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I would like to know if there's a way to remap a value that goes from 0 to 1 constantly like this.

enter image description here

Into those values (those are examples).

enter image description here

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.

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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?)


!!!CAUTION!!!

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!

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  • \$\begingroup\$ Thank you for your very precise answer, I also found that the smoothstep function could help me do this. \$\endgroup\$
    – MaT
    Sep 25 '15 at 6:37
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As @dari said, the smoothstep function is the best solution to achieve what I need.

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