An m x n-dimensional matrix. More...

Public Member Functions
	Matrix (size_t rows, size_t cols)
	This constructor creates a matrix and initializes it with zeros.

	Matrix (const Vertex3 &c1, const Vertex3 &c2, const Vertex3 &c3, bool rowwise)
	Special constructor for a 3x3 matrix.

	Matrix ()=default
	Default constructor.

	Matrix (double value)
	Constructor sets up a matrix 1x1 with the numerical value as entry,.

	Matrix (const Matrix &other)
	Copy constructor.

	Matrix (const Matrix *other)
	Copy constructor.

virtual	~Matrix ()
	Destructor.

void	set (size_t row, size_t col, double value)
	Sets the value of a cell.

void	add (size_t row, size_t col, double value)
	Adds to the value of a cell the passed value.

double	get (size_t row, size_t col) const
	Returns the value of a cell.

void	zeros ()
	This method fills all elements of the matrix with 0.

void	transpose ()
	This method transposes the matrix,.

void	insert (const Matrix &A)
	This method inserts the contents of the other matrix into this matrix. Upper left element is 0,0.

void	insert (const Matrix &A, size_t r, size_t c)
	This method inserts the contents of the Other matrix into this matrix. Upper left element is r,c.

void	diag (double value)
	This method sets all values on the diagonal elements to the desired value.

Status	det (double &det) const
	Calculates the determinant of a matrix.

Status	inverse ()
	Inverts this matrix.

const double *	ref () const
	This method returns the reference to the data array.

double	norm (MatrixNorm norm) const
	This method calculates the condition of the matrix according to the corresponding matrix norm.

double	trace () const
	Returns the sum of the diagonal elements.

Vector	eigen () const
	Returns the Eigen Values of the matrix.

void	print () const
	Prints the content of the matrix on `std::cout`.

size_t	nonZeroElementCount () const
	This method calculates the number of elements that are not 0.0. Currently this is done without EPS.

void	initIdentity ()
	Initializes this transformation as an identity matrix.

void	initWcs (const Vertex3 &extrusion)
	Initializes this matrix as a World Coordinate System (WCS) matrix.

void	initMirroring (const Vertex3 &planePoint, const Vertex3 &planeNormal)
	Initializes this matrix as a mirroring matrix.

void	initMoving (const Vertex3 &distance)
	Initializes this matrix as a translation matrix.

void	initScaling (const Vertex3 &factors)
	Initializes this transformation as scaling by different factors along the x, y, and z axes.

void	initScaling (const Vertex3 &basePoint, double factor)
	Initializes this transformation as scaling around a base point.

void	initRotationZ (double angle)
	Initializes this Transform as a rotation matrix around the Z-axis.

void	initRotation (const Vertex3 &axisPoint, const Vertex3 &axisDirection, double angle)
	Initializes this Transform as a rotation matrix.

void	initLookAt (const jm::Vertex3 &camera, const jm::Vertex3 &center, const jm::Vertex3 &up)
	Initialize this matrix as a "look-at" matrix.

Vertex3	trans (const Vertex3 &vertex) const
	This method transforms the vertex using the 4x4 transformation matrix.

double	trans (double value) const
	This method transforms the number using the 4x4 transformation matrix. X value is used.

double	transAngle (double angle) const
	Transform a rotation angle about the Z-Axis of LCS as usually needed by arcs or texts.

Matrix &	operator= (const Matrix &A)

size_t	rows () const
	This method returns the number of rows.

size_t	cols () const
	This method returns the number of columns.

Static Public Member Functions
static Matrix	generate3x3RotationMatrix (double angle, const Vertex3 &axis)
	This static function generates a 3x3 rotation matrix.

static Matrix	generate3x3RotationXMatrix (double angle)
	This static function generates a 3x3 rotation matrix for a rotation around the X-axis.

static Matrix	generate3x3RotationYMatrix (double angle)
	This static function generates a 3x3 rotation matrix for a rotation around the Y-axis.

static Matrix	generate3x3RotationZMatrix (double angle)
	This static function generates a 3x3 rotation matrix for a rotation around the Z-axis.

static Matrix	generate3x3RotationMatrix (const Vertex3 &u, const Vertex3 &v)
	This static function generates a 3x3 rotation matrix for a rotation from vector u to vector v.

Friends
DllExport friend Matrix	operator* (const Matrix &A, const Matrix &B)
	Implementation of the operator M * M (matrix multiplication).

DllExport friend Matrix	operator* (const double &d, const Matrix &b)
	Implementation of the operator d * M (scalar multiplication).

DllExport friend Vertex3	operator* (const Matrix &A, const Vertex3 &b)
	Implementation of the operator M * v (matrix multiplication with a vector). The matrix must be 3x3.

DllExport friend Matrix	operator+ (const Matrix &A, const Matrix &B)
	Implementation of the operator M + M (matrix addition).

DllExport friend Matrix	operator- (const Matrix &A, const Matrix &B)
	Implementation of the operator M - M (matrix subtraction).

DllExport friend Matrix	operator/ (const Matrix &A, const double &d)
	Implementation of the operator M / d (scalar division).

Detailed Description

An m x n-dimensional matrix.

Constructor & Destructor Documentation

◆ Matrix() [1/6]

jm::Matrix::Matrix	(	size_t	rows,
		size_t	cols
	)

This constructor creates a matrix and initializes it with zeros.

Parameters

rows	Number of rows.
cols	Number of columns.

◆ Matrix() [2/6]

jm::Matrix::Matrix	(	const Vertex3 &	c1,
		const Vertex3 &	c2,
		const Vertex3 &	c3,
		bool	rowwise
	)

Special constructor for a 3x3 matrix.

Parameters

c1	The 1st column of the matrix
c2	The 2nd column of the matrix
c3	The 3rd column of the matrix
rowwise	if `true`, then the matrix is filled row by row otherwise column by column.

◆ Matrix() [3/6]

jm::Matrix::Matrix ( )

default

Default constructor.

◆ Matrix() [4/6]

jm::Matrix::Matrix ( double value )

explicit

Constructor sets up a matrix 1x1 with the numerical value as entry,.

◆ Matrix() [5/6]

jm::Matrix::Matrix ( const Matrix & other )

Copy constructor.

◆ Matrix() [6/6]

jm::Matrix::Matrix ( const Matrix * other )

Copy constructor.

◆ ~Matrix()

virtual jm::Matrix::~Matrix ( )

virtual

Destructor.

Member Function Documentation

◆ add()

void jm::Matrix::add	(	size_t	row,
		size_t	col,
		double	value
	)

Adds to the value of a cell the passed value.

Parameters

row	The 0-based index of the row.
col	The 0-based index of the column.
value	The value to be added to the cell.

◆ cols()

size_t jm::Matrix::cols ( ) const

This method returns the number of columns.

◆ det()

Status jm::Matrix::det ( double & det ) const

Calculates the determinant of a matrix.

This method is currently limited to a maximum of 4x4 matrices.

◆ diag()

void jm::Matrix::diag ( double value )

This method sets all values on the diagonal elements to the desired value.

◆ eigen()

Vector jm::Matrix::eigen ( ) const

Returns the Eigen Values of the matrix.

Currentrly this is restricted to matrices of maximum 3x3.

◆ generate3x3RotationMatrix() [1/2]

static Matrix jm::Matrix::generate3x3RotationMatrix	(	const Vertex3 &	u,
		const Vertex3 &	v
	)

static

This static function generates a 3x3 rotation matrix for a rotation from vector u to vector v.

Parameters

u	The start vector
v	The end vector

◆ generate3x3RotationMatrix() [2/2]

static Matrix jm::Matrix::generate3x3RotationMatrix	(	double	angle,
		const Vertex3 &	axis
	)

static

This static function generates a 3x3 rotation matrix.

Parameters

angle	Angle of rotation in radians
axis	Rotation axis (must be normalized)

◆ generate3x3RotationXMatrix()

static Matrix jm::Matrix::generate3x3RotationXMatrix ( double angle )

static

This static function generates a 3x3 rotation matrix for a rotation around the X-axis.

Parameters

angle Angle of rotation in radians

◆ generate3x3RotationYMatrix()

static Matrix jm::Matrix::generate3x3RotationYMatrix ( double angle )

static

This static function generates a 3x3 rotation matrix for a rotation around the Y-axis.

Parameters

angle Angle of rotation in radians

◆ generate3x3RotationZMatrix()

static Matrix jm::Matrix::generate3x3RotationZMatrix ( double angle )

static

This static function generates a 3x3 rotation matrix for a rotation around the Z-axis.

Parameters

angle Angle of rotation in radians

◆ get()

double jm::Matrix::get	(	size_t	row,
		size_t	col
	)		const

Returns the value of a cell.

Parameters

row	The 0-based index of the row.
col	The 0-based index of the column.

◆ initIdentity()

void jm::Matrix::initIdentity ( )

Initializes this transformation as an identity matrix.

An identity matrix is a square matrix in which all the elements of the principal diagonal are ones and all other elements are zeros. When a vector or point is multiplied by an identity matrix, the result is the same vector or point. This method sets the transformation matrix to an identity matrix, effectively resetting any previous transformations applied.

◆ initLookAt()

void jm::Matrix::initLookAt	(	const jm::Vertex3 &	camera,
		const jm::Vertex3 &	center,
		const jm::Vertex3 &	up
	)

Initialize this matrix as a "look-at" matrix.

Parameters

camera	The camera position
center	The "target" center of the view
up	The up vector (needed for rotation)

◆ initMirroring()

void jm::Matrix::initMirroring	(	const Vertex3 &	planePoint,
		const Vertex3 &	planeNormal
	)

Initializes this matrix as a mirroring matrix.

Parameters

planePoint	The point on the mirror plane.
planeNormal	The normal vector of the mirror plane.

This method initializes the transformation matrix as a mirroring matrix, which reflects points across a mirror plane. The mirror plane is defined by a point on the plane (planePoint) and the normal vector of the plane (planeNormal). The resulting matrix can be used to mirror 3D points and objects.

◆ initMoving()

void jm::Matrix::initMoving ( const Vertex3 & distance )

Initializes this matrix as a translation matrix.

Parameters

distance The distance to translate by.

◆ initRotation()

void jm::Matrix::initRotation	(	const Vertex3 &	axisPoint,
		const Vertex3 &	axisDirection,
		double	angle
	)

Initializes this Transform as a rotation matrix.

Parameters

axisPoint	The origin vector of the rotation axis.
axisDirection	The normalized direction vector of the rotation axis.
angle	The rotation angle in radians.

◆ initRotationZ()

void jm::Matrix::initRotationZ ( double angle )

Initializes this Transform as a rotation matrix around the Z-axis.

Parameters

angle The rotation angle in radians.

◆ initScaling() [1/2]

void jm::Matrix::initScaling	(	const Vertex3 &	basePoint,
		double	factor
	)

Initializes this transformation as scaling around a base point.

Parameters

basePoint	The point around which the scaling is performed.
factor	The scaling factor.

◆ initScaling() [2/2]

void jm::Matrix::initScaling ( const Vertex3 & factors )

Initializes this transformation as scaling by different factors along the x, y, and z axes.

Parameters

factors The scaling factors along the x, y, and z axes.

◆ initWcs()

void jm::Matrix::initWcs ( const Vertex3 & extrusion )

Initializes this matrix as a World Coordinate System (WCS) matrix.

Note: The matrix must be 4x4

Parameters

extrusion The extrusion vector used for the transformation.

This method initializes the transformation matrix as a WCS matrix, which represents the coordinate system transformation from Object Coordinate System (OCS) to WCS. The extrusion vector is used to define the direction of the Z-axis in the WCS. The resulting matrix can be used to transform 3D points and angles from OCS to WCS.

◆ insert() [1/2]

void jm::Matrix::insert ( const Matrix & A )

This method inserts the contents of the other matrix into this matrix. Upper left element is 0,0.

◆ insert() [2/2]

void jm::Matrix::insert	(	const Matrix &	A,
		size_t	r,
		size_t	c
	)

This method inserts the contents of the Other matrix into this matrix. Upper left element is r,c.

◆ inverse()

Status jm::Matrix::inverse ( )

Inverts this matrix.

This method is currently limited to a maximum of 4x4 matrices.

◆ nonZeroElementCount()

size_t jm::Matrix::nonZeroElementCount ( ) const

This method calculates the number of elements that are not 0.0. Currently this is done without EPS.

◆ norm()

double jm::Matrix::norm ( MatrixNorm norm ) const

This method calculates the condition of the matrix according to the corresponding matrix norm.

◆ operator=()

Matrix & jm::Matrix::operator= ( const Matrix & A )

◆ print()

void jm::Matrix::print ( ) const

Prints the content of the matrix on std::cout.

◆ ref()

const double * jm::Matrix::ref ( ) const

This method returns the reference to the data array.

Only needed for efficient access for OpenGL.

◆ rows()

size_t jm::Matrix::rows ( ) const

This method returns the number of rows.

◆ set()

void jm::Matrix::set	(	size_t	row,
		size_t	col,
		double	value
	)

Sets the value of a cell.

Parameters

row	The 0-based index of the row.
col	The 0-based index of the column.
value	The value of the cell.

◆ trace()

double jm::Matrix::trace ( ) const

Returns the sum of the diagonal elements.

◆ trans() [1/2]

Vertex3 jm::Matrix::trans ( const Vertex3 & vertex ) const

This method transforms the vertex using the 4x4 transformation matrix.

Parameters

vertex The input vertex to be transformed.

Returns: The transformed vertex.

◆ trans() [2/2]

double jm::Matrix::trans ( double value ) const

This method transforms the number using the 4x4 transformation matrix. X value is used.

Parameters

value The input number to be transformed.

Returns: The transformed number.

◆ transAngle()

double jm::Matrix::transAngle ( double angle ) const

Transform a rotation angle about the Z-Axis of LCS as usually needed by arcs or texts.

Parameters

angle Rotation angle in radians.

Returns: The transformed angle.

◆ transpose()

void jm::Matrix::transpose ( )

This method transposes the matrix,.

◆ zeros()

void jm::Matrix::zeros ( )

This method fills all elements of the matrix with 0.

Friends And Related Symbol Documentation

◆ operator* [1/3]

DllExport friend Matrix operator*	(	const double &	d,
		const Matrix &	b
	)

friend

Implementation of the operator d * M (scalar multiplication).

◆ operator* [2/3]

DllExport friend Matrix operator*	(	const Matrix &	A,
		const Matrix &	B
	)

friend

Implementation of the operator M * M (matrix multiplication).

◆ operator* [3/3]

DllExport friend Vertex3 operator*	(	const Matrix &	A,
		const Vertex3 &	b
	)

friend

Implementation of the operator M * v (matrix multiplication with a vector). The matrix must be 3x3.

◆ operator+

DllExport friend Matrix operator+	(	const Matrix &	A,
		const Matrix &	B
	)

friend

Implementation of the operator M + M (matrix addition).

◆ operator-

DllExport friend Matrix operator-	(	const Matrix &	A,
		const Matrix &	B
	)

friend

Implementation of the operator M - M (matrix subtraction).

◆ operator/

DllExport friend Matrix operator/	(	const Matrix &	A,
		const double &	d
	)

friend

Implementation of the operator M / d (scalar division).

Public Member Functions

Static Public Member Functions

Friends

Detailed Description

Constructor & Destructor Documentation

◆ Matrix() [1/6]

◆ Matrix() [2/6]

◆ Matrix() [3/6]

◆ Matrix() [4/6]

◆ Matrix() [5/6]

◆ Matrix() [6/6]

◆ ~Matrix()

Member Function Documentation

◆ add()

◆ cols()

◆ det()

◆ diag()

◆ eigen()

◆ generate3x3RotationMatrix() [1/2]

◆ generate3x3RotationMatrix() [2/2]

◆ generate3x3RotationXMatrix()

◆ generate3x3RotationYMatrix()

◆ generate3x3RotationZMatrix()

◆ get()

◆ initIdentity()

◆ initLookAt()

◆ initMirroring()

◆ initMoving()

◆ initRotation()

◆ initRotationZ()

◆ initScaling() [1/2]

◆ initScaling() [2/2]

◆ initWcs()

◆ insert() [1/2]

◆ insert() [2/2]

◆ inverse()

◆ nonZeroElementCount()

◆ norm()

◆ operator=()

◆ print()

◆ ref()

◆ rows()

◆ set()

◆ trace()

◆ trans() [1/2]

◆ trans() [2/2]

◆ transAngle()

◆ transpose()

◆ zeros()

Friends And Related Symbol Documentation

◆ operator* [1/3]

◆ operator* [2/3]

◆ operator* [3/3]

◆ operator+

◆ operator-

◆ operator/