Harmonic Functions for Rotational Symmetry Vector Fields
Representing rotational symmetry vector as a set of vectors is not suitable for design due to lacking of a consistent ordering for measurement. In this paper we introduce a spectral method to find rotation invariant harmonic functions for symmetry vector field design. This method is developed for 3D...
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| Vydáno v: | Computer graphics forum Ročník 35; číslo 7; s. 507 - 516 |
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| Médium: | Journal Article |
| Jazyk: | angličtina |
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Oxford
Blackwell Publishing Ltd
01.10.2016
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| ISSN: | 0167-7055, 1467-8659 |
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| Abstract | Representing rotational symmetry vector as a set of vectors is not suitable for design due to lacking of a consistent ordering for measurement. In this paper we introduce a spectral method to find rotation invariant harmonic functions for symmetry vector field design. This method is developed for 3D vector fields, but it is applicable in 2D. Given the finite symmetry group G of a symmetry vector field v(x) on a 3D domain Ω, we formulate the harmonic function h(s) as a stationary point of group G. Using the real spherical harmonic (SH) bases, we showed the coefficients of the harmonic functions are an eigenvector of the SH rotation matrices corresponding to group G. Instead of solving eigen problems to obtain the eigenvector, we developed a forward constructive method based on orthogonal group theory. The harmonic function found by our method is not only invariant under G, but also expressive and can distinguish different rotations with respect to G. At last, we demonstrate some vector field design results with tetrahedron‐symmetry, cube‐symmetry and dodecahedron‐symmetry groups. |
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| AbstractList | Representing rotational symmetry vector as a set of vectors is not suitable for design due to lacking of a consistent ordering for measurement. In this paper we introduce a spectral method to find rotation invariant harmonic functions for symmetry vector field design. This method is developed for 3D vector fields, but it is applicable in 2D. Given the finite symmetry group G of a symmetry vector field v(x) on a 3D domain [Omega], we formulate the harmonic function h(s) as a stationary point of group G. Using the real spherical harmonic (SH) bases, we showed the coefficients of the harmonic functions are an eigenvector of the SH rotation matrices corresponding to group G. Instead of solving eigen problems to obtain the eigenvector, we developed a forward constructive method based on orthogonal group theory. The harmonic function found by our method is not only invariant under G, but also expressive and can distinguish different rotations with respect to G. At last, we demonstrate some vector field design results with tetrahedron-symmetry, cube-symmetry and dodecahedron-symmetry groups. Representing rotational symmetry vector as a set of vectors is not suitable for design due to lacking of a consistent ordering for measurement. In this paper we introduce a spectral method to find rotation invariant harmonic functions for symmetry vector field design. This method is developed for 3D vector fields, but it is applicable in 2D. Given the finite symmetry group G of a symmetry vector field v(x) on a 3D domain Ω, we formulate the harmonic function h(s) as a stationary point of group G. Using the real spherical harmonic (SH) bases, we showed the coefficients of the harmonic functions are an eigenvector of the SH rotation matrices corresponding to group G. Instead of solving eigen problems to obtain the eigenvector, we developed a forward constructive method based on orthogonal group theory. The harmonic function found by our method is not only invariant under G, but also expressive and can distinguish different rotations with respect to G. At last, we demonstrate some vector field design results with tetrahedron‐symmetry, cube‐symmetry and dodecahedron‐symmetry groups. Representing rotational symmetry vector as a set of vectors is not suitable for design due to lacking of a consistent ordering for measurement. In this paper we introduce a spectral method to find rotation invariant harmonic functions for symmetry vector field design. This method is developed for 3D vector fields, but it is applicable in 2D. Given the finite symmetry group G of a symmetry vector field v (x) on a 3D domain Ω, we formulate the harmonic function h(s) as a stationary point of group G. Using the real spherical harmonic (SH) bases, we showed the coefficients of the harmonic functions are an eigenvector of the SH rotation matrices corresponding to group G. Instead of solving eigen problems to obtain the eigenvector, we developed a forward constructive method based on orthogonal group theory. The harmonic function found by our method is not only invariant under G, but also expressive and can distinguish different rotations with respect to G. At last, we demonstrate some vector field design results with tetrahedron‐symmetry, cube‐symmetry and dodecahedron‐symmetry groups. |
| Author | Bao, Hujun Fang, Xianzhong Huang, Jin Liu, Xinguo Shen, Zhongwei |
| Author_xml | – sequence: 1 givenname: Zhongwei surname: Shen fullname: Shen, Zhongwei organization: State Key Lab of CAD&CG, Zhejiang University – sequence: 2 givenname: Xianzhong surname: Fang fullname: Fang, Xianzhong organization: State Key Lab of CAD&CG, Zhejiang University – sequence: 3 givenname: Xinguo surname: Liu fullname: Liu, Xinguo organization: State Key Lab of CAD&CG, Zhejiang University – sequence: 4 givenname: Hujun surname: Bao fullname: Bao, Hujun organization: State Key Lab of CAD&CG, Zhejiang University – sequence: 5 givenname: Jin surname: Huang fullname: Huang, Jin email: hj@cad.zju.edu.cn, hj@cad.zju.edu.cn organization: State Key Lab of CAD&CG, Zhejiang University |
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| References | Alliez P., Cohen-Steiner D., Devillers O., Lévy B., Desbrun M.: Anisotropic polygonal remeshing. ACM Transactions on Graphics 22, 3 (2003), 485-493. 2 Moakher M.: The Algebra of Fourth-Order Tensors with Application to Diffusion MRI. Springer Berlin Heidelberg, Berlin, Heidelberg, 2009, pp. 57-80. 3 Kuznetsov É. D., Kholshevnikov K.V.: Estimation of the number of extrema of a spherical harmonic. Soviet Astronomy 36, 2 (1992), 220-222. 4 Dong S., Kircher S., Garland M.: Harmonic functions for quadrilateral remeshing of arbitrary manifolds. Computer Aided Geometric Design 22, 5 (July 2005), 392-423. 2 Knöppel F., Crane K., Pinkall U., Schröder P.: Globally optimal direction fields. ACM Transactions on Graphics 32, 4 (July 2013), 59:1-59:10. 3 Li Y., LIu Y., Xu W., Wang W., Guo B.: All-hex meshing using singularity-restricted field. ACM Transactions on Graphics 31, 6 (Nov. 2012), 177:1-177:11. 2, 3 J.F. Cornwell: Group Theory in Physics, Volume I. Academic Press, 1984. 3, 4 Palacios J., Zhang E.: Interactive visualization of rotational symmetry fields on surfaces. IEEE Transactions on Visualization and Computer Graphics 17, 7 (2011), 947-955. 6 Bommes D., Zimmer H., Kobbelt L.: Mixed-integer quadrangulation. ACM Transactions on Graphics 28, 3 (2009), 1-10. 2 Huang J., Zhang M., Ma J., Liu X., Kobbelt L., Bao H.: Spectral quadrangulation with orientation and alignment control. ACM Transactions on Graphics 27, 5 (December 2008), 147:1-147:9. 2 Zheng Y., Doerschuk P.C.: Explicit orthonormal fixed bases for spaces of functions that are totally symmetric under the rotational symmetries of a platonic solid. Acta Crystallographica Section A 52, 2 (1996), 221-235. 3, 4 Schlick C.: An inexpensive brdf model for physically-based rendering. Computer Graphics Forum 13, 3 (1994), 233-246. 2 Jiang T., Huang J., Wang Y., Tong Y., Bao H.: Frame field singularity correction for automatic hexahedralization. IEEE Transactions on Visualization and Computer Graphics 20, 8 (2014), 1189-1199. 2 Palacios J., Zhang E.: Rotational symmetry field design on surfaces. ACM Transaction on Graphics 26, 3 (2007), 55. 1, 2, 3, 6, 8 Zheng Y., Doerschuk P.C.: Explicit computation of orthonormal symmetrized harmonics with application to the identity representation of the icosahedral group. SIAM Journal on Mathematical Analysis 32, 3 (2000), 538-554. 3 Diamanti O., Vaxman A., Panozzo D., Sorkine-Hornung O.: Designing N-polyvector fields with complex polynomials. Computer Graphics Forum 33, 5 (2014), 1-11. 3 Huang J., Tong Y., Wei H., Bao H.: Boundary aligned smooth 3d cross-frame field. ACM Transactions on Graphics 30, 6 (Dec 2011), 143:1-143:8. 1, 2, 3, 5, 6, 8 Sloan P.-P., Kautz J., Snyder J.: Precomputed radiance transfer for real-time rendering in dynamic, low-frequency lighting environments. ACM Transactions on Graphics 21, 3 (July 2002), 527-536. 3 Zhang E., Mischaikow K., Turk G.: Vector field design on surfaces. ACM Transactions on Graphics 25, 4 (Oct. 2006), 1294-1326. 2 Diamanti O., Vaxman A., Panozzo D., Sorkine-Hornung O.: Integrable polyvector fields. ACM Transactions on Graphics 34, 4 (2015), 38. 3 Fisher M., Schröder P., Desbrun M., Hoppe H.: Design of tangent vector fields. ACM Transactions on Graphics 26, 3 (Jul 2007). 2 Nieser M., Reitebuch U., Polthier K.: Cubecover - parameterization of 3d volumes. Computer Graphics Forum 30, 5 (2011), 1397-1406. 2 Ray N., Li W.C., Lévy B., Sheffer A., Alliez P.: Periodic global parameterization. ACM Transactions on Graphics 25, 4 (2006), 1460-1485. 2 2015; 34 1984; I 2010 2009 2011; 30 2008 1996; 52 2005 1992; 36 2003 2002 2011; 17 2005; 22 2012; 31 2009; 28 2014; 20 2001 2000 2013; 32 2000; 32 2008; 27 2006; 25 2002; 21 1994; 13 2015 2014; 33 2003; 22 2007; 26 e_1_2_10_22_2 Kuznetsov É. D. (e_1_2_10_18_2) 1992; 36 Desbrun M. (e_1_2_10_5_2) 2005 Mann S. (e_1_2_10_21_2) 2002 e_1_2_10_19_2 Vyas V. (e_1_2_10_34_2) 2009 e_1_2_10_3_2 e_1_2_10_2_2 e_1_2_10_39_2 e_1_2_10_15_2 Turk G. (e_1_2_10_33_2) 2001 e_1_2_10_38_2 e_1_2_10_4_2 e_1_2_10_16_2 e_1_2_10_37_2 e_1_2_10_7_2 e_1_2_10_36_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_8_2 e_1_2_10_12_2 e_1_2_10_32_2 e_1_2_10_10_2 e_1_2_10_31_2 e_1_2_10_30_2 Polthier K. (e_1_2_10_24_2) 2002 Wei L.‐Y. (e_1_2_10_35_2) 2001 Moakher M. (e_1_2_10_20_2) 2009 Praun E. (e_1_2_10_23_2) 2000 Kazhdan M. (e_1_2_10_17_2) 2003 e_1_2_10_28_2 e_1_2_10_29_2 e_1_2_10_26_2 e_1_2_10_27_2 Cornwell J.F. (e_1_2_10_13_2) 1984 e_1_2_10_25_2 |
| References_xml | – reference: Li Y., LIu Y., Xu W., Wang W., Guo B.: All-hex meshing using singularity-restricted field. ACM Transactions on Graphics 31, 6 (Nov. 2012), 177:1-177:11. 2, 3 – reference: Kuznetsov É. D., Kholshevnikov K.V.: Estimation of the number of extrema of a spherical harmonic. Soviet Astronomy 36, 2 (1992), 220-222. 4 – reference: Zhang E., Mischaikow K., Turk G.: Vector field design on surfaces. ACM Transactions on Graphics 25, 4 (Oct. 2006), 1294-1326. 2 – reference: Jiang T., Huang J., Wang Y., Tong Y., Bao H.: Frame field singularity correction for automatic hexahedralization. IEEE Transactions on Visualization and Computer Graphics 20, 8 (2014), 1189-1199. 2 – reference: Schlick C.: An inexpensive brdf model for physically-based rendering. Computer Graphics Forum 13, 3 (1994), 233-246. 2 – reference: Huang J., Tong Y., Wei H., Bao H.: Boundary aligned smooth 3d cross-frame field. ACM Transactions on Graphics 30, 6 (Dec 2011), 143:1-143:8. 1, 2, 3, 5, 6, 8 – reference: Zheng Y., Doerschuk P.C.: Explicit computation of orthonormal symmetrized harmonics with application to the identity representation of the icosahedral group. SIAM Journal on Mathematical Analysis 32, 3 (2000), 538-554. 3 – reference: Diamanti O., Vaxman A., Panozzo D., Sorkine-Hornung O.: Designing N-polyvector fields with complex polynomials. Computer Graphics Forum 33, 5 (2014), 1-11. 3 – reference: Palacios J., Zhang E.: Rotational symmetry field design on surfaces. ACM Transaction on Graphics 26, 3 (2007), 55. 1, 2, 3, 6, 8 – reference: Huang J., Zhang M., Ma J., Liu X., Kobbelt L., Bao H.: Spectral quadrangulation with orientation and alignment control. ACM Transactions on Graphics 27, 5 (December 2008), 147:1-147:9. 2 – reference: J.F. Cornwell: Group Theory in Physics, Volume I. Academic Press, 1984. 3, 4 – reference: Fisher M., Schröder P., Desbrun M., Hoppe H.: Design of tangent vector fields. ACM Transactions on Graphics 26, 3 (Jul 2007). 2 – reference: Knöppel F., Crane K., Pinkall U., Schröder P.: Globally optimal direction fields. ACM Transactions on Graphics 32, 4 (July 2013), 59:1-59:10. 3 – reference: Palacios J., Zhang E.: Interactive visualization of rotational symmetry fields on surfaces. IEEE Transactions on Visualization and Computer Graphics 17, 7 (2011), 947-955. 6 – reference: Moakher M.: The Algebra of Fourth-Order Tensors with Application to Diffusion MRI. Springer Berlin Heidelberg, Berlin, Heidelberg, 2009, pp. 57-80. 3 – reference: Ray N., Li W.C., Lévy B., Sheffer A., Alliez P.: Periodic global parameterization. ACM Transactions on Graphics 25, 4 (2006), 1460-1485. 2 – reference: Zheng Y., Doerschuk P.C.: Explicit orthonormal fixed bases for spaces of functions that are totally symmetric under the rotational symmetries of a platonic solid. Acta Crystallographica Section A 52, 2 (1996), 221-235. 3, 4 – reference: Sloan P.-P., Kautz J., Snyder J.: Precomputed radiance transfer for real-time rendering in dynamic, low-frequency lighting environments. ACM Transactions on Graphics 21, 3 (July 2002), 527-536. 3 – reference: Alliez P., Cohen-Steiner D., Devillers O., Lévy B., Desbrun M.: Anisotropic polygonal remeshing. ACM Transactions on Graphics 22, 3 (2003), 485-493. 2 – reference: Dong S., Kircher S., Garland M.: Harmonic functions for quadrilateral remeshing of arbitrary manifolds. Computer Aided Geometric Design 22, 5 (July 2005), 392-423. 2 – reference: Diamanti O., Vaxman A., Panozzo D., Sorkine-Hornung O.: Integrable polyvector fields. ACM Transactions on Graphics 34, 4 (2015), 38. 3 – reference: Bommes D., Zimmer H., Kobbelt L.: Mixed-integer quadrangulation. ACM Transactions on Graphics 28, 3 (2009), 1-10. 2 – reference: Nieser M., Reitebuch U., Polthier K.: Cubecover - parameterization of 3d volumes. Computer Graphics Forum 30, 5 (2011), 1397-1406. 2 – start-page: 10:1 year: 2008 end-page: 10:13 – start-page: 517 year: 2000 end-page: 526 – volume: 17 start-page: 947 issue: 7 year: 2011 end-page: 955 article-title: Interactive visualization of rotational symmetry fields on surfaces publication-title: IEEE Transactions on Visualization and Computer Graphics – volume: 30 start-page: 1397 issue: 5 year: 2011 end-page: 1406 article-title: Cubecover ‐ parameterization of 3d volumes publication-title: Computer Graphics Forum – year: 2005 – volume: 34 start-page: 38 issue: 4 year: 2015 article-title: Integrable polyvector fields publication-title: ACM Transactions on Graphics – start-page: 347 year: 2001 end-page: 354 – start-page: 112 year: 2002 end-page: 134 – year: 2003 – start-page: 156 year: 2003 end-page: 164 – start-page: 283 year: 2002 end-page: 290 – volume: 30 start-page: 143:1 issue: 6 year: 2011 end-page: 143:8 article-title: Boundary aligned smooth 3d cross‐frame field publication-title: ACM Transactions on Graphics – volume: 27 start-page: 147:1 issue: 5 year: 2008 end-page: 147:9 article-title: Spectral quadrangulation with orientation and alignment control publication-title: ACM Transactions on Graphics – start-page: 465 year: 2000 end-page: 470 – volume: 31 start-page: 177:1 issue: 6 year: 2012 end-page: 177:11 article-title: All‐hex meshing using singularity‐restricted field publication-title: ACM Transactions on Graphics – start-page: 57 year: 2009 end-page: 80 – volume: 26 issue: 3 year: 2007 article-title: Design of tangent vector fields publication-title: ACM Transactions on Graphics – volume: 33 start-page: 1 issue: 5 year: 2014 end-page: 11 article-title: Designing N‐polyvector fields with complex polynomials publication-title: Computer Graphics Forum – volume: 52 start-page: 221 issue: 2 year: 1996 end-page: 235 article-title: Explicit orthonormal fixed bases for spaces of functions that are totally symmetric under the rotational symmetries of a platonic solid publication-title: Acta Crystallographica Section A – start-page: 191 year: 2002 end-page: 191 – volume: 13 start-page: 233 issue: 3 year: 1994 end-page: 246 article-title: An inexpensive brdf model for physically‐based rendering publication-title: Computer Graphics Forum – volume: 36 start-page: 220 issue: 2 year: 1992 end-page: 222 article-title: Estimation of the number of extrema of a spherical harmonic publication-title: Soviet Astronomy – volume: 25 start-page: 1460 issue: 4 year: 2006 end-page: 1485 article-title: Periodic global parameterization publication-title: ACM Transactions on Graphics – volume: 25 start-page: 1294 issue: 4 year: 2006 end-page: 1326 article-title: Vector field design on surfaces publication-title: ACM Transactions on Graphics – volume: 20 start-page: 1189 issue: 8 year: 2014 end-page: 1199 article-title: Frame field singularity correction for automatic hexahedralization publication-title: IEEE Transactions on Visualization and Computer Graphics – volume: 26 start-page: 55 issue: 3 year: 2007 article-title: Rotational symmetry field design on surfaces publication-title: ACM Transaction on Graphics – volume: 32 start-page: 59:1 issue: 4 year: 2013 end-page: 59:10 article-title: Globally optimal direction fields publication-title: ACM Transactions on Graphics – volume: 28 start-page: 1 issue: 3 year: 2009 end-page: 10 article-title: Mixed‐integer quadrangulation publication-title: ACM Transactions on Graphics – start-page: 118:1 year: 2010 end-page: 118:8 – volume: I year: 1984 – start-page: 355 year: 2001 end-page: 360 – start-page: 377 year: 2009 end-page: 396 – volume: 21 start-page: 527 issue: 3 year: 2002 end-page: 536 article-title: Precomputed radiance transfer for real‐time rendering in dynamic, low‐frequency lighting environments publication-title: ACM Transactions on Graphics – volume: 22 start-page: 485 issue: 3 year: 2003 end-page: 493 article-title: Anisotropic polygonal remeshing publication-title: ACM Transactions on Graphics – volume: 22 start-page: 392 issue: 5 year: 2005 end-page: 423 article-title: Harmonic functions for quadrilateral remeshing of arbitrary manifolds publication-title: Computer Aided Geometric Design – year: 2015 – volume: 32 start-page: 538 issue: 3 year: 2000 end-page: 554 article-title: Explicit computation of orthonormal symmetrized harmonics with application to the identity representation of the icosahedral group publication-title: SIAM Journal on Mathematical Analysis – ident: e_1_2_10_10_2 doi: 10.1145/2070781.2024177 – ident: e_1_2_10_12_2 doi: 10.1145/1409060.1409100 – ident: e_1_2_10_14_2 doi: 10.1109/TVCG.2013.250 – ident: e_1_2_10_15_2 doi: 10.1145/2461912.2462005 – ident: e_1_2_10_9_2 – start-page: 112 volume-title: Mathematical Visualization III year: 2002 ident: e_1_2_10_24_2 – ident: e_1_2_10_31_2 – ident: e_1_2_10_4_2 doi: 10.1016/j.cagd.2005.04.004 – ident: e_1_2_10_26_2 doi: 10.1109/TVCG.2010.121 – start-page: 57 volume-title: The Algebra of Fourth‐Order Tensors with Application to Diffusion MRI year: 2009 ident: e_1_2_10_20_2 – ident: e_1_2_10_29_2 doi: 10.1145/1356682.1356683 – ident: e_1_2_10_6_2 doi: 10.1111/cgf.12426 – volume: 36 start-page: 220 issue: 2 year: 1992 ident: e_1_2_10_18_2 article-title: Estimation of the number of extrema of a spherical harmonic publication-title: Soviet Astronomy – ident: e_1_2_10_22_2 doi: 10.1111/j.1467-8659.2011.02014.x – ident: e_1_2_10_37_2 doi: 10.1137/S0036141098341770 – ident: e_1_2_10_16_2 doi: 10.1145/1242073.1242204 – ident: e_1_2_10_7_2 doi: 10.1145/2766906 – volume-title: Group Theory in Physics year: 1984 ident: e_1_2_10_13_2 – ident: e_1_2_10_39_2 doi: 10.1145/1183287.1183290 – ident: e_1_2_10_27_2 doi: 10.1145/1183287.1183297 – ident: e_1_2_10_25_2 doi: 10.1145/1276377.1276446 – ident: e_1_2_10_3_2 doi: 10.1145/1531326.1531383 – ident: e_1_2_10_32_2 doi: 10.1145/566654.566612 – ident: e_1_2_10_36_2 doi: 10.1107/S0108767395012888 – ident: e_1_2_10_30_2 doi: 10.1111/1467-8659.1330233 – volume-title: ACM SIGGRAPH Courses year: 2005 ident: e_1_2_10_5_2 – ident: e_1_2_10_19_2 doi: 10.1145/2366145.2366196 – ident: e_1_2_10_28_2 – start-page: 347 volume-title: ACM SIGGRAPH year: 2001 ident: e_1_2_10_33_2 – ident: e_1_2_10_2_2 doi: 10.1145/882262.882296 – start-page: 377 volume-title: Proceedings of the 18th International Meshing Roundtable year: 2009 ident: e_1_2_10_34_2 doi: 10.1007/978-3-642-04319-2_22 – start-page: 156 volume-title: Proceedings of the 2003 Eurographics/ACM SIGGRAPH Symposium on Geometry Processing year: 2003 ident: e_1_2_10_17_2 – start-page: 355 volume-title: ACM SIGGRAPH year: 2001 ident: e_1_2_10_35_2 – ident: e_1_2_10_8_2 doi: 10.1145/1276377.1276447 – ident: e_1_2_10_38_2 doi: 10.1145/1833351.1778855 – start-page: 283 volume-title: Proc. of Visualization year: 2002 ident: e_1_2_10_21_2 – start-page: 465 volume-title: ACM SIGGRAPH year: 2000 ident: e_1_2_10_23_2 – ident: e_1_2_10_11_2 doi: 10.1145/344779.345074 |
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| SubjectTerms | Analysis Categories and Subject Descriptors (according to ACM CCS) Eigenvalues Eigenvectors Fields (mathematics) Group dynamics Harmonic functions I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling-Geometric algorithms Image processing systems Invariants Mathematical analysis Spherical harmonics Studies Symmetry Topological manifolds |
| Title | Harmonic Functions for Rotational Symmetry Vector Fields |
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