Class Matrix4

A 4x4 Matrix.

Such a matrix contains a translation and a rotation/scale part. The matrix contains an array of 16 floats, which memory layout is the following.

If you consider the vector (V) matrix (M) multiplication in line : V' = V x M then the memory layout of the matrix is the following, with the translation part [T0,T1,T2] on the bottom :

array[0]array[1]array[2]0 (array[3])
array[4]array[5]array[6]0 (array[7])
array[8]array[9]array[10]0 (array[11])
T0 : array[12]T1 : array[13]T2 : array[14]1 (array[15])

If on the contrary you consider the vector (V) matrix (M) multiplication in column : V' = M x V then the memory layout of the matrix is the following, with the translation part [T0,T1,T2] on the right :
array[0]array[4]array[8]T0 : array[12]
array[1]array[5]array[9]T1 : array[13]
array[2]array[6]array[10]T2 : array[14]
0 (array[3])0 (array[7])0 (array[11])1 (array[15])

The multiplication in column is the convention adopted in the Matrix4 class, when a matrix M2 is multiplied on the left of M1, then any point P transformed by the resulting transformation (P') will be first transformed by M1 and then M2 :
P' = M2 x M1 x P.
Maths

Hierarchy

  • Matrix4

Constructors

constructor

Properties

array

Methods

copy determinant equals getColumn invert isIdentity makeIdentity multiplyLeft multiplyMatrixLeft multiplyMatrixRight multiplyRight multiplyVector3Direction multiplyVector3DirectionXYZ multiplyVector3Position multiplyVector3PositionXYZ multiplyVector4 multiplyVector4XYZW resetToScale rotateX rotateY rotateZ set setQuaternion setTranslation

Constructors

constructor

  • Builds a new Matrix4 from the following memory layout.

    If you consider the matrix vector multiplication in line (V' = V x M), then the following matrix is built (translation [T0,T1,T2] on the bottom) :

    abc0 (d)
    efg0 (h)
    ijk0 (l)
    T0 : mT1 : nT2 : o1 (p)

    If you consider the matrix vector multiplication in column (V' = M x V), then the following matrix is built (translation [T0,T1,T2] on the right) :
    aeiT0 : m
    bfjT1 : n
    cgkT2 : o
    0 (d)0 (h)0 (l)1 (p)

    Returns the newly constructed matrix.

    Returns

    The newly created Matrix4.

    Parameters

    • Optional a: number
      in
      Rotation/scale part.
    • Optional b: number
      in
      Rotation/scale part.
    • Optional c: number
      in
      Rotation/scale part.
    • Optional d: number
      in
      Should be 0.
    • Optional e: number
      in
      Rotation/scale part.
    • Optional f: number
      in
      Rotation/scale part.
    • Optional g: number
      in
      Rotation/scale part.
    • Optional h: number
      in
      Should be 0.
    • Optional i: number
      in
      Rotation/scale part.
    • Optional j: number
      in
      Rotation/scale part.
    • Optional k: number
      in
      Rotation/scale part.
    • Optional l: number
      in
      Should be 0.
    • Optional m: number
      in
      Translation upon x.
    • Optional n: number
      in
      Translation upon y.
    • Optional o: number
      in
      Translation upon z.
    • Optional p: number
      in
      Should be 1.

    Returns Matrix4

Properties

array

array: Float32Array

A 16 float array that contains the values of the matrix.

Methods

copy

  • Copies "this" to pOther matrix.

    If pOther is not supplied, a new Matrix4 is allocated.

    Returns

    The copied matrix.

    Parameters

    • Optional pOut: Matrix4
      out
      The Matrix4 to copy to.

    Returns Matrix4

determinant

  • Computes the matrix determinant.

    Returns

    The determinant of the matrix.

    Returns number

equals

  • Tells if the two matrices are strictly identical.

    Returns

    true if the two matrices are strictly identical.

    Parameters

    • pOtherMatrix: Matrix4
      in
      The other matrix to compare to.

    Returns boolean

getColumn

  • Gets the pColum th "column" of the matrix.

    This function actually takes the column if the Matrix vector multiplication is in column : V' = M x V .

    If you consider the matrix vector multiplication in column (V' = M x V, translation [T0,T1,T2] on the right) :

    aeiT0 : m
    bfjT1 : n
    cgkT2 : o
    0 (d)0 (h)0 (l)1 (p)

    Then getColumn(0) returns (a,b,c).

    If you consider the matrix vector multiplication in line (V' = V x M, translation [T0,T1,T2] on the bottom) :

    abc0 (d)
    efg0 (h)
    ijk0 (l)
    T0 : mT1 : nT2 : o1 (p)

    Then getColumn(0) returns (a,b,c).

    No check is done to ensure pColumn is in the range [0-3].

    Returns

    pOut.

    Parameters

    • pColumn: number
      in
      The column to get in the range [0-3].
    • pOut: Vector3
      out
      The resulting "column" of the matrix.

    Returns Vector3

invert

  • Inverts the transformation and stores the result to pOut.

    If the matrix "this" is non-invertible, then pOut stores a copy of "this".

    If pOut is omitted, the result is stored in "this".

    Returns pOut.

    Returns

    pOut.

    Parameters

    • Optional pOut: Matrix4
      out
      The inverted matrix result.

    Returns Matrix4

isIdentity

  • Tells if the matrix is the identity.

    There is no tolerance on the check, any value other than 0 or 1 in the matrix will make this function return false.

    Returns

    true if the matrix is identity (strictly).

    Returns boolean

makeIdentity

  • Sets this matrix to the identity.

    Returns

    this.

    Returns Matrix4

multiplyLeft

  • Computes the composition of "this" and the matrix represented by the values Mval and stores the result in pOut.

    Any point P transformed by the resulting transformation will first be multiplied by "this", and then Mval.
    Be P' the transformed point of P :
    Depending on your convention : P' = Mval x this x P (hence multiply left)
    or P' = P x this x Mval.

    If pOut is omitted, the result is stored in "this".

    If you consider the matrix vector multiplication in line (V' = V x Mval), then Mval is set to (translation [T0,T1,T2] on the bottom) :

    abc0 (d)
    efg0 (h)
    ijk0 (l)
    T0 : mT1 : nT2 : o1 (p)

    If you consider the matrix vector multiplication in column (V' = Mval x V), then Mval is set (translation [T0,T1,T2] on the right) :
    aeiT0 : m
    bfjT1 : n
    cgkT2 : o
    0 (d)0 (h)0 (l)1 (p)


    Then when using Matrices : 
    this.multiplyMatrixLeft(pSecondTransform, pOut);

    is equivalent to : 
    this.multiplyLeft(
        pSecondTransform.array[0], pSecondTransform.array[1], pSecondTransform.array[2], pSecondTransform.array[3],
        pSecondTransform.array[4], pSecondTransform.array[5], pSecondTransform.array[6], pSecondTransform.array[7],
        pSecondTransform.array[8], pSecondTransform.array[9], pSecondTransform.array[10], pSecondTransform.array[11],
        pSecondTransform.array[12], pSecondTransform.array[13], pSecondTransform.array[14], pSecondTransform.array[15],
        pOut
    );

    Please refer to some matrices courses to get more information.

    Returns

    pOut.

    Parameters

    • a: number
      in
      Rotation/scale part.
    • b: number
      in
      Rotation/scale part.
    • c: number
      in
      Rotation/scale part.
    • d: number
      in
      Should be 0.
    • e: number
      in
      Rotation/scale part.
    • f: number
      in
      Rotation/scale part.
    • g: number
      in
      Rotation/scale part.
    • h: number
      in
      Should be 0.
    • i: number
      in
      Rotation/scale part.
    • j: number
      in
      Rotation/scale part.
    • k: number
      in
      Rotation/scale part.
    • l: number
      in
      Should be 0.
    • m: number
      in
      Translation upon x.
    • n: number
      in
      Translation upon y.
    • o: number
      in
      Translation upon z.
    • p: number
      in
      Should be 1.
    • Optional pOut: Matrix4
      out
      The result of the composition of the matrices.

    Returns Matrix4

multiplyMatrixLeft

  • Computes the composition of "this" and pSecondTransform and stores the result in pOut.

    Any point P transformed by the resulting transformation will first be multiplied by "this", and then pSecondTransform.
    Be P' the transformed point of P :
    Depending on your convention : P' = pSecondTransform x this x P (hence multiply left)
    or P' = P x this x pSecondTransform.


    If pOut is omitted, the result is stored in "this".

    Returns

    pOut.

    Parameters

    • pSecondTransform: Matrix4
      in
      The transform to apply after "this" when transforming points.
    • Optional pOut: Matrix4
      out
      The result of the composition of the matrices.

    Returns Matrix4

multiplyMatrixRight

  • Computes the composition of pFirstTransform and "this" and stores the result in pOut.

    Any point P transformed by the resulting transformation will first be multiplied by pFirstTransform, and then "this".
    Be P' the transformed point of P :
    Depending on your convention : P' = this x pFirstTransform x P (hence multiply right)
    or P' = P x pFirstTransform x this.


    If pOut is omitted, the result is stored in "this".

    Returns

    pOut.

    Parameters

    • pFirstTransform: Matrix4
      in
      The transform to apply first when transforming points.
    • Optional pOut: Matrix4
      out
      The result of the composition of the matrices.

    Returns Matrix4

multiplyRight

  • Computes the composition of the matrix represented by the values Mval and "this" and stores the result in pOut.

    Any point P transformed by the resulting transformation will first be multiplied by Mval, and then "this".
    Be P' the transformed point of P :
    Depending on your convention : P' = this x Mval x P (hence multiply right)
    or P' = P x Mval x this.

    If pOut is omitted, the result is stored in "this".

    If you consider the matrix vector multiplication in line (V' = V x Mval), then Mval is set to (translation [T0,T1,T2] on the bottom) :

    abc0 (d)
    efg0 (h)
    ijk0 (l)
    T0 : mT1 : nT2 : o1 (p)

    If you consider the matrix vector multiplication in column (V' = Mval x V), then Mval is set (translation [T0,T1,T2] on the right) :
    aeiT0 : m
    bfjT1 : n
    cgkT2 : o
    0 (d)0 (h)0 (l)1 (p)


    Then when using Matrices : 
    this.multiplyMatrixRight(pFirstTransform, pOut);

    is equivalent to : 
    this.multiplyRight(
        pFirstTransform.array[0], pFirstTransform.array[1], pFirstTransform.array[2], pFirstTransform.array[3],
        pFirstTransform.array[4], pFirstTransform.array[5], pFirstTransform.array[6], pFirstTransform.array[7],
        pFirstTransform.array[8], pFirstTransform.array[9], pFirstTransform.array[10], pFirstTransform.array[11],
        pFirstTransform.array[12], pFirstTransform.array[13], pFirstTransform.array[14], pFirstTransform.array[15],
        pOut
    );

    Please refer to some matrices courses to get more information.

    Returns

    pOut.

    Parameters

    • a: number
      in
      Rotation/scale part.
    • b: number
      in
      Rotation/scale part.
    • c: number
      in
      Rotation/scale part.
    • d: number
      in
      Should be 0.
    • e: number
      in
      Rotation/scale part.
    • f: number
      in
      Rotation/scale part.
    • g: number
      in
      Rotation/scale part.
    • h: number
      in
      Should be 0.
    • i: number
      in
      Rotation/scale part.
    • j: number
      in
      Rotation/scale part.
    • k: number
      in
      Rotation/scale part.
    • l: number
      in
      Should be 0.
    • m: number
      in
      Translation upon x.
    • n: number
      in
      Translation upon y.
    • o: number
      in
      Translation upon z.
    • p: number
      in
      Should be 1.
    • Optional pOut: Matrix4
      out
      The result of the composition of the matrices.

    Returns Matrix4

multiplyVector3Direction

  • Computes the transformation of the vector pDirection by "this" matrix, and stores the result in pOut.

    pDirection is considered a direction and thus, this is equivalent to using multiplyVector4XYZW(pPoint[0],pPoint[1],pPoint[2],0).

    If pOut is omitted, then pDirection is changed in place.

    Returns pOut.

    Returns

    pOut.

    Parameters

    • pDirection: Vector3
      in
      the vector3 to transform.
    • Optional pOut: Vector3
      out
      the resulting transformed vector.

    Returns Vector3

multiplyVector3DirectionXYZ

  • Computes the transformation of the vector (pX,pY,pZ) by "this" matrix, and stores the result in pOut.

    (pX,pY,pZ) is considered a direction and thus, this is equivalent to using multiplyVector4XYZW(pX,pY,pZ,0).

    Returns pOut.

    Returns

    pOut.

    Parameters

    • pX: number
      in
      x coordinate of the vector3 to transform.
    • pY: number
      in
      y coordinate of the vector3 to transform.
    • pZ: number
      in
      z coordinate of the vector3 to transform.
    • pOut: Vector3
      out
      the resulting transformed vector.

    Returns Vector3

multiplyVector3Position

  • Computes the transformation of the vector pPoint by "this" matrix, and stores the result in pOut.

    pPoint is considered a point and thus, this is equivalent to using multiplyVector4XYZW(pPoint[0],pPoint[1],pPoint[2],1), and computing the homogeneous coordinates of the resulting Vector4 (i.e. dividing all coordinates by the w coordinate of the vector4).

    If pOut is omitted, then pPoint is changed in place.

    Returns pOut.

    Returns

    pOut.

    Parameters

    • pPoint: Vector3
      in
      The vector3 to transform.
    • Optional pOut: Vector3
      out
      The resulting transformed vector.

    Returns Vector3

multiplyVector3PositionXYZ

  • Computes the transformation of the vector (pX,pY,pZ) by "this" matrix, and stores the result in pOut.

    The vector (pX,pY,pZ) is considered a point and thus, this is equivalent to using multiplyVector4XYZW(pX,pY,pZ,1), and computing the homogeneous coordinates of the resulting Vector4 (i.e. dividing all coordinates by the w coordinate of the vector4).

    Returns pOut.

    Returns

    pOut.

    Parameters

    • pX: number
      in
      x coordinate of the vector3 to transform.
    • pY: number
      in
      y coordinate of the vector3 to transform.
    • pZ: number
      in
      z coordinate of the vector3 to transform.
    • pOut: Vector3
      out
      the resulting transformed vector.

    Returns Vector3

multiplyVector4

  • Computes the transformation of pVector by "this" matrix, and stores the result in pOut.

    If pOut is omitted, then pVector is changed in place.

    Returns pOut.

    Returns

    pOut.

    Parameters

    • pVector: Vector4
      in
      The vector4 to transform.
    • Optional pOut: Vector4
      out
      The resulting transformed vector.

    Returns Vector4

multiplyVector4XYZW

  • Computes the transformation of the vector (pX,pY,pZ,pW) by "this" matrix, and stores the result in pOut.

    Returns pOut.

    Returns

    pOut.

    Parameters

    • pX: number
      in
      code>x coordinate of the vector4 to transform.
    • pY: number
      in
      y coordinate of the vector4 to transform.
    • pZ: number
      in
      z coordinate of the vector4 to transform.
    • pW: number
      in
      w coordinate of the vector4 to transform.
    • pOut: Vector4
      out
      The resulting transformed vector.

    Returns Vector4

resetToScale

  • Resets the matrix to be a scale (pX,pY,pZ).

    Returns

    this.

    Parameters

    • pX: number
      in
      x component of the scale to set.
    • pY: number
      in
      y component of the scale to set.
    • pZ: number
      in
      z component of the scale to set.

    Returns Matrix4

rotateX

  • Computes the rotation of "this" around the X axis and stores the result in pOut.

    This computes the composition of "this" and the rotation of pAngle around X.
    Any point P transformed by the resulting transformation will first be multiplied by "this", and then the rotation around X.
    Be P' the transformed point of P, and Rx the rotation around X :
    Depending on your convention : P' = Rx x this x P
    or P' = P x this x Rx.

    If pOut is omitted, the result is stored in "this".

    Returns

    pOut.

    Parameters

    • pAngle: number
      in
      The angle in radian for the rotation around X.
    • Optional pOut: Matrix4
      out
      The result of the rotation of the matrix.

    Returns Matrix4

rotateY

  • Computes the rotation of "this" around the Y axis and stores the result in pOut.

    This computes the composition of "this" and the rotation of pAngle around Y.
    Any point P transformed by the resulting transformation will first be multiplied by "this", and then the rotation around Y.
    Be P' the transformed point of P, and Ry the rotation around Y :
    Depending on your convention : P' = Ry x this x P
    or P' = P x this x Ry.

    If pOut is omitted, the result is stored in "this".

    Returns

    pOut.

    Parameters

    • pAngle: number
      in
      The angle in radian for the rotation around Y.
    • Optional pOut: Matrix4
      out
      The result of the rotation of the matrix.

    Returns Matrix4

rotateZ

  • Computes the rotation of "this" around the Z axis and stores the result in pOut.

    This computes the composition of "this" and the rotation of pAngle around Z.
    Any point P transformed by the resulting transformation will first be multiplied by "this", and then the rotation around Z.
    Be P' the transformed point of P, and Rz the rotation around Z :
    Depending on your convention : P' = Rz x this x P
    or P' = P x this x Rz.

    If pOut is omitted, the result is stored in "this".

    Returns

    pOut.

    Parameters

    • pAngle: number
      in
      The angle in radian for the rotation around Z.
    • Optional pOut: Matrix4
      out
      The result of the rotation of the matrix.

    Returns Matrix4

set

  • Sets values for the matrix.

    If you consider the matrix vector multiplication in line (V' = V x M), then the following matrix is set (translation [T0,T1,T2] on the bottom) :

    abc0 (d)
    efg0 (h)
    ijk0 (l)
    T0 : mT1 : nT2 : o1 (p)

    If you consider the matrix vector multiplication in column (V' = M x V), then the following matrix is set (translation [T0,T1,T2] on the right) :
    aeiT0 : m
    bfjT1 : n
    cgkT2 : o
    0 (d)0 (h)0 (l)1 (p)

    Returns 'this'.

    Returns

    this.

    Parameters

    • Optional a: number
      in
      Rotation/scale part.
    • Optional b: number
      in
      Rotation/scale part.
    • Optional c: number
      in
      Rotation/scale part.
    • Optional d: number
      in
      Should be 0.
    • Optional e: number
      in
      Rotation/scale part.
    • Optional f: number
      in
      Rotation/scale part.
    • Optional g: number
      in
      Rotation/scale part.
    • Optional h: number
      in
      Should be 0.
    • Optional i: number
      in
      Rotation/scale part.
    • Optional j: number
      in
      Rotation/scale part.
    • Optional k: number
      in
      Rotation/scale part.
    • Optional l: number
      in
      Should be 0.
    • Optional m: number
      in
      Translation upon x.
    • Optional n: number
      in
      Translation upon y.
    • Optional o: number
      in
      Translation upon z.
    • Optional p: number
      in
      Should be 1.

    Returns Matrix4

setQuaternion

  • Sets the matrix to be the rotation from the given quaternion values [pX,pY,pZ,pW].

    Returns

    this.

    See

    Quaternion

    Parameters

    • pX: number
      in
      x component of the quaternion.
    • pY: number
      in
      y component of the quaternion.
    • pZ: number
      in
      z component of the quaternion.
    • pW: number
      in
      w component of the quaternion.

    Returns Matrix4

setTranslation

  • Resets the matrix to be a translation.

    The rotation/scale part is set to the identity.

    Returns

    this.

    Parameters

    • pX: number
      in
      x component of the translation.
    • pY: number
      in
      y component of the translation.
    • pZ: number
      in
      z component of the translation.

    Returns Matrix4

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