Other Lerp floating point precision improvement

Hi everyone,

I was reading some changes on microsoft documentation and I found this link: https://learn.microsoft.com/en-us/d...ore-libraries/5.0/vector-lerp-behavior-change

It got me thinking "Isn't Unity uses a+(b-a)*t implementation ?". I cheked it and yes. They do.

So, if you ever encoutered a weird bug while using Lerp on big numbers you can use this implementation instead which is "a*(1-t)+b*t".

 

Just so you know, you actually did not reimplement Mathf.Lerp().

You actually reimplemented

Mathf.LerpUnclamped()

That's a WAAAAAAY different function!!

For comparison:

https://docs.unity3d.com/ScriptReference/Mathf.Lerp.html

https://docs.unity3d.com/ScriptReference/Mathf.LerpUnclamped.html

You may get back to .Lerp() by pre-clamping your

t

term to [0-1]

 

Thank you for pointing it out. I was referring to output implementation. Clamp is done to "t". If I am not mistaken, clampped "t" is still accountable for a floating-point rounding error. But you are right, it was not clear on initial post.

inside Mathf.cs:

 

It should be mentioned that both implementations have advantages and disadvantages. While the classical alpha blend method (

t

and

1-t

) provide the best stability at the extremes, the direction vector approach is better in actually following the line / vector. Doing a normal linear "blend" between two positions could get some jerky in between values that do not necessarily follow a nice straight line.

So I would not recommend to blindly replacing one with the other unless you have a specific reason and you know about all the implications. Which one is better highly depends on the usecase. Unity's lerp could be "improved" by implementing an early exit in case t is greater or equal to 1.


As you can see in this image, this is what a linear blend actually does. The green line is the one in question adn it's a scaled linear combination between A and B. So due to floating point rounding you can imagine that the point on the red line may be slightly off.since it's a combination of those two scaled segments.

The vector approach always has the same stable start point and is adding a scaled version of the red line to the start point. So if something jitters, it jitters along the desired line.