Linear Surface Reconstruction from Discrete Fundamental Forms on Triangle Meshes

We present a linear algorithm to reconstruct the vertex coordinates for a surface mesh given its edge lengths and dihedral angles, unique up to rotation and translation. A local integrability condition for the existence of an immersion of the mesh in 3D Euclidean space is provided, mirroring the fun...

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Veröffentlicht in:	Computer graphics forum Jg. 31; H. 8; S. 2277 - 2287
Hauptverfasser:	Wang, Y., Liu, B., Tong, Y.
Format:	Journal Article
Sprache:	Englisch
Veröffentlicht:	Oxford, UK Blackwell Publishing Ltd 01.12.2012
Schlagworte:	Algorithms Analysis Computer graphics differential coordinates Euclidean space first fundamental forms Gauss equation I.3.5 [Computer Graphics]: Computational Geometry and Object Modelling-Curve Image processing systems Immersion Mathematical analysis Reconstruction second fundamental forms solid and object representations Studies surface surface deformation Theorems Three dimensional Topological manifolds
ISSN:	0167-7055, 1467-8659
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Abstract	We present a linear algorithm to reconstruct the vertex coordinates for a surface mesh given its edge lengths and dihedral angles, unique up to rotation and translation. A local integrability condition for the existence of an immersion of the mesh in 3D Euclidean space is provided, mirroring the fundamental theorem of surfaces in the continuous setting (i.e. Gauss's equation and the Mainardi–Codazzi equations) if we regard edge lengths as the discrete first fundamental form and dihedral angles as the discrete second fundamental form. The resulting sparse linear system to solve for the immersion is derived from the convex optimization of a quadratic energy based on a lift from the immersion in the 3D Euclidean space to the 6D rigid motion space. This discrete representation and linear reconstruction can benefit a wide range of geometry processing tasks such as surface deformation and shape analysis. A rotation‐invariant surface deformation through point and orientation constraints is demonstrated as well. We present a linear algorithm to reconstruct the vertex coordinates for a surface mesh given its edge lengths and dihedral angles, unique up to rotation and translation. A local integrability condition for the existence of an immersion of the mesh in 3D Euclidean space is provided, mirroring the fundamental theorem of surfaces in the continuous setting (i.e., Gauss's equation and the Mainardi‐Codazzi equations) if we regard edge lengths as the discrete first fundamental form and dihedral angles as the discrete second fundamental form.
AbstractList	We present a linear algorithm to reconstruct the vertex coordinates for a surface mesh given its edge lengths and dihedral angles, unique up to rotation and translation. A local integrability condition for the existence of an immersion of the mesh in 3D Euclidean space is provided, mirroring the fundamental theorem of surfaces in the continuous setting (i.e. Gauss's equation and the Mainardi–Codazzi equations) if we regard edge lengths as the discrete first fundamental form and dihedral angles as the discrete second fundamental form. The resulting sparse linear system to solve for the immersion is derived from the convex optimization of a quadratic energy based on a lift from the immersion in the 3D Euclidean space to the 6D rigid motion space. This discrete representation and linear reconstruction can benefit a wide range of geometry processing tasks such as surface deformation and shape analysis. A rotation‐invariant surface deformation through point and orientation constraints is demonstrated as well. We present a linear algorithm to reconstruct the vertex coordinates for a surface mesh given its edge lengths and dihedral angles, unique up to rotation and translation. A local integrability condition for the existence of an immersion of the mesh in 3D Euclidean space is provided, mirroring the fundamental theorem of surfaces in the continuous setting (i.e. Gauss's equation and the Mainardi-Codazzi equations) if we regard edge lengths as the discrete first fundamental form and dihedral angles as the discrete second fundamental form. The resulting sparse linear system to solve for the immersion is derived from the convex optimization of a quadratic energy based on a lift from the immersion in the 3D Euclidean space to the 6D rigid motion space. This discrete representation and linear reconstruction can benefit a wide range of geometry processing tasks such as surface deformation and shape analysis. A rotation-invariant surface deformation through point and orientation constraints is demonstrated as well. [PUBLICATION ABSTRACT] We present a linear algorithm to reconstruct the vertex coordinates for a surface mesh given its edge lengths and dihedral angles, unique up to rotation and translation. A local integrability condition for the existence of an immersion of the mesh in 3D Euclidean space is provided, mirroring the fundamental theorem of surfaces in the continuous setting (i.e. Gauss's equation and the Mainardi-Codazzi equations) if we regard edge lengths as the discrete first fundamental form and dihedral angles as the discrete second fundamental form. The resulting sparse linear system to solve for the immersion is derived from the convex optimization of a quadratic energy based on a lift from the immersion in the 3D Euclidean space to the 6D rigid motion space. This discrete representation and linear reconstruction can benefit a wide range of geometry processing tasks such as surface deformation and shape analysis. A rotation-invariant surface deformation through point and orientation constraints is demonstrated as well. We present a linear algorithm to reconstruct the vertex coordinates for a surface mesh given its edge lengths and dihedral angles, unique up to rotation and translation. A local integrability condition for the existence of an immersion of the mesh in 3D Euclidean space is provided, mirroring the fundamental theorem of surfaces in the continuous setting (i.e., Gauss's equation and the Mainardi-Codazzi equations) if we regard edge lengths as the discrete first fundamental form and dihedral angles as the discrete second fundamental form. We present a linear algorithm to reconstruct the vertex coordinates for a surface mesh given its edge lengths and dihedral angles, unique up to rotation and translation. A local integrability condition for the existence of an immersion of the mesh in 3D Euclidean space is provided, mirroring the fundamental theorem of surfaces in the continuous setting (i.e. Gauss's equation and the Mainardi–Codazzi equations) if we regard edge lengths as the discrete first fundamental form and dihedral angles as the discrete second fundamental form. The resulting sparse linear system to solve for the immersion is derived from the convex optimization of a quadratic energy based on a lift from the immersion in the 3D Euclidean space to the 6D rigid motion space. This discrete representation and linear reconstruction can benefit a wide range of geometry processing tasks such as surface deformation and shape analysis. A rotation‐invariant surface deformation through point and orientation constraints is demonstrated as well. We present a linear algorithm to reconstruct the vertex coordinates for a surface mesh given its edge lengths and dihedral angles, unique up to rotation and translation. A local integrability condition for the existence of an immersion of the mesh in 3D Euclidean space is provided, mirroring the fundamental theorem of surfaces in the continuous setting (i.e., Gauss's equation and the Mainardi‐Codazzi equations) if we regard edge lengths as the discrete first fundamental form and dihedral angles as the discrete second fundamental form.
Author	Tong, Y. Liu, B. Wang, Y.
Author_xml	– sequence: 1 givenname: Y. surname: Wang fullname: Wang, Y. organization: Michigan State University, MI, USA wangyua6@msu.edu, liubeibe@msu.edu, ytong@msu.edu – sequence: 2 givenname: B. surname: Liu fullname: Liu, B. organization: Michigan State University, MI, USA wangyua6@msu.edu, liubeibe@msu.edu, ytong@msu.edu – sequence: 3 givenname: Y. surname: Tong fullname: Tong, Y. organization: Michigan State University, MI, USA wangyua6@msu.edu, liubeibe@msu.edu, ytong@msu.edu
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Cites_doi	10.1111/j.1467-8659.2010.01761.x 10.1111/1467-8659.00580 10.1145/1073204.1073217 10.1017/CBO9780511817977 10.1111/j.1467-8659.2009.01600.x 10.1145/280814.280831 10.1145/1073204.1073219 10.1109/TVCG.2007.1054 10.1016/S0925-7721(99)00032-2 10.1111/j.1467-8659.2011.01974.x 10.1016/j.cagd.2007.07.006 10.1145/1057432.1057456 10.1145/882262.882319 10.1090/gsm/061 10.1145/1015706.1015774 10.1145/1185657.1185665 10.1109/SMI.2004.1314505 10.1080/10586458.1993.10504266
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References	Winkler T., Drieseberg J., Alexa M., Hormann K.: Multi-scale geometry interpolation. Computer Graphics Forum 29 , 2 (May 2010), 309-318. Proceedings of Eurographics. Botsch M., Sorkine O.: On linear variational surface deformation methods. IEEE Transactions on Visualization and Computer Graphics 14 , 1 (2008), 213-230. Chao I., Pinkall U., Sanan P., Schröder P.: A simple geometric model for elastic deformations. ACM Transactions on Graphics (SIGGRAPH) 29 , (July 2010), 38:1-38:6. Desbrun M., Meyer M., Alliez P.: Intrinsic parameterizations of surface meshes. Computer Graphics Forum 21 , (2002), 209-218. Lipman Y., Sorkine O., Levin D., Cohen-Or D.: Linear rotation-invariant coordinates for meshes. ACM Transactions on Graphics 24 , (July 2005), 479-487. Yu Y., Zhou K., Xu D., Shi X., Bao H., Guo B., Shum H.-Y.: Mesh editing with poisson-based gradient field manipulation. ACM Transactions on Graphics (SIGGRAPH) 23 , (2004), 644-651. Baran I., Vlasic D., Grinspun E., Popović J.: Semantic deformation transfer. ACM Transactions on Graphics (SIGGRAPH) 28 (July 2009), 36:1-36:6. Wardetzky M., Bergou M., Harmon D., Zorin D., Grinspun E.: Discrete quadratic curvature energies. Computer Aided Geometric Design 24 , (November 2007), 499-518. Kircher S., Garland M.: Free-form motion processing. ACM Transactions on Graphics 27 , (May 2008), 12:1-12:13. Pauly M., Keiser R., Kobbelt L. P., Gross M.: Shape modeling with point-sampled geometry. ACM Transactions on Graphics 22 , (July 2003), 641-650. Crane K., Desbrun M., Schröder P.: Trivial connections on discrete surfaces. Computer Graphics Forum (SGP) 29 , 5 (2010), 1525-1533. Crane K., Pinkall U., Schröder P.: Spin transformations of discrete surfaces. ACM Transactions on Graphics (SIGGRAPH) 30 , (August 2011), 104:1-104:10. Lipman Y., Cohen-Or D., Gal R., Levin D.: Volume and shape preservation via moving frame manipulation. ACM Transactions on Graphics 26 , (January 2007), 5:1-5:14. Frankel T.: The Geometry of Physics: An Introduction (2nd edition). Cambridge University Press, Cambridge , UK , Nov. 2003. Zhou K., Huang J., Snyder J., Liu X., Bao H., Guo B., Shum H.-Y.: Large mesh deformation using the volumetric graph laplacian. ACM Transactions on Graphics (SIGGRAPH) 24 , (July 2005), 496-503. Ivey T. A., Landsberg J. M.: Cartan for Beginners: Differential Geometry Via Moving Frames and Exterior Differential Systems (Illustrated edition). American Mathematical Society, Rhode Island , USA , 2003. Kobbelt L., Vorsatz J., Seidel H.-P.: Multiresolution hierarchies on unstructured triangle meshes. Computational Geometry: Theory and Applications 14 , 1-3 (1999), 5-24. Fröhlich S., Botsch M.: Example-driven deformations based on discrete shells. Computer Graphics Forum 30 , 8 (December 2011), 2246-2257. Pinkall U., Polthier K.: Computing discrete minimal surfaces and their conjugates. Experimental Mathematics 2 , (1993), 15-36. July 2010 December 2011; 8 July 2009; 36 May 2008 July 2005 June 2003 July 2003 1998 May 2010; 2 1999; 1‐3 2006 2004 1993 August 2011 2003 November 2007 2002 2008; 1 2010; 5 2005; 24 January 2007 e_1_2_10_22_2 e_1_2_10_21_2 Zhou K. (e_1_2_10_26_2) 2005 Botsch M. (e_1_2_10_3_2) 2004 Pauly M. (e_1_2_10_20_2) 2003 Chao I. (e_1_2_10_8_2) 2010 Zayer R. (e_1_2_10_27_2) 2005 Lipman Y. (e_1_2_10_17_2) 2007 Bendels G. H. (e_1_2_10_2_2) 2003 e_1_2_10_18_2 e_1_2_10_4_2 e_1_2_10_16_2 e_1_2_10_13_2 e_1_2_10_6_2 e_1_2_10_14_2 e_1_2_10_9_2 e_1_2_10_11_2 e_1_2_10_12_2 e_1_2_10_10_2 Wardetzky M. (e_1_2_10_23_2) 2007 Lipman Y. (e_1_2_10_19_2) 2005 Kircher S. (e_1_2_10_15_2) 2008 Crane K. (e_1_2_10_7_2) 2011 Baran I. (e_1_2_10_5_2) 2009; 36 e_1_2_10_24_2 e_1_2_10_25_2
References_xml	– reference: Baran I., Vlasic D., Grinspun E., Popović J.: Semantic deformation transfer. ACM Transactions on Graphics (SIGGRAPH) 28 (July 2009), 36:1-36:6. – reference: Pauly M., Keiser R., Kobbelt L. P., Gross M.: Shape modeling with point-sampled geometry. ACM Transactions on Graphics 22 , (July 2003), 641-650. – reference: Yu Y., Zhou K., Xu D., Shi X., Bao H., Guo B., Shum H.-Y.: Mesh editing with poisson-based gradient field manipulation. ACM Transactions on Graphics (SIGGRAPH) 23 , (2004), 644-651. – reference: Lipman Y., Sorkine O., Levin D., Cohen-Or D.: Linear rotation-invariant coordinates for meshes. ACM Transactions on Graphics 24 , (July 2005), 479-487. – reference: Zhou K., Huang J., Snyder J., Liu X., Bao H., Guo B., Shum H.-Y.: Large mesh deformation using the volumetric graph laplacian. ACM Transactions on Graphics (SIGGRAPH) 24 , (July 2005), 496-503. – reference: Chao I., Pinkall U., Sanan P., Schröder P.: A simple geometric model for elastic deformations. ACM Transactions on Graphics (SIGGRAPH) 29 , (July 2010), 38:1-38:6. – reference: Crane K., Pinkall U., Schröder P.: Spin transformations of discrete surfaces. ACM Transactions on Graphics (SIGGRAPH) 30 , (August 2011), 104:1-104:10. – reference: Desbrun M., Meyer M., Alliez P.: Intrinsic parameterizations of surface meshes. Computer Graphics Forum 21 , (2002), 209-218. – reference: Kircher S., Garland M.: Free-form motion processing. ACM Transactions on Graphics 27 , (May 2008), 12:1-12:13. – reference: Lipman Y., Cohen-Or D., Gal R., Levin D.: Volume and shape preservation via moving frame manipulation. ACM Transactions on Graphics 26 , (January 2007), 5:1-5:14. – reference: Botsch M., Sorkine O.: On linear variational surface deformation methods. IEEE Transactions on Visualization and Computer Graphics 14 , 1 (2008), 213-230. – reference: Winkler T., Drieseberg J., Alexa M., Hormann K.: Multi-scale geometry interpolation. Computer Graphics Forum 29 , 2 (May 2010), 309-318. Proceedings of Eurographics. – reference: Crane K., Desbrun M., Schröder P.: Trivial connections on discrete surfaces. Computer Graphics Forum (SGP) 29 , 5 (2010), 1525-1533. – reference: Kobbelt L., Vorsatz J., Seidel H.-P.: Multiresolution hierarchies on unstructured triangle meshes. Computational Geometry: Theory and Applications 14 , 1-3 (1999), 5-24. – reference: Fröhlich S., Botsch M.: Example-driven deformations based on discrete shells. Computer Graphics Forum 30 , 8 (December 2011), 2246-2257. – reference: Frankel T.: The Geometry of Physics: An Introduction (2nd edition). Cambridge University Press, Cambridge , UK , Nov. 2003. – reference: Pinkall U., Polthier K.: Computing discrete minimal surfaces and their conjugates. Experimental Mathematics 2 , (1993), 15-36. – reference: Ivey T. A., Landsberg J. M.: Cartan for Beginners: Differential Geometry Via Moving Frames and Exterior Differential Systems (Illustrated edition). American Mathematical Society, Rhode Island , USA , 2003. – reference: Wardetzky M., Bergou M., Harmon D., Zorin D., Grinspun E.: Discrete quadratic curvature energies. Computer Aided Geometric Design 24 , (November 2007), 499-518. – volume: 2 start-page: 309 year: May 2010 end-page: 318 article-title: Multi‐scale geometry interpolation publication-title: Computer Graphics Forum 29 – start-page: 644 year: 2004 end-page: 651 article-title: Mesh editing with poisson‐based gradient field manipulation publication-title: ACM Transactions on Graphics (SIGGRAPH) 23 – start-page: 181 year: 2004 end-page: 190 – start-page: 479 year: July 2005 end-page: 487 article-title: Linear rotation‐invariant coordinates for meshes publication-title: ACM Transactions on Graphics 24 – volume: 1 start-page: 213 year: 2008 end-page: 230 article-title: On linear variational surface deformation methods publication-title: IEEE Transactions on Visualization and Computer Graphics 14 – start-page: 179 year: 2004 end-page: 188 – year: 2003 – volume: 24 start-page: 601 issue: 3 year: 2005 end-page: 609 – volume: 36 start-page: 1 year: July 2009 end-page: 36:6 article-title: Semantic deformation transfer publication-title: ACM Transactions on Graphics (SIGGRAPH) 28 – start-page: 105 year: 1998 end-page: 114 – volume: 5 start-page: 1525 year: 2010 end-page: 1533 article-title: Trivial connections on discrete surfaces publication-title: Computer Graphics Forum (SGP) 29 – start-page: 209 year: 2002 end-page: 218 article-title: Intrinsic parameterizations of surface meshes publication-title: Computer Graphics Forum 21 – start-page: 104:1 year: August 2011 end-page: 104:10 article-title: Spin transformations of discrete surfaces publication-title: ACM Transactions on Graphics (SIGGRAPH) 30 – start-page: 641 year: July 2003 end-page: 650 article-title: Shape modeling with point‐sampled geometry publication-title: ACM Transactions on Graphics 22 – start-page: 185 year: 2004 end-page: 192 – start-page: 499 year: November 2007 end-page: 518 article-title: Discrete quadratic curvature energies publication-title: Computer Aided Geometric Design 24 – start-page: 15 year: 1993 end-page: 36 article-title: Computing discrete minimal surfaces and their conjugates publication-title: Experimental Mathematics 2 – volume: 8 start-page: 2246 year: December 2011 end-page: 2257 article-title: Example‐driven deformations based on discrete shells publication-title: Computer Graphics Forum 30 – start-page: 38:1 year: July 2010 end-page: 38:6 article-title: A simple geometric model for elastic deformations publication-title: ACM Transactions on Graphics (SIGGRAPH) 29 – volume: 1‐3 start-page: 5 year: 1999 end-page: 24 article-title: Multiresolution hierarchies on unstructured triangle meshes publication-title: Computational Geometry: Theory and Applications 14 – start-page: 496 year: July 2005 end-page: 503 article-title: Large mesh deformation using the volumetric graph laplacian publication-title: ACM Transactions on Graphics (SIGGRAPH) 24 – start-page: 12:1 year: May 2008 end-page: 12:13 article-title: Free‐form motion processing publication-title: ACM Transactions on Graphics 27 – start-page: 5:1 year: January 2007 end-page: 5:14 article-title: Volume and shape preservation via moving frame manipulation publication-title: ACM Transactions on Graphics 26 – year: June 2003 – start-page: 39 year: 2006 end-page: 54 – volume: 36 start-page: 1 year: 2009 ident: e_1_2_10_5_2 article-title: Semantic deformation transfer publication-title: ACM Transactions on Graphics (SIGGRAPH) 28 – start-page: 5:1 year: 2007 ident: e_1_2_10_17_2 article-title: Volume and shape preservation via moving frame manipulation publication-title: ACM Transactions on Graphics 26 – ident: e_1_2_10_6_2 doi: 10.1111/j.1467-8659.2010.01761.x – ident: e_1_2_10_10_2 doi: 10.1111/1467-8659.00580 – volume-title: Symposium on Geometry Processing 2003 year: 2003 ident: e_1_2_10_2_2 – start-page: 479 year: 2005 ident: e_1_2_10_19_2 article-title: Linear rotation‐invariant coordinates for meshes publication-title: ACM Transactions on Graphics 24 doi: 10.1145/1073204.1073217 – ident: e_1_2_10_12_2 doi: 10.1017/CBO9780511817977 – ident: e_1_2_10_24_2 doi: 10.1111/j.1467-8659.2009.01600.x – ident: e_1_2_10_14_2 doi: 10.1145/280814.280831 – start-page: 601 volume-title: Eurographics year: 2005 ident: e_1_2_10_27_2 – start-page: 496 year: 2005 ident: e_1_2_10_26_2 article-title: Large mesh deformation using the volumetric graph laplacian publication-title: ACM Transactions on Graphics (SIGGRAPH) 24 doi: 10.1145/1073204.1073219 – start-page: 12:1 year: 2008 ident: e_1_2_10_15_2 article-title: Free‐form motion processing publication-title: ACM Transactions on Graphics 27 – ident: e_1_2_10_4_2 doi: 10.1109/TVCG.2007.1054 – ident: e_1_2_10_16_2 doi: 10.1016/S0925-7721(99)00032-2 – start-page: 104:1 year: 2011 ident: e_1_2_10_7_2 article-title: Spin transformations of discrete surfaces publication-title: ACM Transactions on Graphics (SIGGRAPH) 30 – ident: e_1_2_10_11_2 doi: 10.1111/j.1467-8659.2011.01974.x – start-page: 499 year: 2007 ident: e_1_2_10_23_2 article-title: Discrete quadratic curvature energies publication-title: Computer Aided Geometric Design 24 doi: 10.1016/j.cagd.2007.07.006 – ident: e_1_2_10_22_2 doi: 10.1145/1057432.1057456 – start-page: 641 year: 2003 ident: e_1_2_10_20_2 article-title: Shape modeling with point‐sampled geometry publication-title: ACM Transactions on Graphics 22 doi: 10.1145/882262.882319 – ident: e_1_2_10_13_2 doi: 10.1090/gsm/061 – ident: e_1_2_10_25_2 doi: 10.1145/1015706.1015774 – start-page: 185 volume-title: Symposium on Geometry Processing 2004 year: 2004 ident: e_1_2_10_3_2 – ident: e_1_2_10_9_2 doi: 10.1145/1185657.1185665 – ident: e_1_2_10_18_2 doi: 10.1109/SMI.2004.1314505 – ident: e_1_2_10_21_2 doi: 10.1080/10586458.1993.10504266 – start-page: 38:1 year: 2010 ident: e_1_2_10_8_2 article-title: A simple geometric model for elastic deformations publication-title: ACM Transactions on Graphics (SIGGRAPH) 29
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Snippet	We present a linear algorithm to reconstruct the vertex coordinates for a surface mesh given its edge lengths and dihedral angles, unique up to rotation and...
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SubjectTerms	Algorithms Analysis Computer graphics differential coordinates Euclidean space first fundamental forms Gauss equation I.3.5 [Computer Graphics]: Computational Geometry and Object Modelling-Curve Image processing systems Immersion Mathematical analysis Reconstruction second fundamental forms solid and object representations Studies surface surface deformation Theorems Three dimensional Topological manifolds
Title	Linear Surface Reconstruction from Discrete Fundamental Forms on Triangle Meshes
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