Representation of a 3D Cartesian coordinate system as a Vector of row vectors. More...

#include <triad.H>

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Public Member Functions
	triad ()
	Default construct as 'unset'.
	triad (const Vector< vector > &vv)
	Construct from components.
	triad (const vector &x, const vector &y, const vector &z)
	Construct from coordinate axes (row vectors).
	triad (const tensor &t)
	Construct from a tensor.
	triad (const vector &pa)
	Construct from a primary axis with the other two unset.
	triad (const quaternion &q)
	Construct from a quaternion.
	triad (Istream &)
	Construct from Istream.
bool	set (const direction d) const
	Is the vector in the direction d set.
bool	set () const
	Are all the vector set.
void	orthogonalise ()
	Inplace orthogonalise so that it is ortho-normal.
void	normalise ()
	Normalise each set axis vector to have a unit magnitude.
void	align (const vector &v)
	Align this triad with the given vector v.
triad	sortxyz () const
	Sort the axes such that they are closest to the x, y and z axes.
	operator quaternion () const
	Convert to a quaternion.
triad	T () const
	Return transpose.
vector	cx () const
	Extract vector for column 0.
vector	cy () const
	Extract vector for column 1.
vector	cz () const
	Extract vector for column 2.
void	operator= (const Vector< vector > &vv)
void	operator= (const tensor &t)
void	operator+= (const triad &t2)
	Add the triad t2 to this triad.
void	orthogonalize ()
	Same as orthogonalise.
void	normalize ()
	Same as normalise.
Public Member Functions inherited from Vector< vector >
	Vector ()=default
	Default construct.
	Vector (const Vector &)=default
	Copy construct.
Vector &	operator= (const Vector &)=default
	Copy assignment.
	Vector (Foam::zero)
	Construct initialized to zero.
	Vector (const VectorSpace< Vector< Cmpt2 >, Cmpt2, 3 > &vs)
	Copy construct from VectorSpace of the same rank.
	Vector (const vector &vx, const vector &vy, const vector &vz)
	Construct from three components.
	Vector (Istream &is)
	Construct from Istream.
const vector &	x () const noexcept
	Access to the vector x component.
const vector &	y () const noexcept
	Access to the vector y component.
const vector &	z () const noexcept
	Access to the vector z component.
vector &	x () noexcept
	Access to the vector x component.
vector &	y () noexcept
	Access to the vector y component.
vector &	z () noexcept
	Access to the vector z component.
const Vector< vector > &	centre (const Foam::UList< Vector< vector > > &) const noexcept
	Return `this` (for point which is a typedef to Vector<scalar>).
scalar	mag () const
	The length (L2-norm) of the vector.
scalar	magSqr () const
	The length (L2-norm) squared of the vector.
scalar	dist (const Vector< vector > &v2) const
	The L2-norm distance from another vector. The mag() of the difference.
scalar	distSqr (const Vector< vector > &v2) const
	The L2-norm distance squared from another vector. The magSqr() of the difference.
Vector< vector > &	normalise (const scalar tol=ROOTVSMALL)
	Inplace normalise the vector by its magnitude.
Vector< vector > &	removeCollinear (const Vector< vector > &unitVec)
	Inplace removal of components that are collinear to the given unit vector.
vector	inner (const Vector< vector > &v2) const
	Scalar-product of `this` with another Vector.
Vector< vector >	cross (const Vector< vector > &v2) const
	Cross-product of `this` with another Vector.
std::enable_if_t< std::is_convertible_v< Cmpt2, vector >, void >	operator+= (const Vector< Cmpt2 > &b)
	Add compatible vector to this.
std::enable_if_t< std::is_convertible_v< Cmpt2, vector >, void >	operator-= (const Vector< Cmpt2 > &b)
	Subtract compatible vector from this.
Public Member Functions inherited from VectorSpace< Form, Cmpt, Ncmpts >
	VectorSpace ()=default
	Default construct.
	VectorSpace (Foam::zero)
	Construct initialized to zero.
	VectorSpace (const VectorSpace< Form, Cmpt, Ncmpts > &vs)
	Copy construct.
template<class Form2, class Cmpt2>
	VectorSpace (const VectorSpace< Form2, Cmpt2, Ncmpts > &)
	Copy construct of a VectorSpace with the same size.
	VectorSpace (Istream &is)
	Construct from Istream.
const Cmpt &	component (const direction) const
Cmpt &	component (const direction)
void	component (Cmpt &, const direction) const
void	replace (const direction, const Cmpt &)
const Cmpt *	cdata () const noexcept
	Return const pointer to the first data element.
Cmpt *	data () noexcept
	Return pointer to the first data element.
void	fill (const Cmpt &s)
	Assign all components to given value.
template<class SubVector, direction BStart>
const ConstBlock< SubVector, BStart >	block () const
const Cmpt &	operator[] (const direction) const
Cmpt &	operator[] (const direction)
void	operator= (const VectorSpace< Form, Cmpt, Ncmpts > &)
void	operator+= (const VectorSpace< Form, Cmpt, Ncmpts > &)
void	operator-= (const VectorSpace< Form, Cmpt, Ncmpts > &)
template<class Form2, class Cmpt2>
void	operator= (const VectorSpace< Form2, Cmpt2, Ncmpts > &)
	Copy assign from a VectorSpace with the same size.
void	operator= (Foam::zero)
void	operator*= (const scalar)
void	operator/= (const scalar)
iterator	begin () noexcept
	Return an iterator (pointer) to begin of VectorSpace.
const_iterator	begin () const noexcept
	Return const_iterator (const pointer) to begin of VectorSpace.
const_iterator	cbegin () const noexcept
	Return const_iterator (const pointer) to begin of VectorSpace.
iterator	end () noexcept
	Return an iterator (pointer) to end of VectorSpace.
const_iterator	end () const noexcept
	Return const_iterator (const pointer) to end of VectorSpace.
const_iterator	cend () const noexcept
	Return const_iterator (const pointer) to end of VectorSpace.
template<class SubVector, Foam::direction BStart>
const Foam::VectorSpace< Form, Cmpt, Ncmpts >::template ConstBlock< SubVector, BStart >	block () const

Static Public Member Functions
static direction	primaryDirection (const vector &v)
	Return the primary direction of the vector v.
static vector	orthogonal (const vector &v1, const vector &v2)
	Return the vector orthogonal to the two provided.
Static Public Member Functions inherited from Vector< vector >
static bool	less_xyz (const Vector< vector > &a, const Vector< vector > &b)
	Lexicographically compare a and b with order (x:y:z).
static bool	less_yzx (const Vector< vector > &a, const Vector< vector > &b)
	Lexicographically compare a and b with order (y:z:x).
static bool	less_zxy (const Vector< vector > &a, const Vector< vector > &b)
	Lexicographically compare a and b with order (z:x:y).
Static Public Member Functions inherited from VectorSpace< Form, Cmpt, Ncmpts >
static constexpr direction	size () noexcept
	The number of elements in the VectorSpace = Ncmpts.
static Form	uniform (const Cmpt &s)
	Return a VectorSpace with all elements = s.

Static Public Attributes
static const triad	I
static const triad	unset
Static Public Attributes inherited from Vector< vector >
static constexpr direction	rank
	Rank of Vector is 1.
Static Public Attributes inherited from VectorSpace< Form, Cmpt, Ncmpts >
static constexpr direction	dim = 3
	Dimensionality of space.
static constexpr direction	nComponents = Ncmpts
	Number of components in this vector space.
static constexpr direction	mRows = Ncmpts
static constexpr direction	nCols = 1
static const char *const	typeName = "spatialVector"
static const char *const	componentNames []
static const Form	zero
static const Form	one
static const Form	max
static const Form	min
static const Form	rootMax
static const Form	rootMin

Friends
Istream &	operator>> (Istream &, triad &)
Ostream &	operator<< (Ostream &, const triad &)

Additional Inherited Members
Public Types inherited from Vector< vector >
typedef Vector< label >	labelType
	Equivalent type of labels used for valid component indexing.
enum	components
	Component labeling enumeration. More...
Public Types inherited from VectorSpace< Form, Cmpt, Ncmpts >
typedef VectorSpace< Form, Cmpt, Ncmpts >	vsType
	VectorSpace type.
typedef Cmpt	cmptType
	Component type.
typedef Cmpt	magType
	Magnitude type.
typedef direction	size_type
	The type to represent the size of a VectorSpace.
typedef Cmpt *	iterator
	Random access iterator for traversing VectorSpace.
typedef const Cmpt *	const_iterator
	Random access iterator for traversing VectorSpace.
Public Attributes inherited from VectorSpace< Form, Cmpt, Ncmpts >
Cmpt	v_ [Ncmpts]
	The components of this vector space.

Detailed Description

Representation of a 3D Cartesian coordinate system as a Vector of row vectors.

See also: Foam::quaternion

Source files

Definition at line 60 of file triad.H.

Constructor & Destructor Documentation

◆ triad() [1/7]

triad ( )

inline

Default construct as 'unset'.

Definition at line 24 of file triadI.H.

References triad(), unset, and Vector< vector >::Vector().

Referenced by operator quaternion(), operator+=(), operator<<, operator>>, sortxyz(), T(), and triad().

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◆ triad() [2/7]

triad ( const Vector< vector > & vv )

inline

Construct from components.

Definition at line 30 of file triadI.H.

References Vector< vector >::Vector().

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◆ triad() [3/7]

triad	(	const vector &	x,
		const vector &	y,
		const vector &	z )

inline

Construct from coordinate axes (row vectors).

Definition at line 36 of file triadI.H.

References Vector< vector >::Vector(), Vector< vector >::x(), Vector< vector >::y(), and Vector< vector >::z().

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◆ triad() [4/7]

triad ( const tensor & t )

inline

Construct from a tensor.

Definition at line 42 of file triadI.H.

References Vector< vector >::Vector(), Vector< vector >::x(), Vector< vector >::y(), and Vector< vector >::z().

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◆ triad() [5/7]

triad ( const vector & pa )

inline

Construct from a primary axis with the other two unset.

Definition at line 48 of file triadI.H.

References operator=(), VectorSpace< Form, Cmpt, Ncmpts >::operator[](), primaryDirection(), and unset.

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◆ triad() [6/7]

triad ( const quaternion & q )

Construct from a quaternion.

Definition at line 84 of file triad.C.

References quaternion::R(), Tensor< Cmpt >::T(), Tensor< Cmpt >::x(), Vector< vector >::x(), Tensor< Cmpt >::y(), Vector< vector >::y(), Tensor< Cmpt >::z(), and Vector< vector >::z().

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◆ triad() [7/7]

triad ( Istream & is )

inline

Construct from Istream.

Definition at line 55 of file triadI.H.

References Vector< vector >::Vector().

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Member Function Documentation

◆ set() [1/2]

bool set ( const direction d ) const

inline

Is the vector in the direction d set.

Definition at line 63 of file triadI.H.

References VectorSpace< Form, Cmpt, Ncmpts >::operator[]().

Referenced by align(), triSurfaceTools::curvatures(), Foam::diff(), normalise(), operator+=(), orthogonalise(), set(), and sortxyz().

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◆ set() [2/2]

bool set ( ) const

inline

Are all the vector set.

Definition at line 69 of file triadI.H.

References set().

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◆ primaryDirection()

Foam::direction primaryDirection ( const vector & v )

inlinestatic

Return the primary direction of the vector v.

Definition at line 75 of file triadI.H.

References Foam::mag(), Vector< vector >::X, Vector< Cmpt >::x(), Vector< vector >::Y, Vector< Cmpt >::y(), Vector< vector >::Z, and Vector< Cmpt >::z().

Referenced by triad().

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◆ orthogonal()

Foam::vector orthogonal	(	const vector &	v1,
		const vector &	v2 )

inlinestatic

Return the vector orthogonal to the two provided.

Definition at line 96 of file triadI.H.

References Foam::mag(), and unset.

Referenced by orthogonalise().

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◆ orthogonalise()

void orthogonalise ( )

Inplace orthogonalise so that it is ortho-normal.

Definition at line 95 of file triad.C.

References Foam::mag(), VectorSpace< Form, Cmpt, Ncmpts >::operator[](), orthogonal(), and set().

Referenced by orthogonalize().

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◆ normalise()

void normalise ( )

inline

Normalise each set axis vector to have a unit magnitude.

Uses vector::normalise with handling of small magnitudes.

Definition at line 117 of file triadI.H.

References set().

Referenced by normalize().

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◆ align()

void align ( const vector & v )

Align this triad with the given vector v.

by rotating the most aligned axis to be coincident with v

Definition at line 235 of file triad.C.

References Foam::mag(), VectorSpace< Form, Cmpt, Ncmpts >::operator[](), R, Foam::rotationTensor(), set(), Foam::transform(), Vector< Cmpt >::x(), Vector< Cmpt >::y(), and Vector< Cmpt >::z().

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◆ sortxyz()

Foam::triad sortxyz ( ) const

Sort the axes such that they are closest to the x, y and z axes.

Definition at line 280 of file triad.C.

References Foam::mag(), VectorSpace< Form, Cmpt, Ncmpts >::operator[](), set(), triad(), x, y, and Vector< vector >::z().

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◆ operator quaternion()

operator quaternion ( ) const

Convert to a quaternion.

References triad(), and Vector< vector >::Vector().

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◆ T()

Foam::triad T ( ) const

inline

Return transpose.

Definition at line 143 of file triadI.H.

References cx(), cy(), cz(), and triad().

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◆ cx()

Foam::vector cx ( ) const

inline

Extract vector for column 0.

Definition at line 125 of file triadI.H.

References x, y, and Vector< vector >::z().

Referenced by T().

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◆ cy()

Foam::vector cy ( ) const

inline

Extract vector for column 1.

Definition at line 131 of file triadI.H.

References x, y, and Vector< vector >::z().

Referenced by T().

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◆ cz()

Foam::vector cz ( ) const

inline

Extract vector for column 2.

Definition at line 137 of file triadI.H.

References x, y, and Vector< vector >::z().

Referenced by T().

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◆ operator=() [1/2]

void operator= ( const Vector< vector > & vv )

inline

Definition at line 151 of file triadI.H.

References Vector< Cmpt >::operator=(), and Vector< vector >::Vector().

Referenced by triad().

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◆ operator=() [2/2]

void operator= ( const tensor & t )

inline

Definition at line 157 of file triadI.H.

References Tensor< Cmpt >::x(), x, Tensor< Cmpt >::y(), y, Tensor< Cmpt >::z(), and Vector< vector >::z().

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◆ operator+=()

void operator+= ( const triad & t2 )

Add the triad t2 to this triad.

without normalising or orthogonalising

Definition at line 172 of file triad.C.

References k, Foam::mag(), VectorSpace< Form, Cmpt, Ncmpts >::operator[](), set(), Foam::sign(), and triad().

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◆ orthogonalize()

void orthogonalize ( )

inline

Same as orthogonalise.

Definition at line 210 of file triad.H.

References orthogonalise().

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◆ normalize()

void normalize ( )

inline

Same as normalise.

Definition at line 215 of file triad.H.

References normalise().

Referenced by triSurfaceTools::curvatures().

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◆ operator>>

Istream & operator>>	(	Istream &	,
		triad &	)

friend

References triad().

◆ operator<<

Ostream & operator<<	(	Ostream &	,
		const triad &	)

friend

References triad().

Member Data Documentation

◆ I

const Foam::triad I

static

Definition at line 106 of file triad.H.

◆ unset

const Foam::triad unset

static

Definition at line 107 of file triad.H.

Referenced by orthogonal(), triad(), triad(), and triSurfaceTools::vertexTriads().

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

src/OpenFOAM/primitives/triad/triad.H
src/OpenFOAM/primitives/triad/triad.C
src/OpenFOAM/primitives/triad/triadI.H

Public Member Functions

Static Public Member Functions

Static Public Attributes

Friends

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ triad() [1/7]

◆ triad() [2/7]

◆ triad() [3/7]

◆ triad() [4/7]

◆ triad() [5/7]

◆ triad() [6/7]

◆ triad() [7/7]

Member Function Documentation

◆ set() [1/2]

◆ set() [2/2]

◆ primaryDirection()

◆ orthogonal()

◆ orthogonalise()

◆ normalise()

◆ align()

◆ sortxyz()

◆ operator quaternion()

◆ T()

◆ cx()

◆ cy()

◆ cz()

◆ operator=() [1/2]

◆ operator=() [2/2]

◆ operator+=()

◆ orthogonalize()

◆ normalize()

Friends And Related Symbol Documentation

◆ operator>>

◆ operator<<

Member Data Documentation

◆ I

◆ unset