This animation, made by Prof. Keenan Crane of Carnegie-Mellon University, shows removing one loop from a smoothly deformable pair of handcuffs from an infinite pole without tearing, breaking, or surfaces passing through one another. The animation was made through the technique of “repulsive shape optimisation”, which is described in technical detail in the following 53 minute video.
Here is a paper describing the technique, “Repulsive Surfaces”, from ACM Transactions on Graphics 2021. The following brief video accompanied the paper.
The narrator of the second video above, explicitly and presciently anticipated this viewer’s impulse to stop watching. He said the video would indicate the easier and more difficult parts and suggested skipping when necessary. I quickly followed through on his anticipation; I stopped watching. I can surely understand how the world’s creators of computer assisted design software would find such information worthwhile and important. I am indeed happy to have perused the descriptions of the embedded videos and glad to know such evolving knowledge exists. However, for me it is all considerably beyond my cognitive abilities. It makes me wish I had had better guides through mathematics back when my brain plasticity was a positive quantity.