This class implements a 4x4 homogeneous transformation matrix using floating point values with the precision specified by type T. More...

#include <HomogenousMatrix4.h>

Inheritance diagram for Ocean::HomogenousMatrixT4< T >:

Public Types
typedef T	Type
	Definition of the used data type.

Public Member Functions
	HomogenousMatrixT4 ()
	Creates a new default HomogenousMatrixT4 object with undefined elements.

	HomogenousMatrixT4 (const HomogenousMatrixT4< T > &matrix)
	Copy constructor.

template<typename U >
	HomogenousMatrixT4 (const HomogenousMatrixT4< U > &matrix)
	Copy constructor for a matrix with difference element data type than T.

	HomogenousMatrixT4 (const bool setToIdentity)
	Creates a new HomogenousMatrixT4.

template<typename U >
	HomogenousMatrixT4 (const U *arrayValues)
	Creates a new HomogenousMatrixT4 object by 16 given floating point values of type U.

	HomogenousMatrixT4 (const T *arrayValues)
	Creates a new HomogenousMatrixT4 object by 16 given floating point values.

template<typename U >
	HomogenousMatrixT4 (const U *arrayValues, const bool valuesRowAligned)
	Creates a new HomogenousMatrixT4 object by an array of at least sixteen elements of float type U.

	HomogenousMatrixT4 (const T *arrayValues, const bool valuesRowAligned)
	Creates a new HomogenousMatrixT4 object by an array of at least sixteen elements.

	HomogenousMatrixT4 (const VectorT3< T > &translation)
	Creates a new HomogenousMatrixT4 object with only a translation.

	HomogenousMatrixT4 (const RotationT< T > &rotation)
	Creates a new HomogenousMatrixT4 object with only a rotation.

	HomogenousMatrixT4 (const EulerT< T > &euler)
	Creates a new HomogenousMatrixT4 object with only a rotation given as Euler rotation.

	HomogenousMatrixT4 (const QuaternionT< T > &rotation)
	Creates a new HomogenousMatrixT4 object with only a rotation given as quaternion.

	HomogenousMatrixT4 (const SquareMatrixT3< T > &rotation)
	Creates a new HomogenousMatrixT4 object with only a rotation given as 3x3 rotation matrix.

	HomogenousMatrixT4 (const SquareMatrixT4< T > &matrix)
	Creates a new HomogenousMatrixT4 object from a 4x4 square matrix.

	HomogenousMatrixT4 (const VectorT3< T > &translation, const RotationT< T > &rotation)
	Creates a new HomogenousMatrixT4 object with a translation and rotation.

	HomogenousMatrixT4 (const std::pair< VectorT3< T >, RotationT< T > > &translationAndRotation)
	Creates a new HomogenousMatrixT4 object with a translation and rotation.

	HomogenousMatrixT4 (const VectorT3< T > &translation, const EulerT< T > &euler)
	Creates a new HomogenousMatrixT4 object with a translation and rotation.

	HomogenousMatrixT4 (const VectorT3< T > &translation, const QuaternionT< T > &rotation)
	Creates a new HomogenousMatrixT4 object with a translation and rotation.

	HomogenousMatrixT4 (const std::pair< VectorT3< T >, QuaternionT< T > > &translationAndRotation)
	Creates a new HomogenousMatrixT4 object with a translation and rotation.

	HomogenousMatrixT4 (const VectorT3< T > &translation, const SquareMatrixT3< T > &rotation)
	Creates a new HomogenousMatrixT4 object with a translation and rotation matrix.

	HomogenousMatrixT4 (const VectorT3< T > &translation, const VectorT3< T > &scale)
	Creates a new HomogenousMatrixT4 object by a translation and a scale.

	HomogenousMatrixT4 (const VectorT3< T > &translation, const RotationT< T > &rotation, const VectorT3< T > &scale)
	Creates a new HomogenousMatrixT4 object by a translation, rotation and scale.

	HomogenousMatrixT4 (const VectorT3< T > &translation, const QuaternionT< T > &rotation, const VectorT3< T > &scale, const VectorT3< T > &shear)
	Creates a new HomogenousMatrixT4 object by a translation, rotation, scale and shear.

	HomogenousMatrixT4 (const VectorT3< T > &translation, const RotationT< T > &rotation, const VectorT3< T > &scale, const VectorT3< T > &shear)
	Creates a new HomogenousMatrixT4 object by a translation, rotation, scale and shear.

	HomogenousMatrixT4 (const VectorT3< T > &translation, const QuaternionT< T > &rotation, const VectorT3< T > &scale)
	Creates a new HomogenousMatrixT4 object by a translation, rotation and scale.

	HomogenousMatrixT4 (const VectorT3< T > &xAxis, const VectorT3< T > &yAxis, const VectorT3< T > &zAxis)
	Creates a new HomogenousMatrixT4 object by three basis vectors.

	HomogenousMatrixT4 (const VectorT3< T > &xAxis, const VectorT3< T > &yAxis, const VectorT3< T > &zAxis, const VectorT3< T > &translation)
	Creates a new HomogenousMatrixT4 object by three basis vectors and a translation vector.

VectorT3< T >	xAxis () const
	Returns the x-axis of the transformation which is the first vector of the upper left 3x3 rotation matrix of this homogeneous 4x4 transformation.

VectorT3< T >	yAxis () const
	Returns the y-axis of the transformation which is the second vector of the upper left 3x3 rotation matrix of this homogeneous 4x4 transformation.

VectorT3< T >	zAxis () const
	Returns the z-axis of the transformation which is the first vector of the upper left 3x3 rotation matrix of this homogeneous 4x4 transformation.

VectorT3< T >	translation () const
	Returns the translation of the transformation.

QuaternionT< T >	rotation () const
	Returns the rotation of the transformation as quaternion.

VectorT3< T >	scale () const
	Returns the scale of the transformation.

bool	decompose (VectorT3< T > &translation, QuaternionT< T > &rotation, VectorT3< T > &scale, VectorT3< T > &shear) const
	Decomposes the transformation matrix into translation, rotation, scale and shear parameters.

SquareMatrixT3< T >	rotationMatrix () const
	Returns the rotation matrix of the transformation.

void	rotationMatrix (T *data, const bool transposed=false) const
	Copies the 3x3 rotation matrix elements of the 4x4 transformation.

SquareMatrixT3< T >	orthonormalRotationMatrix () const
	Returns the 3x3 orthonormal rotation matrix of the 4x4 transformation (by forcing a orthogonal and normalized rotation matrix).

SquareMatrixT4< T >	transposed () const
	Returns the transposed of this matrix.

HomogenousMatrixT4< T >	inverted () const noexcept
	Returns the inverted of this matrix.

bool	invert ()
	Inverts the matrix.

bool	invert (HomogenousMatrixT4< T > &invertedMatrix) const
	Inverts the matrix and returns the result as parameter.

T	determinant () const
	Returns the determinant of the matrix.

T	trace () const
	Returns the trace of the matrix which is the sum of the diagonal elements.

HomogenousMatrixT4< T > &	setTranslation (const VectorT3< T > &translation)
	Sets the translation of this transformation.

HomogenousMatrixT4< T > &	setRotation (const RotationT< T > &rotation)
	Sets the rotation of this transformation.

HomogenousMatrixT4< T > &	setRotation (const QuaternionT< T > &quaternion)
	Sets the rotation of this transformation.

HomogenousMatrixT4< T > &	setRotation (const SquareMatrixT3< T > &matrix)
	Sets the rotation of this transformation.

HomogenousMatrixT4< T > &	applyScale (const VectorT3< T > &scale)
	Applies new scale values.

void	toIdentity ()
	Sets the matrix to the identity matrix.

void	toNull ()
	Sets the matrix to a zero matrix (including the lower right element).

bool	isValid () const
	Returns whether this matrix is a valid homogeneous transformation.

bool	isIdentity () const
	Returns whether this matrix is an identity matrix.

bool	isEqual (const HomogenousMatrixT4< T > &matrix, const T epsilon=NumericT< T >::eps()) const
	Returns whether two matrices are almost identical up to a specified epsilon.

bool	isNull () const
	Returns whether this matrix is a zero matrix (with all elements equal to zero).

const T *	data () const
	Returns a pointer to the internal values.

T *	data ()
	Returns a pointer to the internal values.

void	copyElements (T *arrayValues, const bool valuesRowAligned=false) const
	Copies the elements of this matrix to an array with floating point values of the same type T.

template<typename U >
void	copyElements (U *arrayValues, const bool valuesRowAligned=false) const
	Copies the elements of this matrix to an array with floating point values of the type U.

VectorT3< T >	rotationMatrix (const VectorT3< T > &vector) const
	Transforms a 3D vector by application of only the inner rotation matrix (including scale and shearing) of this transformation.

VectorT3< T >	transposedRotationMatrix (const VectorT3< T > &vector) const
	Transforms a 3D vector by application of only the inner transposed rotation matrix (including scale and shearing) of this transformation.

HomogenousMatrixT4< T > &	operator= (const HomogenousMatrixT4< T > &)=default
	Default copy assignment operator.

bool	operator== (const HomogenousMatrixT4< T > &matrix) const
	Returns whether two transformations are identical up to a small epsilon.

bool	operator!= (const HomogenousMatrixT4< T > &matrix) const
	Returns whether two transformations are not identical up to a small epsilon.

HomogenousMatrixT4< T >	operator* (const HomogenousMatrixT4< T > &matrix) const
	Combines two transformation matrices.

HomogenousMatrixT4< T > &	operator*= (const HomogenousMatrixT4< T > &matrix)
	Combines and assigns two transformation matrices.

HomogenousMatrixT4< T >	operator* (const RotationT< T > &rotation) const
	Combines a transformation with a rotation.

HomogenousMatrixT4< T > &	operator*= (const RotationT< T > &rotation)
	Combines and assigns a transformation with a rotation.

HomogenousMatrixT4< T >	operator* (const QuaternionT< T > &rotation) const
	Combines a transformation with a quaternion rotation.

HomogenousMatrixT4< T > &	operator*= (const QuaternionT< T > &rotation)
	Combines and assigns a transformation with a quaternion rotation.

VectorT3< T >	operator* (const VectorT3< T > &vector) const
	Transforms a 3D vector.

VectorT4< T >	operator* (const VectorT4< T > &vector) const
	Transforms a 4D vector.

T	operator[] (const unsigned int index) const
	Element operator.

T &	operator[] (const unsigned int index)
	Element operator.

T	operator() (const unsigned int row, const unsigned int column) const
	Element operator.

T &	operator() (const unsigned int row, const unsigned int column)
	Element operator.

T	operator() (const unsigned int index) const
	Element operator.

T &	operator() (const unsigned int index)
	Element operator.

const T *	operator() () const
	Access operator.

T *	operator() ()
	Access operator.

size_t	operator() (const HomogenousMatrixT4< T > &matrix) const
	Hash function.

std::vector< HomogenousMatrixT4< float > >	matrices2matrices (const std::vector< HomogenousMatrixT4< float > > &matrices)

std::vector< HomogenousMatrixT4< double > >	matrices2matrices (const std::vector< HomogenousMatrixT4< double > > &matrices)

Static Public Member Functions
template<typename U >
static std::vector< HomogenousMatrixT4< T > >	matrices2matrices (const std::vector< HomogenousMatrixT4< U > > &matrices)
	Converts matrices with specific data type to matrices with different data type.

template<typename U >
static std::vector< HomogenousMatrixT4< T > >	matrices2matrices (const HomogenousMatrixT4< U > *matrices, const size_t size)
	Converts matrices with specific data type to matrices with different data type.

Protected Attributes
T	values_ [16]
	The sixteen values of the transformation matrix.

Friends
template<typename U >
class	HomogenousMatrixT4

Detailed Description

template<typename T>
class Ocean::HomogenousMatrixT4< T >

This class implements a 4x4 homogeneous transformation matrix using floating point values with the precision specified by type T.

The values are stored in a column major/aligned order with indices:
| 0  4  8  12 |
| 1  5  9  13 |
| 2  6  10 14 |
| 3  7  11 15 |

This matrix allows homogeneous transformations only.
With basis vectors (rx1, ry1, rz1), (rx2, ry2, rz2), (rx3, ry3, rz3), and translation vector (tx, ty, tz):
| rx1 rx2 rx3 tx |
| ry1 ry2 ry3 ty |
| rz1 rz2 rz3 tz |
|  0   0   0   1 |

Template Parameters

T	Data type of matrix elements

See also: HomogenousMatrix4, HomogenousMatrixF4, HomogenousMatrixD4.

Member Typedef Documentation

◆ Type

template<typename T >

typedef T Ocean::HomogenousMatrixT4< T >::Type

Definition of the used data type.

Constructor & Destructor Documentation

◆ HomogenousMatrixT4() [1/27]

template<typename T >

Ocean::HomogenousMatrixT4< T >::HomogenousMatrixT4 ( )

inline

Creates a new default HomogenousMatrixT4 object with undefined elements.

Beware: This matrix is neither a zero nor an entity matrix!

◆ HomogenousMatrixT4() [2/27]

template<typename T >

Ocean::HomogenousMatrixT4< T >::HomogenousMatrixT4 ( const HomogenousMatrixT4< T > & matrix )

inline

Copy constructor.

Parameters

matrix The matrix to copy

◆ HomogenousMatrixT4() [3/27]

template<typename T >

template<typename U >

Ocean::HomogenousMatrixT4< T >::HomogenousMatrixT4 ( const HomogenousMatrixT4< U > & matrix )

inlineexplicit

Copy constructor for a matrix with difference element data type than T.

Parameters

matrix The matrix to copy

Template Parameters

U	The element data type of the second matrix

◆ HomogenousMatrixT4() [4/27]

template<typename T >

Ocean::HomogenousMatrixT4< T >::HomogenousMatrixT4 ( const bool setToIdentity )

inlineexplicit

Creates a new HomogenousMatrixT4.

Beware: The zero matrix will hold a zero in the lower right corner which must be set explicitly later to create a valid matrix.
Only constructors explicitly set the lower right value to 1 like e.g., the constructor building a matrix from a rotation or translation and so on.

Parameters

setToIdentity True, to create a identity matrix; False, to set a zero matrix

◆ HomogenousMatrixT4() [5/27]

template<typename T >

template<typename U >

Ocean::HomogenousMatrixT4< T >::HomogenousMatrixT4 ( const U * arrayValues )

explicit

Creates a new HomogenousMatrixT4 object by 16 given floating point values of type U.

Parameters

arrayValues The array with 16 matrix elements of type U

◆ HomogenousMatrixT4() [6/27]

template<typename T >

Ocean::HomogenousMatrixT4< T >::HomogenousMatrixT4 ( const T * arrayValues )

explicit

Creates a new HomogenousMatrixT4 object by 16 given floating point values.

Parameters

arrayValues The array with 16 matrix elements

◆ HomogenousMatrixT4() [7/27]

template<typename T >

template<typename U >

Ocean::HomogenousMatrixT4< T >::HomogenousMatrixT4	(	const U *	arrayValues,
		const bool	valuesRowAligned
	)

Creates a new HomogenousMatrixT4 object by an array of at least sixteen elements of float type U.

Parameters

arrayValues	The sixteen matrix elements defining the new matrix, must be valid
valuesRowAligned	True, if the given values are stored in a row aligned order; False, if the values are stored in a column aligned order (which is the default case for this matrix)

Template Parameters

U	The floating point type of the given elements

◆ HomogenousMatrixT4() [8/27]

template<typename T >

Ocean::HomogenousMatrixT4< T >::HomogenousMatrixT4	(	const T *	arrayValues,
		const bool	valuesRowAligned
	)

Creates a new HomogenousMatrixT4 object by an array of at least sixteen elements.

Parameters

valuesRowAligned	True, if the given values are stored in a row aligned order; False, if the values are stored in a column aligned order (which is the default case for this matrix)
arrayValues	The sixteen matrix elements defining the new matrix, must be valid

◆ HomogenousMatrixT4() [9/27]

template<typename T >

Ocean::HomogenousMatrixT4< T >::HomogenousMatrixT4 ( const VectorT3< T > & translation )

explicit

Creates a new HomogenousMatrixT4 object with only a translation.

Parameters

translation The translation of the resulting transformation

◆ HomogenousMatrixT4() [10/27]

template<typename T >

Ocean::HomogenousMatrixT4< T >::HomogenousMatrixT4 ( const RotationT< T > & rotation )

explicit

Creates a new HomogenousMatrixT4 object with only a rotation.

Parameters

rotation The angle-axis rotation of the resulting transformation

◆ HomogenousMatrixT4() [11/27]

template<typename T >

Ocean::HomogenousMatrixT4< T >::HomogenousMatrixT4 ( const EulerT< T > & euler )

explicit

Creates a new HomogenousMatrixT4 object with only a rotation given as Euler rotation.

Parameters

euler The euler rotation of the resulting transformation

◆ HomogenousMatrixT4() [12/27]

template<typename T >

Ocean::HomogenousMatrixT4< T >::HomogenousMatrixT4 ( const QuaternionT< T > & rotation )

explicit

Creates a new HomogenousMatrixT4 object with only a rotation given as quaternion.

Parameters

rotation The rotation of the resulting transformation

◆ HomogenousMatrixT4() [13/27]

template<typename T >

Ocean::HomogenousMatrixT4< T >::HomogenousMatrixT4 ( const SquareMatrixT3< T > & rotation )

explicit

Creates a new HomogenousMatrixT4 object with only a rotation given as 3x3 rotation matrix.

Parameters

rotation 3x3 rotation matrix

◆ HomogenousMatrixT4() [14/27]

template<typename T >

Ocean::HomogenousMatrixT4< T >::HomogenousMatrixT4 ( const SquareMatrixT4< T > & matrix )

explicit

Creates a new HomogenousMatrixT4 object from a 4x4 square matrix.

Parameters

matrix The 4x4 square matrix

◆ HomogenousMatrixT4() [15/27]

template<typename T >

Ocean::HomogenousMatrixT4< T >::HomogenousMatrixT4	(	const VectorT3< T > &	translation,
		const RotationT< T > &	rotation
	)

Creates a new HomogenousMatrixT4 object with a translation and rotation.

The resulting transformation can be written as the following matrix multiplication:

HomogenousMatrix4(translation, rotation) == HomogenousMatrix4(translation) * HomogenousMatrix4(rotation)

Parameters

translation	The translation of the resulting transformation
rotation	The rotation of the resulting transformation, must be valid

◆ HomogenousMatrixT4() [16/27]

template<typename T >

Ocean::HomogenousMatrixT4< T >::HomogenousMatrixT4 ( const std::pair< VectorT3< T >, RotationT< T > > & translationAndRotation )

explicit

Creates a new HomogenousMatrixT4 object with a translation and rotation.

Parameters

translationAndRotation The pair of translation and rotation of the resulting transformation

◆ HomogenousMatrixT4() [17/27]

template<typename T >

Ocean::HomogenousMatrixT4< T >::HomogenousMatrixT4	(	const VectorT3< T > &	translation,
		const EulerT< T > &	euler
	)

Creates a new HomogenousMatrixT4 object with a translation and rotation.

The resulting transformation can be written as the following matrix multiplication:

HomogenousMatrix4(translation, euler) == HomogenousMatrix4(translation) * HomogenousMatrix4(euler)

Parameters

translation	The translation of the resulting transformation
euler	The euler rotation of the resulting transformation, must be valid

◆ HomogenousMatrixT4() [18/27]

template<typename T >

Ocean::HomogenousMatrixT4< T >::HomogenousMatrixT4	(	const VectorT3< T > &	translation,
		const QuaternionT< T > &	rotation
	)

Creates a new HomogenousMatrixT4 object with a translation and rotation.

The resulting transformation can be written as the following matrix multiplication:

HomogenousMatrix4(translation, rotation) == HomogenousMatrix4(translation) * HomogenousMatrix4(rotation)

Parameters

translation	The translation of the resulting transformation
rotation	The quaternion rotation of the resulting transformation, must be valid

◆ HomogenousMatrixT4() [19/27]

template<typename T >

Ocean::HomogenousMatrixT4< T >::HomogenousMatrixT4 ( const std::pair< VectorT3< T >, QuaternionT< T > > & translationAndRotation )

explicit

Creates a new HomogenousMatrixT4 object with a translation and rotation.

Parameters

translationAndRotation The pair of translation and rotation of the resulting transformation

◆ HomogenousMatrixT4() [20/27]

template<typename T >

Ocean::HomogenousMatrixT4< T >::HomogenousMatrixT4	(	const VectorT3< T > &	translation,
		const SquareMatrixT3< T > &	rotation
	)

Creates a new HomogenousMatrixT4 object with a translation and rotation matrix.

The resulting transformation can be written as the following matrix multiplication:

HomogenousMatrix4(translation, rotation) == HomogenousMatrix4(translation) * HomogenousMatrix4(rotation)

Parameters

translation	The translation of the resulting transformation
rotation	The rotation matrix of the resulting transformation, must be valid

◆ HomogenousMatrixT4() [21/27]

template<typename T >

Ocean::HomogenousMatrixT4< T >::HomogenousMatrixT4	(	const VectorT3< T > &	translation,
		const VectorT3< T > &	scale
	)

Creates a new HomogenousMatrixT4 object by a translation and a scale.

Parameters

translation	The translation of the resulting transformation
scale	The scale of the resulting transformation

◆ HomogenousMatrixT4() [22/27]

template<typename T >

Ocean::HomogenousMatrixT4< T >::HomogenousMatrixT4	(	const VectorT3< T > &	translation,
		const RotationT< T > &	rotation,
		const VectorT3< T > &	scale
	)

Creates a new HomogenousMatrixT4 object by a translation, rotation and scale.

Parameters

translation	The translation of the resulting transformation
rotation	The rotation of the resulting transformation, must be valid
scale	The scale of the resulting transformation

◆ HomogenousMatrixT4() [23/27]

template<typename T >

Ocean::HomogenousMatrixT4< T >::HomogenousMatrixT4	(	const VectorT3< T > &	translation,
		const QuaternionT< T > &	rotation,
		const VectorT3< T > &	scale,
		const VectorT3< T > &	shear
	)

Creates a new HomogenousMatrixT4 object by a translation, rotation, scale and shear.

Parameters

translation	The translation of the resulting transformation
rotation	The rotation of the resulting transformation as unit quaternion, must be valid
scale	The scale of the resulting transformation
shear	The shear of the resulting transformation with order (xy, xz, yz)

◆ HomogenousMatrixT4() [24/27]

template<typename T >

Ocean::HomogenousMatrixT4< T >::HomogenousMatrixT4	(	const VectorT3< T > &	translation,
		const RotationT< T > &	rotation,
		const VectorT3< T > &	scale,
		const VectorT3< T > &	shear
	)

Creates a new HomogenousMatrixT4 object by a translation, rotation, scale and shear.

Parameters

translation	The translation of the resulting transformation
rotation	The rotation of the resulting transformation, must be valid
scale	The scale of the resulting transformation
shear	The shear of the resulting transformation with order (xy, xz, yz)

◆ HomogenousMatrixT4() [25/27]

template<typename T >

Ocean::HomogenousMatrixT4< T >::HomogenousMatrixT4	(	const VectorT3< T > &	translation,
		const QuaternionT< T > &	rotation,
		const VectorT3< T > &	scale
	)

Creates a new HomogenousMatrixT4 object by a translation, rotation and scale.

Parameters

translation	The translation of the resulting transformation
rotation	The quaternion rotation of the resulting transformation, must be valid
scale	The scale of the resulting transformation

◆ HomogenousMatrixT4() [26/27]

template<typename T >

Ocean::HomogenousMatrixT4< T >::HomogenousMatrixT4	(	const VectorT3< T > &	xAxis,
		const VectorT3< T > &	yAxis,
		const VectorT3< T > &	zAxis
	)

Creates a new HomogenousMatrixT4 object by three basis vectors.

Parameters

xAxis	First basis vector
yAxis	Second basis vector
zAxis	Third basis vector

◆ HomogenousMatrixT4() [27/27]

template<typename T >

Ocean::HomogenousMatrixT4< T >::HomogenousMatrixT4	(	const VectorT3< T > &	xAxis,
		const VectorT3< T > &	yAxis,
		const VectorT3< T > &	zAxis,
		const VectorT3< T > &	translation
	)

Creates a new HomogenousMatrixT4 object by three basis vectors and a translation vector.

Parameters

xAxis	First basis vector
yAxis	Second basis vector
zAxis	Third basis vector
translation	The translation vector

Member Function Documentation

◆ applyScale()

template<typename T >

HomogenousMatrixT4< T > & Ocean::HomogenousMatrixT4< T >::applyScale ( const VectorT3< T > & scale )

Applies new scale values.

Parameters

scale The new scale values which are applied to the inner 3x3 rotation matrix

Returns: Reference to this transformation matrix

◆ copyElements() [1/2]

template<typename T >

void Ocean::HomogenousMatrixT4< T >::copyElements	(	T *	arrayValues,
		const bool	valuesRowAligned = `false`
	)		const

inline

Copies the elements of this matrix to an array with floating point values of the same type T.

Parameters

arrayValues	Array with 16 floating point values of type T receiving the elements of this matrix, must be valid
valuesRowAligned	True, if the target values are stored in a row aligned order; False, if the values are stored in a column aligned order (which is the default case for this matrix)

◆ copyElements() [2/2]

template<typename T >

template<typename U >

void Ocean::HomogenousMatrixT4< T >::copyElements	(	U *	arrayValues,
		const bool	valuesRowAligned = `false`
	)		const

inline

Copies the elements of this matrix to an array with floating point values of the type U.

Parameters

arrayValues	Array with 16 floating point values of type U receiving the elements of this matrix, must be valid
valuesRowAligned	True, if the target values are stored in a row aligned order; False, if the values are stored in a column aligned order (which is the default case for this matrix)

◆ data() [1/2]

template<typename T >

T * Ocean::HomogenousMatrixT4< T >::data ( )

inline

Returns a pointer to the internal values.

Returns: The pointer to the internal values, always valid

◆ data() [2/2]

template<typename T >

const T * Ocean::HomogenousMatrixT4< T >::data ( ) const

inline

Returns a pointer to the internal values.

Returns: The pointer to the internal values, always valid

◆ decompose()

template<typename T >

bool Ocean::HomogenousMatrixT4< T >::decompose	(	VectorT3< T > &	translation,
		QuaternionT< T > &	rotation,
		VectorT3< T > &	scale,
		VectorT3< T > &	shear
	)		const

Decomposes the transformation matrix into translation, rotation, scale and shear parameters.

Parameters

translation	The returning translation parameter
rotation	The returning rotation parameter as quaternion
scale	The returning scale parameter
shear	The returning shear parameter with order (xy, xz, yz)

Returns: True, if succeeded (otherwise the transformation matrix has a zero-scaling axis and the translation is decomposed only)

◆ determinant()

template<typename T >

T Ocean::HomogenousMatrixT4< T >::determinant ( ) const

Returns the determinant of the matrix.

Returns: Matrix determinant

◆ invert() [1/2]

template<typename T >

bool Ocean::HomogenousMatrixT4< T >::invert ( )

Inverts the matrix.

Returns: True, if the matrix could be inverted (because the matrix was not singular)

◆ invert() [2/2]

template<typename T >

bool Ocean::HomogenousMatrixT4< T >::invert ( HomogenousMatrixT4< T > & invertedMatrix ) const

Inverts the matrix and returns the result as parameter.

Parameters

invertedMatrix The resulting inverted matrix

Returns: True, if the matrix could be inverted because the matrix is not singular

See also: inverted(), solve().

◆ inverted()

template<typename T >

HomogenousMatrixT4< T > Ocean::HomogenousMatrixT4< T >::inverted ( ) const

noexcept

Returns the inverted of this matrix.

This matrix must not be singular, ensure that the matrix is invertible before calling this function.
Even better: avoid the usage of this function and call invert() instead.
In case, this matrix is not invertible, this matrix will be returned instead.

Returns: The inverted matrix see invert().

◆ isEqual()

template<typename T >

bool Ocean::HomogenousMatrixT4< T >::isEqual	(	const HomogenousMatrixT4< T > &	matrix,
		const T	epsilon = `NumericT<T>::eps()`
	)		const

inline

Returns whether two matrices are almost identical up to a specified epsilon.

Parameters

matrix	Second matrix that will be checked
epsilon	The epsilon threshold to be used, with range [0, infinity)

Returns: True, if so

◆ isIdentity()

template<typename T >

bool Ocean::HomogenousMatrixT4< T >::isIdentity ( ) const

Returns whether this matrix is an identity matrix.

Returns: True, if so

See also: toIdentity().

◆ isNull()

template<typename T >

bool Ocean::HomogenousMatrixT4< T >::isNull ( ) const

Returns whether this matrix is a zero matrix (with all elements equal to zero).

Returns: True, if so

See also: toNull().

◆ isValid()

template<typename T >

bool Ocean::HomogenousMatrixT4< T >::isValid ( ) const

Returns whether this matrix is a valid homogeneous transformation.

Returns: True, if so

◆ matrices2matrices() [1/4]

template<typename T >

template<typename U >

std::vector< HomogenousMatrixT4< T > > Ocean::HomogenousMatrixT4< T >::matrices2matrices	(	const HomogenousMatrixT4< U > *	matrices,
		const size_t	size
	)

inlinestatic

Converts matrices with specific data type to matrices with different data type.

Parameters

matrices	The matrices to convert
size	The number of matrices to convert

Returns: The converted matrices

Template Parameters

U	The element data type of the matrices to convert

◆ matrices2matrices() [2/4]

std::vector< HomogenousMatrixT4< double > > Ocean::HomogenousMatrixT4< double >::matrices2matrices ( const std::vector< HomogenousMatrixT4< double > > & matrices )

inline

◆ matrices2matrices() [3/4]

std::vector< HomogenousMatrixT4< float > > Ocean::HomogenousMatrixT4< float >::matrices2matrices ( const std::vector< HomogenousMatrixT4< float > > & matrices )

inline

◆ matrices2matrices() [4/4]

template<typename T >

template<typename U >

std::vector< HomogenousMatrixT4< T > > Ocean::HomogenousMatrixT4< T >::matrices2matrices ( const std::vector< HomogenousMatrixT4< U > > & matrices )

inlinestatic

Converts matrices with specific data type to matrices with different data type.

Parameters

matrices The matrices to convert

Returns: The converted matrices

Template Parameters

U	The element data type of the matrices to convert

◆ operator!=()

template<typename T >

bool Ocean::HomogenousMatrixT4< T >::operator!= ( const HomogenousMatrixT4< T > & matrix ) const

inline

Returns whether two transformations are not identical up to a small epsilon.

Parameters

matrix Right operand

Returns: True, if so

◆ operator()() [1/7]

template<typename T >

T * Ocean::HomogenousMatrixT4< T >::operator() ( )

inline

Access operator.

Returns: Pointer to the internal values

◆ operator()() [2/7]

template<typename T >

const T * Ocean::HomogenousMatrixT4< T >::operator() ( ) const

inline

Access operator.

Returns: Pointer to the internal values

◆ operator()() [3/7]

template<typename T >

size_t Ocean::HomogenousMatrixT4< T >::operator() ( const HomogenousMatrixT4< T > & matrix ) const

inline

Hash function.

Parameters

matrix The matrix for which the hash value will be determined

Returns: The resulting hash value

◆ operator()() [4/7]

template<typename T >

T & Ocean::HomogenousMatrixT4< T >::operator() ( const unsigned int index )

inline

Element operator.

Parameters

index The index of the element to return [0, 15]

Returns: Specified element

◆ operator()() [5/7]

template<typename T >

T Ocean::HomogenousMatrixT4< T >::operator() ( const unsigned int index ) const

inline

Element operator.

Parameters

index The index of the element to return [0, 15]

Returns: Specified element

◆ operator()() [6/7]

template<typename T >

T & Ocean::HomogenousMatrixT4< T >::operator()	(	const unsigned int	row,
		const unsigned int	column
	)

inline

Element operator.

Parameters

row	The row of the element to return [0, 3]
column	The column of the element to return [0, 3]

Returns: Specified element

◆ operator()() [7/7]

template<typename T >

T Ocean::HomogenousMatrixT4< T >::operator()	(	const unsigned int	row,
		const unsigned int	column
	)		const

inline

Element operator.

Parameters

row	The row of the element to return [0, 3]
column	The column of the element to return [0, 3]

Returns: Specified element

◆ operator*() [1/5]

template<typename T >

HomogenousMatrixT4< T > Ocean::HomogenousMatrixT4< T >::operator* ( const HomogenousMatrixT4< T > & matrix ) const

Combines two transformation matrices.

Parameters

matrix Right transformation matrix

Returns: Combined transformation matrix

◆ operator*() [2/5]

template<typename T >

HomogenousMatrixT4< T > Ocean::HomogenousMatrixT4< T >::operator* ( const QuaternionT< T > & rotation ) const

Combines a transformation with a quaternion rotation.

Parameters

rotation The quaternion rotation to combine, must be valid

Returns: Combined transformation matrix

◆ operator*() [3/5]

template<typename T >

HomogenousMatrixT4< T > Ocean::HomogenousMatrixT4< T >::operator* ( const RotationT< T > & rotation ) const

Combines a transformation with a rotation.

Parameters

rotation The rotation to combine, must be valid

Returns: Combined transformation matrix

◆ operator*() [4/5]

template<typename T >

VectorT3< T > Ocean::HomogenousMatrixT4< T >::operator* ( const VectorT3< T > & vector ) const

inline

Transforms a 3D vector.

The vector will be extended with a 1.0 as fourth element and de-homogenized afterwards.

Parameters

vector The vector to transform

Returns: Resulting transformed and homogenized 3D vector

◆ operator*() [5/5]

template<typename T >

VectorT4< T > Ocean::HomogenousMatrixT4< T >::operator* ( const VectorT4< T > & vector ) const

inline

Transforms a 4D vector.

Parameters

vector The vector to transform

Returns: The resulting transformed 4D vector

◆ operator*=() [1/3]

template<typename T >

HomogenousMatrixT4< T > & Ocean::HomogenousMatrixT4< T >::operator*= ( const HomogenousMatrixT4< T > & matrix )

inline

Combines and assigns two transformation matrices.

Parameters

matrix Right transformation matrix

Returns: Reference to this transformation matrix

◆ operator*=() [2/3]

template<typename T >

HomogenousMatrixT4< T > & Ocean::HomogenousMatrixT4< T >::operator*= ( const QuaternionT< T > & rotation )

inline

Combines and assigns a transformation with a quaternion rotation.

Parameters

rotation The quaternion rotation to combine, must be valid

Returns: Reference to this transformation matrix

◆ operator*=() [3/3]

template<typename T >

HomogenousMatrixT4< T > & Ocean::HomogenousMatrixT4< T >::operator*= ( const RotationT< T > & rotation )

inline

Combines and assigns a transformation with a rotation.

Parameters

rotation The rotation to combine, must be valid

Returns: Reference to this transformation matrix

◆ operator=()

template<typename T >

HomogenousMatrixT4< T > & Ocean::HomogenousMatrixT4< T >::operator= ( const HomogenousMatrixT4< T > & )

default

Default copy assignment operator.

Returns: Reference to this object

◆ operator==()

template<typename T >

bool Ocean::HomogenousMatrixT4< T >::operator== ( const HomogenousMatrixT4< T > & matrix ) const

Returns whether two transformations are identical up to a small epsilon.

Parameters

matrix Right operand

Returns: True, if so

◆ operator[]() [1/2]

template<typename T >

T & Ocean::HomogenousMatrixT4< T >::operator[] ( const unsigned int index )

inline

Element operator.

Parameters

index The index of the element to return [0, 15]

Returns: Specified element

◆ operator[]() [2/2]

template<typename T >

T Ocean::HomogenousMatrixT4< T >::operator[] ( const unsigned int index ) const

inline

Element operator.

Parameters

index The index of the element to return [0, 15]

Returns: Specified element

◆ orthonormalRotationMatrix()

template<typename T >

SquareMatrixT3< T > Ocean::HomogenousMatrixT4< T >::orthonormalRotationMatrix ( ) const

Returns the 3x3 orthonormal rotation matrix of the 4x4 transformation (by forcing a orthogonal and normalized rotation matrix).

All vectors of the resulting rotation matrix have unit length.

Returns: The normalized rotation matrix

◆ rotation()

template<typename T >

QuaternionT< T > Ocean::HomogenousMatrixT4< T >::rotation ( ) const

Returns the rotation of the transformation as quaternion.

Returns: Rotation

◆ rotationMatrix() [1/3]

template<typename T >

SquareMatrixT3< T > Ocean::HomogenousMatrixT4< T >::rotationMatrix ( ) const

inline

Returns the rotation matrix of the transformation.

Returns: Rotation matrix containing scale

◆ rotationMatrix() [2/3]

template<typename T >

VectorT3< T > Ocean::HomogenousMatrixT4< T >::rotationMatrix ( const VectorT3< T > & vector ) const

inline

Transforms a 3D vector by application of only the inner rotation matrix (including scale and shearing) of this transformation.

Parameters

vector The vector to be transformed

Returns: Transformed 3D vector

◆ rotationMatrix() [3/3]

template<typename T >

void Ocean::HomogenousMatrixT4< T >::rotationMatrix	(	T *	data,
		const bool	transposed = `false`
	)		const

inline

Copies the 3x3 rotation matrix elements of the 4x4 transformation.

Parameters

data	The buffer receiving the nine rotation matrix elements, must be valid
transposed	True, to copy the transposed rotation matrix (to copy the array into a row major buffer); False, to copy the matrix into a column major buffer

◆ scale()

template<typename T >

VectorT3< T > Ocean::HomogenousMatrixT4< T >::scale ( ) const

Returns the scale of the transformation.

Returns: Transformation scale

◆ setRotation() [1/3]

template<typename T >

HomogenousMatrixT4< T > & Ocean::HomogenousMatrixT4< T >::setRotation ( const QuaternionT< T > & quaternion )

Sets the rotation of this transformation.

Parameters

quaternion The quaternion rotation to set, must be valid

Returns: Reference to this transformation matrix

◆ setRotation() [2/3]

template<typename T >

HomogenousMatrixT4< T > & Ocean::HomogenousMatrixT4< T >::setRotation ( const RotationT< T > & rotation )

Sets the rotation of this transformation.

Parameters

rotation The rotation to set, must be valid

Returns: Reference to this transformation matrix

◆ setRotation() [3/3]

template<typename T >

HomogenousMatrixT4< T > & Ocean::HomogenousMatrixT4< T >::setRotation ( const SquareMatrixT3< T > & matrix )

Sets the rotation of this transformation.

Parameters

matrix The 3x3 rotation matrix to set

Returns: Reference to this transformation matrix

◆ setTranslation()

template<typename T >

HomogenousMatrixT4< T > & Ocean::HomogenousMatrixT4< T >::setTranslation ( const VectorT3< T > & translation )

inline

Sets the translation of this transformation.

Parameters

translation The translation to set

Returns: Reference to this transformation matrix

◆ toIdentity()

template<typename T >

void Ocean::HomogenousMatrixT4< T >::toIdentity ( )

inline

Sets the matrix to the identity matrix.

See also: isIdentity().

◆ toNull()

template<typename T >

void Ocean::HomogenousMatrixT4< T >::toNull ( )

inline

Sets the matrix to a zero matrix (including the lower right element).

See also: isNull();

◆ trace()

template<typename T >

T Ocean::HomogenousMatrixT4< T >::trace ( ) const

inline

Returns the trace of the matrix which is the sum of the diagonal elements.

Returns: Trace of the matrix

◆ translation()

template<typename T >

VectorT3< T > Ocean::HomogenousMatrixT4< T >::translation ( ) const

inline

Returns the translation of the transformation.

Returns: Translation

◆ transposed()

template<typename T >

SquareMatrixT4< T > Ocean::HomogenousMatrixT4< T >::transposed ( ) const

Returns the transposed of this matrix.

Returns: Transposed matrix as square 4x4 matrix

◆ transposedRotationMatrix()

template<typename T >

VectorT3< T > Ocean::HomogenousMatrixT4< T >::transposedRotationMatrix ( const VectorT3< T > & vector ) const

inline

Transforms a 3D vector by application of only the inner transposed rotation matrix (including scale and shearing) of this transformation.

Parameters

vector The vector to be transformed

Returns: Transformed 3D vector

◆ xAxis()

template<typename T >

VectorT3< T > Ocean::HomogenousMatrixT4< T >::xAxis ( ) const

inline

Returns the x-axis of the transformation which is the first vector of the upper left 3x3 rotation matrix of this homogeneous 4x4 transformation.

Returns: The x-axis of this transformation

◆ yAxis()

template<typename T >

VectorT3< T > Ocean::HomogenousMatrixT4< T >::yAxis ( ) const

inline

Returns the y-axis of the transformation which is the second vector of the upper left 3x3 rotation matrix of this homogeneous 4x4 transformation.

Returns: The y-axis of this transformation

◆ zAxis()

template<typename T >

VectorT3< T > Ocean::HomogenousMatrixT4< T >::zAxis ( ) const

inline

Returns the z-axis of the transformation which is the first vector of the upper left 3x3 rotation matrix of this homogeneous 4x4 transformation.

Returns: The z-axis of this transformation

Friends And Related Symbol Documentation

◆ HomogenousMatrixT4

template<typename T >

template<typename U >

friend class HomogenousMatrixT4

friend

Field Documentation

◆ values_

template<typename T >

T Ocean::HomogenousMatrixT4< T >::values_[16]

protected

The sixteen values of the transformation matrix.

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

Public Types

Public Member Functions

Static Public Member Functions

Protected Attributes

Friends

Detailed Description

Member Typedef Documentation

◆ Type

Constructor & Destructor Documentation

◆ HomogenousMatrixT4() [1/27]

◆ HomogenousMatrixT4() [2/27]

◆ HomogenousMatrixT4() [3/27]

◆ HomogenousMatrixT4() [4/27]

◆ HomogenousMatrixT4() [5/27]

◆ HomogenousMatrixT4() [6/27]

◆ HomogenousMatrixT4() [7/27]

◆ HomogenousMatrixT4() [8/27]

◆ HomogenousMatrixT4() [9/27]

◆ HomogenousMatrixT4() [10/27]

◆ HomogenousMatrixT4() [11/27]

◆ HomogenousMatrixT4() [12/27]

◆ HomogenousMatrixT4() [13/27]

◆ HomogenousMatrixT4() [14/27]

◆ HomogenousMatrixT4() [15/27]

◆ HomogenousMatrixT4() [16/27]

◆ HomogenousMatrixT4() [17/27]

◆ HomogenousMatrixT4() [18/27]

◆ HomogenousMatrixT4() [19/27]

◆ HomogenousMatrixT4() [20/27]

◆ HomogenousMatrixT4() [21/27]

◆ HomogenousMatrixT4() [22/27]

◆ HomogenousMatrixT4() [23/27]

◆ HomogenousMatrixT4() [24/27]

◆ HomogenousMatrixT4() [25/27]

◆ HomogenousMatrixT4() [26/27]

◆ HomogenousMatrixT4() [27/27]

Member Function Documentation

◆ applyScale()

◆ copyElements() [1/2]

◆ copyElements() [2/2]

◆ data() [1/2]

◆ data() [2/2]

◆ decompose()

◆ determinant()

◆ invert() [1/2]

◆ invert() [2/2]

◆ inverted()

◆ isEqual()

◆ isIdentity()

◆ isNull()

◆ isValid()

◆ matrices2matrices() [1/4]

◆ matrices2matrices() [2/4]

◆ matrices2matrices() [3/4]

◆ matrices2matrices() [4/4]

◆ operator!=()

◆ operator()() [1/7]

◆ operator()() [2/7]

◆ operator()() [3/7]

◆ operator()() [4/7]

◆ operator()() [5/7]

◆ operator()() [6/7]

◆ operator()() [7/7]

◆ operator*() [1/5]

◆ operator*() [2/5]

◆ operator*() [3/5]

◆ operator*() [4/5]

◆ operator*() [5/5]

◆ operator*=() [1/3]

◆ operator*=() [2/3]

◆ operator*=() [3/3]

◆ operator=()

◆ operator==()

◆ operator[]() [1/2]

◆ operator[]() [2/2]

◆ orthonormalRotationMatrix()

◆ rotation()

◆ rotationMatrix() [1/3]

◆ rotationMatrix() [2/3]

◆ rotationMatrix() [3/3]