Question

I was curious if there was an elegant way to do this, aside from just calculating the distance from the point to each side and finding the minimum.

Some things I’ve thought about:
If it’s a square, we can just draw the diagonals and figure out which of the 4 regions the point falls on. Each of these region corresponds to a closest side.

Perhaps we can divide up the rectangle into squares and go somewhere from there?

It seems an alternative solution would be too complicated and not worth looking for.

Answer 1

For rectangle you can use following regions: