Polyhedral patterns
Publication date
2015-11-01
Authors
Jiang, Caigui
Tang, Chengcheng
Vaxman, A.
Wonka, Peter
Pottmann, Helmut
Editors
Advisors
Supervisors
Document Type
Article
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License
taverne
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.
Keywords
Architectural geometry, Discrete differential geometry, Polyhedral meshes, Wallpaper tiling groups, Taverne, Computer Graphics and Computer-Aided Design
Citation
Jiang, C, Tang, C, Vaxman, A, Wonka, P & Pottmann, H 2015, 'Polyhedral patterns', ACM Transactions on Graphics, vol. 34, no. 6, 172. https://doi.org/10.1145/2816795.2818077