This is less of a graphics question per se and more of a general math
question. Suppose you have an interval [a,b] and a point p in this interval.
Additionally, you have another interval [c,d] and a point p' in this
interval. Given that a, b, c, d, p, and p' all represent real numbers, what
is the general formula for deriving p' from p?
The classic example I happened to think of is the Celsius to Fahrenheit
conversion, in which [a,b] is [0,100] and [c,d] is [32,212]. Suppose that p
= 50. Then p' = (9/5)*p + 32 = 122.
This general strategy doesn't seem to work for an arbitrary scale, though.
Following the C-to-F guidelines, I couldn't seem to derive a formula for
converting, say, [1,4] to [3,7].