I’ve noticed when talking to various Unity users (and browsing the forums) there seems to be a bit of confusion about the purpose of the Lerp methods, and how and when to use them. This isn’t too surprising given that the documentation on Lerp is bizarre (it uses Time.time as a t value, something that by the end of this tutorial you’d know is somewhat odd). I’ve also supplied a Unity webplayer below to visualize how Lerp works.
Lerp stands for Linear Interpolation. Unity has a family of Lerp methods that all function pretty much the same way but have different applications: Mathf.Lerp, Vector3.Lerp, Color.Lerp, and Quaternion.Lerp.
Lerp essentially lets you pick two values, a from and to value, and then select a t value that returns an interpolation between the from and to. The t value is clamped between 0 and 1 (regardless of what you put in the method as a parameter) so you can think of it like a percentage; 0.4 is 40%, 0.6 is 60%, and so on. This leads to the idea of thinking that when you run Lerp on a from and to values, you will get a value t percent between the two. Lets look at some examples.
Mathf.Lerp(0, 100, 0.5f)
This is trivial. We can read this as asking Lerp to give us the value 50% between 0 and 100. This will return 50.
Mathf.Lerp(50, 80, 0.3f)
This will return the value 30% between 50 and 80, which is 59. To make Lerp’s inner workings less opaque, you can actually verify these values using simple arithmetic. You really just need to get the range between the two values, multiply that by the t value and then add that to the from value. For the example above you would do.
range : 80 - 50 = 30 distance by t value : 30 * 0.3 = 9 interpolated value : 50 + 9 = 59
(The above is in pseudocode and not C#)
As stated above, the other Lerp methods work in pretty much the same way. Vector3.Lerp has you select two Vector3s for the from and to values, Color.Lerp uses Colors (duh), Quaternion.Lerp, rotations.
You don’t always have the luxury of having the t value easily supplied for you. Often when using Lerp you are attempting to relate two different values to each other. An example of this would be simulating camera shake when a player is nearby a cannon firing: the further the player is away from the cannon, the less the camera shakes. Therefore there is a clear relation between the distance the player is from the cannon and the magnitude of the camera shake. (This example is based on the cannons from the Mario 64 HD project I built, specifically the FiringCannon class.)
Unity supplies a method named InverseLerp. InverseLerp takes a from and to parameter, and then a value parameter which should be somewhere between from and to. I’ll do an example before we try it out on the camera shake problem stated above.
Mathf.InverseLerp(30, 60, 45);
We can read this as “how far is 45 between 30 and 60?” This will return 0.5, as 45 is halfway between 30 and 60.
For our cannon, lets assume we have some CameraShake(float magnitude) method that we will use. We will state that the maximum shake magnitude is 20, and the minimum is 0. We will also say that the maximum distance the player can be from the cannon and still feel the shake is 50, and the minimum 0. Let’s solve this.
float t = Mathf.InverseLerp(0, 50, Vector3.Distance(cannon.position, player.position));
Where cannon and player are Transforms. This will give us a t value that is 0 when the player is immediately beside the cannon, and 1 when the player’s distance is 50 or greater. We now need to get the proper shake magnitude.
Mathf.Lerp(20, 0, t);
You’ll notice that the from value is larger than the to value. This perfectly acceptable and is done because we want the shake magnitude to be a maximum when the player’s distance is 0 (and the t value is 0) and at a minimum when the player’s distance is 50 or greater (and the t value is 1). If for whatever reason you need the from value to be the smaller of the two, you can always invert t by subtracting it from 1.
I’ve added a demo below showing Lerping between two values (Mathf.Lerp), positions (Vector3.Lerp) and colors (Color.Lerp), with the t value controlled by the slider. Hopefully this will clear up how Lerp works and has demonstrated how useful a method it is.
