This template class is used to represent spatial matrices. More...

Useful functions
SBDTypePhysicalMatrix33< Quantity00 >	m00
	The top left 3x3 matrix.

SBDTypePhysicalMatrix33< Quantity01 >	m01
	The top right 3x3 matrix.

SBDTypePhysicalMatrix33< Quantity10 >	m10
	The bottom left 3x3 matrix.

SBDTypePhysicalMatrix33< Quantity11 >	m11
	The bottom right 3x3 matrix.

static const SBDTypePhysicalMatrix66< Quantity00, Quantity01, Quantity10, Quantity11 >	zero
	The zero physical matrix.

static const SBDTypePhysicalMatrix66< Quantity00, Quantity01, Quantity10, Quantity11 >	identity
	The identity physical matrix.

void	print () const
	Prints the spatial matrix.

void	setZero ()
	Sets the matrix to zero.

void	symmetrize ()
	Makes the matrix symmetric.

void	setIdentity ()
	Sets the matrix to identity.

SBDTypePhysicalMatrix66< Quantity00, Quantity10, Quantity01, Quantity11 >	transpose () const
	Returns the transpose.

void	transpose (SBDTypePhysicalMatrix66< Quantity00, Quantity10, Quantity01, Quantity11 > &result) const
	Sets `result` to the transpose of the matrix.

SBDTypePhysicalMatrix66< Quantity00, Quantity01, Quantity10, Quantity11 >	doubleSymmetricPart () const
	Returns twice the symmetric part of the matrix.

Constructors
	SBDTypePhysicalMatrix66 ()
	he default constructor initializes all components to zero

	SBDTypePhysicalMatrix66 (const SBDTypePhysicalMatrix33< Quantity00 > &mat00, const SBDTypePhysicalMatrix33< Quantity01 > &mat01, const SBDTypePhysicalMatrix33< Quantity10 > &mat10, const SBDTypePhysicalMatrix33< Quantity11 > &mat11)
	Constructs a spatial matrix from four 3x3 matrices.

	SBDTypePhysicalMatrix66 (const SBDTypePhysicalMatrix66< Quantity00, Quantity01, Quantity10, Quantity11 > &mat)
	Copy constructor.

Serialization
virtual void	serialize (SBCSerializer *serializer, const SBVersionNumber &sdkVersionNumber=SB_SDK_VERSION_NUMBER) const
	Serializes the matrix using the provided `serializer`.

virtual void	unserialize (SBCSerializer *serializer, const SBVersionNumber &sdkVersionNumber=SB_SDK_VERSION_NUMBER)
	Unserializes the matrix using the provided `serializer`.

Accessors
SBDTypePhysicalVector6< Quantity00, Quantity10 >	getE1 () const
	Returns the first column of the spatial matrix.

SBDTypePhysicalVector6< Quantity00, Quantity10 >	getE2 () const
	Returns the second column of the spatial matrix.

SBDTypePhysicalVector6< Quantity00, Quantity10 >	getE3 () const
	Returns the third column of the spatial matrix.

SBDTypePhysicalVector6< Quantity01, Quantity11 >	getE4 () const
	Returns the fourth column of the spatial matrix.

SBDTypePhysicalVector6< Quantity01, Quantity11 >	getE5 () const
	Returns the fifth column of the spatial matrix.

SBDTypePhysicalVector6< Quantity01, Quantity11 >	getE6 () const
	Returns the sixth column of the spatial matrix.

SBDTypePhysicalMatrix66< SBQuantity::dimensionless, SBQuantity::dimensionless, SBQuantity::dimensionless, SBQuantity::dimensionless >	getValue () const
	Returns a dimensionless physical matrix whose components are equal to those of this physical matrix.

void	setValue (const SBDTypePhysicalMatrix66< SBQuantity::dimensionless, SBQuantity::dimensionless, SBQuantity::dimensionless, SBQuantity::dimensionless > &u)
	Sets the components of this physical matrix equal to those of the dimensionless physical matrix `u`.

Operators
SBDTypePhysicalMatrix66< Quantity00, Quantity01, Quantity10, Quantity11 > &	operator= (const SBDTypePhysicalMatrix66< Quantity00, Quantity01, Quantity10, Quantity11 > &mat)
	Copy assignment.

SBDTypePhysicalMatrix66< Quantity00, Quantity01, Quantity10, Quantity11 >	operator+ (const SBDTypePhysicalMatrix66< Quantity00, Quantity01, Quantity10, Quantity11 > &mat) const
	Returns the sum of the spatial matrix with the `mat` spatial matrix.

void	operator+= (const SBDTypePhysicalMatrix66 &mat)
	Adds the `mat` spatial matrix to this spatial matrix.

SBDTypePhysicalMatrix66< Quantity00, Quantity01, Quantity10, Quantity11 >	operator- (const SBDTypePhysicalMatrix66< Quantity00, Quantity01, Quantity10, Quantity11 > &mat) const
	Returns the subtraction of the spatial matrix from the `mat` spatial matrix.

void	operator-= (const SBDTypePhysicalMatrix66 &mat)
	Subtracts the `mat` spatial matrix from this spatial matrix.

SBDTypePhysicalMatrix66< Quantity00, Quantity01, Quantity10, Quantity11 >	operator- () const
	Returns the opposite of the spatial matrix.

template<typename QuantityA , typename QuantityL >
SBDTypePhysicalVector6< typename SBQuantityProduct2< Quantity00, QuantityA >::Type, typename SBQuantityProduct2< Quantity10, QuantityA >::Type >	operator* (const SBDTypePhysicalVector6< QuantityA, QuantityL > &v) const
	Returns the product of this spatial matrix with the spatial vector `v`.

SBDTypePhysicalMatrix66< Quantity00, Quantity01, Quantity10, Quantity11 >	operator* (double d) const
	Returns the product of this spatial matrix with double `d`.

SBDTypePhysicalMatrix66< Quantity00, Quantity01, Quantity10, Quantity11 >	operator/ (double d) const
	Returns the division of this spatial matrix by double `d`.

template<typename Quantity >
SBDTypePhysicalMatrix66< Quantity00, Quantity01, Quantity10, Quantity11 > &	operator*= (Quantity d) const
	Multiplies this spatial matrix with physical quantity `d`.

template<typename Quantity >
SBDTypePhysicalMatrix66< Quantity00, Quantity01, Quantity10, Quantity11 > &	operator/= (Quantity d) const
	Divides this spatial matrix by physical quantity `d`.

bool	operator== (const SBDTypePhysicalMatrix66< Quantity00, Quantity01, Quantity10, Quantity11 > &mat) const
	Returns true if this spatial matrix is equal to spatial matrix `mat` (component-wise)

bool	operator!= (const SBDTypePhysicalMatrix66< Quantity00, Quantity01, Quantity10, Quantity11 > &mat) const
	Returns true if this spatial matrix is different from spatial matrix `mat` (component-wise)

Detailed Description

template<typename Quantity00, typename Quantity01, typename Quantity10, typename Quantity11>
class SBDTypePhysicalMatrix66< Quantity00, Quantity01, Quantity10, Quantity11 >

Template Parameters

Quantity00	The quantity type of the top left 3x3 block
Quantity01	The quantity type of the top right 3x3 block
Quantity10	The quantity type of the bottom left 3x3 block
Quantity11	The quantity type of the bottom right 3x3 block

This template class represents spatial matrices, i.e. 6x6 matrices typically used to describe rigid or articulated inertias and inverse inertias. Spatial matrices are physical quantities, and thus use SAMSON's unit system. In a spatial matrix (e.g. an inertia matrix), the 3x3 blocks may have different units, so that spatial matrices are defined by four units, and the SBDTypePhysicalMatrix66 template class is parameterized by four types: Quantity00, Quantity01, Quantity10 and Quantity11.

Most of the time, developers of SAMSON Extensions do not have to use this template, but may directly use some predefined types, e.g. SBMatrix66 (dimensionless spatial matrix), SBInertia66 (spatial inertia) or SBInverseInertia66 (spatial inverse inertia).

Short name: SBPhysicalMatrix66

See also: SAMSON's unit system; SBDTypePhysicalMatrix33; SBDTypePhysicalVector6

Constructor & Destructor Documentation

◆ SBDTypePhysicalMatrix66()

template<typename Quantity00 , typename Quantity01 , typename Quantity10 , typename Quantity11 >

SBDTypePhysicalMatrix66< Quantity00, Quantity01, Quantity10, Quantity11 >::SBDTypePhysicalMatrix66	(	const SBDTypePhysicalMatrix33< Quantity00 > &	mat00,
		const SBDTypePhysicalMatrix33< Quantity01 > &	mat01,
		const SBDTypePhysicalMatrix33< Quantity10 > &	mat10,
		const SBDTypePhysicalMatrix33< Quantity11 > &	mat11
	)

inline

Parameters

mat00	The top left 3x3 block
mat01	The top right 3x3 block
mat10	The bottom left 3x3 block
mat11	The bottom right 3x3 block

This constructor initializes a spatial matrix from four 3x3 matrices

Member Function Documentation

◆ operator*() [1/2]

template<typename Quantity00 , typename Quantity01 , typename Quantity10 , typename Quantity11 >

template<typename QuantityA , typename QuantityL >

SBDTypePhysicalVector6< typename SBQuantityProduct2< Quantity00, QuantityA >::Type, typename SBQuantityProduct2< Quantity10, QuantityA >::Type > SBDTypePhysicalMatrix66< Quantity00, Quantity01, Quantity10, Quantity11 >::operator* ( const SBDTypePhysicalVector6< QuantityA, QuantityL > & v ) const

inline

Parameters

v	A spatial vector

This function returns the product of this spatial matrix with the spatial vector v. SAMSON's unit system checks that the units in the spatial matrix and the spatial vector are compatible.

◆ operator*() [2/2]

template<typename Quantity00 , typename Quantity01 , typename Quantity10 , typename Quantity11 >

SBDTypePhysicalMatrix66< Quantity00, Quantity01, Quantity10, Quantity11 > SBDTypePhysicalMatrix66< Quantity00, Quantity01, Quantity10, Quantity11 >::operator* ( double d ) const

inline

Parameters

d A double

This function returns the product of this spatial matrix with double d.

◆ operator*=()

template<typename Quantity00 , typename Quantity01 , typename Quantity10 , typename Quantity11 >

template<typename Quantity >

SBDTypePhysicalMatrix66< Quantity00, Quantity01, Quantity10, Quantity11 > & SBDTypePhysicalMatrix66< Quantity00, Quantity01, Quantity10, Quantity11 >::operator*= ( Quantity d ) const

inline

Parameters

d	A dimensionless physical quantity or a numeric type (i.e. int, float, double, etc)

◆ operator+()

template<typename Quantity00 , typename Quantity01 , typename Quantity10 , typename Quantity11 >

SBDTypePhysicalMatrix66< Quantity00, Quantity01, Quantity10, Quantity11 > SBDTypePhysicalMatrix66< Quantity00, Quantity01, Quantity10, Quantity11 >::operator+ ( const SBDTypePhysicalMatrix66< Quantity00, Quantity01, Quantity10, Quantity11 > & mat ) const

inline

Parameters

mat	A spatial matrix

This function returns the sum of the spatial matrix with the mat spatial matrix. Both spatial matrices must have identical units.

◆ operator+=()

template<typename Quantity00 , typename Quantity01 , typename Quantity10 , typename Quantity11 >

void SBDTypePhysicalMatrix66< Quantity00, Quantity01, Quantity10, Quantity11 >::operator+= ( const SBDTypePhysicalMatrix66< Quantity00, Quantity01, Quantity10, Quantity11 > & mat )

inline

Parameters

mat	A spatial matrix

This function adds the mat spatial matrix to this spatial matrix. Both spatial matrices must have identical units.

◆ operator-() [1/2]

template<typename Quantity00 , typename Quantity01 , typename Quantity10 , typename Quantity11 >

SBDTypePhysicalMatrix66< Quantity00, Quantity01, Quantity10, Quantity11 > SBDTypePhysicalMatrix66< Quantity00, Quantity01, Quantity10, Quantity11 >::operator- ( ) const

inline

This function returns the opposite of the spatial matrix.

◆ operator-() [2/2]

template<typename Quantity00 , typename Quantity01 , typename Quantity10 , typename Quantity11 >

SBDTypePhysicalMatrix66< Quantity00, Quantity01, Quantity10, Quantity11 > SBDTypePhysicalMatrix66< Quantity00, Quantity01, Quantity10, Quantity11 >::operator- ( const SBDTypePhysicalMatrix66< Quantity00, Quantity01, Quantity10, Quantity11 > & mat ) const

inline

Parameters

mat	A spatial matrix

This function returns the subtraction of the spatial matrix from the mat spatial matrix. Both spatial matrices must have identical units.

◆ operator-=()

template<typename Quantity00 , typename Quantity01 , typename Quantity10 , typename Quantity11 >

void SBDTypePhysicalMatrix66< Quantity00, Quantity01, Quantity10, Quantity11 >::operator-= ( const SBDTypePhysicalMatrix66< Quantity00, Quantity01, Quantity10, Quantity11 > & mat )

inline

Parameters

mat	A spatial matrix

This function subtracts the mat spatial matrix from this spatial matrix. Both spatial matrices must have identical units.

◆ operator/()

template<typename Quantity00 , typename Quantity01 , typename Quantity10 , typename Quantity11 >

SBDTypePhysicalMatrix66< Quantity00, Quantity01, Quantity10, Quantity11 > SBDTypePhysicalMatrix66< Quantity00, Quantity01, Quantity10, Quantity11 >::operator/ ( double d ) const

inline

Parameters

d A double

This function returns the division of this spatial matrix by double d.

◆ operator/=()

template<typename Quantity00 , typename Quantity01 , typename Quantity10 , typename Quantity11 >

template<typename Quantity >

SBDTypePhysicalMatrix66< Quantity00, Quantity01, Quantity10, Quantity11 > & SBDTypePhysicalMatrix66< Quantity00, Quantity01, Quantity10, Quantity11 >::operator/= ( Quantity d ) const

inline

Parameters

d	A dimensionless physical quantity or a numeric type (i.e. int, float, double, etc)

◆ print()

template<typename Quantity00 , typename Quantity01 , typename Quantity10 , typename Quantity11 >

void SBDTypePhysicalMatrix66< Quantity00, Quantity01, Quantity10, Quantity11 >::print ( ) const

inline

This function prints the spatial matrix.

◆ symmetrize()

template<typename Quantity00 , typename Quantity01 , typename Quantity10 , typename Quantity11 >

void SBDTypePhysicalMatrix66< Quantity00, Quantity01, Quantity10, Quantity11 >::symmetrize ( )

inline

Makes the matrix symmetric by replacing it with the half-sum of itself and its transpose: \(\mathbf{M}:=\frac{\mathbf{M}+\mathbf{M}^T}{2}\)

◆ transpose()

template<typename Quantity00 , typename Quantity01 , typename Quantity10 , typename Quantity11 >

void SBDTypePhysicalMatrix66< Quantity00, Quantity01, Quantity10, Quantity11 >::transpose ( SBDTypePhysicalMatrix66< Quantity00, Quantity10, Quantity01, Quantity11 > & result ) const

inline

Parameters

result The spatial matrix which becomes equal to the transpose of this matrix This function exists for efficiency reasons, to avoid the cost of an object construction.

Useful functions

Constructors

Serialization

Accessors

Operators

Detailed Description

Constructor & Destructor Documentation

◆ SBDTypePhysicalMatrix66()

Member Function Documentation

◆ operator*() [1/2]

◆ operator*() [2/2]

◆ operator*=()

◆ operator+()

◆ operator+=()

◆ operator-() [1/2]

◆ operator-() [2/2]

◆ operator-=()

◆ operator/()

◆ operator/=()

◆ print()

◆ symmetrize()

◆ transpose()