Unity: How to Normalize a Vector

Overview

Vectors play a fundamental role in various fields. These fields include mathematics, physics, computer science, and game development. A vector represents both magnitude (or size) and direction.

Normalization is a standard operation. This operation allows us to compare the direction of two vectors. In this article, you will learn what vector normalization is. You will learn why normalizing a vector is important. And, you will get to see some different methods to normalize a vector in Unity - both in C# and in a shader.

This is a series on Unity Physics. We recommend reading the series in order.

1. Unity Physics
2. Unity Collision Detection
3. Character Controller and Input Systems
4. Rigidbody Mass in Unity
5. How to add Friction to a Rigidbody
6. Cylinder Collider in Unity
7. Box Collider in Unity
8. Box Cast in Unity
9. Sorting Layers
10. Get the distance between two objects
11. How to normalize a vector

Introduction

Before diving into vector normalization, let us first understand the context.

In this section, we will explain what a vector is. And, we will look into why we want to normalize it.

In simple terms, a vector is an object that represents the magnitude and direction of a line in space. The magnitude means the size, or total length, of the vector.

You can have 2D, 3D, or n-dimensional vectors. Developers use vectors to describe velocity, force, and position. They also use vectors to describe direction.

I will give an example. A game developer uses a vector to describe the view direction of a camera. Let’s imagine that the camera looks straight ahead. In that case, the view direction (x, y, z) is equal to (0, 0, 1). They also use vectors to describe the direction in which a character should move. And, they use vectors to compare the position of two objects.

What is Vector Normalization?

Vector normalization is the process of transforming any vector into a unit vector.

A unit vector is a vector with a length (or magnitude) of 1 unit. When we normalize a vector, we throw away the original magnitude. But, we keep the direction.

Why would we want to throw away some information? Well, this helps us when using other operations to compare two vectors.

For example, you can use the dot product to compare two vectors. The dot product helps us understand how much the two vectors point in the same direction.

This also helps when you want an input vector to be the same length in every direction. In Unity, you will normalize a player’s input. This makes sure that the player moves the same speed in every direction.