Polyhedral patterns | Zendy

Caigui Jiang | Zendy; Chengcheng Tang | Zendy; Amir Vaxman | Zendy; Peter Wonka | Zendy; Helmut Pottmann | Zendy

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Polyhedral patterns

Author(s) -

Caigui Jiang,

Chengcheng Tang,

Amir Vaxman,

Peter Wonka,

Helmut Pottmann

Publication year - 2015

Publication title -

acm transactions on graphics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 2.153

H-Index - 218

eISSN - 1557-7368

pISSN - 0730-0301

DOI - 10.1145/2816795.2818077

Subject(s) - homogeneous space , invariant (physics) , curvature , planar , computer science , mathematics , polyhedron , geometry , computer graphics (images) , mathematical physics

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

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