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The obvious one is modulation/multiplication of each axis by different pitch, or dedicating different bits for each axis (in computer terms)

But are there known smarter methods? i.e. normalized distribution where the higher number the higher length/distance of the position, via some kind of fibonnaci sequence based algoritm? In simple terms, some kind "equation" that distributes encoded points evenly in each direction with steadily increasing radius.

If such exists, are they useful or limited? Can you calculate radius or add two positions without decoding the number back into 3D axis?

Note: I couldn't find much about this on google (not fully sure which terms to use for this)

johnick
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  • Can you please elaborate a little bit on your "obvious" encoding, in particular the modulation one? – Andreas Lenz Nov 21 '21 at 08:21
  • It's more common when it comes to programming, eg. z100+y10+x allows you to encode 10 units width 3D space – johnick Nov 21 '21 at 08:26
  • @Varun Vejalla There are bijections between $\mathbb{R}$ and $\mathbb{R}^n$, see e.g. https://math.stackexchange.com/questions/243590/bijection-from-mathbb-r-to-mathbb-rn . But I don't think this is what the OP is looking for. – Andreas Lenz Nov 21 '21 at 08:30
  • @AndreasLenz Interesting, I thought this was impossible - I'll delete my earlier comment. – Varun Vejalla Nov 21 '21 at 16:41

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I think the way most software is build it is much easier to just use 3 different numbers. Clever software allows you to treat the 3 numbers as a vector and do vector/ matrix based operation with them. That seems to be a lot more helpful than encoding the three numbers into one.

One could define a number of differnt ways to encode 3 numbers into one but as far as I know none of them are in any way useful for applications.

quarague
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