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.
Bibliographical noteKAUST Repository Item: Exported on 2020-10-01
Acknowledgements: 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.