I would like to know if there's a way to remap a value that goes from 0 to 1 constantly like this.
Into those values (those are examples).
This might be some function transformation but I can't find the way to do that. I've tried using a lookup texture but in my opinion this is not the best solution.
Thank you very much.
Okay so what you have is something like f(t)=(colour from gradient) as t goes from 0 to 1
This gives a nice smooth gradient, Where as if you take an auxiliary function, say a(t)=t^2 you'll notice this also goes between 0 and 1 (as t goes from 0 to 1 but it starts much slower then gets much faster.
You can compose the two, by using f(a(t)) this "alters the speed" that t changes if you will.
If f(t) has gradient 1 (uniformly, as the gradient increases at a constant rate, it must be 1 to go from the far ends of the colour gradient over a time of "1")
then f(a(t)) has gradient a'(t)f'(a(t)) which if a(t):=t^2 gives a rate of change of:
2t which at t=0.25 has gradient 0.5 (half the rate of change of the "normal" gradient) and at t=0.75 it has a gradient of 1.5 which is 50% faster than the usual one.
Using different a(t) you can get different effects
(someone else was asking about altering rates of change earlier, Can I use sin or cos for the non uniform rotation in unity 5? but for some reason I got a comment-less downvote, this is a similar question right?)
Take a function like:
f(t) = { 5t if 0<= t < 0.1
{ 0.5+5(t-0.1)/9 if 0.1 <= t <= 1
This will have a shape like:
1 1
| ___/ |
| ____/ |
| ____/ |
| / |
| / |
|/ |
+------------------+
0 1
It'll rise really sharply as we go from 0 to 0.1 then increase slowly to 1.
If we differentiate this we get:
f'(t) = { 5 if 0<= t < 0.1
{ 5/9 if 0.1 <= t <= 1
Which has a graph something like this:
|
| _________
|
|___
|
+------------
Notice the jump, it is NOT continuous, which will be apparent in the result.
Don't fret though, there are plenty of "smooth" functions to choose from!
As @dari said, the smoothstep function is the best solution to achieve what I need.
