gp_Mat Class Reference

Describes a three column, three row matrix. This sort of object is used in various vectorial or matrix computations. More...

#include <gp_Mat.hxx>

Public Member Functions
constexpr	gp_Mat () noexcept
	Creates a matrix with null coefficients.
constexpr	gp_Mat (const double theA11, const double theA12, const double theA13, const double theA21, const double theA22, const double theA23, const double theA31, const double theA32, const double theA33) noexcept
	gp_Mat (const gp_XYZ &theCol1, const gp_XYZ &theCol2, const gp_XYZ &theCol3)
	Creates a matrix. theCol1, theCol2, theCol3 are the 3 columns of the matrix.
void	SetCol (const int theCol, const gp_XYZ &theValue)
	Assigns the three coordinates of theValue to the column of index theCol of this matrix. Raises OutOfRange if theCol < 1 or theCol > 3.
void	SetCols (const gp_XYZ &theCol1, const gp_XYZ &theCol2, const gp_XYZ &theCol3)
	Assigns the number triples theCol1, theCol2, theCol3 to the three columns of this matrix.
void	SetCross (const gp_XYZ &theRef)
	Modifies the matrix M so that applying it to any number triple (X, Y, Z) produces the same result as the cross product of theRef and the number triple (X, Y, Z): i.e.: M * {X,Y,Z}t = theRef.Cross({X, Y ,Z}) this matrix is anti symmetric. To apply this matrix to the triplet {XYZ} is the same as to do the cross product between the triplet theRef and the triplet {XYZ}. Note: this matrix is anti-symmetric.
constexpr void	SetDiagonal (const double theX1, const double theX2, const double theX3) noexcept
	Modifies the main diagonal of the matrix.
void	SetDot (const gp_XYZ &theRef) noexcept
	Modifies this matrix so that applying it to any number triple (X, Y, Z) produces the same result as the scalar product of theRef and the number triple (X, Y, Z): this * (X,Y,Z) = theRef.(X,Y,Z) Note: this matrix is symmetric.
constexpr void	SetIdentity () noexcept
	Modifies this matrix so that it represents the Identity matrix.
void	SetRotation (const gp_XYZ &theAxis, const double theAng)
	Modifies this matrix so that it represents a rotation. theAng is the angular value in radians and the XYZ axis gives the direction of the rotation. Raises ConstructionError if XYZ.Modulus() <= Resolution().
void	SetRow (const int theRow, const gp_XYZ &theValue)
	Assigns the three coordinates of Value to the row of index theRow of this matrix. Raises OutOfRange if theRow < 1 or theRow > 3.
void	SetRows (const gp_XYZ &theRow1, const gp_XYZ &theRow2, const gp_XYZ &theRow3)
	Assigns the number triples theRow1, theRow2, theRow3 to the three rows of this matrix.
constexpr void	SetScale (const double theS) noexcept
	Modifies the matrix so that it represents a scaling transformation, where theS is the scale factor. :
void	SetValue (const int theRow, const int theCol, const double theValue)
	Assigns <theValue> to the coefficient of row theRow, column theCol of this matrix. Raises OutOfRange if theRow < 1 or theRow > 3 or theCol < 1 or theCol > 3.
gp_XYZ	Column (const int theCol) const
	Returns the column of theCol index. Raises OutOfRange if theCol < 1 or theCol > 3.
constexpr double	Determinant () const noexcept
	Computes the determinant of the matrix.
gp_XYZ	Diagonal () const
	Returns the main diagonal of the matrix.
gp_XYZ	Row (const int theRow) const
	returns the row of theRow index. Raises OutOfRange if theRow < 1 or theRow > 3
const double &	Value (const int theRow, const int theCol) const
	Returns the coefficient of range (theRow, theCol) Raises OutOfRange if theRow < 1 or theRow > 3 or theCol < 1 or theCol > 3.
const double &	operator() (const int theRow, const int theCol) const
double &	ChangeValue (const int theRow, const int theCol)
	Returns the coefficient of range (theRow, theCol) Raises OutOfRange if theRow < 1 or theRow > 3 or theCol < 1 or theCol > 3.
double &	operator() (const int theRow, const int theCol)
constexpr bool	IsSingular () const noexcept
	The Gauss LU decomposition is used to invert the matrix (see Math package) so the matrix is considered as singular if the largest pivot found is lower or equal to Resolution from gp.
constexpr void	Add (const gp_Mat &theOther) noexcept
constexpr void	operator+= (const gp_Mat &theOther) noexcept
constexpr gp_Mat	Added (const gp_Mat &theOther) const noexcept
	Computes the sum of this matrix and the matrix theOther for each coefficient of the matrix : <me>.Coef(i,j) + <theOther>.Coef(i,j).
constexpr gp_Mat	operator+ (const gp_Mat &theOther) const noexcept
constexpr void	Divide (const double theScalar)
constexpr void	operator/= (const double theScalar)
constexpr gp_Mat	Divided (const double theScalar) const
	Divides all the coefficients of the matrix by Scalar.
constexpr gp_Mat	operator/ (const double theScalar) const
void	Invert ()
gp_Mat	Inverted () const
	Inverses the matrix and raises if the matrix is singular.
constexpr gp_Mat	Multiplied (const gp_Mat &theOther) const noexcept
	Computes the product of two matrices <me> * <Other>.
constexpr gp_Mat	operator* (const gp_Mat &theOther) const noexcept
constexpr void	Multiply (const gp_Mat &theOther) noexcept
	Computes the product of two matrices <me> = <Other> * <me>.
constexpr void	operator*= (const gp_Mat &theOther) noexcept
constexpr void	PreMultiply (const gp_Mat &theOther) noexcept
constexpr gp_Mat	Multiplied (const double theScalar) const noexcept
constexpr gp_Mat	operator* (const double theScalar) const noexcept
constexpr void	Multiply (const double theScalar) noexcept
	Multiplies all the coefficients of the matrix by Scalar.
constexpr void	operator*= (const double theScalar) noexcept
void	Power (const int N)
gp_Mat	Powered (const int theN) const
	Computes <me> = <me> * <me> * .......* <me>, theN time. if theN = 0 <me> = Identity if theN < 0 <me> = <me>.Invert() ........... <me>.Invert(). If theN < 0 an exception will be raised if the matrix is not inversible.
constexpr void	Subtract (const gp_Mat &theOther) noexcept
constexpr void	operator-= (const gp_Mat &theOther) noexcept
constexpr gp_Mat	Subtracted (const gp_Mat &theOther) const noexcept
	cOmputes for each coefficient of the matrix : <me>.Coef(i,j) - <theOther>.Coef(i,j)
constexpr gp_Mat	operator- (const gp_Mat &theOther) const noexcept
void	Transpose ()
gp_Mat	Transposed () const
	Transposes the matrix. A(j, i) -> A (i, j).
void	DumpJson (Standard_OStream &theOStream, int theDepth=-1) const
	Dumps the content of me into the stream.

Detailed Description

Describes a three column, three row matrix. This sort of object is used in various vectorial or matrix computations.

Constructor & Destructor Documentation

gp_Mat() [1/3]

gp_Mat::gp_Mat ( )

inlineconstexprnoexcept

Creates a matrix with null coefficients.

gp_Mat() [2/3]

gp_Mat::gp_Mat ( const double theA11, const double theA12, const double theA13, const double theA21, const double theA22, const double theA23, const double theA31, const double theA32, const double theA33 )

inlineconstexprnoexcept

gp_Mat() [3/3]

gp_Mat::gp_Mat	(	const gp_XYZ &	theCol1,
		const gp_XYZ &	theCol2,
		const gp_XYZ &	theCol3 )

Creates a matrix. theCol1, theCol2, theCol3 are the 3 columns of the matrix.

Member Function Documentation

Add()

void gp_Mat::Add ( const gp_Mat & theOther )

inlineconstexprnoexcept

Added()

gp_Mat gp_Mat::Added ( const gp_Mat & theOther ) const

inlinenodiscardconstexprnoexcept

Computes the sum of this matrix and the matrix theOther for each coefficient of the matrix : <me>.Coef(i,j) + <theOther>.Coef(i,j).

ChangeValue()

double & gp_Mat::ChangeValue ( const int theRow, const int theCol )

inline

Returns the coefficient of range (theRow, theCol) Raises OutOfRange if theRow < 1 or theRow > 3 or theCol < 1 or theCol > 3.

Column()

gp_XYZ gp_Mat::Column

(

const int

theCol

)

const

Returns the column of theCol index. Raises OutOfRange if theCol < 1 or theCol > 3.

Determinant()

double gp_Mat::Determinant ( ) const

inlineconstexprnoexcept

Computes the determinant of the matrix.

Diagonal()

gp_XYZ gp_Mat::Diagonal

(

)

const

Returns the main diagonal of the matrix.

Divide()

void gp_Mat::Divide ( const double theScalar )

inlineconstexpr

Divided()

gp_Mat gp_Mat::Divided ( const double theScalar ) const

inlinenodiscardconstexpr

Divides all the coefficients of the matrix by Scalar.

DumpJson()

void gp_Mat::DumpJson	(	Standard_OStream &	theOStream,
		int	theDepth = -1 ) const

Dumps the content of me into the stream.

Invert()

void gp_Mat::Invert

(

)

Inverted()

gp_Mat gp_Mat::Inverted ( ) const

nodiscard

Inverses the matrix and raises if the matrix is singular.

• Invert assigns the result to this matrix, while
• Inverted creates a new one. Warning The Gauss LU decomposition is used to invert the matrix. Consequently, the matrix is considered as singular if the largest pivot found is less than or equal to gp::Resolution(). Exceptions Standard_ConstructionError if this matrix is singular, and therefore cannot be inverted.

IsSingular()

bool gp_Mat::IsSingular ( ) const

inlineconstexprnoexcept

The Gauss LU decomposition is used to invert the matrix (see Math package) so the matrix is considered as singular if the largest pivot found is lower or equal to Resolution from gp.

Multiplied() [1/2]

gp_Mat gp_Mat::Multiplied ( const double theScalar ) const

inlinenodiscardconstexprnoexcept

Multiplied() [2/2]

gp_Mat gp_Mat::Multiplied ( const gp_Mat & theOther ) const

inlinenodiscardconstexprnoexcept

Computes the product of two matrices <me> * <Other>.

Multiply() [1/2]

void gp_Mat::Multiply ( const double theScalar )

inlineconstexprnoexcept

Multiplies all the coefficients of the matrix by Scalar.

Multiply() [2/2]

void gp_Mat::Multiply ( const gp_Mat & theOther )

inlineconstexprnoexcept

Computes the product of two matrices <me> = <Other> * <me>.

operator()() [1/2]

double & gp_Mat::operator() ( const int theRow, const int theCol )

inline

operator()() [2/2]

const double & gp_Mat::operator() ( const int theRow, const int theCol ) const

inline

operator*() [1/2]

gp_Mat gp_Mat::operator* ( const double theScalar ) const

inlinenodiscardconstexprnoexcept

operator*() [2/2]

gp_Mat gp_Mat::operator* ( const gp_Mat & theOther ) const

inlinenodiscardconstexprnoexcept

operator*=() [1/2]

void gp_Mat::operator*= ( const double theScalar )

inlineconstexprnoexcept

operator*=() [2/2]

void gp_Mat::operator*= ( const gp_Mat & theOther )

inlineconstexprnoexcept

operator+()

gp_Mat gp_Mat::operator+ ( const gp_Mat & theOther ) const

inlinenodiscardconstexprnoexcept

operator+=()

void gp_Mat::operator+= ( const gp_Mat & theOther )

inlineconstexprnoexcept

operator-()

gp_Mat gp_Mat::operator- ( const gp_Mat & theOther ) const

inlinenodiscardconstexprnoexcept

operator-=()

void gp_Mat::operator-= ( const gp_Mat & theOther )

inlineconstexprnoexcept

operator/()

gp_Mat gp_Mat::operator/ ( const double theScalar ) const

inlinenodiscardconstexpr

operator/=()

void gp_Mat::operator/= ( const double theScalar )

inlineconstexpr

Power()

void gp_Mat::Power

(

const int

N

)

Powered()

gp_Mat gp_Mat::Powered ( const int theN ) const

inlinenodiscard

Computes <me> = <me> * <me> * .......* <me>, theN time. if theN = 0 <me> = Identity if theN < 0 <me> = <me>.Invert() ........... <me>.Invert(). If theN < 0 an exception will be raised if the matrix is not inversible.

PreMultiply()

void gp_Mat::PreMultiply ( const gp_Mat & theOther )

inlineconstexprnoexcept

Row()

gp_XYZ gp_Mat::Row

(

const int

theRow

)

const

returns the row of theRow index. Raises OutOfRange if theRow < 1 or theRow > 3

SetCol()

void gp_Mat::SetCol	(	const int	theCol,
		const gp_XYZ &	theValue )

Assigns the three coordinates of theValue to the column of index theCol of this matrix. Raises OutOfRange if theCol < 1 or theCol > 3.

SetCols()

void gp_Mat::SetCols	(	const gp_XYZ &	theCol1,
		const gp_XYZ &	theCol2,
		const gp_XYZ &	theCol3 )

Assigns the number triples theCol1, theCol2, theCol3 to the three columns of this matrix.

SetCross()

void gp_Mat::SetCross

(

const gp_XYZ &

theRef

)

Modifies the matrix M so that applying it to any number triple (X, Y, Z) produces the same result as the cross product of theRef and the number triple (X, Y, Z): i.e.: M * {X,Y,Z}t = theRef.Cross({X, Y ,Z}) this matrix is anti symmetric. To apply this matrix to the triplet {XYZ} is the same as to do the cross product between the triplet theRef and the triplet {XYZ}. Note: this matrix is anti-symmetric.

SetDiagonal()

void gp_Mat::SetDiagonal ( const double theX1, const double theX2, const double theX3 )

inlineconstexprnoexcept

Modifies the main diagonal of the matrix.

<me>.Value (1, 1) = theX1
<me>.Value (2, 2) = theX2
<me>.Value (3, 3) = theX3

The other coefficients of the matrix are not modified.

SetDot()

void gp_Mat::SetDot ( const gp_XYZ & theRef )

noexcept

Modifies this matrix so that applying it to any number triple (X, Y, Z) produces the same result as the scalar product of theRef and the number triple (X, Y, Z): this * (X,Y,Z) = theRef.(X,Y,Z) Note: this matrix is symmetric.

SetIdentity()

void gp_Mat::SetIdentity ( )

inlineconstexprnoexcept

Modifies this matrix so that it represents the Identity matrix.

SetRotation()

void gp_Mat::SetRotation	(	const gp_XYZ &	theAxis,
		const double	theAng )

Modifies this matrix so that it represents a rotation. theAng is the angular value in radians and the XYZ axis gives the direction of the rotation. Raises ConstructionError if XYZ.Modulus() <= Resolution().

SetRow()

void gp_Mat::SetRow	(	const int	theRow,
		const gp_XYZ &	theValue )

Assigns the three coordinates of Value to the row of index theRow of this matrix. Raises OutOfRange if theRow < 1 or theRow > 3.

SetRows()

void gp_Mat::SetRows	(	const gp_XYZ &	theRow1,
		const gp_XYZ &	theRow2,
		const gp_XYZ &	theRow3 )

Assigns the number triples theRow1, theRow2, theRow3 to the three rows of this matrix.

SetScale()

void gp_Mat::SetScale ( const double theS )

inlineconstexprnoexcept

Modifies the matrix so that it represents a scaling transformation, where theS is the scale factor. :

        | theS    0.0  0.0 |
<me> =  | 0.0   theS   0.0 |
        | 0.0  0.0   theS  |

SetValue()

void gp_Mat::SetValue ( const int theRow, const int theCol, const double theValue )

inline

Assigns <theValue> to the coefficient of row theRow, column theCol of this matrix. Raises OutOfRange if theRow < 1 or theRow > 3 or theCol < 1 or theCol > 3.

Subtract()

void gp_Mat::Subtract ( const gp_Mat & theOther )

inlineconstexprnoexcept

Subtracted()

gp_Mat gp_Mat::Subtracted ( const gp_Mat & theOther ) const

inlinenodiscardconstexprnoexcept

cOmputes for each coefficient of the matrix : <me>.Coef(i,j) - <theOther>.Coef(i,j)

Transpose()

void gp_Mat::Transpose ( )

inline

Transposed()

gp_Mat gp_Mat::Transposed ( ) const

inlinenodiscard

Transposes the matrix. A(j, i) -> A (i, j).

Value()

const double & gp_Mat::Value ( const int theRow, const int theCol ) const

inline

Returns the coefficient of range (theRow, theCol) Raises OutOfRange if theRow < 1 or theRow > 3 or theCol < 1 or theCol > 3.

---

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

• gp_Mat.hxx