The question of the most dense possible packaging of the same spheres, initially answered by Johannes Kepler in 1611, remains unresolved for 3D objects of various sizes and forms. However, a group of researchers from MIT and Inkbit, led by Wojciech Matusik, has presented a new computing methodology called “dense, without mutual overlap and scalable spectral packaging” (SSP) that addresses this challenge. The technique will be presented at the SIGGRAPH 2023 conference, the largest conference on computer graphics and interactive methods.
The SSP approach involves the “querselization” of the container, represented as a 3D network of small cubes or stakes. The algorithm then calculates the number of free stakes for each object and determines where they can be placed without intersecting with other objects. The researchers use a metric designed to maximize packaging density.
The final step of the SSP algorithm ensures that each object can reach its designated place and can be separated from other objects during unpacking. By utilizing fast Fourier conversion (FFT), the team was able to greatly accelerate the packaging process.
In a demonstration example, the new algorithm successfully placed 670 objects in 40 seconds, achieving a packaging density of approximately 36%. In just 2 hours, it placed 6,596 objects with a packaging density of 37.30%. “The density we achieve, close to 40%, is much better than what traditional algorithms can achieve, and the process is also faster,” says Matusik.
Benesh Benesh, a professor of computer sciences at the University of Purdue, comments, “This is a breakthrough solution to the long-standing problem of effectively organizing 3D objects.”
The technique is potentially valuable for companies involved in storage and shipping, where various objects are regularly packaged in boxes of different sizes. However, Matusik and his colleagues are particularly interested in applying this methodology to 3D printing. “By increasing the packaging density, we can improve the overall efficiency of the printing process and reduce the cost of manufacturing parts,” he adds.
Although the problem of optimal arrangement for deformed or articulated objects remains unsolved, future work may provide solutions.