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> complicated math

Is it though? Isn't the final shape just a paraboloid, like a parabolic antenna with the hoop in the focal point?

It's optimizing for an average of shots from more or less arbitrary locations, so it's not necessarily a perfect parabaloid.

The average of paraboloids is more or less a paraboloid too

The video justifies that it isn't: that paraboloids work to focus straight lines but not parabolic basketball trajectories.