# Module: mat4

4x4 Matrix

Source:
  - mat4.js, line 23

### Methods

#### (static) add(out, a, b) → {mat4}

Adds two mat4's

##### Parameters:

Name | Type | Description
--- | --- | ---
`out` | mat4 | the receiving matrix
`a` | mat4 | the first operand
`b` | mat4 | the second operand

Source:
  - mat4.js, line 1516

##### Returns:

out

Type
  mat4

#### (static) adjoint(out, a) → {mat4}

Calculates the adjugate of a mat4

##### Parameters:

Name | Type | Description
--- | --- | ---
`out` | mat4 | the receiving matrix
`a` | mat4 | the source matrix

Source:
  - mat4.js, line 328

##### Returns:

out

Type
  mat4

#### (static) clone(a) → {mat4}

Creates a new mat4 initialized with values from an existing matrix

##### Parameters:

Name | Type | Description
--- | --- | ---
`a` | mat4 | matrix to clone

Source:
  - mat4.js, line 60

##### Returns:

a new 4x4 matrix

Type
  mat4

#### (static) copy(out, a) → {mat4}

Copy the values from one mat4 to another

##### Parameters:

Name | Type | Description
--- | --- | ---
`out` | mat4 | the receiving matrix
`a` | mat4 | the source matrix

Source:
  - mat4.js, line 88

##### Returns:

out

Type
  mat4

#### (static) create() → {mat4}

Creates a new identity mat4

Source:
  - mat4.js, line 33

##### Returns:

a new 4x4 matrix

Type
  mat4

#### (static) determinant(a) → {Number}

Calculates the determinant of a mat4

##### Parameters:

Name | Type | Description
--- | --- | ---
`a` | mat4 | the source matrix

Source:
  - mat4.js, line 359

##### Returns:

determinant of a

Type
  Number

#### (static) equals(a, b) → {Boolean}

Returns whether or not the matrices have approximately the same elements in the same position.

##### Parameters:

Name | Type | Description
--- | --- | ---
`a` | mat4 | The first matrix.
`b` | mat4 | The second matrix.

Source:
  - mat4.js, line 1642

##### Returns:

True if the matrices are equal, false otherwise.

Type
  Boolean

#### (static) exactEquals(a, b) → {Boolean}

Returns whether or not the matrices have exactly the same elements in the same position (when compared with ===)

##### Parameters:

Name | Type | Description
--- | --- | ---
`a` | mat4 | The first matrix.
`b` | mat4 | The second matrix.

Source:
  - mat4.js, line 1628

##### Returns:

True if the matrices are equal, false otherwise.

Type
  Boolean

#### (static) frob(a) → {Number}

Returns Frobenius norm of a mat4

##### Parameters:

Name | Type | Description
--- | --- | ---
`a` | mat4 | the matrix to calculate Frobenius norm of

Source:
  - mat4.js, line 1504

##### Returns:

Frobenius norm

Type
  Number

#### (static) fromQuat(out, q) → {mat4}

Calculates a 4x4 matrix from the given quaternion

##### Parameters:

Name | Type | Description
--- | --- | ---
`out` | mat4 | mat4 receiving operation result
`q` | quat | Quaternion to create matrix from

Source:
  - mat4.js, line 1167

##### Returns:

out

Type
  mat4

#### (static) fromRotation(out, rad, axis) → {mat4}

Creates a matrix from a given angle around a given axis This is equivalent to (but much faster than): mat4.identity(dest); mat4.rotate(dest, dest, rad, axis);

##### Parameters:

Name | Type | Description
--- | --- | ---
`out` | mat4 | mat4 receiving operation result
`rad` | Number | the angle to rotate the matrix by
`axis` | vec3 | the axis to rotate around

Source:
  - mat4.js, line 756

##### Returns:

out

Type
  mat4

#### (static) fromRotationTranslation(out, q, v) → {mat4}

Creates a matrix from a quaternion rotation and vector translation This is equivalent to (but much faster than): mat4.identity(dest); mat4.translate(dest, vec); let quatMat = mat4.create(); quat4.toMat4(quat, quatMat); mat4.multiply(dest, quatMat);

##### Parameters:

Name | Type | Description
--- | --- | ---
`out` | mat4 | mat4 receiving operation result
`q` | quat4 | Rotation quaternion
`v` | vec3 | Translation vector

Source:
  - mat4.js, line 912

##### Returns:

out

Type
  mat4

#### (static) fromRotationTranslationScale(out, q, v, s) → {mat4}

Creates a matrix from a quaternion rotation, vector translation and vector scale This is equivalent to (but much faster than): mat4.identity(dest); mat4.translate(dest, vec); let quatMat = mat4.create(); quat4.toMat4(quat, quatMat); mat4.multiply(dest, quatMat); mat4.scale(dest, scale)

##### Parameters:

Name | Type | Description
--- | --- | ---
`out` | mat4 | mat4 receiving operation result
`q` | quat4 | Rotation quaternion
`v` | vec3 | Translation vector
`s` | vec3 | Scaling vector

Source:
  - mat4.js, line 1054

##### Returns:

out

Type
  mat4

#### (static) fromRotationTranslationScaleOrigin(out, q, v, s, o) → {mat4}

Creates a matrix from a quaternion rotation, vector translation and vector scale, rotating and scaling around the given origin This is equivalent to (but much faster than): mat4.identity(dest); mat4.translate(dest, vec); mat4.translate(dest, origin); let quatMat = mat4.create(); quat4.toMat4(quat, quatMat); mat4.multiply(dest, quatMat); mat4.scale(dest, scale) mat4.translate(dest, negativeOrigin);

##### Parameters:

Name | Type | Description
--- | --- | ---
`out` | mat4 | mat4 receiving operation result
`q` | quat4 | Rotation quaternion
`v` | vec3 | Translation vector
`s` | vec3 | Scaling vector
`o` | vec3 | The origin vector around which to scale and rotate

Source:
  - mat4.js, line 1114

##### Returns:

out

Type
  mat4

#### (static) fromScaling(out, v) → {mat4}

Creates a matrix from a vector scaling This is equivalent to (but much faster than): mat4.identity(dest); mat4.scale(dest, dest, vec);

##### Parameters:

Name | Type | Description
--- | --- | ---
`out` | mat4 | mat4 receiving operation result
`v` | vec3 | Scaling vector

Source:
  - mat4.js, line 724

##### Returns:

out

Type
  mat4

#### (static) fromTranslation(out, v) → {mat4}

Creates a matrix from a vector translation This is equivalent to (but much faster than): mat4.identity(dest); mat4.translate(dest, dest, vec);

##### Parameters:

Name | Type | Description
--- | --- | ---
`out` | mat4 | mat4 receiving operation result
`v` | vec3 | Translation vector

Source:
  - mat4.js, line 693

##### Returns:

out

Type
  mat4

#### (static) fromValues(m00, m01, m02, m03, m10, m11, m12, m13, m20, m21, m22, m23, m30, m31, m32, m33) → {mat4}

Create a new mat4 with the given values

##### Parameters:

Name | Type | Description
--- | --- | ---
`m00` | Number | Component in column 0, row 0 position (index 0)
`m01` | Number | Component in column 0, row 1 position (index 1)
`m02` | Number | Component in column 0, row 2 position (index 2)
`m03` | Number | Component in column 0, row 3 position (index 3)
`m10` | Number | Component in column 1, row 0 position (index 4)
`m11` | Number | Component in column 1, row 1 position (index 5)
`m12` | Number | Component in column 1, row 2 position (index 6)
`m13` | Number | Component in column 1, row 3 position (index 7)
`m20` | Number | Component in column 2, row 0 position (index 8)
`m21` | Number | Component in column 2, row 1 position (index 9)
`m22` | Number | Component in column 2, row 2 position (index 10)
`m23` | Number | Component in column 2, row 3 position (index 11)
`m30` | Number | Component in column 3, row 0 position (index 12)
`m31` | Number | Component in column 3, row 1 position (index 13)
`m32` | Number | Component in column 3, row 2 position (index 14)
`m33` | Number | Component in column 3, row 3 position (index 15)

Source:
  - mat4.js, line 129

##### Returns:

A new mat4

Type
  mat4

#### (static) fromXRotation(out, rad) → {mat4}

Creates a matrix from the given angle around the X axis This is equivalent to (but much faster than): mat4.identity(dest); mat4.rotateX(dest, dest, rad);

##### Parameters:

Name | Type | Description
--- | --- | ---
`out` | mat4 | mat4 receiving operation result
`rad` | Number | the angle to rotate the matrix by

Source:
  - mat4.js, line 803

##### Returns:

out

Type
  mat4

#### (static) fromYRotation(out, rad) → {mat4}

Creates a matrix from the given angle around the Y axis This is equivalent to (but much faster than): mat4.identity(dest); mat4.rotateY(dest, dest, rad);

##### Parameters:

Name | Type | Description
--- | --- | ---
`out` | mat4 | mat4 receiving operation result
`rad` | Number | the angle to rotate the matrix by

Source:
  - mat4.js, line 838

##### Returns:

out

Type
  mat4

#### (static) fromZRotation(out, rad) → {mat4}

Creates a matrix from the given angle around the Z axis This is equivalent to (but much faster than): mat4.identity(dest); mat4.rotateZ(dest, dest, rad);

##### Parameters:

Name | Type | Description
--- | --- | ---
`out` | mat4 | mat4 receiving operation result
`rad` | Number | the angle to rotate the matrix by

Source:
  - mat4.js, line 873

##### Returns:

out

Type
  mat4

#### (static) frustum(out, left, right, bottom, top, near, far) → {mat4}

Generates a frustum matrix with the given bounds

##### Parameters:

Name | Type | Description
--- | --- | ---
`out` | mat4 | mat4 frustum matrix will be written into
`left` | Number | Left bound of the frustum
`right` | Number | Right bound of the frustum
`bottom` | Number | Bottom bound of the frustum
`top` | Number | Top bound of the frustum
`near` | Number | Near bound of the frustum
`far` | Number | Far bound of the frustum

Source:
  - mat4.js, line 1218

##### Returns:

out

Type
  mat4

#### (static) getRotation(out, mat) → {quat}

Returns a quaternion representing the rotational component of a transformation matrix. If a matrix is built with fromRotationTranslation, the returned quaternion will be the same as the quaternion originally supplied.

##### Parameters:

Name | Type | Description
--- | --- | ---
`out` | quat | Quaternion to receive the rotation component
`mat` | mat4 | Matrix to be decomposed (input)

Source:
  - mat4.js, line 1003

##### Returns:

out

Type
  quat

#### (static) getScaling(out, mat) → {vec3}

Returns the scaling factor component of a transformation matrix. If a matrix is built with fromRotationTranslationScale with a normalized Quaternion paramter, the returned vector will be the same as the scaling vector originally supplied.

##### Parameters:

Name | Type | Description
--- | --- | ---
`out` | vec3 | Vector to receive scaling factor component
`mat` | mat4 | Matrix to be decomposed (input)

Source:
  - mat4.js, line 976

##### Returns:

out

Type
  vec3

#### (static) getTranslation(out, mat) → {vec3}

Returns the translation vector component of a transformation matrix. If a matrix is built with fromRotationTranslation, the returned vector will be the same as the translation vector originally supplied.

##### Parameters:

Name | Type | Description
--- | --- | ---
`out` | vec3 | Vector to receive translation component
`mat` | mat4 | Matrix to be decomposed (input)

Source:
  - mat4.js, line 958

##### Returns:

out

Type
  vec3

#### (static) identity(out) → {mat4}

Set a mat4 to the identity matrix

##### Parameters:

Name | Type | Description
--- | --- | ---
`out` | mat4 | the receiving matrix

Source:
  - mat4.js, line 199

##### Returns:

out

Type
  mat4

#### (static) invert(out, a) → {mat4}

Inverts a mat4

##### Parameters:

Name | Type | Description
--- | --- | ---
`out` | mat4 | the receiving matrix
`a` | mat4 | the source matrix

Source:
  - mat4.js, line 274

##### Returns:

out

Type
  mat4

#### (static) lookAt(out, eye, center, up) → {mat4}

Generates a look-at matrix with the given eye position, focal point, and up axis

##### Parameters:

Name | Type | Description
--- | --- | ---
`out` | mat4 | mat4 frustum matrix will be written into
`eye` | vec3 | Position of the viewer
`center` | vec3 | Point the viewer is looking at
`up` | vec3 | vec3 pointing up

Source:
  - mat4.js, line 1355

##### Returns:

out

Type
  mat4

#### (static) mul()

Alias for mat4.multiply

Source:
  - mat4.js, line 1675

#### (static) multiply(out, a, b) → {mat4}

Multiplies two mat4s

##### Parameters:

Name | Type | Description
--- | --- | ---
`out` | mat4 | the receiving matrix
`a` | mat4 | the first operand
`b` | mat4 | the second operand

Source:
  - mat4.js, line 390

##### Returns:

out

Type
  mat4

#### (static) multiplyScalar(out, a, b) → {mat4}

Multiply each element of the matrix by a scalar.

##### Parameters:

Name | Type | Description
--- | --- | ---
`out` | mat4 | the receiving matrix
`a` | mat4 | the matrix to scale
`b` | Number | amount to scale the matrix's elements by

Source:
  - mat4.js, line 1572

##### Returns:

out

Type
  mat4

#### (static) multiplyScalarAndAdd(out, a, b, scale) → {mat4}

Adds two mat4's after multiplying each element of the second operand by a scalar value.

##### Parameters:

Name | Type | Description
--- | --- | ---
`out` | mat4 | the receiving vector
`a` | mat4 | the first operand
`b` | mat4 | the second operand
`scale` | Number | the amount to scale b's elements by before adding

Source:
  - mat4.js, line 1601

##### Returns:

out

Type
  mat4

#### (static) ortho(out, left, right, bottom, top, near, far) → {mat4}

Generates a orthogonal projection matrix with the given bounds

##### Parameters:

Name | Type | Description
--- | --- | ---
`out` | mat4 | mat4 frustum matrix will be written into
`left` | number | Left bound of the frustum
`right` | number | Right bound of the frustum
`bottom` | number | Bottom bound of the frustum
`top` | number | Top bound of the frustum
`near` | number | Near bound of the frustum
`far` | number | Far bound of the frustum

Source:
  - mat4.js, line 1323

##### Returns:

out

Type
  mat4

#### (static) perspective(out, fovy, aspect, near, far) → {mat4}

Generates a perspective projection matrix with the given bounds

##### Parameters:

Name | Type | Description
--- | --- | ---
`out` | mat4 | mat4 frustum matrix will be written into
`fovy` | number | Vertical field of view in radians
`aspect` | number | Aspect ratio. typically viewport width/height
`near` | number | Near bound of the frustum
`far` | number | Far bound of the frustum

Source:
  - mat4.js, line 1251

##### Returns:

out

Type
  mat4

#### (static) perspectiveFromFieldOfView(out, fov, near, far) → {mat4}

Generates a perspective projection matrix with the given field of view. This is primarily useful for generating projection matrices to be used with the still experiemental WebVR API.

##### Parameters:

Name | Type | Description
--- | --- | ---
`out` | mat4 | mat4 frustum matrix will be written into
`fov` | Object | Object containing the following values: upDegrees, downDegrees, leftDegrees, rightDegrees
`near` | number | Near bound of the frustum
`far` | number | Far bound of the frustum

Source:
  - mat4.js, line 1284

##### Returns:

out

Type
  mat4

#### (static) rotate(out, a, rad, axis) → {mat4}

Rotates a mat4 by the given angle around the given axis

##### Parameters:

Name | Type | Description
--- | --- | ---
`out` | mat4 | the receiving matrix
`a` | mat4 | the matrix to rotate
`rad` | Number | the angle to rotate the matrix by
`axis` | vec3 | the axis to rotate around

Source:
  - mat4.js, line 499

##### Returns:

out

Type
  mat4

#### (static) rotateX(out, a, rad) → {mat4}

Rotates a matrix by the given angle around the X axis

##### Parameters:

Name | Type | Description
--- | --- | ---
`out` | mat4 | the receiving matrix
`a` | mat4 | the matrix to rotate
`rad` | Number | the angle to rotate the matrix by

Source:
  - mat4.js, line 561

##### Returns:

out

Type
  mat4

#### (static) rotateY(out, a, rad) → {mat4}

Rotates a matrix by the given angle around the Y axis

##### Parameters:

Name | Type | Description
--- | --- | ---
`out` | mat4 | the receiving matrix
`a` | mat4 | the matrix to rotate
`rad` | Number | the angle to rotate the matrix by

Source:
  - mat4.js, line 604

##### Returns:

out

Type
  mat4

#### (static) rotateZ(out, a, rad) → {mat4}

Rotates a matrix by the given angle around the Z axis

##### Parameters:

Name | Type | Description
--- | --- | ---
`out` | mat4 | the receiving matrix
`a` | mat4 | the matrix to rotate
`rad` | Number | the angle to rotate the matrix by

Source:
  - mat4.js, line 647

##### Returns:

out

Type
  mat4

#### (static) scale(out, a, v) → {mat4}

Scales the mat4 by the dimensions in the given vec3 not using vectorization

##### Parameters:

Name | Type | Description
--- | --- | ---
`out` | mat4 | the receiving matrix
`a` | mat4 | the matrix to scale
`v` | vec3 | the vec3 to scale the matrix by

Source:
  - mat4.js, line 468

##### Returns:

out

Type
  mat4

#### (static) set(out, m00, m01, m02, m03, m10, m11, m12, m13, m20, m21, m22, m23, m30, m31, m32, m33) → {mat4}

Set the components of a mat4 to the given values

##### Parameters:

Name | Type | Description
--- | --- | ---
`out` | mat4 | the receiving matrix
`m00` | Number | Component in column 0, row 0 position (index 0)
`m01` | Number | Component in column 0, row 1 position (index 1)
`m02` | Number | Component in column 0, row 2 position (index 2)
`m03` | Number | Component in column 0, row 3 position (index 3)
`m10` | Number | Component in column 1, row 0 position (index 4)
`m11` | Number | Component in column 1, row 1 position (index 5)
`m12` | Number | Component in column 1, row 2 position (index 6)
`m13` | Number | Component in column 1, row 3 position (index 7)
`m20` | Number | Component in column 2, row 0 position (index 8)
`m21` | Number | Component in column 2, row 1 position (index 9)
`m22` | Number | Component in column 2, row 2 position (index 10)
`m23` | Number | Component in column 2, row 3 position (index 11)
`m30` | Number | Component in column 3, row 0 position (index 12)
`m31` | Number | Component in column 3, row 1 position (index 13)
`m32` | Number | Component in column 3, row 2 position (index 14)
`m33` | Number | Component in column 3, row 3 position (index 15)

Source:
  - mat4.js, line 172

##### Returns:

out

Type
  mat4

#### (static) str(a) → {String}

Returns a string representation of a mat4

##### Parameters:

Name | Type | Description
--- | --- | ---
`a` | mat4 | matrix to represent as a string

Source:
  - mat4.js, line 1491

##### Returns:

string representation of the matrix

Type
  String

#### (static) sub()

Alias for mat4.subtract

Source:
  - mat4.js, line 1681

#### (static) subtract(out, a, b) → {mat4}

Subtracts matrix b from matrix a

##### Parameters:

Name | Type | Description
--- | --- | ---
`out` | mat4 | the receiving matrix
`a` | mat4 | the first operand
`b` | mat4 | the second operand

Source:
  - mat4.js, line 1544

##### Returns:

out

Type
  mat4

#### (static) targetTo(out, eye, center, up) → {mat4}

Generates a matrix that makes something look at something else.

##### Parameters:

Name | Type | Description
--- | --- | ---
`out` | mat4 | mat4 frustum matrix will be written into
`eye` | vec3 | Position of the viewer
`center` | vec3 | Point the viewer is looking at
`up` | vec3 | vec3 pointing up

Source:
  - mat4.js, line 1442

##### Returns:

out

Type
  mat4

#### (static) translate(out, a, v) → {mat4}

Translate a mat4 by the given vector

##### Parameters:

Name | Type | Description
--- | --- | ---
`out` | mat4 | the receiving matrix
`a` | mat4 | the matrix to translate
`v` | vec3 | vector to translate by

Source:
  - mat4.js, line 431

##### Returns:

out

Type
  mat4

#### (static) transpose(out, a) → {mat4}

Transpose the values of a mat4

##### Parameters:

Name | Type | Description
--- | --- | ---
`out` | mat4 | the receiving matrix
`a` | mat4 | the source matrix

Source:
  - mat4.js, line 226

##### Returns:

out

Type
  mat4