Mat4

class cee.Mat4()

An immutable 4x4 matrix

Matrices are stored internally as a one dimensional array for performance reasons.

The mapping of matrix elements to indices of this internal array is as follows:

| m00  m01  m02  m03 |     | 0  4   8  12 |
| m10  m11  m12  m13 |     | 1  5   9  13 |
| m20  m21  m22  m23 |     | 2  6  10  14 |
| m30  m31  m32  m33 |     | 3  7  11  15 |

This is consistent with the way matrices are represented in WebGL. To exemplify, translation values are stored in elements 12,13,14; see figure below

| 1  0  0 Tx |
| 0  1  0 Ty |
| 0  0  1 Tz |
| 0  0  0  1 |

From the OpenGL red book (page 68) v’ = M*v

| X'|   | 1  0  0 Tx |   | X |
| Y'|   | 0  1  0 Ty |   | Y |
| Z'| = | 0  0  1 Tz | * | Z |
| 1 |   | 0  0  0  1 |   | 1 |

Note that this class is immutable.

Constructors

Methods

Constructors

Mat4.constructor()

Creates the matrix. Default is an identity matrix.

Return type:

Mat4

Methods

equals

Mat4.equals(other)
Arguments:

  • other (Mat4) – None

Returns true if the matrices are equal

Return type:

boolean

getAsArray

Mat4.getAsArray()

Returns a reference to the internal array storing the matrix values.

The array will be ordered as follows:

| m00  m01  m02  m03 |     | 0  4   8  12 |
| m10  m11  m12  m13 |     | 1  5   9  13 |
| m20  m21  m22  m23 |     | 2  6  10  14 |
| m30  m31  m32  m33 |     | 3  7  11  15 |
Return type:

ArrayLike <number>

getInverse

Mat4.getInverse()

Returns this inverse of this matrix.

If this matrix is not invertible, returns a zero matrix.

Return type:

Mat4

getRowCol

Mat4.getRowCol(row, col)
Arguments:

  • row (number) – None

  • col (number) – None

Returns the value at the given row and column

Return type:

number

isIdentity

Mat4.isIdentity()

Returns true if the matrix is an identity matrix

Return type:

boolean

static fromArray

Mat4.fromArray(array)
Arguments:

  • array (ArrayLike) – None

Returns a matrix initialized with the values in the passed array

The array must be ordered as follows:

| m00  m01  m02  m03 |     | 0  4   8  12 |
| m10  m11  m12  m13 |     | 1  5   9  13 |
| m20  m21  m22  m23 |     | 2  6  10  14 |
| m30  m31  m32  m33 |     | 3  7  11  15 |
Return type:

Mat4

static fromCoordSystemAxes

Mat4.fromCoordSystemAxes(xAxis, yAxis, zAxis)
Arguments:

  • xAxis (Vec3Like) – Orientation of x axis

  • yAxis (Vec3Like) – Orientation of y axis

  • zAxis (Vec3Like) – Orientation of z axis

Returns a rotation matrix that will align the global X, Y and Z axes with the specified axes.

Note that at least one axis must be specified and all specified axes must be normalized. If two or three axes are specified, they must be orthogonal to each other.

Return type:

Mat4

static fromElements

Mat4.fromElements(m00, m01, m02, m03, m10, m11, m12, m13, m20, m21, m22, m23, m30, m31, m32, m33)
Arguments:

  • m00 (number) – None

  • m01 (number) – None

  • m02 (number) – None

  • m03 (number) – None

  • m10 (number) – None

  • m11 (number) – None

  • m12 (number) – None

  • m13 (number) – None

  • m20 (number) – None

  • m21 (number) – None

  • m22 (number) – None

  • m23 (number) – None

  • m30 (number) – None

  • m31 (number) – None

  • m32 (number) – None

  • m33 (number) – None

Returns a transformation matrix containing the given element values

| m00  m01  m02  m03 |
| m10  m11  m12  m13 |
| m20  m21  m22  m23 |
| m30  m31  m32  m33 |
Return type:

Mat4

static fromRotation

Mat4.fromRotation(axis, angle)
Arguments:

  • axis (Vec3Like) – None

  • angle (number) – None

Returns a transformation matrix containing only rotation, specified as a rotation around the given axis

Return type:

Mat4

static fromScaling

Mat4.fromScaling(scale)
Arguments:

Returns a transformation matrix containing only the given scaling

| Sx 0  0  0 |
| 0  Sy 0  0 |
| 0  0  Sz 0 |
| 0  0  0  1 |
Return type:

Mat4

static fromTranslation

Mat4.fromTranslation(trans)
Arguments:

Returns a transformation matrix containing only the given translation

Will set m03 to x, m13 to y, and m23 to z, resulting in the following matrix

| 1  0  0 Tx |
| 0  1  0 Ty |
| 0  0  1 Tz |
| 0  0  0  1 |
Return type:

Mat4

static multiply

Mat4.multiply(matrices)
Arguments:

  • matrices ([Mat4]) – None

Multiplies given matrices.

Return type:

Mat4

static translatePostMultiply

Mat4.translatePostMultiply(M, tv)
Arguments:

Adds translation to the given matrix M by post-multiplying it with a matrix containing the given translation tv.

This has the effect of performing the multiplication M’ = M x T

Return type:

Mat4

static translatePreMultiply

Mat4.translatePreMultiply(M, tv)
Arguments:

Adds translation to the given matrix M by pre-multiplying it with a matrix containing the given translation tv.

This has the effect of performing the multiplication M’ = T x M

Return type:

Mat4