The objective of this line of research is to find efficient algorithms for packing an irregularly shaped part with irregular or regular shapes. This falls under geometric packing, a class of mathematical optimization problems with the goal of finding a combination of small objects (bins) that fit a large target (container). Geometric packing in 3D is an understudied field with significant implications in transforming design for sustainable, distributed, and obfuscated compositional manufacturing.
Potential approaches can be partitioning a volume successively into the largest inscribed cubes, few base cubes whose planes cut the outer boundary into covering segments, and a skeleton whose line segments act as principal axes of part body segments (similar to the human body). Examples of the first two approach are shown below.
![](https://i0.wp.com/coefs.charlotte.edu/mdinar/files/2023/11/Picture2.png?ssl=1)
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![](https://coefs.charlotte.edu/mdinar/files/2023/11/Picture3-1.png)
If we succeed in improving and scaling this approach, we help solve a fundamental mathematical problem in synergy with other transformational research. One potential application is in sustainable manufacturing, where we create new functional parts by reusing existing non-functional components or pieces of scrap material. Such an open-ended problem is significantly challenging to solve algorithmically, but humans can creatively tackle it. The examples below show how few participants in an exploratory study created a coat-hanger, book shelf, and a pully from sprues, gates, and miscast parts in a foundry.
![](https://i2.wp.com/coefs.charlotte.edu/mdinar/files/2023/11/Picture4.jpg?ssl=1)
![](https://i1.wp.com/coefs.charlotte.edu/mdinar/files/2023/11/Picture5.jpg?ssl=1)
![](https://i0.wp.com/coefs.charlotte.edu/mdinar/files/2023/11/Picture6.jpg?ssl=1)