I created this project as a short experiment into drawing images using magnets in a grid pattern. The motivation was to create a screen that can accurately display an images in magnetic sand using only electromagnets below a sand-filled tray. The magnets can vary their strength by changing the voltage flowing through them, but that is all.
This simulation uses metaballs (https://en.wikipedia.org/wiki/Metaballs) to act as a naive approximation for the behaivior of an electromagnet. This works because magnetic fields merge in a similar way to metaballs (ignoring field lines), but metaballs are much much faster to calculate.
The algorithm works as follows:
1: Take an input picture and run edge detection on it
2: Take the edge detected image and make the regions inside of the outline black and the regions
outside the outline white.
3: Find magnets within the black region, all other magnets are set to strength 0. This is because
no magnet outside the region of the image should be turned on. It will always make the
approximation worse.
4: Out of the set of all magnets inside the region, iterate over them and shift their
strength up or down slightly to increase the accuracy of the image. The accuracy is measured
as the difference between the amount of accurate pixels in the magnet image and the accurate pixels in the
original. As the algorithm runs it makes smaller and smaller changes each iteration.
If this is the input image:
And the magnet accuracy is set to 10x15 (meaning that you have a grid of 10 by 15 magnets to work with), the program will output:
Unfortunately, I never used this system with a real magnet array because the cost and time to create one is too much, however working on this project I have learned a lot about image processing as well as the math behind metaballs!