not sure why i found this fascinating. i was working a geospatial mapping project and stumbled on this tangent
It makes sense because the real world is isotopic. Rectangular is presumptuous to some extent where high frequency information will be found.
What’s really cool as that the basis of support in the frequency domain has the same shape as your sampling function.
And generally speaking, the perfect shape would be a circle because you can fit the maximum amount of bandlimited noise into that space. Orientation really shouldn’t matter. It’s stranger that it does.
My dude I have like five publications in the space. But yeah I’m just some guy on the Internet. I just wish I had more opportunities to talk about it.
It started in high school when I had a side job catching dragonflies. They did experiments on their eyes, which have a hexagonal shape. It was being done to research new imaging systems. Later on I worked on some of the mathematical theory for image processing operations, namely how to perform operations like convolution in sampling systems that have non orthogonal basis vectors. Typically you represent these operations using matrix arithmetic but it doesn’t work when your sampling basis is not orthogonal.
I would like to identify those specific operations but I’m pretty much the only guy who would turn up in the search results, so I’m not sure how much more specific I can get. It is unfortunate. To my knowledge I have the fastest convolution implementations for non-rectangular two dimensional sample systems. It’s kind of a lonely research area. It’s a shame.