by Honghua Li ∑ Ibraheem Alhashim ∑ Hao Zhang ∑ Ariel Shamir ∑ Daniel Cohen-Or

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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 objectís 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.