Polyhedral patterns

Handle URI:
http://hdl.handle.net/10754/622588
Title:
Polyhedral patterns
Authors:
Jiang, Caigui ( 0000-0002-1342-4094 ) ; Tang, Chengcheng ( 0000-0002-4875-6670 ) ; Vaxman, Amir; Wonka, Peter ( 0000-0003-0627-9746 ) ; Pottmann, Helmut ( 0000-0002-3195-9316 )
Abstract:
We study the design and optimization of polyhedral patterns, which are patterns of planar polygonal faces on freeform surfaces. Working with polyhedral patterns is desirable in architectural geometry and industrial design. However, the classical tiling patterns on the plane must take on various shapes in order to faithfully and feasibly approximate curved surfaces. We define and analyze the deformations these tiles must undertake to account for curvature, and discover the symmetries that remain invariant under such deformations. We propose a novel method to regularize polyhedral patterns while maintaining these symmetries into a plethora of aesthetic and feasible patterns.
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division; Computer Science Program; Applied Mathematics and Computational Science Program; Visual Computing Center (VCC); TU Wien, KAUST, Saudi Arabia
Citation:
Jiang C, Tang C, Vaxman A, Wonka P, Pottmann H (2015) Polyhedral patterns. ACM Transactions on Graphics 34: 1–12. Available: http://dx.doi.org/10.1145/2816795.2818077.
Publisher:
Association for Computing Machinery (ACM)
Issue Date:
27-Oct-2015
DOI:
10.1145/2816795.2818077
Type:
Article
ISSN:
0730-0301
Sponsors:
We thank the anonymous reviewers for their insightful comments and suggestions for improving the paper. This research was supported by the Visual Computing Center (VCC) at KAUST and by the Austrian Science Fund (FWF) via grants P23735-N13 and I706-N26 (DFG-Collaborative Research Center, TRR 109, Discretization in Geometry and Dynamics). Caigui Jiang and Chengcheng Tang were supported by KAUST baseline funding.
Appears in Collections:
Articles; Applied Mathematics and Computational Science Program; Computer Science Program; Visual Computing Center (VCC); Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorJiang, Caiguien
dc.contributor.authorTang, Chengchengen
dc.contributor.authorVaxman, Amiren
dc.contributor.authorWonka, Peteren
dc.contributor.authorPottmann, Helmuten
dc.date.accessioned2017-01-02T09:55:31Z-
dc.date.available2017-01-02T09:55:31Z-
dc.date.issued2015-10-27en
dc.identifier.citationJiang C, Tang C, Vaxman A, Wonka P, Pottmann H (2015) Polyhedral patterns. ACM Transactions on Graphics 34: 1–12. Available: http://dx.doi.org/10.1145/2816795.2818077.en
dc.identifier.issn0730-0301en
dc.identifier.doi10.1145/2816795.2818077en
dc.identifier.urihttp://hdl.handle.net/10754/622588-
dc.description.abstractWe study the design and optimization of polyhedral patterns, which are patterns of planar polygonal faces on freeform surfaces. Working with polyhedral patterns is desirable in architectural geometry and industrial design. However, the classical tiling patterns on the plane must take on various shapes in order to faithfully and feasibly approximate curved surfaces. We define and analyze the deformations these tiles must undertake to account for curvature, and discover the symmetries that remain invariant under such deformations. We propose a novel method to regularize polyhedral patterns while maintaining these symmetries into a plethora of aesthetic and feasible patterns.en
dc.description.sponsorshipWe thank the anonymous reviewers for their insightful comments and suggestions for improving the paper. This research was supported by the Visual Computing Center (VCC) at KAUST and by the Austrian Science Fund (FWF) via grants P23735-N13 and I706-N26 (DFG-Collaborative Research Center, TRR 109, Discretization in Geometry and Dynamics). Caigui Jiang and Chengcheng Tang were supported by KAUST baseline funding.en
dc.publisherAssociation for Computing Machinery (ACM)en
dc.subjectArchitectural geometryen
dc.subjectDiscrete differential geometryen
dc.subjectPolyhedral meshesen
dc.subjectWallpaper tiling groupsen
dc.titlePolyhedral patternsen
dc.typeArticleen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.contributor.departmentComputer Science Programen
dc.contributor.departmentApplied Mathematics and Computational Science Programen
dc.contributor.departmentVisual Computing Center (VCC)en
dc.contributor.departmentTU Wien, KAUST, Saudi Arabiaen
dc.contributor.institutionTU Wien, Utrecht University, Netherlandsen
kaust.authorJiang, Caiguien
kaust.authorTang, Chengchengen
kaust.authorWonka, Peteren
kaust.authorPottmann, Helmuten
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