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

constructor

Methods

equals
getAsArray
getInverse
getRowCol
isIdentity
fromArray
fromCoordSystemAxes
fromElements
fromRotation
fromScaling
fromTranslation
multiply
translatePostMultiply
translatePreMultiply

Constructors

constructor

cee.Mat4.constructor()

Creates the matrix. Default is an identity matrix.

Return type: cee.Mat4

Methods

equals

cee.Mat4.equals(other)

Returns true if the matrices are equal

Arguments

other (cee.Mat4) –

Return type

boolean

getAsArray

cee.Mat4.getAsArray()

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

Return type: ArrayLike[number]

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 |

getInverse

cee.Mat4.getInverse()

Returns this inverse of this matrix.

Return type: cee.Mat4

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

getRowCol

cee.Mat4.getRowCol(row, col)

Returns the value at the given row and column

Arguments

row (number) –
col (number) –

Return type

number

isIdentity

cee.Mat4.isIdentity()

Returns true if the matrix is an identity matrix

Return type: boolean

fromArray

cee.Mat4.fromArray(array)

Returns a matrix initialized with the values in the passed array

Arguments

array (ArrayLike[number]) –

Return type

cee.Mat4

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 |

fromCoordSystemAxes

cee.Mat4.fromCoordSystemAxes(xAxis, yAxis, zAxis)

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

Arguments

xAxis (cee.Vec3Like) – Orientation of x axis
yAxis (cee.Vec3Like) – Orientation of y axis
zAxis (cee.Vec3Like) – Orientation of z axis

Return type

cee.Mat4

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.

fromElements

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

Returns a transformation matrix containing the given element values

Arguments

m00 (number) –
m01 (number) –
m02 (number) –
m03 (number) –
m10 (number) –
m11 (number) –
m12 (number) –
m13 (number) –
m20 (number) –
m21 (number) –
m22 (number) –
m23 (number) –
m30 (number) –
m31 (number) –
m32 (number) –
m33 (number) –

Return type

cee.Mat4

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

fromRotation

cee.Mat4.fromRotation(axis, angle)

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

Arguments

axis (cee.Vec3Like) –
angle (number) –

Return type

cee.Mat4

fromScaling

cee.Mat4.fromScaling(scale)

Returns a transformation matrix containing only the given scaling

Arguments

scale (cee.Vec3Like) –

Return type

cee.Mat4

  | Sx 0  0  0 |
  | 0  Sy 0  0 |
  | 0  0  Sz 0 |
  | 0  0  0  1 |

fromTranslation

cee.Mat4.fromTranslation(trans)

Returns a transformation matrix containing only the given translation

Arguments

trans (cee.Vec3Like) –

Return type

cee.Mat4

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 |

multiply

cee.Mat4.multiply(matrices)

Multiplies given matrices.

Arguments

matrices ([cee.Mat4]) –

Return type

cee.Mat4

translatePostMultiply

cee.Mat4.translatePostMultiply(M, tv)

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

Arguments

M (cee.Mat4) –
tv (cee.Vec3Like) –

Return type

cee.Mat4

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

translatePreMultiply

cee.Mat4.translatePreMultiply(M, tv)

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

Arguments

M (cee.Mat4) –
tv (cee.Vec3Like) –

Return type

cee.Mat4

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