Hi there I am trying to find a 3D equation that follows some properties, I am having a bit of difficulty. I am unsure how to describe what the equation looks like but here goes:
The equation should be some b which is equal to two variables f and p. f and p must be in the same range and are independent of one another. So f in range [0,1] and p in range [0,1] but this can be whatever. But I will assume that f and p are in the range of [0,1] for my description.
When the value of f and p are near each other, that is f - p is close to 0. I want the equation to have the following behaviour which is best described with examples: -- if f = 0, p = o then b = 0 -- if f = 0.1, p = 0.1 then b = 0.1 -- if f = 0.2, p = 0.2 then b = 0.2 -- if f = 0.3, p = 0.3 then b = 0.3 -- if f = 0.4, p = 0.4 then b = 0.4 -- if f = 0.5, p = 0.5 then b = 0.5 -- if f = 0.6, p = 0.6 then b = 0.4 -- if f = 0.7, p = 0.7 then b = 0.3 -- if f = 0.8, p = 0.8 then b = 0.2 -- if f = 0.9, p = 0.9 then b = 0.1 -- if f = 1, p = 1 then b = 1 (Note that is f and p are close but not equal then b should stay close to this behavior)
As the values for f and p differ the equation should then have the following behavior: -- When f > p, as f - p gets greater, b should decrease as some rate relative to (f - p) -- When f < p , as p - f gets greater, b should increase at some rate relative to (p-f)
As an example we would have say: -- f = 0.55 and p = 0.5, b = 0.45 (b should drop slightly as f increases here) then -- f = 0.6 and p = 0.5, b = 0.4 (b drop even more) but if p increases -- f = 0.6 and p = 0.55 then b = 0.45 (It increases again as p increases)
Then the other way for p > f: -- let p = 0.55 and f = 0.45 then b = 0.55 then -- p = 0.6 and f = 0.4 then b = 0.6 or if f increases -- p = 0.6 and f = 0.5 then b = 0.5 (or near there it decreases as f increases)
I have attached a terrible picture I tried to draw which shows the first behavior in the green line (b = P(B) in this picture, f = Fk and p = Pk). It almost looks like a curve for similar values of p and f then on each "side" of the green line we should have b increasing as p outgrows f and we should have b decreasing as f outgrows p.
Thanks to anyone who gives this a read of is willing to help! Thanks.
