Building LEGO sculptures requires accounting for the target object's shape, colors, and stability. In particular, finding a good layout of LEGO bricks that prevents the sculpture from collapsing (due to its own weight) is usually challenging, and it becomes increasingly difficult as the target object becomes larger or more complex. We devise a force-based analysis for estimating physical stability of a given sculpture. Unlike previous techniques for Legolization, which typically use heuristic-based metrics for stability estimation, our force-based metric gives 1) an ordering in the strength so that we know which structure is more stable, and 2) a threshold for stability so that we know which one is stable enough. In addition, our stability analysis tells us the weak portion of the sculpture. Building atop our stability analysis, we present a layout refinement algorithm that iteratively improves the structure around the weak portion, allowing for automatic generation of a LEGO brick layout from a given 3D model, accounting for color information, required workload (in terms of the number of bricks) and physical stability. We demonstrate the success of our method with real LEGO sculptures built up from a wide variety of 3D models, and compare against previous methods.

LEGO, stability-aware design, fabrication

We thank anonymous reviewers for encouragements and thoughtful suggestions. We thank Christopher Batty, Gabriel Cirio, Anne Fleming and Eitan Grinspun for helping to prepare the final version of this paper. We thank Intel for donating computing hardware. Figures 2 (a) to (d) are courtesy of Robin Sather - Brickville DesignWorks - LEGO Certified Professional Builder. Figure 2 (e) is courtesy of the LEGO club of The University of Tokyo.

We thank the providers of the free 3D models used in this paper: GIRAFFE from Archive 3D; SNAIL and TABLE from TF3DM. We thank student volunteers from National Taiwan University for helping to build the LEGO sculptures: Chin-Yu Chien, Chi-Hao Hsieh, Tsung-HungWu, Kang Jao, Jia-Yu Tsai, Che-Chun Hsu, FanWang, Wei-Tse Lee, Yung-Ta Lin, Li-Ming Yang, Long-Fei Lin, Xiao-Feng Jian, Kai-Han Chang, and Ming-Shiuan Chen. We thankWei-Ting Lin for helping to capture the photos and videos. We used Mitsuba [Jakob 2010] for rendering synthesized images.

This work was supported in part by the JSPS Postdoctoral Fellowships for Research Abroad, Ministry of Science and Technology (MOST103-2218-E-002-030, MOST103-2221-E-002-158-MY3) and Intel.