This class implements a 3x3 square matrix. More...

Inheritance diagram for Ocean::SquareMatrixT3< T >:

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

Public Member Functions
	SquareMatrixT3 ()
	Creates a new SquareMatrixT3 object with undefined elements. More...

	SquareMatrixT3 (const SquareMatrixT3< T > &matrix)=default
	Copy constructor. More...

template<typename U >
	SquareMatrixT3 (const SquareMatrixT3< U > &matrix)
	Copy constructor for a matrix with difference element data type than T. More...

	SquareMatrixT3 (const bool setToIdentity)
	Creates a new SquareMatrixT3 object. More...

	SquareMatrixT3 (const EulerT< T > &euler)
	Creates a new SquareMatrixT3 rotation matrix by a given Euler rotation. More...

	SquareMatrixT3 (const RotationT< T > &rotation)
	Creates a new 3x3 matrix object by a given angle-axis rotation. More...

	SquareMatrixT3 (const QuaternionT< T > &quaternion)
	Creates a new 3x3 matrix object by a given quaternion rotation. More...

	SquareMatrixT3 (const VectorT3< T > &xAxis, const VectorT3< T > &yAxis, const VectorT3< T > &zAxis)
	Creates a new SquareMatrixT3 object by three axes. More...

	SquareMatrixT3 (const VectorT3< T > &diagonal)
	Creates a new SquareMatrixT3 object by a given diagonal vector. More...

template<typename U >
	SquareMatrixT3 (const U *arrayValues)
	Creates a new SquareMatrixT3 object by nine elements of float type U. More...

	SquareMatrixT3 (const T *arrayValues)
	Creates a new SquareMatrixT3 object by nine elements. More...

template<typename U >
	SquareMatrixT3 (const U *arrayValues, const bool valuesRowAligned)
	Creates a new SquareMatrixT3 object by nine elements. More...

	SquareMatrixT3 (const T *arrayValues, const bool valuesRowAligned)
	Creates a new SquareMatrixT3 object by nine elements. More...

	SquareMatrixT3 (const HomogenousMatrixT4< T > &transformation)
	Creates a 3x3 rotation matrix by a given 4x4 homogeneous transformation. More...

	SquareMatrixT3 (const SquareMatrixT4< T > &transformation)
	Creates a 3x3 square matrix by a given 4x4 square transformation. More...

	SquareMatrixT3 (const T &m00, const T &m10, const T &m20, const T &m01, const T &m11, const T &m21, const T &m02, const T &m12, const T &m22)
	Creates a 3x3 rotation matrix by 9 given matrix elements. More...

SquareMatrixT3< T >	transposed () const
	Returns the transposed of this matrix. More...

void	transpose ()
	Transposes the matrix. More...

SquareMatrixT3< T >	inverted () const
	Returns the inverted matrix of this matrix. More...

bool	invert ()
	Inverts this matrix in place. More...

bool	invert (SquareMatrixT3< T > &invertedMatrix) const
	Inverts the matrix and returns the result as parameter. More...

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

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

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

void	toNull ()
	Sets the matrix to a zero matrix. More...

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

bool	isNull () const
	Returns whether this matrix is a zero matrix. More...

bool	isSingular () const
	Returns whether this matrix is singular (and thus cannot be inverted). More...

bool	isSimilarity () const
	Returns true if this matrix is a similarity transformation. More...

bool	isAffine () const
	Returns true if this matrix is a affine transformation. More...

bool	isHomography () const
	Returns true if this matrix is perspective transform/homography. More...

bool	isOrthonormal (const T epsilon=NumericT< T >::eps()) const
	Returns whether this matrix is an orthonormal matrix. More...

bool	isSymmetric (const T epsilon=NumericT< T >::eps()) const
	Returns whether this matrix is symmetric. More...

bool	isEqual (const SquareMatrixT3< T > &matrix, const T eps=NumericT< T >::eps()) const
	Returns whether two matrices are almost identical up to a specified epsilon. More...

VectorT3< T >	xAxis () const
	Returns the x axis which is the first column of the matrix. More...

VectorT3< T >	yAxis () const
	Returns the y axis which is the middle column of the matrix. More...

VectorT3< T >	zAxis () const
	Returns the z axis which is the last column of the matrix. More...

SquareMatrixT3< T >	orthonormalMatrix () const
	Returns the orthonormal matrix of this matrix by scaling the x-axis and adjusting y- and z-axis. More...

bool	eigenValues (T *eigenValues) const
	Determines the eigen values of this matrix. More...

bool	eigenSystem (T eigenValues, VectorT3< T > eigenVectors) const
	Performs an eigen value analysis. More...

VectorT3< T >	diagonal () const
	Returns a 3d vector with values of the matrix diagonal. More...

bool	solve (const VectorT3< T > &b, VectorT3< T > &x) const
	Solve a simple 3x3 system of linear equations: Ax = b Beware: The system of linear equations is assumed to be fully determined. More...

T	absSum () const
	Calculates the sum of absolute value of elements. More...

T	sum () const
	Calculates the sum of elements. More...

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

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

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 type U. More...

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

bool	multiply (const VectorT2< T > &vector, VectorT2< T > &result) const
	Multiplies a 2D vector with this matrix (from the right). More...

SquareMatrixT3< T >	transposedMultiply (const SquareMatrixT3< T > &right) const
	Multiplies this transposed matrix with a second matrix. More...

SquareMatrixT3< T > &	operator= (const SquareMatrixT3< T > &)=default
	Default copy assignment operator. More...

bool	operator== (const SquareMatrixT3< T > &matrix) const
	Returns whether two matrices are identical up to a small epsilon. More...

bool	operator!= (const SquareMatrixT3< T > &matrix) const
	Returns whether two matrices are not identical up to a small epsilon. More...

SquareMatrixT3< T >	operator+ (const SquareMatrixT3< T > &matrix) const
	Adds two matrices. More...

SquareMatrixT3< T > &	operator+= (const SquareMatrixT3< T > &matrix)
	Adds and assigns two matrices. More...

SquareMatrixT3< T >	operator- (const SquareMatrixT3< T > &matrix) const
	Subtracts two matrices. More...

SquareMatrixT3< T > &	operator-= (const SquareMatrixT3< T > &matrix)
	Subtracts and assigns two matrices. More...

SquareMatrixT3< T >	operator- () const
	Returns the negative matrix of this matrix (all matrix elements are multiplied by -1). More...

OCEAN_FORCE_INLINE SquareMatrixT3< T >	operator* (const SquareMatrixT3< T > &matrix) const
	Multiplies two matrices. More...

OCEAN_FORCE_INLINE SquareMatrixT3< T > &	operator*= (const SquareMatrixT3< T > &matrix)
	Multiplies and assigns two matrices. More...

OCEAN_FORCE_INLINE VectorT2< T >	operator* (const VectorT2< T > &vector) const
	Multiply operator for a 2D vector. More...

OCEAN_FORCE_INLINE VectorT3< T >	operator* (const VectorT3< T > &vector) const
	Multiply operator for a 3D vector. More...

OCEAN_FORCE_INLINE SquareMatrixT3< T >	operator* (const T value) const
	Multiplies this matrix with a scalar value. More...

SquareMatrixT3< T > &	operator*= (const T value)
	Multiplies and assigns this matrix with a scalar value. More...

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

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

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

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

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

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

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

T *	operator() ()
	Access operator. More...

size_t	operator() (const SquareMatrixT3< T > &matrix) const
	Hash function. More...

OCEAN_FORCE_INLINE VectorT3< double >	operator* (const VectorT3< double > &vector) const

OCEAN_FORCE_INLINE VectorT3< float >	operator* (const VectorT3< float > &vector) const

void	multiply (const SquareMatrixT3< float > &matrix, const VectorT3< float > vectors, VectorT3< float > results, const size_t number)

std::vector< SquareMatrixT3< float > >	matrices2matrices (const std::vector< SquareMatrixT3< float > > &matrices)

std::vector< SquareMatrixT3< double > >	matrices2matrices (const std::vector< SquareMatrixT3< double > > &matrices)

template<typename U >
std::vector< SquareMatrixT3< T > >	matrices2matrices (const SquareMatrixT3< U > *matrices, const size_t size)

Static Public Member Functions
static SquareMatrixT3< T >	skewSymmetricMatrix (const VectorT3< T > &vector)
	Creates a skew symmetric 3x3 matrix for a specific vector. More...

static size_t	elements ()
	Returns the number of elements this matrix has. More...

static void	multiply (const SquareMatrixT3< T > &matrix, const VectorT2< T > vectors, VectorT2< T > results, const size_t number)
	Multiplies several 2D vectors with a given 3x3 matrix. More...

static void	multiply (const SquareMatrixT3< T > &matrix, const VectorT3< T > vectors, VectorT3< T > results, const size_t number)
	Multiplies several 3D vectors with a given 3x3 matrix. More...

template<typename U >
static SquareMatricesT3< T >	matrices2matrices (const SquareMatricesT3< U > &matrices)
	Converts matrices with specific data type to matrices with different data type. More...

template<typename U >
static SquareMatricesT3< T >	matrices2matrices (const SquareMatrixT3< U > *matrices, const size_t size)
	Converts matrices with specific data type to matrices with different data type. More...

Protected Attributes
T	values_ [9]
	The nine values of the matrix. More...

Friends
template<typename U >
class	SquareMatrixT3

Detailed Description

template<typename T>
class Ocean::SquareMatrixT3< T >

This class implements a 3x3 square matrix.

The matrix can be applied as e.g., rotation matrix for 3D vectors or can represent a Homography and so on.
The values are stored in a column aligned order with indices:

| 0 3 6 |
| 1 4 7 |
| 2 5 8 |

Template Parameters

T	Data type of matrix elements

See also: SquareMatrix3, SquareMatrixF3, SquareMatrixD3, Rotation, Euler, Quaternion, ExponentialMap.

Member Typedef Documentation

◆ Type

template<typename T >

typedef T Ocean::SquareMatrixT3< T >::Type

Definition of the used data type.

Constructor & Destructor Documentation

◆ SquareMatrixT3() [1/16]

template<typename T >

Ocean::SquareMatrixT3< T >::SquareMatrixT3

inline

Creates a new SquareMatrixT3 object with undefined elements.

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

◆ SquareMatrixT3() [2/16]

template<typename T >

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

default

Copy constructor.

Parameters

matrix The matrix to copy

◆ SquareMatrixT3() [3/16]

template<typename T >

template<typename U >

Ocean::SquareMatrixT3< T >::SquareMatrixT3 ( const SquareMatrixT3< 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

◆ SquareMatrixT3() [4/16]

template<typename T >

Ocean::SquareMatrixT3< T >::SquareMatrixT3 ( const bool setToIdentity )

explicit

Creates a new SquareMatrixT3 object.

Parameters

setToIdentity Determines whether a entity matrix will be created, otherwise the matrix is initialized with zeros

◆ SquareMatrixT3() [5/16]

template<typename T >

Ocean::SquareMatrixT3< T >::SquareMatrixT3 ( const EulerT< T > & euler )

explicit

Creates a new SquareMatrixT3 rotation matrix by a given Euler rotation.

Parameters

euler Euler rotation to create a rotation matrix from, must be valid

Rotation matrix around x-axis R(x): [ 1 0 0 ] [ 0 cos -sin ] [ 0 sin cos ]

Rotation matrix around y-axis R(y): [ cos 0 sin ] [ 0 1 0 ] [ -sin 0 cos ]

Rotation matrix around z-axis R(z): [ cos -sin 0 ] [ sin cos 0 ] [ 0 0 1 ]

Combined rotation matrix for R(y)R(x)R(z) [ cy cz + sx sy sz cz sx sy - cy sz cx sy ] [ cx sz cx cz -sx ] [ -cz sy + cy sx sz cy cz sx + sy sz cx cy ]

◆ SquareMatrixT3() [6/16]

template<typename T >

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

explicit

Creates a new 3x3 matrix object by a given angle-axis rotation.

Parameters

rotation The angle-axis rotation to create a matrix from, must be valid

◆ SquareMatrixT3() [7/16]

template<typename T >

Ocean::SquareMatrixT3< T >::SquareMatrixT3 ( const QuaternionT< T > & quaternion )

explicit

Creates a new 3x3 matrix object by a given quaternion rotation.

Parameters

quaternion The quaternion rotation to create a matrix from, must be valid

◆ SquareMatrixT3() [8/16]

template<typename T >

Ocean::SquareMatrixT3< T >::SquareMatrixT3	(	const VectorT3< T > &	xAxis,
		const VectorT3< T > &	yAxis,
		const VectorT3< T > &	zAxis
	)

Creates a new SquareMatrixT3 object by three axes.

Parameters

xAxis	First column of the matrix
yAxis	Middle column of the matrix
zAxis	Last column of the matrix

◆ SquareMatrixT3() [9/16]

template<typename T >

Ocean::SquareMatrixT3< T >::SquareMatrixT3 ( const VectorT3< T > & diagonal )

explicit

Creates a new SquareMatrixT3 object by a given diagonal vector.

Parameters

diagonal The diagonal vector for the new matrix

◆ SquareMatrixT3() [10/16]

template<typename T >

template<typename U >

Ocean::SquareMatrixT3< T >::SquareMatrixT3 ( const U * arrayValues )

explicit

Creates a new SquareMatrixT3 object by nine elements of float type U.

Parameters

arrayValues The nine matrix elements defining the new matrix, must be valid

Template Parameters

U	The floating point type of the given elements

◆ SquareMatrixT3() [11/16]

template<typename T >

Ocean::SquareMatrixT3< T >::SquareMatrixT3 ( const T * arrayValues )

explicit

Creates a new SquareMatrixT3 object by nine elements.

Parameters

arrayValues The nine matrix elements defining the new matrix, must be valid

◆ SquareMatrixT3() [12/16]

template<typename T >

template<typename U >

Ocean::SquareMatrixT3< T >::SquareMatrixT3	(	const U *	arrayValues,
		const bool	valuesRowAligned
	)

Creates a new SquareMatrixT3 object by nine elements.

Parameters

arrayValues	The nine 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

◆ SquareMatrixT3() [13/16]

template<typename T >

Ocean::SquareMatrixT3< T >::SquareMatrixT3	(	const T *	arrayValues,
		const bool	valuesRowAligned
	)

Creates a new SquareMatrixT3 object by nine elements.

Parameters

arrayValues	The nine 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)

◆ SquareMatrixT3() [14/16]

template<typename T >

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

explicit

Creates a 3x3 rotation matrix by a given 4x4 homogeneous transformation.

Parameters

transformation The transformation to create a 3x3 rotation matrix from

◆ SquareMatrixT3() [15/16]

template<typename T >

Ocean::SquareMatrixT3< T >::SquareMatrixT3 ( const SquareMatrixT4< T > & transformation )

explicit

Creates a 3x3 square matrix by a given 4x4 square transformation.

Parameters

transformation The transformation to create a 3x3 square matrix from

◆ SquareMatrixT3() [16/16]

template<typename T >

Ocean::SquareMatrixT3< T >::SquareMatrixT3	(	const T &	m00,
		const T &	m10,
		const T &	m20,
		const T &	m01,
		const T &	m11,
		const T &	m21,
		const T &	m02,
		const T &	m12,
		const T &	m22
	)

explicit

Creates a 3x3 rotation matrix by 9 given matrix elements.

Parameters

m00	Element of the first row and first column
m10	Element of the second row and first column
m20	Element of the third row and first column
m01	Element of the first row and second column
m11	Element of the second row and second column
m21	Element of the third row and second column
m02	Element of the first row and third column
m12	Element of the second row and third column
m22	Element of the third row and third column

Member Function Documentation

◆ absSum()

template<typename T >

T Ocean::SquareMatrixT3< T >::absSum

inline

Calculates the sum of absolute value of elements.

Returns: Sum of absolute value of elements

◆ copyElements() [1/2]

template<typename T >

void Ocean::SquareMatrixT3< T >::copyElements	(	T *	arrayValues,
		const bool	valuesRowAligned = `false`
	)		const

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

Parameters

arrayValues	Array with 9 floating point values of type T receiving the elements of this matrix
valuesRowAligned	True, if the target values are stored in a row aligned order; False, if the target values are stored in a column aligned order

◆ copyElements() [2/2]

template<typename T >

template<typename U >

void Ocean::SquareMatrixT3< T >::copyElements	(	U *	arrayValues,
		const bool	valuesRowAligned = `false`
	)		const

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

Parameters

arrayValues	Array with 9 floating point values of type U receiving the elements of this matrix
valuesRowAligned	True, if the target values are stored in a row aligned order; False, if the target values are stored in a column aligned order

Template Parameters

U	Floating point type

◆ data() [1/2]

template<typename T >

T * Ocean::SquareMatrixT3< T >::data

inline

Returns a pointer to the internal values.

Returns: Pointer to the internal values

◆ data() [2/2]

template<typename T >

const T * Ocean::SquareMatrixT3< T >::data

inline

Returns a pointer to the internal values.

Returns: Pointer to the internal values

◆ determinant()

template<typename T >

T Ocean::SquareMatrixT3< T >::determinant

Returns the determinant of the matrix.

Returns: Matrix determinant

◆ diagonal()

template<typename T >

VectorT3< T > Ocean::SquareMatrixT3< T >::diagonal

Returns a 3d vector with values of the matrix diagonal.

Returns: Vector with diagonal values

◆ eigenSystem()

template<typename T >

bool Ocean::SquareMatrixT3< T >::eigenSystem	(	T *	eigenValues,
		VectorT3< T > *	eigenVectors
	)		const

Performs an eigen value analysis.

Parameters

eigenValues	The three resulting eigen values, sorted: the highest first
eigenVectors	The three corresponding eigen vectors

Returns: True, if succeeded

Computation of the characteristic polynomial

    [ a b c ]
A = [ d e f ]
    [ g h i ]

            [ a-x   b    c  ]
A - x * E = [  d   e-x   f  ]
            [  g    h   i-x ]

Polynomial = Det|A - x * E| = 0
           = (a - x) * (e - x)          * (i - x) + bfg + cdh - g * (e - x) * c  - h * f * (a - x)  - (i - x) * d * b
           = (ae - a * x - e * x + x^2) * (i - x) + bfg + cdh - g * (ec - c * x) - h * (fa - f * x) - d * (ib - x * b)
           = aei - ae * x - ai * x + a * x^2 - ei * x + e * x^2 + i * x^2 - x^3 + bfg + cdh - gec + gc * x - hfa + hf * x - dib + db * x
           = -x^3 + (a + e + i) * x^2 + (-ae - ai - ei + gc + hf + db) * x + aei + bfg + cdh - gec - hfa - dib
           = x^3 - (a + e + i) * x^2 - (-ae - ai - ei + gc + hf + db) * x - aei - bfg - cdh + gec + hfa + dib
           = a1x^3 + a2x^2 + a3x + a4 = 0

Determination of the eigen vectors (vx, vy, vz):
            [ a-x   b    c  ]   [ vx ]
A - x * E = [  d   e-x   f  ] * [ vy ] = 0
            [  g    h   i-x ]   [ vz ]
We can apply the cross product to find a vector that is perpendicular to the two top rows of the matrix A - x * E

◆ eigenValues()

template<typename T >

bool Ocean::SquareMatrixT3< T >::eigenValues ( T * eigenValues ) const

Determines the eigen values of this matrix.

Parameters

eigenValues The three resulting eigen values, sorted: the highest first

Returns: True, if succeeded

Computation of the characteristic polynomial


    [ a b c ]
A = [ d e f ]
    [ g h i ]

            [ a-x   b    c  ]
A - x * E = [  d   e-x   f  ]
            [  g    h   i-x ]

Polynomial = Det|A - x * E| = 0
           = (a - x) * (e - x)          * (i - x) + bfg + cdh - g * (e - x) * c  - h * f * (a - x)  - (i - x) * d * b
           = (ae - a * x - e * x + x^2) * (i - x) + bfg + cdh - g * (ec - c * x) - h * (fa - f * x) - d * (ib - x * b)
           = aei - ae * x - ai * x + a * x^2 - ei * x + e * x^2 + i * x^2 - x^3 + bfg + cdh - gec + gc * x - hfa + hf * x - dib + db * x
           = -x^3 + (a + e + i) * x^2 + (-ae - ai - ei + gc + hf + db) * x + aei + bfg + cdh - gec - hfa - dib
           = x^3 - (a + e + i) * x^2 - (-ae - ai - ei + gc + hf + db) * x - aei - bfg - cdh + gec + hfa + dib
           = a1x^3 + a2x^2 + a3x + a4 = 0

◆ elements()

template<typename T >

size_t Ocean::SquareMatrixT3< T >::elements

inlinestatic

Returns the number of elements this matrix has.

Returns: The number of elements, always 9

◆ invert() [1/2]

template<typename T >

bool Ocean::SquareMatrixT3< T >::invert

Inverts this matrix in place.

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

See also: inverted(), solve().

◆ invert() [2/2]

template<typename T >

bool Ocean::SquareMatrixT3< T >::invert ( SquareMatrixT3< T > & invertedMatrix ) const

Inverts the matrix and returns the result as parameter.

Parameters

invertedMatrix The resulting inverted matrix

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

See also: inverted(), solve().

◆ inverted()

template<typename T >

SquareMatrixT3< T > Ocean::SquareMatrixT3< T >::inverted

Returns the inverted matrix of this matrix.

This matrix must not be singular.
Beware: This function does not throw an exception if the matrix cannot be inverted.
Thus, 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 also: invert(), isSingular().

◆ isAffine()

template<typename T >

bool Ocean::SquareMatrixT3< T >::isAffine

inline

Returns true if this matrix is a affine transformation.

In order to be considered affine, the matrix mustn't be singular and the last row must be equivalent to [0 0 1].

Returns: True, if this matrix is an affine transformation, otherwise false

◆ isEqual()

template<typename T >

bool Ocean::SquareMatrixT3< T >::isEqual	(	const SquareMatrixT3< T > &	matrix,
		const T	eps = `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
eps	The epsilon threshold to be used, with range [0, infinity)

Returns: True, if so

◆ isHomography()

template<typename T >

bool Ocean::SquareMatrixT3< T >::isHomography

inline

Returns true if this matrix is perspective transform/homography.

In order to be considered a homography, the matrix mustn't be singular and the bottom-right matrix element must be nonzero.

Returns: True, if this matrix is a homography, otherwise false

◆ isIdentity()

template<typename T >

bool Ocean::SquareMatrixT3< T >::isIdentity

Returns whether this matrix is an identity matrix.

Returns: True, if so

See also: toIdentity().

◆ isNull()

template<typename T >

bool Ocean::SquareMatrixT3< T >::isNull

Returns whether this matrix is a zero matrix.

Returns: True, if so

See also: toNull().

◆ isOrthonormal()

template<typename T >

bool Ocean::SquareMatrixT3< T >::isOrthonormal ( const T epsilon = NumericT<T>::eps() ) const

Returns whether this matrix is an orthonormal matrix.

Parameters

epsilon The epsilon threshold to be used, with range [0, infinity)

Returns: True, if so

◆ isSimilarity()

template<typename T >

bool Ocean::SquareMatrixT3< T >::isSimilarity

inline

Returns true if this matrix is a similarity transformation.

A similarity transformation has four degrees of freedom and contains a rotation, a scale, and a 2D translation and is not singular.
The 3x3 matrix representing the similarity transformation has the following layout:

| a  -b  tx |
| b   a  ty |
| 0   0   1 |

Returns: True, if this matrix is a similarity transformation, otherwise false

◆ isSingular()

template<typename T >

bool Ocean::SquareMatrixT3< T >::isSingular

inline

Returns whether this matrix is singular (and thus cannot be inverted).

A matrix is singular if the determinant of a matrix is 0.

Returns: True, if so

◆ isSymmetric()

template<typename T >

bool Ocean::SquareMatrixT3< T >::isSymmetric ( const T epsilon = NumericT<T>::eps() ) const

inline

Returns whether this matrix is symmetric.

Parameters

epsilon The epsilon threshold to be used, with range [0, infinity)

Returns: True, if so

◆ matrices2matrices() [1/5]

template<typename T >

template<typename U >

SquareMatricesT3< T > Ocean::SquareMatrixT3< T >::matrices2matrices ( const SquareMatricesT3< 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

◆ matrices2matrices() [2/5]

template<typename T >

template<typename U >

static SquareMatricesT3<T> Ocean::SquareMatrixT3< T >::matrices2matrices	(	const SquareMatrixT3< 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() [3/5]

template<typename T >

template<typename U >

std::vector< SquareMatrixT3<T> > Ocean::SquareMatrixT3< T >::matrices2matrices	(	const SquareMatrixT3< U > *	matrices,
		const size_t	size
	)

inline

◆ matrices2matrices() [4/5]

std::vector< SquareMatrixT3< double > > Ocean::SquareMatrixT3< double >::matrices2matrices ( const std::vector< SquareMatrixT3< double > > & matrices )

inline

◆ matrices2matrices() [5/5]

std::vector< SquareMatrixT3< float > > Ocean::SquareMatrixT3< float >::matrices2matrices ( const std::vector< SquareMatrixT3< float > > & matrices )

inline

◆ multiply() [1/4]

void Ocean::SquareMatrixT3< float >::multiply	(	const SquareMatrixT3< float > &	matrix,
		const VectorT3< float > *	vectors,
		VectorT3< float > *	results,
		const size_t	number
	)

inline

◆ multiply() [2/4]

template<typename T >

void Ocean::SquareMatrixT3< T >::multiply	(	const SquareMatrixT3< T > &	matrix,
		const VectorT2< T > *	vectors,
		VectorT2< T > *	results,
		const size_t	number
	)

static

Multiplies several 2D vectors with a given 3x3 matrix.

Each 2D vector is interpreted as a 3D vector with third component equal to 1.
The final result will be de-homogenized to provide a 2D vector result.

Parameters

matrix	The matrix to be used for multiplication
vectors	The input vectors that will be multiplied, may be nullptr if number is 0
results	The resulting output (multiplied/transformed) vectors, with same number as the provided input vectors
number	The number of provided vectors (input and output), with range [0, infinity)

◆ multiply() [3/4]

template<typename T >

void Ocean::SquareMatrixT3< T >::multiply	(	const SquareMatrixT3< T > &	matrix,
		const VectorT3< T > *	vectors,
		VectorT3< T > *	results,
		const size_t	number
	)

static

Multiplies several 3D vectors with a given 3x3 matrix.

Parameters

matrix	The matrix to be used for multiplication
vectors	The input vectors that will be multiplied, may be nullptr if number is 0
results	The resulting output (multiplied/transformed) vectors, with same number as the provided input vectors
number	The number of provided vectors (input and output), with range [0, infinity)

◆ multiply() [4/4]

template<typename T >

bool Ocean::SquareMatrixT3< T >::multiply	(	const VectorT2< T > &	vector,
		VectorT2< T > &	result
	)		const

inline

Multiplies a 2D vector with this matrix (from the right).

The 2D vector is interpreted as a 3D vector with third component equal to 1.
This function is equivalent with the corresponding multiplication operator but returns False if the dot product between the augmented vector and the last row is zero.
The multiplication result will be de-homogenized to provide a 2D vector result, if possible.
Actually this function does:

Parameters

vector	The vector to be multiplied/transformed
result	The de-homogenized resulting 2D vector, if this function succeeds

Returns: True, if the dot product between the augmented vector and the last row is non-zero; False, otherwise

See also: operator*(const VectorT2<T>& vector).

| x' | | 0 3 6 | | x | | y' | = | 1 4 7 | * | y | | 1 | | 2 5 8 | | 1 |

◆ operator!=()

template<typename T >

bool Ocean::SquareMatrixT3< T >::operator!= ( const SquareMatrixT3< T > & matrix ) const

inline

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

Parameters

matrix Right operand

Returns: True, if so

◆ operator()() [1/7]

template<typename T >

T * Ocean::SquareMatrixT3< T >::operator()

inline

Access operator.

Returns: Pointer to the internal values

◆ operator()() [2/7]

template<typename T >

const T * Ocean::SquareMatrixT3< T >::operator()

inline

Access operator.

Returns: Pointer to the internal values

◆ operator()() [3/7]

template<typename T >

size_t Ocean::SquareMatrixT3< T >::operator() ( const SquareMatrixT3< 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::SquareMatrixT3< T >::operator() ( const unsigned int index )

inline

Element operator.

Beware: No range check will be done!

Parameters

index The index of the element to return [0, 8]

Returns: Specified element

◆ operator()() [5/7]

template<typename T >

T Ocean::SquareMatrixT3< T >::operator() ( const unsigned int index ) const

inline

Element operator.

Beware: No range check will be done!

Parameters

index The index of the element to return [0, 8]

Returns: Specified element

◆ operator()() [6/7]

template<typename T >

T & Ocean::SquareMatrixT3< T >::operator()	(	const unsigned int	row,
		const unsigned int	column
	)

inline

Element operator.

Beware: No range check will be done!

Parameters

row	The row of the element to return [0, 2]
column	The column of the element to return [0, 2]

Returns: Specified element

◆ operator()() [7/7]

template<typename T >

T Ocean::SquareMatrixT3< T >::operator()	(	const unsigned int	row,
		const unsigned int	column
	)		const

inline

Element operator.

Beware: No range check will be done!

Parameters

row	The row of the element to return [0, 2]
column	The column of the element to return [0, 2]

Returns: Specified element

◆ operator*() [1/6]

template<typename T >

OCEAN_FORCE_INLINE SquareMatrixT3< T > Ocean::SquareMatrixT3< T >::operator* ( const SquareMatrixT3< T > & matrix ) const

Multiplies two matrices.

Parameters

matrix Right operand

Returns: Product matrix

◆ operator*() [2/6]

template<typename T >

SquareMatrixT3< T > Ocean::SquareMatrixT3< T >::operator* ( const T value ) const

Multiplies this matrix with a scalar value.

Parameters

value Right operand

Returns: Resulting matrix

◆ operator*() [3/6]

template<typename T >

OCEAN_FORCE_INLINE VectorT2< T > Ocean::SquareMatrixT3< T >::operator* ( const VectorT2< T > & vector ) const

Multiply operator for a 2D vector.

The 2D vector is interpreted as a 3D vector with third component equal to 1.
The final result will be de-homogenized to provide a 2D vector result.
Beware the dot product between the last row and the (augmented) vector must not be zero!

Parameters

vector Right operand, vector to be multiplied from the right

Returns: Resulting 2D vector

See also: multiply().

| x' | | 0 3 6 | | x | | y' | = | 1 4 7 | * | y | | 1 | | 2 5 8 | | 1 |

◆ operator*() [4/6]

OCEAN_FORCE_INLINE VectorT3< double > Ocean::SquareMatrixT3< double >::operator* ( const VectorT3< double > & vector ) const

◆ operator*() [5/6]

OCEAN_FORCE_INLINE VectorT3< float > Ocean::SquareMatrixT3< float >::operator* ( const VectorT3< float > & vector ) const

◆ operator*() [6/6]

template<typename T >

OCEAN_FORCE_INLINE VectorT3< T > Ocean::SquareMatrixT3< T >::operator* ( const VectorT3< T > & vector ) const

Multiply operator for a 3D vector.

Parameters

vector Right operand

Returns: Resulting 3D vector

◆ operator*=() [1/2]

template<typename T >

SquareMatrixT3< T > & Ocean::SquareMatrixT3< T >::operator*= ( const SquareMatrixT3< T > & matrix )

inline

Multiplies and assigns two matrices.

Parameters

matrix Right operand

Returns: Reference to this object

◆ operator*=() [2/2]

template<typename T >

SquareMatrixT3< T > & Ocean::SquareMatrixT3< T >::operator*= ( const T value )

Multiplies and assigns this matrix with a scalar value.

Parameters

value right operand

Returns: Reference to this object

◆ operator+()

template<typename T >

SquareMatrixT3< T > Ocean::SquareMatrixT3< T >::operator+ ( const SquareMatrixT3< T > & matrix ) const

Adds two matrices.

Parameters

matrix Right operand

Returns: Sum matrix

◆ operator+=()

template<typename T >

SquareMatrixT3< T > & Ocean::SquareMatrixT3< T >::operator+= ( const SquareMatrixT3< T > & matrix )

Adds and assigns two matrices.

Parameters

matrix Right operand

Returns: Reference to this object

◆ operator-() [1/2]

template<typename T >

SquareMatrixT3< T > Ocean::SquareMatrixT3< T >::operator-

inline

Returns the negative matrix of this matrix (all matrix elements are multiplied by -1).

Returns: Resulting negative matrix

◆ operator-() [2/2]

template<typename T >

SquareMatrixT3< T > Ocean::SquareMatrixT3< T >::operator- ( const SquareMatrixT3< T > & matrix ) const

Subtracts two matrices.

Parameters

matrix Right operand

Returns: Difference matrix

◆ operator-=()

template<typename T >

SquareMatrixT3< T > & Ocean::SquareMatrixT3< T >::operator-= ( const SquareMatrixT3< T > & matrix )

Subtracts and assigns two matrices.

Parameters

matrix Right operand

Returns: Reference to this object

◆ operator=()

template<typename T >

SquareMatrixT3<T>& Ocean::SquareMatrixT3< T >::operator= ( const SquareMatrixT3< T > & )

default

Default copy assignment operator.

Returns: Reference to this object

◆ operator==()

template<typename T >

bool Ocean::SquareMatrixT3< T >::operator== ( const SquareMatrixT3< T > & matrix ) const

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

Parameters

matrix Right operand

Returns: True, if so

◆ operator[]() [1/2]

template<typename T >

T & Ocean::SquareMatrixT3< T >::operator[] ( const unsigned int index )

inline

Element operator.

Beware: No range check will be done!

Parameters

index The index of the element to return [0, 8]

Returns: Specified element

◆ operator[]() [2/2]

template<typename T >

T Ocean::SquareMatrixT3< T >::operator[] ( const unsigned int index ) const

inline

Element operator.

Beware: No range check will be done!

Parameters

index The index of the element to return [0, 8]

Returns: Specified element

◆ orthonormalMatrix()

template<typename T >

SquareMatrixT3< T > Ocean::SquareMatrixT3< T >::orthonormalMatrix

Returns the orthonormal matrix of this matrix by scaling the x-axis and adjusting y- and z-axis.

This matrix must not be singular.

Returns: An orthonormal version of this matrix

◆ skewSymmetricMatrix()

template<typename T >

SquareMatrixT3< T > Ocean::SquareMatrixT3< T >::skewSymmetricMatrix ( const VectorT3< T > & vector )

inlinestatic

Creates a skew symmetric 3x3 matrix for a specific vector.

The skew symmetric matrix allows to calculate the cross product of the specified vector with a second vector by a matrix multiplication.
That means: skewSymmetricMatrix(vectorA) * vectorB == vectorA.cross(vectorB)
The final matrix has the following form for a vector (v0, v1, v2):

|  0   -v2    v1 |
| v2     0   -v0 |
| -v1   v0     0 |

Parameters

vector The vector for which the skew symmetric matrix will be created

Returns: Resulting matrix

◆ solve()

template<typename T >

bool Ocean::SquareMatrixT3< T >::solve	(	const VectorT3< T > &	b,
		VectorT3< T > &	x
	)		const

inline

Solve a simple 3x3 system of linear equations: Ax = b Beware: The system of linear equations is assumed to be fully determined.

Parameters

b	The right-hand side vector
x	The resulting solution vector

Returns: True, if the solution is valid, otherwise false

See also: invert(), inverted().

◆ sum()

template<typename T >

T Ocean::SquareMatrixT3< T >::sum

inline

Calculates the sum of elements.

Returns: Sum of elements

◆ toIdentity()

template<typename T >

void Ocean::SquareMatrixT3< T >::toIdentity

inline

Sets the matrix to the identity matrix.

See also: isIdentity().

◆ toNull()

template<typename T >

void Ocean::SquareMatrixT3< T >::toNull

inline

Sets the matrix to a zero matrix.

See also: isNull();

◆ trace()

template<typename T >

T Ocean::SquareMatrixT3< T >::trace

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

Returns: Trace of the matrix

◆ transpose()

template<typename T >

void Ocean::SquareMatrixT3< T >::transpose

Transposes the matrix.

◆ transposed()

template<typename T >

SquareMatrixT3< T > Ocean::SquareMatrixT3< T >::transposed

Returns the transposed of this matrix.

Returns: Transposed matrix

◆ transposedMultiply()

template<typename T >

SquareMatrixT3< T > Ocean::SquareMatrixT3< T >::transposedMultiply ( const SquareMatrixT3< T > & right ) const

Multiplies this transposed matrix with a second matrix.

Actually, the following matrix will be returned: (*this).transposed() * right.

Parameters

right Matrix to multiply

Returns: Matrix product

◆ xAxis()

template<typename T >

VectorT3< T > Ocean::SquareMatrixT3< T >::xAxis

Returns the x axis which is the first column of the matrix.

Returns: Vector with the first column

◆ yAxis()

template<typename T >

VectorT3< T > Ocean::SquareMatrixT3< T >::yAxis

Returns the y axis which is the middle column of the matrix.

Returns: Vector with the middle column

◆ zAxis()

template<typename T >

VectorT3< T > Ocean::SquareMatrixT3< T >::zAxis

Returns the z axis which is the last column of the matrix.

Returns: Vector with the last column

Friends And Related Function Documentation

◆ SquareMatrixT3

template<typename T >

template<typename U >

friend class SquareMatrixT3

friend

Field Documentation

◆ values_

template<typename T >

T Ocean::SquareMatrixT3< T >::values_[9]

protected

The nine values of the 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

template<typename T> class Ocean::SquareMatrixT3< T >

Member Typedef Documentation

◆ Type

Constructor & Destructor Documentation

◆ SquareMatrixT3() [1/16]

◆ SquareMatrixT3() [2/16]

◆ SquareMatrixT3() [3/16]

◆ SquareMatrixT3() [4/16]

◆ SquareMatrixT3() [5/16]

◆ SquareMatrixT3() [6/16]

◆ SquareMatrixT3() [7/16]

◆ SquareMatrixT3() [8/16]

◆ SquareMatrixT3() [9/16]

◆ SquareMatrixT3() [10/16]

◆ SquareMatrixT3() [11/16]

◆ SquareMatrixT3() [12/16]

◆ SquareMatrixT3() [13/16]

◆ SquareMatrixT3() [14/16]

◆ SquareMatrixT3() [15/16]

◆ SquareMatrixT3() [16/16]

Member Function Documentation

◆ absSum()

◆ copyElements() [1/2]

◆ copyElements() [2/2]

◆ data() [1/2]

◆ data() [2/2]

◆ determinant()

◆ diagonal()

◆ eigenSystem()

◆ eigenValues()

◆ elements()

◆ invert() [1/2]

◆ invert() [2/2]

◆ inverted()

◆ isAffine()

◆ isEqual()

◆ isHomography()

◆ isIdentity()

◆ isNull()

◆ isOrthonormal()

◆ isSimilarity()

◆ isSingular()

◆ isSymmetric()

◆ matrices2matrices() [1/5]

◆ matrices2matrices() [2/5]

◆ matrices2matrices() [3/5]

◆ matrices2matrices() [4/5]

◆ matrices2matrices() [5/5]

◆ multiply() [1/4]

◆ multiply() [2/4]

◆ multiply() [3/4]

◆ multiply() [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*() [1/6]

◆ operator*() [2/6]

◆ operator*() [3/6]

◆ operator*() [4/6]

◆ operator*() [5/6]

◆ operator*() [6/6]

◆ operator*=() [1/2]

◆ operator*=() [2/2]

◆ operator+()

◆ operator+=()

◆ operator-() [1/2]

◆ operator-() [2/2]

◆ operator-=()

◆ operator=()

template<typename T>
class Ocean::SquareMatrixT3< T >