Construction and Fabrication of Reversible Shape Transforms

SHUHUA LI (1,2), ALI MAHDAVI-AMIRI (1), RUIZHEN HU (3), CHANGQING ZOU (5), OLIVER VAN KAICK (4), XIUPING LIU (1), HUI HUANG (6), HAO ZHANG (1)

(1) Simon Fraser University, (2) Dalian University of Technology, (3) Shenzhen University, (4) Carleton University, (5) University of Maryland, College Park, (6) Shenzhen University


Abstract

We study a new and elegant instance of geometric dissection of 2D shapes: reversible hinged dissection, which corresponds to a dual transform between two shapes where one of them can be dissected in its interior and then inverted inside-out, with hinges on the shape boundary, to reproduce the other shape, and vice versa. We call such a transform reversible inside-out transform or RIOT. Since it is rare for two shapes to possess even a rough RIOT, let alone an exact one, we develop both a RIOT construction algorithm and a quick filtering mechanism to pick, from a shape collection, potential shape pairs that are likely to possess the transform. Our construction algorithm is fully automatic. It computes an approximate RIOT between two given input 2D shapes, whose boundaries can undergo slight deformations, while the filtering scheme picks good inputs for the construction. Furthermore, we add properly designed hinges and connectors to the shape pieces and fabricate them using a 3D printer so that they can be played as an assembly puzzle. With many interesting and fun RIOT pairs constructed from shapes found online, we demonstrate that our method significantly expands the range of shapes to be considered for RIOT, a seemingly impossible shape transform, and offers a practical way to construct and physically realize these transforms.

[Paper (50.2 MB)] [Supplementary Material (136 MB) ]

Video

RIOT.mp4

Bibtex

@article{li2018riot,title={Construction and Fabrication of Reversible Shape Transforms},author={Shuhua Li, Ali Mahdavi-Amiri, Ruizhen Hu, Han Liu, Changquin Zou, Oliver Van Kaick, Xiuping Liu, Hui Huang, Hao Zhang},journal={ACM Transactions on Graphics (TOG)},volume={37},number={6},year={2018},publisher={ACM}}

Acknowledgement

We thank the anonymous reviewers for their valuable comments. This work was supported in parts by China Scholarship Council, NSERC Canada (611370, 611649, 2015-05407), NSFC (61528208, 61602311, 61522213, 61432003, 61370143), GD Science and Technology Program (2015A030312015), Shenzhen Innovation Program (JCYJ20170302153208613, KQJSCX20170727101233642), and gift funds from Adobe. We would also like to thank Richard Bartels, and Akshay Gadi Patil for proofreading and helpful comments and Kai Yang for his artistic works to texture our results.
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