Version: 2022.2
  • C#


struct in UnityEngine


Implemented in:UnityEngine.CoreModule

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A standard 4x4 transformation matrix.

A transformation matrix can perform arbitrary linear 3D transformations (i.e. translation, rotation, scale, shear etc.) and perspective transformations using homogenous coordinates. You rarely use matrices in scripts; most often using Vector3s, Quaternions and functionality of Transform class is more straightforward. Plain matrices are used in special cases like setting up nonstandard camera projection.

In Unity, several Transform, Camera, Material, Graphics and GL functions use Matrix4x4.

Matrices in Unity are column major; i.e. the position of a transformation matrix is in the last column, and the first three columns contain x, y, and z-axes. Data is accessed as: row + (column*4). Matrices can be indexed like 2D arrays but note that in an expression like mat[a, b], a refers to the row index, while b refers to the column index.

using UnityEngine;

public class ExampleScript : MonoBehaviour { void Start() { // get matrix from the Transform var matrix = transform.localToWorldMatrix; // get position from the last column var position = new Vector3(matrix[0,3], matrix[1,3], matrix[2,3]); Debug.Log("Transform position from matrix is: " + position); } }

Static Properties

identityReturns the identity matrix (Read Only).
zeroReturns a matrix with all elements set to zero (Read Only).


decomposeProjectionThis property takes a projection matrix and returns the six plane coordinates that define a projection frustum.
determinantThe determinant of the matrix. (Read Only)
inverseThe inverse of this matrix. (Read Only)
isIdentityChecks whether this is an identity matrix. (Read Only)
lossyScaleAttempts to get a scale value from the matrix. (Read Only)
rotationAttempts to get a rotation quaternion from this matrix.
this[int,int]Access element at [row, column].
transposeReturns the transpose of this matrix (Read Only).

Public Methods

GetColumnGet a column of the matrix.
GetPositionGet position vector from the matrix.
GetRowReturns a row of the matrix.
MultiplyPointTransforms a position by this matrix (generic).
MultiplyPoint3x4Transforms a position by this matrix (fast).
MultiplyVectorTransforms a direction by this matrix.
SetColumnSets a column of the matrix.
SetRowSets a row of the matrix.
SetTRSSets this matrix to a translation, rotation and scaling matrix.
ToStringReturns a formatted string for this matrix.
TransformPlaneReturns a plane that is transformed in space.
ValidTRSChecks if this matrix is a valid transform matrix.

Static Methods

FrustumThis function returns a projection matrix with viewing frustum that has a near plane defined by the coordinates that were passed in.
Inverse3DAffineComputes the inverse of a 3D affine matrix.
LookAtCreate a "look at" matrix.
OrthoCreate an orthogonal projection matrix.
PerspectiveCreate a perspective projection matrix.
RotateCreates a rotation matrix.
ScaleCreates a scaling matrix.
TranslateCreates a translation matrix.
TRSCreates a translation, rotation and scaling matrix.


operator *Multiplies two matrices.