A row major 4x4 transformation matrix. More...

Public Member Functions
Vector3	GetAxis (int index)
	Requests an axis or column from the matrix, dropping the last row.
void	SetAxis (int index, Vector3 axis)
	Set an axis or column from the matrix.
void	InitRotationX (float angle)
	Sets this matrix to a rotation matrix around the X axis.
void	InitRotationY (float angle)
	Sets this matrix to a rotation matrix around the Y axis.
void	InitRotationZ (float angle)
	Sets this matrix to a rotation matrix around the Z axis.
void	InitTranslationMatrix (Vector3 trans)
	Initialise a translation matrix, no rotation or scale.
void	InitRotation (float angleX, float angleY, float angleZ)
	Initialise this matrix from the given Euler angles.
void	InitRotationTranslation (float angleX, float angleY, float angleZ, Vector3 trans)
	Initialise this matrix from the given Euler angles and translation.
void	InitScaling (Vector3 scale)
	Initialise this matrix as a scaling matrix.
void	ApplyScaling (Vector3 scaling)
	Scales the matrix basis vectors.
Vector3	RemoveScale ()
	Removes scaling from the matrix basis vectors.
void	InitLookAt (Vector3 eye, Vector3 target, Vector3 axisUp, int forwardAxisIndex=1, int upAxisIndex=2)
	Initialise this matrix as a model or camera matrix.
void	Transpose ()
	Transpose this matrix.
void	Invert ()
	Inverse this matrix.
void	RigidBodyInvert ()
	Calculate the inverse of a rigid body matrix (no skew or scaling).
Vector3	Transform (Vector3 v)
	Apply this transformation to the vector v .
Vector3	Rotate (Vector3 v)
	Transforms the vector v by the rotation component of this matrix.
Static Public Member Functions
static Matrix4	All (float val)
	Create a matrix with all components set to val .
static Matrix4	IdentityMatrix ()
	The 4x4 identity matrix.
static Matrix4	RotationX (float angle)
	Builds a rotation matrix around the X axis.
static Matrix4	RotationY (float angle)
	Sets this matrix to a rotation matrix around the Y axis.
static Matrix4	RotationZ (float angle)
	Sets this matrix to a rotation matrix around the Z axis.
static Matrix4	TranslationMatrix (Vector3 trans)
	Create a translation matrix, no rotation or scale.
static Matrix4	Rotation (float angleX, float angleY, float angleZ)
	Build a rotation matrix from the given Euler angles.
static Matrix4	RotationTranslation (float angleX, float angleY, float angleZ, Vector3 trans)
	Build a transformation matrix from the given Euler angles and translation.
static Matrix4	Scaling (Vector3 scale)
	Initialise a scaling matrix.
static Matrix4	LookAt (Vector3 eye, Vector3 target, Vector3 axisUp, int forwardAxisIndex=1, int upAxisIndex=2)
	Create a model or camera matrix at eye looking at target .
static Vector3	operator* (Matrix4 a, Vector3 v)
	Calculates the transformation `Av`.
static Matrix4	operator* (Matrix4 a, Matrix4 b)
	Calculates the matrix product of two 4x4 matrices.
Static Public Attributes
static Matrix4	Zero = All(0.0f)
	A matrix with all zero components.
static Matrix4	Identity = IdentityMatrix()
	The 4x4 identity matrix.
Properties
float	this[int index] `[get, set]`
	Indexing accessor across the range [0, 15].
float	this[int r, int c] `[get, set]`
	Row/column indexing accessor.
float	Determinant `[get]`
	Calculate the determinant of this matrix.
Vector3	AxisX `[get, set]`
	Get/set the conceptual X axis from this matrix.
Vector3	AxisY `[get, set]`
	Get/set the conceptual Y axis from this matrix.
Vector3	AxisZ `[get, set]`
	Get/set the conceptual Z axis from this matrix.
Vector3	Translation `[get, set]`
	Get/set the conceptual translation axis from this matrix.
Vector3	Scale `[get]`
	Calculate the per axis scaling of this matrix.
Matrix4	Transposed `[get]`
	Return the transpose of this matrix.
Matrix4	Inverse `[get]`
	Get the inverse of this matrix.
Matrix4	RigidBodyInverse `[get]`
	Get the inverse of a rigid body matrix (no skew or scaling).

Detailed Description

A row major 4x4 transformation matrix.

The matrix is laid out as follows:

          | m00  m01  m02  m03 |   |  0   1   2   3 |   | xx  yx  zx  tx |
      M = | m10  m11  m12  m13 | = |  4   5   6   7 | = | xy  yy  zy  ty |
          | m20  m21  m22  m23 |   |  8   9  10  11 |   | xz  yz  zz  tz |
          | m30  m31  m32  m33 |   | 12  13  14  15 |   |  0   0   0   1 |

Where (xx, xy, xz) are the components of the X axis. Similarly, yn and zn form the Y axis and Z axis of the basis vectors respectively. Finally, (tx, ty, tz) is the translation.

Member Function Documentation

static Matrix4 Tes::Maths::Matrix4::All ( float val ) [inline, static]

Create a matrix with all components set to val .

Parameters:

val	The value to assign to each component.

Returns:: The matrix with all components val .

void Tes::Maths::Matrix4::ApplyScaling ( Vector3 scaling ) [inline]

Scales the matrix basis vectors.

The translation column is left unmodified.

Parameters:

scaling Per axis scaling. Each coordinate corresponds to a column of the matrix.

Vector3 Tes::Maths::Matrix4::GetAxis ( int index ) [inline]

Requests an axis or column from the matrix, dropping the last row.

A Vector4 class is need to properly extract the whole column.

Parameters:

index The axis/column index [0, 3]

Returns:: The requested axis.

static Matrix4 Tes::Maths::Matrix4::IdentityMatrix ( ) [inline, static]

The 4x4 identity matrix.

Returns:: The identity matrix.

void Tes::Maths::Matrix4::InitLookAt	(	Vector3	eye,
		Vector3	target,
		Vector3	axisUp,
		int	forwardAxisIndex = `1`,
		int	upAxisIndex = `2`
	)		`[inline]`

Initialise this matrix as a model or camera matrix.

LookAt(Vector3, Vector3, Vector3, int, int).

Parameters:

eye	The position of the eye/camera.
target	The target to look at. Should not be equal to eye .
axisUp	The axis defining the initial up vector. Must be normalised.
forwardAxisIndex	The index of the forward axis. This is to point at target .
upAxisIndex	The index of the up axis. Must not be equal to forwardAxisIndex .

void Tes::Maths::Matrix4::InitRotation	(	float	angleX,
		float	angleY,
		float	angleZ
	)		`[inline]`

Initialise this matrix from the given Euler angles.

Parameters:

angleX	The rotation around the X axis (radians).
angleY	The rotation around the Y axis (radians).
angleZ	The rotation around the Z axis (radians).

void Tes::Maths::Matrix4::InitRotationTranslation	(	float	angleX,
		float	angleY,
		float	angleZ,
		Vector3	trans
	)		`[inline]`

Initialise this matrix from the given Euler angles and translation.

Parameters:

angleX	The rotation around the X axis (radians).
angleY	The rotation around the Y axis (radians).
angleZ	The rotation around the Z axis (radians).
trans	The translation component for matrix.

void Tes::Maths::Matrix4::InitRotationX ( float angle ) [inline]

Sets this matrix to a rotation matrix around the X axis.

Parameters:

angle The rotation angle (radians)

void Tes::Maths::Matrix4::InitRotationY ( float angle ) [inline]

Sets this matrix to a rotation matrix around the Y axis.

Parameters:

angle The rotation angle (radians)

void Tes::Maths::Matrix4::InitRotationZ ( float angle ) [inline]

Sets this matrix to a rotation matrix around the Z axis.

Parameters:

angle The rotation angle (radians)

void Tes::Maths::Matrix4::InitScaling ( Vector3 scale ) [inline]

Initialise this matrix as a scaling matrix.

Parameters:

scale The scaling factor. Each coordinate corresponds to one of the first three columns of the matrix.

void Tes::Maths::Matrix4::InitTranslationMatrix ( Vector3 trans ) [inline]

Initialise a translation matrix, no rotation or scale.

Parameters:

trans The translation to apply.

void Tes::Maths::Matrix4::Invert ( ) [inline]

Inverse this matrix.

Undefined behaviour for singular matrices.

static Matrix4 Tes::Maths::Matrix4::LookAt	(	Vector3	eye,
		Vector3	target,
		Vector3	axisUp,
		int	forwardAxisIndex = `1`,
		int	upAxisIndex = `2`
	)		`[inline, static]`

Create a model or camera matrix at eye looking at target .

Supports specifying the up and forward axes (inferring the left/right axis), where the indices [0, 1, 2] correspond to the axes (X, Y, Z).

The default behaviour is to use Y as the forward axis and Z as up.

Parameters:

eye	The position of the eye/camera.
target	The target to look at. Should not be equal to eye .
axisUp	The axis defining the initial up vector. Must be normalised.
forwardAxisIndex	The index of the forward axis. This is to point at target .
upAxisIndex	The index of the up axis. Must not be equal to forwardAxisIndex .

Returns:: A model matrix at eye pointing at target . Returns identity if there are errors in the specification of forwardAxisIndex and upAxisIndex .

static Matrix4 Tes::Maths::Matrix4::operator*	(	Matrix4	a,
		Matrix4	b
	)		`[inline, static]`

Calculates the matrix product of two 4x4 matrices.

Conceptually, when the resulting matrix transforms a vector, the matrix b is applied first, then a .

Parameters:

a	A matrix operand.
b	A matrix operand.

Returns:: The matrix product of a and b .

static Vector3 Tes::Maths::Matrix4::operator*	(	Matrix4	a,
		Vector3	v
	)		`[inline, static]`

Calculates the transformation Av.

Parameters:

a	The transformation matrix.
v	The vector to transform.

Returns:: The matrix product Av where A is this matrix and v is the vector argument.

Vector3 Tes::Maths::Matrix4::RemoveScale ( ) [inline]

Removes scaling from the matrix basis vectors.

Returns:: The scale before modification.

void Tes::Maths::Matrix4::RigidBodyInvert ( ) [inline]

Calculate the inverse of a rigid body matrix (no skew or scaling).

Performs a matrix transpose and negates the translation.

Vector3 Tes::Maths::Matrix4::Rotate ( Vector3 v ) [inline]

Transforms the vector v by the rotation component of this matrix.

No translation is applied.

Parameters:

v	The vector to rotate.

Returns:: Av, where A is this matrix converted to a 3x3 rotation matrix (no translation).

FIXME: remove scaling effects.

static Matrix4 Tes::Maths::Matrix4::Rotation	(	float	angleX,
		float	angleY,
		float	angleZ
	)		`[inline, static]`

Build a rotation matrix from the given Euler angles.

Parameters:

angleX	The rotation around the X axis (radians).
angleY	The rotation around the Y axis (radians).
angleZ	The rotation around the Z axis (radians).

Returns:: The rotation matrix.

static Matrix4 Tes::Maths::Matrix4::RotationTranslation	(	float	angleX,
		float	angleY,
		float	angleZ,
		Vector3	trans
	)		`[inline, static]`

Build a transformation matrix from the given Euler angles and translation.

Parameters:

angleX	The rotation around the X axis (radians).
angleY	The rotation around the Y axis (radians).
angleZ	The rotation around the Z axis (radians).
trans	The translation component for matrix.

Returns:: The transformation matrix.

static Matrix4 Tes::Maths::Matrix4::RotationX ( float angle ) [inline, static]

Builds a rotation matrix around the X axis.

Parameters:

angle The rotation angle (radians)

Returns:: The rotation matrix.

static Matrix4 Tes::Maths::Matrix4::RotationY ( float angle ) [inline, static]

Sets this matrix to a rotation matrix around the Y axis.

Parameters:

angle The rotation angle (radians)

static Matrix4 Tes::Maths::Matrix4::RotationZ ( float angle ) [inline, static]

Sets this matrix to a rotation matrix around the Z axis.

Parameters:

angle The rotation angle (radians)

static Matrix4 Tes::Maths::Matrix4::Scaling ( Vector3 scale ) [inline, static]

Initialise a scaling matrix.

Parameters:

scale The scaling factor. Each coordinate corresponds to a column of the matrix.

void Tes::Maths::Matrix4::SetAxis	(	int	index,
		Vector3	axis
	)		`[inline]`

Set an axis or column from the matrix.

The last row is set to either zero for columns [0, 2] and 1 for column 3. A Vector4 class is need to properly set the whole column.

Parameters:

index	The axis/column index [0, 3]
axis	The axis value.

Vector3 Tes::Maths::Matrix4::Transform ( Vector3 v ) [inline]

Apply this transformation to the vector v .

Parameters:

v	The vector to transform.

Returns:: The matrix product Av where A is this matrix and v is the vector argument.

static Matrix4 Tes::Maths::Matrix4::TranslationMatrix ( Vector3 trans ) [inline, static]

Create a translation matrix, no rotation or scale.

Parameters:

trans The translation to apply.

Returns:: The constructed translation matrix.

Property Documentation

Vector3 Tes::Maths::Matrix4::AxisX [get, set]

Get/set the conceptual X axis from this matrix.

This equates to column 0.

Vector3 Tes::Maths::Matrix4::AxisY [get, set]

Get/set the conceptual Y axis from this matrix.

This equates to column 1.

Vector3 Tes::Maths::Matrix4::AxisZ [get, set]

Get/set the conceptual Z axis from this matrix.

This equates to column 2.

float Tes::Maths::Matrix4::Determinant [get]

Calculate the determinant of this matrix.

Not a cheap operation.

Matrix4 Tes::Maths::Matrix4::Inverse [get]

Get the inverse of this matrix.

Undefined behaviour for singular matrices.

Matrix4 Tes::Maths::Matrix4::RigidBodyInverse [get]

Get the inverse of a rigid body matrix (no skew or scaling).

Performs a matrix transpose and negates the translation.

float Tes::Maths::Matrix4::this[int index] [get, set]

Indexing accessor across the range [0, 15].

See class documentation on the matrix layout.

Parameters:

index The component index [0, 15].

Returns:: The requested component.

Exceptions:

IndexOutOfRangeException Thrown when index is out of range.

float Tes::Maths::Matrix4::this[int r, int c] [get, set]

Row/column indexing accessor.

Valid row and column ranges are: [0, 3].

See class documentation on the matrix layout.

Parameters:

r	The row index [0, 3].
c	The column index [0, 3].

Returns:: The requested component.

Exceptions:

IndexOutOfRangeException Thrown when r or c are out of range.

Vector3 Tes::Maths::Matrix4::Translation [get, set]

Get/set the conceptual translation axis from this matrix.

This equates to column 3.

The documentation for this struct was generated from the following file:

Matrix4.cs

Public Member Functions

Static Public Member Functions

Static Public Attributes

Properties

Detailed Description

Member Function Documentation

Property Documentation