  Sequential assembly with geometric primitives has drawn attention in robotics
and 3D vision since it yields a practical blueprint to construct a target
shape. However, due to its combinatorial property, a greedy method falls short
of generating a sequence of volumetric primitives. To alleviate this
consequence induced by a huge number of feasible combinations, we propose a
combinatorial 3D shape generation framework. The proposed framework reflects an
important aspect of human generation processes in real life -- we often create
a 3D shape by sequentially assembling unit primitives with geometric
constraints. To find the desired combination regarding combination evaluations,
we adopt Bayesian optimization, which is able to exploit and explore
efficiently the feasible regions constrained by the current primitive
placements. An evaluation function conveys global structure guidance for an
assembly process and stability in terms of gravity and external forces
simultaneously. Experimental results demonstrate that our method successfully
generates combinatorial 3D shapes and simulates more realistic generation
processes. We also introduce a new dataset for combinatorial 3D shape
generation. All the codes are available at
\url{https://github.com/POSTECH-CVLab/Combinatorial-3D-Shape-Generation}.
