Matrix4x4

One value that stores where something is, which way it faces and how big it is. You'll mostly meet it when drawing meshes from code or writing shaders.

Do I need this?

Usually not. A Transform already handles position, rotation and scale for GameObjects. You need Matrix4x4 when there is no Transform, for example when you draw a mesh with Graphics.RenderMesh, or when you pass placement data to a shader.

You never have to fill in the 16 numbers yourself. Give Unity a position, rotation and scale and it builds the matrix.

Local vs world space

Local space = measured from the object itself. World space = measured from the centre of the scene. A cup's local position says where it sits on the table; its world position says where it is in the room. A matrix converts local into world.

The members you'll use

Example

Attach to any object and check the Console.

using UnityEngine;

public class MatrixExample : MonoBehaviour
{
    void Start()
    {
        // Move 10 right, turn 90° to the right, double the size
        Matrix4x4 m = Matrix4x4.TRS(new Vector3(10, 0, 0),
                                    Quaternion.Euler(0, 90, 0),
                                    Vector3.one * 2);

        Vector3 point = m.MultiplyPoint3x4(Vector3.forward); // (12, 0, 0)
        Vector3 dir   = m.MultiplyVector(Vector3.forward);    // (2, 0, 0): not moved by 10
        Debug.Log($"point {point}, direction {dir}");

        Vector3 back = m.inverse.MultiplyPoint3x4(point);     // about (0, 0, 1) again
        Debug.Log(back);
    }
}

The point (0,0,1) was scaled to (0,0,2), turned to (2,0,0), then moved to (12,0,0). The direction got the same scale and turn, but no move.

Combining matrices: order matters

You can combine two matrices with *. Read it right to left: in parent * child, the child's recipe happens first, then the parent's. Swapping them gives a different answer, just like "turn then walk" ends somewhere different from "walk then turn".

Matrix4x4 parent = Matrix4x4.TRS(new Vector3(5, 0, 0), Quaternion.Euler(0, 90, 0), Vector3.one);
Matrix4x4 child  = Matrix4x4.Translate(new Vector3(0, 0, 2));  // 2 forward
Vector3 p = (parent * child).MultiplyPoint3x4(Vector3.zero);    // (7, 0, 0)

Going further

• Normals (arrows pointing out of a surface) need special care if the scale is uneven, like (1, 3, 1). Use m.inverse.transpose.MultiplyVector(normal).normalized.
• Camera projection matrices add perspective. For those, use MultiplyPoint, not MultiplyPoint3x4.

Common Mistakes

• Using new Matrix4x4() as "no change". It's all zeros and squashes everything to a point. Use Matrix4x4.identity.
• Using MultiplyPoint3x4 on a velocity or direction. It gets moved as well. Use MultiplyVector.
• Multiplying in the wrong order and getting an object that orbits instead of sitting still.

See also

• Transform
• Quaternion
• Procedural Meshes

This page is a simplified, AI-assisted interpretation. For the complete and authoritative reference, see the official documentation.