4x4 Matrix

Format: column-major, when typed out it looks like row-major

The matrices are being post multiplied.

Format: column-major, when typed out it looks like row-major

The matrices are being post multiplied.

### 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 |

##### 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 |

##### 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 |

##### 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 |

##### Returns:

out

- Type
- mat4

#### (static) create() → {mat4}

Creates a new identity mat4

##### 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 |

##### 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. |

##### 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. |

##### 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 |

##### 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 |

##### Returns:

out

- Type
- mat4

#### (static) fromQuat2(out, a) → {mat4}

Creates a new mat4 from a dual quat.

##### Parameters:

Name | Type | Description |
---|---|---|

`out` |
mat4 | Matrix |

`a` |
quat2 | Dual Quaternion |

##### Returns:

mat4 receiving operation result

- 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 |

##### 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 |

##### 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 |

##### 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 |

##### 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 |

##### 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 |

##### 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) |

##### 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 |

##### 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 |

##### 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 |

##### 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 |

##### 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) |

##### 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) |

##### 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) |

##### Returns:

out

- Type
- vec3

#### (static) identity(out) → {mat4}

Set a mat4 to the identity matrix

##### Parameters:

Name | Type | Description |
---|---|---|

`out` |
mat4 | the receiving matrix |

##### 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 |

##### 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.
If you want a matrix that actually makes an object look at another object, you should use targetTo instead.

##### 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 |

##### Returns:

out

- Type
- mat4

#### (static) mul()

Alias for mat4.multiply

#### (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 |

##### 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 |

##### 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 |

##### 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 |

##### Returns:

out

- Type
- mat4

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

Generates a perspective projection matrix with the given bounds.
Passing null/undefined/no value for far will generate infinite projection matrix.

##### 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, can be null or Infinity |

##### 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 |

##### 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 |

##### 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 |

##### 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 |

##### 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 |

##### 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 |

##### 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) |

##### 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 |

##### Returns:

string representation of the matrix

- Type
- String

#### (static) sub()

Alias for mat4.subtract

#### (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 |

##### 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 |

##### 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 |

##### 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 |

##### Returns:

out

- Type
- mat4