SIGGRAPH Asia 2012
Honghua Li Ibraheem Alhashim Hao Zhang Ariel Shamir Daniel Cohen-Or
Simon Fraser University National University of Defense Technology
Interdisciplinary Center Tel Aviv University


We introduce the geometric problem of stackabilization: how to geometrically modify a 3D object so that it is more amenable to stacking. Given a 3D object and a stacking direction, we define a measure of stackability, which is derived from the gap between the lower and upper envelopes of the object in a stacking configuration along the stacking direction. The main challenge in stackabilization lies in the desire to modify the object's geometry only subtly so that the intended functionality and aesthetic appearance of the original object are not significantly affected. We present an automatic algorithm to deform a 3D object to meet a target stackability score using energy minimization. The optimized energy accounts for both the scales of the deformation parameters as well as the preservation of pre-existing geometric and structural properties in the object, e.g., symmetry, as a means of maintaining its functionality. We also present an intelligent editing tool that assists a modeler when modifying a given 3D object to improve its stackability. Finally, we explore a few fun variations of the stackabilization problem.


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@article {Li_siga12,
title = {Stackabilization},
author = {Honghua Li and Ibraheem Alhashim and Hao Zhang and Ariel Shamir and Daniel Cohen-Or},
journal = {ACM Transactions on Graphics, (Proc. of SIGGRAPH Asia 2012)},
volume = {31},
number = {6},
year = {2012}


We thank the anonymous reviewers for their valuable comments. We thank Yanir Kleinman for initial testing of the stackabilization concept, to Kai Xu for discussion on the controller deformation code, and to all the participants of the user study. This work is supported in part by grants from China Scholarship Council, National Science and Engineering Research Council of Canada (No. 611370), the Israel Ministry of Science and Education, and the Israel Science Foundation (No. 324/11).