A row major 3x3 rotation matrix. More...

#include <3esmatrix3.h>

Public Member Functions
	Matrix3 ()
	Empty constructor; contents are undefined.

	Matrix3 (const T *array9)
	Array initialisation constructor from an array of at least 9 elements. More...

	Matrix3 (const Matrix3< T > &other)
	Copy constructor. More...

template<typename Q >
	Matrix3 (const Matrix3< Q > &other)
	Copy constructor from a different numeric type. More...

	Matrix3 (const T &rc00, const T &rc01, const T &rc02, const T &rc10, const T &rc11, const T &rc12, const T &rc20, const T &rc21, const T &rc22)
	Per element constructor, specifying each row in order. More...

T &	operator() (int r, int c)
	Row/column access. More...

const T &	operator() (int r, int c) const
	Row/column immutable access. More...

T &	operator[] (int index)
	Indexing operator (no bounds checking). More...

const T &	operator[] (int index) const
	Indexing operator (no bounds checking). More...

Matrix3< T > &	initRotationX (const T &angle)

Matrix3< T > &	initRotationY (const T &angle)

Matrix3< T > &	initRotationZ (const T &angle)

Matrix3< T > &	initRotation (const T &x, const T &y, const T &z)

Matrix3< T > &	initScaling (const Vector3< T > &scale)

Matrix3< T > &	initLookAt (const Vector3< T > &eye, const Vector3< T > &target, const Vector3< T > &axisUp, int forwardAxisIndex=1, int upAxisIndex=2)
	Initialise this matrix as a model or camera matrix. More...

Matrix3< T > &	transpose ()
	Transposes this matrix. More...

Matrix3< T >	transposed () const
	Returns the transpose of this matrix, leaving this matrix unchanged. More...

Matrix3< T > &	invert ()
	Inverts this matrix. More...

Matrix3< T >	inverse () const
	Returns the inverse of this matrix, leaving this matrix unchanged. More...

T	getAdjoint (Matrix3< T > &adj) const
	Gets the adjoint of this matrix. More...

Matrix3< T > &	rigidBodyInvert ()
	Inverts this matrix assuming this matrix represents a rigid body transformation. More...

Matrix3< T >	rigidBodyInverse () const
	Returns the inverse of this matrix assuming this is a rigid body transformation. More...

T	determinant () const
	Calculates the determinant of this matrix. More...

Vector3< T >	axisX () const
	Returns the X axis of this matrix (elements (0, 0), (1, 0), (2, 0)). More...

Vector3< T >	axisY () const
	Returns the Y axis of this matrix (elements (0, 1), (1, 1), (2, 1)). More...

Vector3< T >	axisZ () const
	Returns the Z axis of this matrix (elements (0, 2), (1, 2), (2, 2)). More...

Vector3< T >	axis (int index) const
	Returns one of the axes of this matrix. More...

Matrix3< T > &	setAxisX (const Vector3< T > &axis)
	Sets the X axis of this matrix. More...

Matrix3< T > &	setAxisY (const Vector3< T > &axis)
	Sets the Y axis of this matrix. More...

Matrix3< T > &	setAxisZ (const Vector3< T > &axis)
	Sets the Z axis of this matrix. More...

Matrix3< T > &	setAxis (int index, const Vector3< T > &axis)
	Sets the indexed axis of this matrix. More...

Vector3< T >	scale () const
	Returns the scale contained in this matrix. More...

Matrix3< T > &	scale (const Vector3< T > &scaling)
	Scales this matrix, adjusting the scale of each rotation, but leaving the translation. More...

Vector3< T >	transform (const Vector3< T > &v) const
	Transforms the vector `v` by this matrix. More...

Vector3< T >	rotate (const Vector3< T > &v) const
	An alias for `transform()`. More...

Static Public Member Functions
static Matrix3< T >	rotationX (const T &angle)
	Create a matrix which represents a rotation around the X axis. More...

static Matrix3< T >	rotationY (const T &angle)
	Create a matrix which represents a rotation around the Y axis. More...

static Matrix3< T >	rotationZ (const T &angle)
	Create a matrix which represents a rotation around the Z axis. More...

static Matrix3< T >	rotation (const T &x, const T &y, const T &z)
	Create a matrix which represents a rotation around each axis (Euler angles). More...

static Matrix3< T >	scaling (const Vector3< T > &scale)
	Create a scaling matrix. More...

static Matrix3< T >	lookAt (const Vector3< T > &eye, const Vector3< T > &target, const Vector3< T > &axisUp, int forwardAxisIndex=1, int upAxisIndex=2)
	Create a model or camera matrix at `eye` looking at `target`. More...

Public Attributes
union {
T rc [3][3]
	Row/column indexing representation.

T m [9]
	Array representation.

};

Static Public Attributes
static const Matrix3< T >	zero
	A matrix with all zero elements.

static const Matrix3< T >	identity
	The identity matrix.

Detailed Description

template<typename T>
class tes::Matrix3< T >

A row major 3x3 rotation matrix.

The matrix is laid out as follows:

    | rc00  rc01  rc02  |   |  0   1   2 |   | xx  yx  zx |
M = | rc10  rc11  rc12  | = |  3   4   5 | = | xy  yy  zy |
    | rc20  rc21  rc22  |   |  6   7   8 |   | xz  yz  zz |

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.

Constructor & Destructor Documentation

◆ Matrix3() [1/4]

template<typename T>

tes::Matrix3< T >::Matrix3 ( const T * array9 )

Array initialisation constructor from an array of at least 9 elements.

No bounds checking.

Parameters

array9 The array of at least 9 value to initialise from.

◆ Matrix3() [2/4]

template<typename T>

tes::Matrix3< T >::Matrix3 ( const Matrix3< T > & other )

Copy constructor.

Parameters

other The matrix to copy from.

◆ Matrix3() [3/4]

template<typename T>

template<typename Q >

tes::Matrix3< T >::Matrix3 ( const Matrix3< Q > & other )

Copy constructor from a different numeric type.

Parameters

other The matrix to copy from.

◆ Matrix3() [4/4]

template<typename T>

tes::Matrix3< T >::Matrix3	(	const T &	rc00,
		const T &	rc01,
		const T &	rc02,
		const T &	rc10,
		const T &	rc11,
		const T &	rc12,
		const T &	rc20,
		const T &	rc21,
		const T &	rc22
	)

Per element constructor, specifying each row in order.

Parameters

rc00	Element at row/column 00
rc01	Element at row/column 01
rc02	Element at row/column 02
rc10	Element at row/column 10
rc11	Element at row/column 11
rc12	Element at row/column 12
rc20	Element at row/column 20
rc21	Element at row/column 21
rc22	Element at row/column 22

Member Function Documentation

◆ axis()

template<typename T>

Vector3<T> tes::Matrix3< T >::axis ( int index ) const

Returns one of the axes of this matrix.

Parameters

index The index of the axis of interest. 0 => X, 1 => Y, 2 => Z.

Returns: The axis of interest.

Referenced by tes::Matrix3< T >::initLookAt().

◆ axisX()

template<typename T>

Vector3<T> tes::Matrix3< T >::axisX ( ) const

Returns the X axis of this matrix (elements (0, 0), (1, 0), (2, 0)).

Returns: The X axis.

Referenced by tes::Matrix3< T >::initLookAt().

◆ axisY()

template<typename T>

Vector3<T> tes::Matrix3< T >::axisY ( ) const

Returns the Y axis of this matrix (elements (0, 1), (1, 1), (2, 1)).

Returns: The Y axis.

Referenced by tes::Matrix3< T >::initLookAt().

◆ axisZ()

template<typename T>

Vector3<T> tes::Matrix3< T >::axisZ ( ) const

Returns the Z axis of this matrix (elements (0, 2), (1, 2), (2, 2)).

Returns: The Z axis.

Referenced by tes::Matrix3< T >::initLookAt().

◆ determinant()

template<typename T>

T tes::Matrix3< T >::determinant ( ) const

Calculates the determinant of this matrix.

Returns: The determinant.

Referenced by tes::Matrix3< T >::initLookAt().

◆ getAdjoint()

template<typename T>

T tes::Matrix3< T >::getAdjoint ( Matrix3< T > & adj ) const

Gets the adjoint of this matrix.

Parameters

[out] m The adjoint is written here.

Returns: The determinant.

Referenced by tes::Matrix3< T >::initLookAt().

◆ initLookAt()

template<typename T>

Matrix3<T>& tes::Matrix3< T >::initLookAt	(	const Vector3< T > &	eye,
		const Vector3< T > &	target,
		const Vector3< T > &	axisUp,
		int	forwardAxisIndex = `1`,
		int	upAxisIndex = `2`
	)

inline

Initialise this matrix as a model or camera matrix.

See also: lookAt().

Parameters

eye	The position of the eye/camera (dropped after rotation is calculated).
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: this

◆ inverse()

template<typename T>

Matrix3<T> tes::Matrix3< T >::inverse ( ) const

Returns the inverse of this matrix, leaving this matrix unchanged.

Returns: The inverse of this matrix.

Referenced by tes::Matrix3< T >::initLookAt().

◆ invert()

template<typename T>

Matrix3<T>& tes::Matrix3< T >::invert ( )

Inverts this matrix.

Returns: This matrix after the operation.

Referenced by tes::Matrix3< T >::initLookAt().

◆ lookAt()

template<typename T>

static Matrix3<T> tes::Matrix3< T >::lookAt	(	const Vector3< T > &	eye,
		const Vector3< T > &	target,
		const Vector3< T > &	axisUp,
		int	forwardAxisIndex = `1`,
		int	upAxisIndex = `2`
	)

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.

Note: the resulting matrix can only represent the rotation part of the matrix and the eye translation is essentially dropped. Use Matrix4 where the translation is required.

Parameters

eye	The position of the eye/camera (dropped after rotation is calculated).
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.

Referenced by tes::Matrix3< T >::initLookAt(), and tes::Matrix3< T >::operator[]().

◆ operator()() [1/2]

template<typename T>

T& tes::Matrix3< T >::operator()	(	int	r,
		int	c
	)

inline

Row/column access.

Not bounds checked.

Parameters

r	The row to access [0, 2]
c	The column to access [0, 2].

References tes::Matrix3< T >::rc.

◆ operator()() [2/2]

template<typename T>

const T& tes::Matrix3< T >::operator()	(	int	r,
		int	c
	)		const

inline

Row/column immutable access.

Not bounds checked.

Parameters

r	The row to access [0, 2]
c	The column to access [0, 2].

References tes::Matrix3< T >::rc.

◆ operator[]() [1/2]

template<typename T>

T& tes::Matrix3< T >::operator[] ( int index )

inline

Indexing operator (no bounds checking).

Parameters

index The element to access [0, 9].

Returns: The matrix element at index.

References tes::Matrix3< T >::m.

◆ operator[]() [2/2]

template<typename T>

const T& tes::Matrix3< T >::operator[] ( int index ) const

inline

Indexing operator (no bounds checking).

Parameters

index The element to access [0, 9].

Returns: The matrix element at index.

References tes::Matrix3< T >::lookAt(), tes::Matrix3< T >::m, tes::Matrix3< T >::rotation(), tes::Matrix3< T >::rotationX(), tes::Matrix3< T >::rotationY(), tes::Matrix3< T >::rotationZ(), tes::Matrix3< T >::scale(), and tes::Matrix3< T >::scaling().

◆ rigidBodyInverse()

template<typename T>

Matrix3<T> tes::Matrix3< T >::rigidBodyInverse ( ) const

Returns the inverse of this matrix assuming this is a rigid body transformation.

See rigidBodyInvert().

Returns: The inverse of this matrix.

Referenced by tes::Matrix3< T >::initLookAt().

◆ rigidBodyInvert()

template<typename T>

Matrix3<T>& tes::Matrix3< T >::rigidBodyInvert ( )

Inverts this matrix assuming this matrix represents a rigid body transformation.

A rigid body transformation contains no skewing. That is, the basis vectors are orthogonal.

The inverse is calculated by transposing the rotation and inverting the translation.

Returns: This matrix after the operation.

Referenced by tes::Matrix3< T >::initLookAt().

◆ rotate()

template<typename T>

Vector3<T> tes::Matrix3< T >::rotate ( const Vector3< T > & v ) const

An alias for transform().

Returns: Av, where A is this matrix.

Referenced by tes::Matrix3< T >::initLookAt().

◆ rotation()

template<typename T>

static Matrix3<T> tes::Matrix3< T >::rotation	(	const T &	x,
		const T &	y,
		const T &	z
	)

static

Create a matrix which represents a rotation around each axis (Euler angles).

Rotations are applied in x, y, z order.

Parameters

x	Rotation around the X axis (radians).
y	Rotation around the Y axis (radians).
z	Rotation around the Z axis (radians).

Returns: The rotation matrix.

Referenced by tes::Matrix3< T >::operator[]().

◆ rotationX()

template<typename T>

static Matrix3<T> tes::Matrix3< T >::rotationX ( const T & angle )

static

Create a matrix which represents a rotation around the X axis.

Parameters

angle The rotation angle in radians.

Returns: The rotation matrix.

Referenced by tes::Matrix3< T >::operator[]().

◆ rotationY()

template<typename T>

static Matrix3<T> tes::Matrix3< T >::rotationY ( const T & angle )

static

Create a matrix which represents a rotation around the Y axis.

Parameters

angle The rotation angle in radians.

Returns: The rotation matrix.

Referenced by tes::Matrix3< T >::operator[]().

◆ rotationZ()

template<typename T>

static Matrix3<T> tes::Matrix3< T >::rotationZ ( const T & angle )

static

Create a matrix which represents a rotation around the Z axis.

Parameters

angle The rotation angle in radians.

Returns: The rotation matrix.

Referenced by tes::Matrix3< T >::operator[]().

◆ scale() [1/2]

template<typename T>

Vector3<T> tes::Matrix3< T >::scale ( ) const

Returns the scale contained in this matrix.

This is the length of each axis.

Returns: The scale of each rotation axis in this matrix.

Referenced by tes::Matrix3< T >::initLookAt(), and tes::Matrix3< T >::operator[]().

◆ scale() [2/2]

template<typename T>

Matrix3<T>& tes::Matrix3< T >::scale ( const Vector3< T > & scaling )

Scales this matrix, adjusting the scale of each rotation, but leaving the translation.

Parameters

scaling The scaling to apply.

Returns: This matrix after the operation.

◆ scaling()

template<typename T>

static Matrix3<T> tes::Matrix3< T >::scaling ( const Vector3< T > & scale )

static

Create a scaling matrix.

Parameters

scale The scaling to apply along each axis.

Returns: The scaling matrix.

Referenced by tes::Matrix3< T >::operator[]().

◆ setAxis()

template<typename T>

Matrix3<T>& tes::Matrix3< T >::setAxis	(	int	index,
		const Vector3< T > &	axis
	)

Sets the indexed axis of this matrix.

See axis().

Parameters

index	The index of the axis of interest. 0 => X, 1 => Y, 2 => Z.
axis	The value to set the axis to.

Returns: This matrix after the operation.

Referenced by tes::Matrix3< T >::initLookAt().

◆ setAxisX()

template<typename T>

Matrix3<T>& tes::Matrix3< T >::setAxisX ( const Vector3< T > & axis )

Sets the X axis of this matrix.

See axisX().

Parameters

axis	The value to set the axis to.

Returns: This matrix after the operation.

Referenced by tes::Matrix3< T >::initLookAt().

◆ setAxisY()

template<typename T>

Matrix3<T>& tes::Matrix3< T >::setAxisY ( const Vector3< T > & axis )

Sets the Y axis of this matrix.

See axisY().

Parameters

axis	The value to set the axis to.

Returns: This matrix after the operation.

Referenced by tes::Matrix3< T >::initLookAt().

◆ setAxisZ()

template<typename T>

Matrix3<T>& tes::Matrix3< T >::setAxisZ ( const Vector3< T > & axis )

Sets the Z axis of this matrix.

See axisZ().

Parameters

axis	The value to set the axis to.

Returns: This matrix after the operation.

Referenced by tes::Matrix3< T >::initLookAt().

◆ transform()

template<typename T>

Vector3<T> tes::Matrix3< T >::transform ( const Vector3< T > & v ) const

Transforms the vector v by this matrix.

Returns: Av, where A is this matrix.

Referenced by tes::Matrix3< T >::initLookAt().

◆ transpose()

template<typename T>

Matrix3<T>& tes::Matrix3< T >::transpose ( )

Transposes this matrix.

Returns: This matrix after the operation.

Referenced by tes::Matrix3< T >::initLookAt().

◆ transposed()

template<typename T>

Matrix3<T> tes::Matrix3< T >::transposed ( ) const

Returns the transpose of this matrix, leaving this matrix unchanged.

Returns: The transpose of this matrix.

Referenced by tes::Matrix3< T >::initLookAt().

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

3esmatrix3.h

Public Member Functions

Static Public Member Functions

Public Attributes

Static Public Attributes

Detailed Description

template<typename T> class tes::Matrix3< T >

Constructor & Destructor Documentation

◆ Matrix3() [1/4]

◆ Matrix3() [2/4]

◆ Matrix3() [3/4]

◆ Matrix3() [4/4]

Member Function Documentation

◆ axis()

◆ axisX()

◆ axisY()

◆ axisZ()

◆ determinant()

◆ getAdjoint()

◆ initLookAt()

◆ inverse()

◆ invert()

◆ lookAt()

◆ operator()() [1/2]

◆ operator()() [2/2]

◆ operator[]() [1/2]

◆ operator[]() [2/2]

◆ rigidBodyInverse()

◆ rigidBodyInvert()

◆ rotate()

◆ rotation()

◆ rotationX()

◆ rotationY()

◆ rotationZ()

◆ scale() [1/2]

◆ scale() [2/2]

◆ scaling()

◆ setAxis()

◆ setAxisX()

◆ setAxisY()

◆ setAxisZ()

◆ transform()

◆ transpose()

◆ transposed()

template<typename T>
class tes::Matrix3< T >