Describes a unit vector in 3D space. This unit vector is also called "Direction". See Also gce_MakeDir which provides functions for more complex unit vector constructions Geom_Direction which provides additional functions for constructing unit vectors and works, in particular, with the parametric equations of unit vectors. More...

#include <gp_Dir.hxx>

Public Types
enum class	D { X , Y , Z , NX , NY , NZ }
	Standard directions in 3D space for optimized constexpr construction. More...

Public Member Functions
constexpr	gp_Dir () noexcept
	Creates a direction corresponding to X axis.

constexpr	gp_Dir (const D theDir) noexcept
	Creates a direction from a standard direction enumeration.

constexpr	gp_Dir (const gp_Vec &theV)
	Normalizes the vector theV and creates a direction. Raises ConstructionError if theV.Magnitude() <= Resolution.

constexpr	gp_Dir (const gp_XYZ &theCoord)
	Creates a direction from a triplet of coordinates. Raises ConstructionError if theCoord.Modulus() <= Resolution from gp.

constexpr	gp_Dir (const double theXv, const double theYv, const double theZv)
	Creates a direction with its 3 cartesian coordinates. Raises ConstructionError if std::sqrt(theXvtheXv + theYvtheYv + theZvtheZv) <= Resolution Modification of the direction's coordinates If std::sqrt (theXvtheXv + theYvtheYv + theZvtheZv) <= Resolution from gp where theXv, theYv ,theZv are the new coordinates it is not possible to construct the direction and the method raises the exception ConstructionError.

constexpr	gp_Dir (const gp_Dir &) noexcept=default

constexpr	gp_Dir (gp_Dir &&) noexcept=default

constexpr gp_Dir &	operator= (const gp_Dir &) noexcept=default

constexpr gp_Dir &	operator= (gp_Dir &&) noexcept=default

constexpr void	SetCoord (const int theIndex, const double theXi)
	For this unit vector, assigns the value Xi to:

constexpr void	SetCoord (const double theXv, const double theYv, const double theZv)
	For this unit vector, assigns the values theXv, theYv and theZv to its three coordinates. Remember that all the coordinates of a unit vector are implicitly modified when any single one is changed directly.

constexpr void	SetX (const double theX)
	Assigns the given value to the X coordinate of this unit vector.

constexpr void	SetY (const double theY)
	Assigns the given value to the Y coordinate of this unit vector.

constexpr void	SetZ (const double theZ)
	Assigns the given value to the Z coordinate of this unit vector.

constexpr void	SetXYZ (const gp_XYZ &theCoord)
	Assigns the three coordinates of theCoord to this unit vector.

constexpr double	Coord (const int theIndex) const
	Returns the coordinate of range theIndex : theIndex = 1 => X is returned theIndex = 2 => Y is returned theIndex = 3 => Z is returned Exceptions Standard_OutOfRange if theIndex is not 1, 2, or 3.

constexpr void	Coord (double &theXv, double &theYv, double &theZv) const noexcept
	Returns for the unit vector its three coordinates theXv, theYv, and theZv.

constexpr double	X () const noexcept
	Returns the X coordinate for a unit vector.

constexpr double	Y () const noexcept
	Returns the Y coordinate for a unit vector.

constexpr double	Z () const noexcept
	Returns the Z coordinate for a unit vector.

constexpr const gp_XYZ &	XYZ () const noexcept
	for this unit vector, returns its three coordinates as a number triple.

bool	IsEqual (const gp_Dir &theOther, const double theAngularTolerance) const
	Returns True if the angle between the two directions is lower or equal to theAngularTolerance.

bool	IsNormal (const gp_Dir &theOther, const double theAngularTolerance) const
	Returns True if the angle between this unit vector and the unit vector theOther is equal to Pi/2 (normal).

bool	IsOpposite (const gp_Dir &theOther, const double theAngularTolerance) const
	Returns True if the angle between this unit vector and the unit vector theOther is equal to Pi (opposite).

bool	IsParallel (const gp_Dir &theOther, const double theAngularTolerance) const
	Returns true if the angle between this unit vector and the unit vector theOther is equal to 0 or to Pi. Note: the tolerance criterion is given by theAngularTolerance.

double	Angle (const gp_Dir &theOther) const
	Computes the angular value in radians between <me> and <theOther>. This value is always positive in 3D space. Returns the angle in the range [0, PI].

double	AngleWithRef (const gp_Dir &theOther, const gp_Dir &theVRef) const
	Computes the angular value between <me> and <theOther>. <theVRef> is the direction of reference normal to <me> and <theOther> and its orientation gives the positive sense of rotation. If the cross product <me> ^ <theOther> has the same orientation as <theVRef> the angular value is positive else negative. Returns the angular value in the range -PI and PI (in radians). Raises DomainError if <me> and <theOther> are not parallel this exception is raised when <theVRef> is in the same plane as <me> and <theOther> The tolerance criterion is Resolution from package gp.

constexpr void	Cross (const gp_Dir &theRight)
	Computes the cross product between two directions Raises the exception ConstructionError if the two directions are parallel because the computed vector cannot be normalized to create a direction.

constexpr void	operator^= (const gp_Dir &theRight)

constexpr gp_Dir	Crossed (const gp_Dir &theRight) const
	Computes the triple vector product. <me> ^ (V1 ^ V2) Raises the exception ConstructionError if V1 and V2 are parallel or <me> and (V1^V2) are parallel because the computed vector can't be normalized to create a direction.

constexpr gp_Dir	operator^ (const gp_Dir &theRight) const

constexpr void	CrossCross (const gp_Dir &theV1, const gp_Dir &theV2)

constexpr gp_Dir	CrossCrossed (const gp_Dir &theV1, const gp_Dir &theV2) const
	Computes the double vector product this ^ (theV1 ^ theV2).

constexpr double	Dot (const gp_Dir &theOther) const noexcept
	Computes the scalar product.

constexpr double	operator* (const gp_Dir &theOther) const noexcept

constexpr double	DotCross (const gp_Dir &theV1, const gp_Dir &theV2) const noexcept
	Computes the triple scalar product <me> * (theV1 ^ theV2). Warnings : The computed vector theV1' = theV1 ^ theV2 is not normalized to create a unitary vector. So this method never raises an exception even if theV1 and theV2 are parallel.

constexpr void	Reverse () noexcept

constexpr gp_Dir	Reversed () const noexcept
	Reverses the orientation of a direction geometric transformations Performs the symmetrical transformation of a direction with respect to the direction V which is the center of the symmetry.

constexpr gp_Dir	operator- () const noexcept

void	Mirror (const gp_Dir &theV) noexcept

gp_Dir	Mirrored (const gp_Dir &theV) const noexcept
	Performs the symmetrical transformation of a direction with respect to the direction theV which is the center of the symmetry.

void	Mirror (const gp_Ax1 &theA1) noexcept

gp_Dir	Mirrored (const gp_Ax1 &theA1) const noexcept
	Performs the symmetrical transformation of a direction with respect to an axis placement which is the axis of the symmetry.

void	Mirror (const gp_Ax2 &theA2) noexcept

gp_Dir	Mirrored (const gp_Ax2 &theA2) const noexcept
	Performs the symmetrical transformation of a direction with respect to a plane. The axis placement theA2 locates the plane of the symmetry : (Location, XDirection, YDirection).

void	Rotate (const gp_Ax1 &theA1, const double theAng)

gp_Dir	Rotated (const gp_Ax1 &theA1, const double theAng) const
	Rotates a direction. theA1 is the axis of the rotation. theAng is the angular value of the rotation in radians.

void	Transform (const gp_Trsf &theT)

gp_Dir	Transformed (const gp_Trsf &theT) const
	Transforms a direction with a "Trsf" from gp. Warnings : If the scale factor of the "Trsf" theT is negative then the direction <me> is reversed.

void	DumpJson (Standard_OStream &theOStream, int theDepth=-1) const
	Dumps the content of me into the stream.

bool	InitFromJson (const Standard_SStream &theSStream, int &theStreamPos)
	Inits the content of me from the stream.

Detailed Description

Describes a unit vector in 3D space. This unit vector is also called "Direction". See Also gce_MakeDir which provides functions for more complex unit vector constructions Geom_Direction which provides additional functions for constructing unit vectors and works, in particular, with the parametric equations of unit vectors.

Member Enumeration Documentation

◆ D

enum class gp_Dir::D

strong

Standard directions in 3D space for optimized constexpr construction.

Enumerator
X	Direction along positive X axis (1, 0, 0)
Y	Direction along positive Y axis (0, 1, 0)
Z	Direction along positive Z axis (0, 0, 1)
NX	Direction along negative X axis (-1, 0, 0)
NY	Direction along negative Y axis (0, -1, 0)
NZ	Direction along negative Z axis (0, 0, -1)

Constructor & Destructor Documentation

◆ gp_Dir() [1/7]

constexpr gp_Dir::gp_Dir ( )

inlineconstexprnoexcept

Creates a direction corresponding to X axis.

◆ gp_Dir() [2/7]

constexpr gp_Dir::gp_Dir ( const D theDir )

inlineexplicitconstexprnoexcept

Creates a direction from a standard direction enumeration.

◆ gp_Dir() [3/7]

constexpr gp_Dir::gp_Dir ( const gp_Vec & theV )

inlineconstexpr

Normalizes the vector theV and creates a direction. Raises ConstructionError if theV.Magnitude() <= Resolution.

Note: Constexpr-compatible when input is already normalized.

◆ gp_Dir() [4/7]

constexpr gp_Dir::gp_Dir ( const gp_XYZ & theCoord )

inlineconstexpr

Creates a direction from a triplet of coordinates. Raises ConstructionError if theCoord.Modulus() <= Resolution from gp.

Note: Constexpr-compatible when input is already normalized.

◆ gp_Dir() [5/7]

constexpr gp_Dir::gp_Dir	(	const double	theXv,
		const double	theYv,
		const double	theZv )

inlineconstexpr

Creates a direction with its 3 cartesian coordinates. Raises ConstructionError if std::sqrt(theXv*theXv + theYv*theYv + theZv*theZv) <= Resolution Modification of the direction's coordinates If std::sqrt (theXv*theXv + theYv*theYv + theZv*theZv) <= Resolution from gp where theXv, theYv ,theZv are the new coordinates it is not possible to construct the direction and the method raises the exception ConstructionError.

Note: Constexpr-compatible when input is already normalized.

◆ gp_Dir() [6/7]

constexpr gp_Dir::gp_Dir ( const gp_Dir & )

constexprdefaultnoexcept

◆ gp_Dir() [7/7]

constexpr gp_Dir::gp_Dir ( gp_Dir && )

constexprdefaultnoexcept

Member Function Documentation

◆ Angle()

double gp_Dir::Angle ( const gp_Dir & theOther ) const

Computes the angular value in radians between <me> and <theOther>. This value is always positive in 3D space. Returns the angle in the range [0, PI].

◆ AngleWithRef()

double gp_Dir::AngleWithRef	(	const gp_Dir &	theOther,
		const gp_Dir &	theVRef ) const

Computes the angular value between <me> and <theOther>. <theVRef> is the direction of reference normal to <me> and <theOther> and its orientation gives the positive sense of rotation. If the cross product <me> ^ <theOther> has the same orientation as <theVRef> the angular value is positive else negative. Returns the angular value in the range -PI and PI (in radians). Raises DomainError if <me> and <theOther> are not parallel this exception is raised when <theVRef> is in the same plane as <me> and <theOther> The tolerance criterion is Resolution from package gp.

◆ Coord() [1/2]

constexpr double gp_Dir::Coord ( const int theIndex ) const

inlineconstexpr

Returns the coordinate of range theIndex : theIndex = 1 => X is returned theIndex = 2 => Y is returned theIndex = 3 => Z is returned Exceptions Standard_OutOfRange if theIndex is not 1, 2, or 3.

◆ Coord() [2/2]

constexpr void gp_Dir::Coord	(	double &	theXv,
		double &	theYv,
		double &	theZv ) const

inlineconstexprnoexcept

Returns for the unit vector its three coordinates theXv, theYv, and theZv.

◆ Cross()

constexpr void gp_Dir::Cross ( const gp_Dir & theRight )

inlineconstexpr

Computes the cross product between two directions Raises the exception ConstructionError if the two directions are parallel because the computed vector cannot be normalized to create a direction.

Note: Constexpr-compatible when result is already normalized.

◆ CrossCross()

constexpr void gp_Dir::CrossCross	(	const gp_Dir &	theV1,
		const gp_Dir &	theV2 )

inlineconstexpr

Note: Constexpr-compatible when result is already normalized.

◆ CrossCrossed()

constexpr gp_Dir gp_Dir::CrossCrossed	(	const gp_Dir &	theV1,
		const gp_Dir &	theV2 ) const

inlineconstexpr

Computes the double vector product this ^ (theV1 ^ theV2).

CrossCrossed creates a new unit vector. Exceptions Standard_ConstructionError if:
theV1 and theV2 are parallel, or
this unit vector and (theV1 ^ theV2) are parallel. This is because, in these conditions, the computed vector is null and cannot be normalized.
Note
Constexpr-compatible when result is already normalized.

◆ Crossed()

constexpr gp_Dir gp_Dir::Crossed ( const gp_Dir & theRight ) const

inlineconstexpr

Computes the triple vector product. <me> ^ (V1 ^ V2) Raises the exception ConstructionError if V1 and V2 are parallel or <me> and (V1^V2) are parallel because the computed vector can't be normalized to create a direction.

Note: Constexpr-compatible when result is already normalized.

◆ Dot()

constexpr double gp_Dir::Dot ( const gp_Dir & theOther ) const

inlineconstexprnoexcept

Computes the scalar product.

◆ DotCross()

constexpr double gp_Dir::DotCross	(	const gp_Dir &	theV1,
		const gp_Dir &	theV2 ) const

inlineconstexprnoexcept

Computes the triple scalar product <me> * (theV1 ^ theV2). Warnings : The computed vector theV1' = theV1 ^ theV2 is not normalized to create a unitary vector. So this method never raises an exception even if theV1 and theV2 are parallel.

◆ DumpJson()

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

Dumps the content of me into the stream.

◆ InitFromJson()

bool gp_Dir::InitFromJson	(	const Standard_SStream &	theSStream,
		int &	theStreamPos )

Inits the content of me from the stream.

◆ IsEqual()

bool gp_Dir::IsEqual	(	const gp_Dir &	theOther,
		const double	theAngularTolerance ) const

inline

Returns True if the angle between the two directions is lower or equal to theAngularTolerance.

◆ IsNormal()

bool gp_Dir::IsNormal	(	const gp_Dir &	theOther,
		const double	theAngularTolerance ) const

inline

Returns True if the angle between this unit vector and the unit vector theOther is equal to Pi/2 (normal).

◆ IsOpposite()

bool gp_Dir::IsOpposite	(	const gp_Dir &	theOther,
		const double	theAngularTolerance ) const

inline

Returns True if the angle between this unit vector and the unit vector theOther is equal to Pi (opposite).

◆ IsParallel()

bool gp_Dir::IsParallel	(	const gp_Dir &	theOther,
		const double	theAngularTolerance ) const

inline

Returns true if the angle between this unit vector and the unit vector theOther is equal to 0 or to Pi. Note: the tolerance criterion is given by theAngularTolerance.

◆ Mirror() [1/3]

void gp_Dir::Mirror ( const gp_Ax1 & theA1 )

noexcept

◆ Mirror() [2/3]

void gp_Dir::Mirror ( const gp_Ax2 & theA2 )

noexcept

◆ Mirror() [3/3]

void gp_Dir::Mirror ( const gp_Dir & theV )

noexcept

◆ Mirrored() [1/3]

gp_Dir gp_Dir::Mirrored ( const gp_Ax1 & theA1 ) const

noexcept

Performs the symmetrical transformation of a direction with respect to an axis placement which is the axis of the symmetry.

◆ Mirrored() [2/3]

gp_Dir gp_Dir::Mirrored ( const gp_Ax2 & theA2 ) const

noexcept

Performs the symmetrical transformation of a direction with respect to a plane. The axis placement theA2 locates the plane of the symmetry : (Location, XDirection, YDirection).

◆ Mirrored() [3/3]

gp_Dir gp_Dir::Mirrored ( const gp_Dir & theV ) const

noexcept

Performs the symmetrical transformation of a direction with respect to the direction theV which is the center of the symmetry.

◆ operator*()

constexpr double gp_Dir::operator* ( const gp_Dir & theOther ) const

inlineconstexprnoexcept

◆ operator-()

constexpr gp_Dir gp_Dir::operator- ( ) const

inlineconstexprnoexcept

◆ operator=() [1/2]

constexpr gp_Dir & gp_Dir::operator= ( const gp_Dir & )

constexprdefaultnoexcept

◆ operator=() [2/2]

constexpr gp_Dir & gp_Dir::operator= ( gp_Dir && )

constexprdefaultnoexcept

◆ operator^()

constexpr gp_Dir gp_Dir::operator^ ( const gp_Dir & theRight ) const

inlineconstexpr

◆ operator^=()

constexpr void gp_Dir::operator^= ( const gp_Dir & theRight )

inlineconstexpr

◆ Reverse()

constexpr void gp_Dir::Reverse ( )

inlineconstexprnoexcept

◆ Reversed()

constexpr gp_Dir gp_Dir::Reversed ( ) const

inlineconstexprnoexcept

Reverses the orientation of a direction geometric transformations Performs the symmetrical transformation of a direction with respect to the direction V which is the center of the symmetry.

◆ Rotate()

void gp_Dir::Rotate	(	const gp_Ax1 &	theA1,
		const double	theAng )

inline

◆ Rotated()

gp_Dir gp_Dir::Rotated	(	const gp_Ax1 &	theA1,
		const double	theAng ) const

inline

Rotates a direction. theA1 is the axis of the rotation. theAng is the angular value of the rotation in radians.

◆ SetCoord() [1/2]

constexpr void gp_Dir::SetCoord	(	const double	theXv,
		const double	theYv,
		const double	theZv )

inlineconstexpr

For this unit vector, assigns the values theXv, theYv and theZv to its three coordinates. Remember that all the coordinates of a unit vector are implicitly modified when any single one is changed directly.

Note: Constexpr-compatible when input is already normalized.

◆ SetCoord() [2/2]

constexpr void gp_Dir::SetCoord	(	const int	theIndex,
		const double	theXi )

inlineconstexpr

For this unit vector, assigns the value Xi to:

the X coordinate if theIndex is 1, or
the Y coordinate if theIndex is 2, or
the Z coordinate if theIndex is 3, and then normalizes it. Warning: Remember that all the coordinates of a unit vector are implicitly modified when any single one is changed directly. Exceptions Standard_OutOfRange if theIndex is not 1, 2, or 3. Standard_ConstructionError if either of the following is less than or equal to gp::Resolution():
std::sqrt(Xv*Xv + Yv*Yv + Zv*Zv), or
the modulus of the number triple formed by the new value theXi and the two other coordinates of this vector that were not directly modified.
Note
Constexpr-compatible when result is already normalized.

◆ SetX()

constexpr void gp_Dir::SetX ( const double theX )

inlineconstexpr

Assigns the given value to the X coordinate of this unit vector.

Note: Constexpr-compatible when result is already normalized.

◆ SetXYZ()

constexpr void gp_Dir::SetXYZ ( const gp_XYZ & theCoord )

inlineconstexpr

Assigns the three coordinates of theCoord to this unit vector.

Note: Constexpr-compatible when input is already normalized.

◆ SetY()

constexpr void gp_Dir::SetY ( const double theY )

inlineconstexpr

Assigns the given value to the Y coordinate of this unit vector.

Note: Constexpr-compatible when result is already normalized.

◆ SetZ()

constexpr void gp_Dir::SetZ ( const double theZ )

inlineconstexpr

Assigns the given value to the Z coordinate of this unit vector.

Note: Constexpr-compatible when result is already normalized.

◆ Transform()

void gp_Dir::Transform ( const gp_Trsf & theT )

◆ Transformed()

gp_Dir gp_Dir::Transformed ( const gp_Trsf & theT ) const

inline

Transforms a direction with a "Trsf" from gp. Warnings : If the scale factor of the "Trsf" theT is negative then the direction <me> is reversed.

◆ X()

constexpr double gp_Dir::X ( ) const

inlineconstexprnoexcept

Returns the X coordinate for a unit vector.

◆ XYZ()

constexpr const gp_XYZ & gp_Dir::XYZ ( ) const

inlineconstexprnoexcept

for this unit vector, returns its three coordinates as a number triple.

◆ Y()

constexpr double gp_Dir::Y ( ) const

inlineconstexprnoexcept

Returns the Y coordinate for a unit vector.

◆ Z()

constexpr double gp_Dir::Z ( ) const

inlineconstexprnoexcept

Returns the Z coordinate for a unit vector.

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

gp_Dir.hxx

Public Types

Public Member Functions

Detailed Description

Member Enumeration Documentation

◆ D

Constructor & Destructor Documentation

◆ gp_Dir() [1/7]

◆ gp_Dir() [2/7]

◆ gp_Dir() [3/7]

◆ gp_Dir() [4/7]

◆ gp_Dir() [5/7]

◆ gp_Dir() [6/7]

◆ gp_Dir() [7/7]

Member Function Documentation

◆ Angle()

◆ AngleWithRef()

◆ Coord() [1/2]

◆ Coord() [2/2]

◆ Cross()

◆ CrossCross()

◆ CrossCrossed()

◆ Crossed()

◆ Dot()

◆ DotCross()

◆ DumpJson()

◆ InitFromJson()

◆ IsEqual()

◆ IsNormal()

◆ IsOpposite()

◆ IsParallel()

◆ Mirror() [1/3]

◆ Mirror() [2/3]

◆ Mirror() [3/3]

◆ Mirrored() [1/3]

◆ Mirrored() [2/3]

◆ Mirrored() [3/3]

◆ operator*()

◆ operator-()

◆ operator=() [1/2]

◆ operator=() [2/2]

◆ operator^()

◆ operator^=()

◆ Reverse()

◆ Reversed()

◆ Rotate()

◆ Rotated()

◆ SetCoord() [1/2]

◆ SetCoord() [2/2]

◆ SetX()

◆ SetXYZ()

◆ SetY()

◆ SetZ()

◆ Transform()

◆ Transformed()

◆ X()

◆ XYZ()

◆ Y()

◆ Z()