QuadCover - Surface Parameterization using Branched Coverings

We introduce an algorithm for the automatic computation of global parameterizations on arbitrary simplicial 2‐manifolds, whose parameter lines are guided by a given frame field, for example, by principal curvature frames. The parameter lines are globally continuous and allow a remeshing of the surfa...

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Published in:	Computer graphics forum Vol. 26; no. 3; pp. 375 - 384
Main Authors:	Kälberer, Felix, Nieser, Matthias, Polthier, Konrad
Format:	Journal Article
Language:	English
Published:	Oxford, UK Blackwell Publishing Ltd 01.09.2007
Subjects:	Algorithms and systems Computer graphics Geometric algorithms Hierarchy and geometric transformations I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling, Hierarchy and geometric transformations, Geometric algorithms, languages, and systems languages Studies
ISSN:	0167-7055, 1467-8659
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Abstract	We introduce an algorithm for the automatic computation of global parameterizations on arbitrary simplicial 2‐manifolds, whose parameter lines are guided by a given frame field, for example, by principal curvature frames. The parameter lines are globally continuous and allow a remeshing of the surface into quadrilaterals. The algorithm converts a given frame field into a single vector field on a branched covering of the 2‐manifold and generates an integrable vector field by a Hodge decomposition on the covering space. Except for an optional smoothing and alignment of the initial frame field, the algorithm is fully automatic and generates high quality quadrilateral meshes.
AbstractList	We introduce an algorithm for the automatic computation of global parameterizations on arbitrary simplicial 2‐manifolds, whose parameter lines are guided by a given frame field, for example, by principal curvature frames. The parameter lines are globally continuous and allow a remeshing of the surface into quadrilaterals. The algorithm converts a given frame field into a single vector field on a branched covering of the 2‐manifold and generates an integrable vector field by a Hodge decomposition on the covering space. Except for an optional smoothing and alignment of the initial frame field, the algorithm is fully automatic and generates high quality quadrilateral meshes. We introduce an algorithm for the automatic computation of global parameterizations on arbitrary simplicial 2-manifolds, whose parameter lines are guided by a given frame field, for example, by principal curvature frames. The parameter lines are globally continuous and allow a remeshing of the surface into quadrilaterals. The algorithm converts a given frame field into a single vector field on a branched covering of the 2-manifold and generates an integrable vector field by a Hodge decomposition on the covering space. Except for an optional smoothing and alignment of the initial frame field, the algorithm is fully automatic and generates high quality quadrilateral meshes. [PUBLICATION ABSTRACT]
Author	Kälberer, Felix Nieser, Matthias Polthier, Konrad
Author_xml	– sequence: 1 givenname: Felix surname: Kälberer fullname: Kälberer, Felix organization: Freie Universität Berlin – sequence: 2 givenname: Matthias surname: Nieser fullname: Nieser, Matthias organization: Freie Universität Berlin – sequence: 3 givenname: Konrad surname: Polthier fullname: Polthier, Konrad organization: Freie Universität Berlin
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References_xml	– reference: Marinov M., Kobbelt L.: A robust two-step procedure for quad-dominant remeshing. Computer Graphics Forum 25, 3 (2006), 537U-546. – reference: Ray N., Li W. C., Lévy B., Sheffer A., Alliez P.Periodic global parameterization. ACM Trans. Graph. 25, 4 (2006), 1460-1485. – reference: Kharevych L., Springborn B., Schröder P.: Discrete conformal mappings via circle patterns. ACM Transactions on Graphics 25, 2 (2006). – reference: Dong S., Kircher S., Garland M.Harmonic functions for quadrilateral remeshing of arbitrary manifolds. Comp. Aided Design 22, 4 (2005), 392-423. – reference: Fulton W.: Algebraic Topology, A first course. Springer Verlag, 1995. – reference: Cohen-Steiner D., Morvan J.-M.: Restricted delaunay triangulations and normal cycle. In Proc. of Symp. on Comp. Geom. (2003), ACM Press, pp. 312-321. – reference: Hildebrandt K., Polthier K.Anisotropic filtering of non-linear surface features. Computer Graphics Forum 23, 3 (2004), 391-400. – reference: Jost J.: Compact Riemann Surfaces. Springer, 2002. – reference: Farkas H. M., Kra I.: Riemann Surfaces. Springer Verlag, 1980. – start-page: 191 year: 2006 end-page: 200 – start-page: 127 year: 2003 end-page: 137 – start-page: 517 year: 2000 end-page: 526 – year: 1980 – volume: 25 start-page: 1460 issue: 4 year: 2006 end-page: 1485 article-title: Periodic global parameterization publication-title: ACM Trans. Graph. – year: 2002 – start-page: 201 year: 2006 end-page: 210 – year: 2006 – volume: 23 start-page: 391 issue: 3 year: 2004 end-page: 400 article-title: Anisotropic filtering of non‐linear surface features publication-title: Computer Graphics Forum – start-page: 485 year: 2003 end-page: 493 – year: 1995 – start-page: 113 year: 2003 end-page: 134 – volume: 22 start-page: 392 issue: 4 year: 2005 end-page: 423 article-title: Harmonic functions for quadrilateral remeshing of arbitrary manifolds publication-title: Comp. Aided Design – volume: 25 start-page: 2 year: 2006 article-title: Discrete conformal mappings via circle patterns publication-title: ACM Transactions on Graphics – start-page: 207 year: 2004 end-page: 216 – year: January 2006 – start-page: 193 year: 2004 end-page: 203 – volume: 25 start-page: 537U issue: 3 year: 2006 end-page: 546 article-title: A robust two‐step procedure for quad‐dominant remeshing publication-title: Computer Graphics Forum – start-page: 312 year: 2003 end-page: 321 – ident: e_1_2_7_10_2 doi: 10.1111/j.1467-8659.2004.00770.x – volume-title: Algebraic Topology, A first course. year: 1995 ident: e_1_2_7_8_2 doi: 10.1007/978-1-4612-4180-5 – ident: e_1_2_7_14_2 – ident: e_1_2_7_19_2 – ident: e_1_2_7_12_2 doi: 10.1007/978-3-662-04745-3 – ident: e_1_2_7_6_2 doi: 10.1016/j.cagd.2005.04.004 – ident: e_1_2_7_5_2 doi: 10.1145/1179352.1141993 – ident: e_1_2_7_18_2 doi: 10.1145/1183287.1183297 – ident: e_1_2_7_2_2 doi: 10.1145/882262.882296 – ident: e_1_2_7_3_2 doi: 10.1145/1057432.1057459 – start-page: 312 volume-title: Restricted delaunay triangulations and normal cycle year: 2003 ident: e_1_2_7_4_2 – ident: e_1_2_7_11_2 doi: 10.1145/344779.345074 – ident: e_1_2_7_13_2 doi: 10.1145/1138450.1138461 – ident: e_1_2_7_15_2 doi: 10.1109/PCCGA.2004.1348351 – ident: e_1_2_7_17_2 doi: 10.1007/978-3-662-05105-4_6 – ident: e_1_2_7_7_2 doi: 10.1007/978-1-4684-9930-8 – ident: e_1_2_7_9_2 – ident: e_1_2_7_20_2 – ident: e_1_2_7_16_2 doi: 10.1111/j.1467-8659.2006.00973.x
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Snippet	We introduce an algorithm for the automatic computation of global parameterizations on arbitrary simplicial 2‐manifolds, whose parameter lines are guided by a... We introduce an algorithm for the automatic computation of global parameterizations on arbitrary simplicial 2-manifolds, whose parameter lines are guided by a...
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SubjectTerms	Algorithms and systems Computer graphics Geometric algorithms Hierarchy and geometric transformations I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling, Hierarchy and geometric transformations, Geometric algorithms, languages, and systems languages Studies
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