Foldabilizing Furniture
*Honghua Li1 *Ruizhen Hu1,2,3 Ibraheem Alhashim1 Hao Zhang1 (*joint first authors)
1Simon Fraser University 2VisuCA/SIAT 3Zhejiang University


We introduce the foldabilization problem for space-saving furniture design. Namely, given a 3D object representing a piece of furniture, our goal is to apply a minimum amount of modification to the object so that it can be folded to save space --- the object is thus foldabilized. We focus on one instance of the problem where folding is with respect to a prescribed folding direction and allowed object modifications include hinge insertion and part shrinking.

We develop an automatic algorithm for foldabilization by formulating and solving a nested optimization problem operating at two granularity levels of the input shape. Specifically, the input shape is first partitioned into a set of integral folding units. For each unit, we construct a graph which encodes conflict relations, e.g., collisions, between foldings implied by various patch foldabilizations within the unit. Finding a minimum-cost foldabilization with a conflict-free folding is an instance of the maximum-weight independent set problem. In the outer loop of the optimization, we process the folding units in an optimized ordering where the units are sorted based on estimated foldabilization costs. We show numerous foldabilization results computed at interactive speed and 3D-print physical prototypes of these results to demonstrate manufacturability.


@article {Li_sig15,
title = {Foldabilizing Furniture},
author = {Honghua Li and Ruizhen Hu and Ibraheem Alhashim and Hao Zhang}
journal = {ACM Transactions on Graphics, (Proc. of SIGGRAPH 2015)},
year = {2015},
volume = {34},
number = {4},
articleno = {90}


We thank the anonymous reviewers for their valuable comments and suggestions. We are grateful to Lu Lin for printing the models in Figure 24. Thanks also go to Daniel Cohen-Or, Tao Ju, and Ariel Shamir for some initial discussions. This work is supported in part by grants from Natural Sciences and Engineering Research Council of Canada (No. 611370 and No. 611649), GRAND NCE, NSFC (61232011), National 973 Program (2014CB360503), and Shenzhen Key Lab (CXB201104220029A).

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