Tip: Scaling a range of numbers with a known min and max value

■ Scaling a range of numbers with a known min and max value

Let's say you want to scale a range [min,max] to [a,b]. You're looking for a (continuous) function that satisfies

f(min) = a
f(max) = b

In your case, a would be 1 and b would be 30, but let's start with something simpler and try to map [min,max] into the range [0,1].

Putting min into a function and getting out 0 could be accomplished with

f(x) = x - min   ===>   f(min) = min - min = 0

So that's almost what we want. But putting in max would give us max - min when we actually want 1. So we'll have to scale it:

        x - min                                  max - min
f(x) = ---------   ===>   f(min) = 0;  f(max) =  --------- = 1
       max - min                                 max - min

which is what we want. So we need to do a translation and a scaling. Now if instead we want to get arbitrary values of a and b, we need something a little more complicated:

       (b-a)(x - min)
f(x) = --------------  + a
          max - min

You can verify that putting in min for x now gives a, and putting in max gives b.

You might also notice that (b-a)/(max-min) is a scaling factor between the size of the new range and the size of the original range. So really we are first translating x by -min, scaling it to the correct factor, and then translating it back up to the new minimum value of a.

Hope this helps.

http://stackoverflow.com/questions/5294955/how-to-scale-down-a-range-of-numbers-with-a-known-min-and-max-value