Linear Interpolation Problem

Unity Engine
1

Hello, I have the following problem.

How can I interpolate from a given value A to a value B relative to a given initial value X to a end value Y

where A = 0, B = 100

and X = 0.1 and Y=0

In other words:

When my input is 0.1, my output is 0
When my input is 0, my output is 100

Mathematically:
f(0.1) = 0
f(0) = 100
I need to find the function f

I think the solution is LERP but I dont know how to use it for this, and maybe is not even lerp.

Thanks for your help.

2

The answer is indeed Mathf.Lerp but you have to scale your particular input first.

The way Mathf.Lerp( a, b, c) works, it will give you a value between a and b depending on the value of c ranging from 0.0 to 1.0

Since your input is 0.1 to 0.0, you can scale that to be 0 to 1 by inverting and scaling it:

float alpha = (0.1f - input) * 10.0f

That will make alpha be from 0 to 1 as long as input goes from 0.1 to 0.0.

Then your result is just

float result = Mathf.Lerp( 0.0f, 100.0f, alpha);
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3

That is an awesome response, Thanks a lot

4

I see that normalizing the value from 0.1 to 0 is easy in this case, is there a method to find this normalization formula for arbitrary values?

Lets say those are defined at runtime

5

Generally if a value goes from A to B, and A and B are different values, you can rescale that value to range from 0 to 1 with the following formula:

float output = (input - A) / (B - A);

Substituting to the above reply I made, you get

float output = (input - 0.1f) / (0.0f - 0.1f);

or…

float output = (input - 0.1f) / -0.1f;

or…

float output = (0.1f - input) / 0.1f;

or…

float output = (0.1f - input) * 10f;

Math is cool. If I’m lucky I didn’t screw any of that math up. I’m sure someone will let me know if I did! Good night.

6

That is perfect! Thanks a lot.
I was wondering where that 10 came from, I didnt noticed it was the inverse of 1/10

Thanks again for your help. Good Night

1 Like