Linear Interpolation

Checked with version: 4

-

Difficulty: Beginner

When making games it can sometimes be useful to linearly interpolate between two values. This is done with a function called Lerp. Linearly interpolating is finding a value that is some percentage between two given values. For example, we could linearly interpolate between the numbers 3 and 5 by 50% to get the number 4. This is because 4 is 50% of the way between 3 and 5.

In Unity there are several Lerp functions that can be used for different types. For the example we have just used, the equivalent would be the Mathf.Lerp function and would look like this:

Code snippet

// In this case, result = 4
float result = Mathf.Lerp (3f, 5f, 0.5f);

The Mathf.Lerp function takes 3 float parameters: one representing the value to interpolate from; another representing the value to interpolate to and a final float representing how far to interpolate. In this case, the interpolation value is 0.5 which means 50%. If it was 0, the function would return the ‘from’ value and if it was 1 the function would return the ‘to’ value.

Other examples of Lerp functions include Color.Lerp and Vector3.Lerp. These work in exactly the same way as Mathf.Lerp but the ‘from’ and ‘to’ values are of type Color and Vector3 respectively. The third parameter in each case is still a float representing how much to interpolate. The result of these functions is finding a colour that is some blend of two given colours and a vector that is some percentage of the way between the two given vectors.

Let’s look at another example:

Code snippet

Vector3 from = new Vector3 (1f, 2f, 3f);
Vector3 to = new Vector3 (5f, 6f, 7f);

// Here result = (4, 5, 6)
Vector3 result = Vector3.Lerp (from, to, 0.75f);

In this case the result is (4, 5, 6) because 4 is 75% of the way between 1 and 5; 5 is 75% of the way between 2 and 6 and 6 is 75% of the way between 3 and 7.

The same principle is applied when using Color.Lerp. In the Color struct, colours are represented by 4 floats representing red, blue, green and alpha. When using Lerp, these floats are interpolated just as with Mathf.Lerp and Vector3.Lerp.

Under some circumstances Lerp functions can be used to smooth a value over time. Consider the following piece of code:

Code snippet

void Update ()
{
    light.intensity = Mathf.Lerp(light.intensity, 8f, 0.5f);
}

If the intensity of the light starts off at 0 then after the first update it will be set to 4. The next frame it will be set to 6, then to 7, then to 7.5 and so on. Thus over several frames, the lights intensity will tend towards 8 but the rate of it’s change will slow as it approaches its target. Note that this happens over the course of several frames. If we wanted this to not be frame rate dependent then we could use the following code:

Code snippet

void Update ()
{
    light.intensity = Mathf.Lerp(light.intensity, 8f, 0.5f * Time.deltaTime);
}

This would mean the change to intensity would happen per second instead of per frame.

Please note that when smoothing a value it is often best to use the SmoothDamp function. Only use Lerp for smoothing if you are sure of the effect you want.

Related tutorials

Related documentation

Scripting

  1. Scripts as Behaviour Components
  2. Variables and Functions
  3. Conventions and Syntax
  4. C# vs JS syntax
  5. IF Statements
  6. Loops
  7. Scope and Access Modifiers
  8. Awake and Start
  9. Update and FixedUpdate
  10. Vector Maths
  11. Enabling and Disabling Components
  12. Activating GameObjects
  13. Translate and Rotate
  14. Look At
  15. Linear Interpolation
  16. Destroy
  17. GetButton and GetKey
  18. GetAxis
  19. OnMouseDown
  20. GetComponent
  21. Delta Time
  22. Data Types
  23. Classes
  24. Instantiate
  25. Arrays
  26. Invoke
  27. Enumerations
  28. Switch Statements
  1. Properties
  2. Ternary Operator
  3. Statics
  4. Method Overloading
  5. Generics
  6. Inheritance
  7. Polymorphism
  8. Member Hiding
  9. Overriding
  10. Interfaces
  11. Extension Methods
  12. Namespaces
  13. Lists and Dictionaries
  14. Coroutines
  15. Quaternions
  16. Delegates
  17. Attributes
  18. Events
  1. Building a Custom Inspector
  2. The DrawDefaultInspector Function
  3. Adding Buttons to a Custom Inspector
  1. MonoDevelop's Debugger
  2. Good Coding Practices in Unity
  3. Unity Editor Extensions – Menu Items
  4. Creating Meshes
  1. AssetBundles and the AssetBundle Manager
  2. Mastering Unity Project Folder Structure - Version Control Systems
  1. Installing Tools for Unity Development
  2. Building your first Unity Game with Visual Studio
  3. Editing Unity games in Visual Studio
  4. Debugging Unity games in Visual Studio
  5. Graphics debugging Unity games in Visual Studio
  6. Taking Unity games to Universal Windows Platform
  7. Testing Unity games on Android in Visual Studio
  1. Scripting Primer and Q&A
  2. Scripting Primer and Q&A - Continued
  3. Scripting Primer and Q&A - Continued (Again)
  4. Persistence - Saving and Loading Data
  5. Object Pooling
  6. Introduction to Scriptable Objects
  7. How to communicate between Scripts and GameObjects
  8. Coding in Unity for the Absolute Beginner
  9. Sound Effects & Scripting
  10. Editor Scripting Intro
  11. Writing Plugins
  12. Property Drawers & Custom Inspectors
  13. Events: Creating a simple messaging system
  14. Ability System with Scriptable Objects
  15. Character Select System with Scriptable Objects
  1. Intro and Setup
  2. Data Classes
  3. Menu Screen
  4. Game UI
  5. Answer Button
  6. Displaying Questions
  7. Click To Answer
  8. Ending The Game and Q&A
  1. Intro To Part Two
  2. High Score with PlayerPrefs
  3. Serialization and Game Data
  4. Loading Game Data via JSON
  5. Loading and Saving via Editor Script
  6. Game Data Editor GUI
  7. Question and Answer
  1. Overview and Goals
  2. Localization Data
  3. Dictionary, JSON and Streaming Assets
  4. Localization Manager
  5. Startup Manager
  6. Localized Text Component
  7. Localized Text Editor Script
  8. Localization Q&A
  1. Introduction and Session Goals
  2. Particle Launcher
  3. Particle Collisions
  4. ParticleLauncher Script
  5. Particle Collisions and Scripting
  6. Random Particle Colors
  7. Drawing Decals with Particles
  8. Collecting Particle Information For Display
  9. Displaying Particles Via Script
  10. Droplet Decals
  11. Questions and Answers