Why Use .normalize()? — Understanding Vector Normalization through Three.js and Blender

What is Normalization?

Normalization is the process of maintaining the direction of a vector unchanged while making its length 1. It discards «how far you go» and retains only «which direction you point». Thus, normalized vectors are used when representing information where direction is more important than magnitude, such as direction, view direction, normal, and movement input vectors.

Mathematically, it is the vector v divided by its magnitude |v|. A vector like (3, 4, 0) has a length of 5, so when normalized, it becomes (0.6, 0.8, 0). The length becomes 1, but the direction remains the same.

Why Grids Don't Have This Issue

Grid-based games like chess, old Pokémon games, and turn-based strategy simulations don't require normalization. Such game worlds are not truly continuous spaces. One square left, one square right, one diagonal square each «distance differently» mathematically, but within the game's rules, they all count as «one move». Even if the diagonal measures √2 ≈ 1.41 mathematically, if the rule defines it as «one square», that's the standard. The exact distance value isn't what's crucial here, it's the rule that's important, eliminating concerns like «isn't diagonal faster?»

What Happens Without Normalization in Three.js Space

The space in Three.js is entirely different. Coordinates are (x, y, z), values are all Floats, and movement is by distance computation, not «squares». The issue becomes clear without normalization.

Consider pressing W + D keys simultaneously. The input vector is (1, 1), and the length of this vector is √2 ≈ 1.41. Within one frame, linear movement travels 1 unit, but diagonal movement travels 1.41 units. This isn't just a perceivable speed issue; it's an actual change in positional values.

This difference can lead to significant issues. Moving diagonally across thin walls or corners can cause collision detection bugs where walls are passed through in one frame, and characters moving diagonally to the same destination always arriving first. This is not a speed setting error but a gain in distance.

So We Use Normalization

In free movement games, this is often the flow. First, input is interpreted as directional intent. (1, 1) means «want to go diagonally». Applying .normalize() to this results in (0.707, 0.707). Then, you multiply it by speed.

After normalization, rightward movement (1, 0), upward movement (0, 1), and diagonal movement (1, 1) all have a length of 1. You appear to move diagonally, but by position value standards, you always travel the same distance.

The Real Reason to Apply Scale in Blender

Here's where Blender reconnects. The Normal Vector in Blender indicates the direction a face is pointing during lighting calculations. This normal is calculated under the premise that its length is always 1.

If you increase scale and don't Apply Scale, internal vector lengths increase too. The normal no longer only represents «directional value».

Lighting calculations utilize the Dot Product. When both the face normal and light direction vector have a length of 1, the dot product results in a value between -1 ~ 1, which maps to the brightness we expect. However, if a face's normal length is 100 and the light's direction length is 50, the dot product results in 5000. This causes the screen to turn white, colors to pop bizarrely, or shading to appear disrupted. Apply Scale effectively means «reset these vectors to a length of 1 standard».

Caution in Three.js

.normalize() alters the original vector directly.

If you need to maintain the position or force magnitude, you must copy it first.

At first, not knowing this, many experience their object flying towards the origin when calling .normalize() directly on position vectors.

Real Situations Where Normalization is Commonly Encountered in Three.js

You don't need to apply it everywhere. However, when the word «direction» arises, it's almost mandatory.

Creating Custom Movement Logic

Using controllers like OrbitControls, it's easy to think there's almost no need to use .normalize() initially as it's handled internally. However, the story changes when directly crafting movement logic accepting keyboard input or click coordinates. Simple coordinate movements like clearly define «how much to move», so normalization isn't required. However, movements with specific directions or movements based on camera directions or input vectors must use it.

Without normalization, the speed value varies with distance. The closer the goal, the slower it moves, resulting in strange speeds where objects farther away move faster.

Mouse Interaction (Raycaster)

When crafting 3D web interactions with Three.js, Raycaster is almost always used. A seemingly invisible laser shot from the mouse position into the screen is the directional vector. Internally, raycaster.setFromCamera(mouse, camera) assumes the direction vector is normalized. Insert an unnormalized vector, and click detection occurs in peculiar places or ray extends excessively affecting performance.

Directly Handling Shaders or Materials

When using built-in materials like MeshStandardMaterial or , Three.js internally normalizes all normals and directional vectors. However, strong distortions like or writing directly means you must manage it yourself.

In shaders, numbers directly translate to screen results. Missing normalization causes excessive brightness, color distortion, or flickering outcomes frame by frame.

Normalization maintains a fair distance standard for movement and a brightness standard for lighting. It intentionally separates direction and magnitude, effectively indicating «this value only represents direction». Ultimately, .normalize() serves to control the values' size, maintaining a consistent calculation standard. If a situation requires only direction, it's naturally accompanied by this process.

• #Three.js
• #WebGL