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November 16th, 2017, 03:15 AM   #1
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Need some help with coordinate conversion scheme

For those familiar with my other threads, those threads were purely for fun, this one is meant in complete seriousness however. (though not sure if this is the right place for it)

I have a scheme for giving a coordinate address for 2d space with a single number, much like Spiral Honeycomb Mosaic, but for a square grid and simplified.

Take a square with address 0. Slice it into quadrants. The top left quadrant is 00, the top right quadrant is 02, the bottom left quadrant is 01, and the bottom right quadrant is 03. With the coordinate as base 4, each digit of the coordinate address is at a particular depth of recursion.

Firgure,
00 02 20 22
01 03 21 23

10 12 30 32
11 13 31 33

This is stacked to as many levels as required, filling the entire square with infinite addresses while maintaining locality.

Further, when represented as binary, simple logic can be used to find the address of neighboring cells of the same depth.

This makes it useful for computers.

However, I need some way to convert from this single number address to the X,Y address of Cartesian coordinates (though with quadrant one as the upper left quadrant since this is all for use on computers with potential for computer images).

However, I have no idea how to do this. I don't know about space filling curves, which is the only math I can think of that might apply.

What do you guys think? And can anyone help me figure this out?
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