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.
%0 Journal Article
%1 Jiang:2015:PP:2816795.2818077
%A Jiang, Caigui
%A Tang, Chengcheng
%A Vaxman, Amir
%A Wonka, Peter
%A Pottmann, Helmut
%C New York, NY, USA
%D 2015
%I ACM
%J ACM Trans. Graph.
%K 2015 architecture graphics polygon siggraph
%N 6
%P 172:1--172:12
%R 10.1145/2816795.2818077
%T Polyhedral Patterns
%U http://doi.acm.org/10.1145/2816795.2818077
%V 34
%X 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.
@article{Jiang:2015:PP:2816795.2818077,
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.},
acmid = {2818077},
added-at = {2018-04-23T13:34:27.000+0200},
address = {New York, NY, USA},
articleno = {172},
author = {Jiang, Caigui and Tang, Chengcheng and Vaxman, Amir and Wonka, Peter and Pottmann, Helmut},
biburl = {https://www.bibsonomy.org/bibtex/2befa78ab2ee596e0743d893ab30254b1/achakraborty},
description = {Polyhedral patterns},
doi = {10.1145/2816795.2818077},
interhash = {090b34d82767ce396a5e6373f6f471d9},
intrahash = {befa78ab2ee596e0743d893ab30254b1},
issn = {0730-0301},
issue_date = {November 2015},
journal = {ACM Trans. Graph.},
keywords = {2015 architecture graphics polygon siggraph},
month = oct,
number = 6,
numpages = {12},
pages = {172:1--172:12},
publisher = {ACM},
timestamp = {2018-04-23T13:34:27.000+0200},
title = {Polyhedral Patterns},
url = {http://doi.acm.org/10.1145/2816795.2818077},
volume = 34,
year = 2015
}