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

Constructors

constructor

new Matrix4(a?, b?, c?, d?, e?, f?, g?, h?, i?, j?, k?, l?, m?, n?, o?, p?): Matrix4
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) :

a b c 0 (d)

e f g 0 (h)

i j k 0 (l)

T0 : m T1 : n T2 : o 1 (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) :

a e i T0 : m

b f j T1 : n

c g k T2 : o

0 (d) 0 (h) 0 (l) 1 (p)

Returns the newly constructed matrix.
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
The newly created Matrix4.

Properties

array

array: Float32Array

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

Methods

copy

copy(pOut?): Matrix4
Copies this to pOther matrix.

If pOther is not supplied, a new Matrix4 is allocated.
Parameters
- Optional pOut: Matrix4
  out
  The Matrix4 to copy to.
Returns Matrix4
The copied matrix.

determinant

determinant(): number
Computes the matrix determinant.

Returns number
The determinant of the matrix.

equals

equals(pOtherMatrix): boolean
Tells if the two matrices are strictly identical.
Parameters
- pOtherMatrix: Matrix4
  in
  The other matrix to compare to.
Returns boolean
true if the two matrices are strictly identical.

fromJSON

fromJSON(pMatrixData): boolean
Sets the content of the Matrix4 from a former call to toJSON.
Parameters
- pMatrixData: string | Object
  in
  Internal Matrix4 data to set.
Returns boolean
true if the data is set.

getColumn

getColumn(pColumn, pOut): Vector3
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) :

a e i T0 : m

b f j T1 : n

c g k T2 : 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) :

a b c 0 (d)

e f g 0 (h)

i j k 0 (l)

T0 : m T1 : n T2 : o 1 (p)

Then getColumn(0) returns (a,b,c).
No check is done to ensure pColumn is in the range [0-3].
Parameters
- pColumn: number
  in
  The column to get in the range [0-3].
- pOut: Vector3
  out
  The resulting "column" of the matrix.
Returns Vector3
pOut.

invert

invert(pOut?): Matrix4
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.
Parameters
- Optional pOut: Matrix4
  out
  The inverted matrix result.
Returns Matrix4
pOut.

isIdentity

isIdentity(): boolean
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 boolean
true if the matrix is identity (strictly).

makeIdentity

makeIdentity(): this
Sets this matrix to the identity.

Returns this
this.

multiplyLeft

multiplyLeft(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, pOut?): Matrix4
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) :

a b c 0 (d)

e f g 0 (h)

i j k 0 (l)

T0 : m T1 : n T2 : o 1 (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) :

a e i T0 : m

b f j T1 : n

c g k T2 : 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.
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
pOut.

multiplyMatrixLeft

multiplyMatrixLeft(pSecondTransform, pOut?): Matrix4
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.
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
pOut.

multiplyMatrixRight

multiplyMatrixRight(pFirstTransform, pOut?): Matrix4
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.
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
pOut.

multiplyRight

multiplyRight(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, pOut?): Matrix4
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) :

a b c 0 (d)

e f g 0 (h)

i j k 0 (l)

T0 : m T1 : n T2 : o 1 (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) :

a e i T0 : m

b f j T1 : n

c g k T2 : 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.
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
pOut.

multiplyVector3Direction

multiplyVector3Direction(pDirection, pOut?): Vector3
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.
Parameters
- pDirection: Vector3
  in
  the vector3 to transform.
- Optional pOut: Vector3
  out
  the resulting transformed vector.
Returns Vector3
pOut.

multiplyVector3DirectionXYZ

multiplyVector3DirectionXYZ(pX, pY, pZ, pOut): Vector3
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.
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
pOut.

multiplyVector3Position

multiplyVector3Position(pPoint, pOut?): Vector3
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.
Parameters
- pPoint: Vector3
  in
  The vector3 to transform.
- Optional pOut: Vector3
  out
  The resulting transformed vector.
Returns Vector3
pOut.

multiplyVector3PositionXYZ

multiplyVector3PositionXYZ(pX, pY, pZ, pOut): Vector3
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.
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
pOut.

multiplyVector4

multiplyVector4(pVector, pOut?): Vector4
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.
Parameters
- pVector: Vector4
  in
  The vector4 to transform.
- Optional pOut: Vector4
  out
  The resulting transformed vector.
Returns Vector4
pOut.

multiplyVector4XYZW

multiplyVector4XYZW(pX, pY, pZ, pW, pOut): Vector4
Computes the transformation of the vector (pX,pY,pZ,pW) by this matrix, and stores the result in pOut.

Returns pOut.
Parameters
- pX: number
  in
  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
pOut.

resetToScale

resetToScale(pX, pY, pZ): this
Resets the matrix to be a scale (pX,pY,pZ).
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 this
this.

rotateX

rotateX(pAngle, pOut?): Matrix4
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.
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
pOut.

rotateY

rotateY(pAngle, pOut?): Matrix4
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.
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
pOut.

rotateZ

rotateZ(pAngle, pOut?): Matrix4
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.
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
pOut.

set

set(a?, b?, c?, d?, e?, f?, g?, h?, i?, j?, k?, l?, m?, n?, o?, p?): this
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) :

a b c 0 (d)

e f g 0 (h)

i j k 0 (l)

T0 : m T1 : n T2 : o 1 (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) :

a e i T0 : m

b f j T1 : n

c g k T2 : o

0 (d) 0 (h) 0 (l) 1 (p)

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 this
this.

setQuaternion

setQuaternion(pX, pY, pZ, pW): this
Sets the matrix to be the rotation from the given quaternion values [pX,pY,pZ,pW].

The translation is reset to (0,0,0).
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 this
this.

See
Quaternion

setQuaternionPart

setQuaternionPart(pX, pY, pZ, pW): this
Sets the matrix to be the rotation from the given quaternion values [pX,pY,pZ,pW].

The translation is left unchanged.
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 this
this.

See
Quaternion

setRotationPart

setRotationPart(a, b, c, e, f, g, i, j, k): this
Sets the matrix to be the rotation from the given values.

The translation is left unchanged.

See set to get information on the memory layout.

Returns this.
Parameters
- a: number
  in
  Rotation/scale part.
- b: number
  in
  Rotation/scale part.
- c: number
  in
  Rotation/scale part.
- e: number
  in
  Rotation/scale part.
- f: number
  in
  Rotation/scale part.
- g: number
  in
  Rotation/scale part.
- i: number
  in
  Rotation/scale part.
- j: number
  in
  Rotation/scale part.
- k: number
  in
  Rotation/scale part.
Returns this
this.

setRotationPartFromMatrix

setRotationPartFromMatrix(pMatrix): this
Sets the matrix to be the rotation from the given matrix.

The translation is left unchanged.
Parameters
- pMatrix: Matrix4
  in
  The matrix to copy data from.
Returns this
this.

setTranslation

setTranslation(pX, pY, pZ): this
Resets the matrix to be a translation.

The rotation/scale part is reset to the identity.
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 this
this.

setTranslationPart

setTranslationPart(pX, pY, pZ): this
Sets the translation part of the matrix.

The rotation/scale part is left unchanged.
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 this
this.

setTranslationPartFromMatrix

setTranslationPartFromMatrix(pMatrix): this
Copies the translation part of the matrix.

The rotation/scale part is left unchanged.
Parameters
- pMatrix: Matrix4
  in
  The matrix to copy.
Returns this
this.

toJSON

toJSON(pKey?): Object
Serializes the given Matrix4 to JSON.
Parameters
- Optional pKey: any
  in
  Unused.
Returns Object
The JSON representation of the object.

transpose3x3

transpose3x3(pOutMatrix?): Matrix4
Computes the transpose of the rotation part. This is useful for inverting a rotation matrix.

The translation is left unchanged (no copy of translation).
Parameters
- Optional pOutMatrix: Matrix4
  out
  The matrix that will receive the transpose (the translation part is left unchanged).
Returns Matrix4
pOutMatrix.

a	b	c	0 (d)
e	f	g	0 (h)
i	j	k	0 (l)
T0 : m	T1 : n	T2 : o	1 (p)

a	e	i	T0 : m
b	f	j	T1 : n
c	g	k	T2 : o
0 (d)	0 (h)	0 (l)	1 (p)

a	e	i	T0 : m
b	f	j	T1 : n
c	g	k	T2 : o
0 (d)	0 (h)	0 (l)	1 (p)

a	b	c	0 (d)
e	f	g	0 (h)
i	j	k	0 (l)
T0 : m	T1 : n	T2 : o	1 (p)

Class Matrix4

Index

Constructors

Properties

Methods

Constructors

constructor

Parameters

Returns Matrix4

Properties

array

Methods

copy

Parameters

Returns Matrix4

determinant

Returns number

equals

Parameters

Returns boolean

fromJSON

Parameters

Returns boolean

getColumn

Parameters

Returns Vector3

invert

Parameters

Returns Matrix4

isIdentity

Returns boolean

makeIdentity

Returns this

multiplyLeft

Parameters

Returns Matrix4

multiplyMatrixLeft

Parameters

Returns Matrix4

multiplyMatrixRight

Parameters

Returns Matrix4

multiplyRight

Parameters

Returns Matrix4

multiplyVector3Direction

Parameters

Returns Vector3

multiplyVector3DirectionXYZ

Parameters

Returns Vector3

multiplyVector3Position

Parameters

Returns Vector3

multiplyVector3PositionXYZ

Parameters

Returns Vector3

multiplyVector4

Parameters

Returns Vector4

multiplyVector4XYZW

Parameters

Returns Vector4

resetToScale

Parameters

Returns this

rotateX

Parameters

Returns Matrix4

rotateY

Parameters

Returns Matrix4

rotateZ

Parameters

Returns Matrix4

set

Parameters

Returns this

setQuaternion

Parameters