Question

I’m trying to come up with a formular which converts one number spectrum into another.
For example:

0 - 800 to -1 - 1

Where 0 = -1, 200 = -0.5, 400 = 0, 600 = 0.5, 800 = 1, and so on.

The difficult part for me seems to be the negative range.

Answer 1

If your ranges are a0, a1 and b0, b1, then you want x to go to

((x-a0)/(a1-a0)) * (b1-b0) + b0

Basically, (x-a0) is how far over you are from the lower side of the first range, and (x-a0)/(a1-a0) divides by the width of the range so the number is now normalized to [0, 1]. After that, we multiply by (b1-b0) to expand the range to the new scale, and add b0 to shift it over.

For example:

>>> a0, a1 = 0.0, 800.0
>>> b0, b1 = -1.0, 1.0
>>> 
>>> x = 400 # should go to 0
>>> x-a0
400.0
>>> (x-a0)/(a1-a0)
0.5
>>> (x-a0)/(a1-a0) * (b1-b0)
1.0
>>> (x-a0)/(a1-a0) * (b1-b0) + b0
0.0
>>> x = 0 # should go to -1
>>> (x-a0)/(a1-a0) * (b1-b0) + b0
-1.0
>>> x = 800 # should go to 1
>>> (x-a0)/(a1-a0) * (b1-b0) + b0
1.0