2012.03153.x http://doi.org/10.1111/j.1467-8659.2012.03153.x . .

O. Weber , , , C. Gotsman . . Controllable conformal maps for shape deformation and interpolation . . ACM Trans. Graph. , , 2010 . . 29 ( ( 4 ): ): Article 78 DOI: 10.1145/1778765.1778815 http://doi.org/10.1145/1778765.1778815 . .

T. Winkler , , , J. Drieseberg , , , M. Alexa , , , 等 . . Multiscale geometry interpolation . . Comput. Graph. Forum , , 2010 . . 29 ( ( 2 ): ): 309 - - 318 . . DOI: 10.1111/j.1467-8659.2009.01600.x http://doi.org/10.1111/j.1467-8659.2009.01600.x . .

Y.Z. Yu , , , K. Zhou , , , D. Xu , , , 等 . . Mesh editing with Poisson-based gradient field manipulation . . ACM Trans. Graph. , , 2004 . . 23 ( ( 3 ): ): 644 - - 651 . . DOI: 10.1145/1015706.1015774 http://doi.org/10.1145/1015706.1015774 . .

M. Zhang , , , W. Zeng , , , S.Q. Xin , , , 等 . . Stable geodesic surface signatures . . Tsinghua Sci. Technol. , , 2012 . . 17 ( ( 4 ): ): 471 - - 480 . . DOI: 10.1109/TST.2012.6297593 http://doi.org/10.1109/TST.2012.6297593 . .

D. Zorin , , , P. Schröber , , , W. Sweldens . . Interactive multiresolution mesh editing . . Proc. 24th Annual Conf. on Computer Graphics and Interactive Techniques , , 1997 . . p.259 - - 268 . . DOI: 10.1145/258734.258863 http://doi.org/10.1145/258734.258863 . .

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