Describes a coordinate system in 3D space. Unlike a gp_Ax2 coordinate system, a gp_Ax3 can be right-handed ("direct sense") or left-handed ("indirect sense"). A coordinate system is defined by: More...

#include <gp_Ax3.hxx>

Public Member Functions
constexpr	gp_Ax3 () noexcept
	Creates an object corresponding to the reference coordinate system (OXYZ).
	gp_Ax3 (const gp_Ax2 &theA)
	Creates a coordinate system from a right-handed coordinate system.
	gp_Ax3 (const gp_Pnt &theP, const gp_Dir &theN, const gp_Dir &theVx)
	Creates a right handed axis placement with the "Location" point theP and two directions, theN gives the "Direction" and theVx gives the "XDirection". Raises ConstructionError if theN and theVx are parallel (same or opposite orientation).
constexpr	gp_Ax3 (const gp_Pnt &theP, const gp_Dir::D theN, const gp_Dir::D theVx) noexcept
	Creates an axis placement with standard directions. This constructor allows constexpr and noexcept construction when using standard directions.
	gp_Ax3 (const gp_Pnt &theP, const gp_Dir &theV)
	Creates an axis placement with the "Location" point <theP> and the normal direction <theV>.
constexpr	gp_Ax3 (const gp_Pnt &theP, const gp_Dir::D theV) noexcept
	Creates an axis placement with the given location point and standard direction.
constexpr	gp_Ax3 (const gp_Dir::D theV) noexcept
	Creates an axis placement at the origin with the given standard direction.
constexpr void	XReverse () noexcept
	Reverses the X direction of <me>.
constexpr void	YReverse () noexcept
	Reverses the Y direction of <me>.
constexpr void	ZReverse () noexcept
	Reverses the Z direction of <me>.
void	SetAxis (const gp_Ax1 &theA1)
	Assigns the origin and "main Direction" of the axis theA1 to this coordinate system, then recomputes its "X Direction" and "Y Direction". Note:
void	SetDirection (const gp_Dir &theV)
	Changes the main direction of this coordinate system, then recomputes its "X Direction" and "Y Direction". Note:
constexpr void	SetLocation (const gp_Pnt &theP) noexcept
	Changes the "Location" point (origin) of <me>.
void	SetXDirection (const gp_Dir &theVx)
	Changes the "Xdirection" of <me>. The main direction "Direction" is not modified, the "Ydirection" is modified. If <theVx> is not normal to the main direction then <XDirection> is computed as follows XDirection = Direction ^ (theVx ^ Direction). Raises ConstructionError if <theVx> is parallel (same or opposite orientation) to the main direction of <me>.
void	SetYDirection (const gp_Dir &theVy)
	Changes the "Ydirection" of <me>. The main direction is not modified but the "Xdirection" is changed. If <theVy> is not normal to the main direction then "YDirection" is computed as follows YDirection = Direction ^ (<theVy> ^ Direction). Raises ConstructionError if <theVy> is parallel to the main direction of <me>.
double	Angle (const gp_Ax3 &theOther) const
	Computes the angular value between the main direction of <me> and the main direction of <theOther>. Returns the angle between 0 and PI in radians.
constexpr const gp_Ax1 &	Axis () const noexcept
	Returns the main axis of <me>. It is the "Location" point and the main "Direction".
gp_Ax2	Ax2 () const
	Computes a right-handed coordinate system with the same "X Direction" and "Y Direction" as those of this coordinate system, then recomputes the "main Direction". If this coordinate system is right-handed, the result returned is the same coordinate system. If this coordinate system is left-handed, the result is reversed.
constexpr const gp_Dir &	Direction () const noexcept
	Returns the main direction of <me>.
constexpr const gp_Pnt &	Location () const noexcept
	Returns the "Location" point (origin) of <me>.
constexpr const gp_Dir &	XDirection () const noexcept
	Returns the "XDirection" of <me>.
constexpr const gp_Dir &	YDirection () const noexcept
	Returns the "YDirection" of <me>.
constexpr bool	Direct () const
	Returns True if the coordinate system is right-handed. i.e. XDirection().Crossed(YDirection()).Dot(Direction()) > 0.
bool	IsCoplanar (const gp_Ax3 &theOther, const double theLinearTolerance, const double theAngularTolerance) const
	Returns True if . the distance between the "Location" point of <me> and <theOther> is lower or equal to theLinearTolerance and . the distance between the "Location" point of <theOther> and <me> is lower or equal to theLinearTolerance and . the main direction of <me> and the main direction of <theOther> are parallel (same or opposite orientation).
bool	IsCoplanar (const gp_Ax1 &theA1, const double theLinearTolerance, const double theAngularTolerance) const
	Returns True if . the distance between <me> and the "Location" point of theA1 is lower of equal to theLinearTolerance and . the distance between theA1 and the "Location" point of <me> is lower or equal to theLinearTolerance and . the main direction of <me> and the direction of theA1 are normal.
void	Mirror (const gp_Pnt &theP) noexcept
gp_Ax3	Mirrored (const gp_Pnt &theP) const noexcept
	Performs the symmetrical transformation of an axis placement with respect to the point theP which is the center of the symmetry. Warnings : The main direction of the axis placement is not changed. The "XDirection" and the "YDirection" are reversed. So the axis placement stay right handed.
void	Mirror (const gp_Ax1 &theA1) noexcept
gp_Ax3	Mirrored (const gp_Ax1 &theA1) const noexcept
	Performs the symmetrical transformation of an axis placement with respect to an axis placement which is the axis of the symmetry. The transformation is performed on the "Location" point, on the "XDirection" and "YDirection". The resulting main "Direction" is the cross product between the "XDirection" and the "YDirection" after transformation.
void	Mirror (const gp_Ax2 &theA2) noexcept
gp_Ax3	Mirrored (const gp_Ax2 &theA2) const noexcept
	Performs the symmetrical transformation of an axis placement with respect to a plane. The axis placement <theA2> locates the plane of the symmetry: (Location, XDirection, YDirection). The transformation is performed on the "Location" point, on the "XDirection" and "YDirection". The resulting main "Direction" is the cross product between the "XDirection" and the "YDirection" after transformation.
void	Rotate (const gp_Ax1 &theA1, const double theAng)
gp_Ax3	Rotated (const gp_Ax1 &theA1, const double theAng) const
	Rotates an axis placement. <theA1> is the axis of the rotation. theAng is the angular value of the rotation in radians.
void	Scale (const gp_Pnt &theP, const double theS)
gp_Ax3	Scaled (const gp_Pnt &theP, const double theS) const
	Applies a scaling transformation on the axis placement. The "Location" point of the axisplacement is modified. Warnings: If the scale <theS> is negative : . the main direction of the axis placement is not changed. . The "XDirection" and the "YDirection" are reversed. So the axis placement stay right handed.
void	Transform (const gp_Trsf &theT)
gp_Ax3	Transformed (const gp_Trsf &theT) const
	Transforms an axis placement with a Trsf. The "Location" point, the "XDirection" and the "YDirection" are transformed with theT. The resulting main "Direction" of <me> is the cross product between the "XDirection" and the "YDirection" after transformation.
constexpr void	Translate (const gp_Vec &theV) noexcept
constexpr gp_Ax3	Translated (const gp_Vec &theV) const noexcept
	Translates an axis plaxement in the direction of the vector <theV>. The magnitude of the translation is the vector's magnitude.
constexpr void	Translate (const gp_Pnt &theP1, const gp_Pnt &theP2) noexcept
constexpr gp_Ax3	Translated (const gp_Pnt &theP1, const gp_Pnt &theP2) const noexcept
	Translates an axis placement from the point <theP1> to the point <theP2>.
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 coordinate system in 3D space. Unlike a gp_Ax2 coordinate system, a gp_Ax3 can be right-handed ("direct sense") or left-handed ("indirect sense"). A coordinate system is defined by:

its origin (also referred to as its "Location point"), and
three orthogonal unit vectors, termed the "X Direction", the "Y Direction" and the "Direction" (also referred to as the "main Direction"). The "Direction" of the coordinate system is called its "main Direction" because whenever this unit vector is modified, the "X Direction" and the "Y Direction" are recomputed. However, when we modify either the "X Direction" or the "Y Direction", "Direction" is not modified. "Direction" is also the "Z Direction". The "main Direction" is always parallel to the cross product of its "X Direction" and "Y Direction". If the coordinate system is right-handed, it satisfies the equation: "main Direction" = "X Direction" ^ "Y Direction" and if it is left-handed, it satisfies the equation: "main Direction" = -"X Direction" ^ "Y Direction" A coordinate system is used:
to describe geometric entities, in particular to position them. The local coordinate system of a geometric entity serves the same purpose as the STEP function "axis placement three axes", or
to define geometric transformations. Note:
We refer to the "X Axis", "Y Axis" and "Z Axis", respectively, as the axes having:
the origin of the coordinate system as their origin, and
the unit vectors "X Direction", "Y Direction" and "main Direction", respectively, as their unit vectors.
The "Z Axis" is also the "main Axis".
gp_Ax2 is used to define a coordinate system that must be always right-handed.

Constructor & Destructor Documentation

◆ gp_Ax3() [1/7]

gp_Ax3::gp_Ax3 ( )

inlineconstexprnoexcept

Creates an object corresponding to the reference coordinate system (OXYZ).

◆ gp_Ax3() [2/7]

gp_Ax3::gp_Ax3 ( const gp_Ax2 & theA )

inline

Creates a coordinate system from a right-handed coordinate system.

◆ gp_Ax3() [3/7]

gp_Ax3::gp_Ax3	(	const gp_Pnt &	theP,
		const gp_Dir &	theN,
		const gp_Dir &	theVx )

inline

Creates a right handed axis placement with the "Location" point theP and two directions, theN gives the "Direction" and theVx gives the "XDirection". Raises ConstructionError if theN and theVx are parallel (same or opposite orientation).

◆ gp_Ax3() [4/7]

gp_Ax3::gp_Ax3	(	const gp_Pnt &	theP,
		const gp_Dir::D	theN,
		const gp_Dir::D	theVx )

inlineconstexprnoexcept

Creates an axis placement with standard directions. This constructor allows constexpr and noexcept construction when using standard directions.

◆ gp_Ax3() [5/7]

gp_Ax3::gp_Ax3	(	const gp_Pnt &	theP,
		const gp_Dir &	theV )

Creates an axis placement with the "Location" point <theP> and the normal direction <theV>.

◆ gp_Ax3() [6/7]

gp_Ax3::gp_Ax3	(	const gp_Pnt &	theP,
		const gp_Dir::D	theV )

inlineconstexprnoexcept

Creates an axis placement with the given location point and standard direction.

◆ gp_Ax3() [7/7]

gp_Ax3::gp_Ax3 ( const gp_Dir::D theV )

inlineexplicitconstexprnoexcept

Creates an axis placement at the origin with the given standard direction.

Member Function Documentation

◆ Angle()

double gp_Ax3::Angle ( const gp_Ax3 & theOther ) const

inline

Computes the angular value between the main direction of <me> and the main direction of <theOther>. Returns the angle between 0 and PI in radians.

◆ Ax2()

gp_Ax2 gp_Ax3::Ax2 ( ) const

inline

Computes a right-handed coordinate system with the same "X Direction" and "Y Direction" as those of this coordinate system, then recomputes the "main Direction". If this coordinate system is right-handed, the result returned is the same coordinate system. If this coordinate system is left-handed, the result is reversed.

◆ Axis()

const gp_Ax1 & gp_Ax3::Axis ( ) const

inlineconstexprnoexcept

Returns the main axis of <me>. It is the "Location" point and the main "Direction".

◆ Direct()

bool gp_Ax3::Direct ( ) const

inlineconstexpr

Returns True if the coordinate system is right-handed. i.e. XDirection().Crossed(YDirection()).Dot(Direction()) > 0.

◆ Direction()

const gp_Dir & gp_Ax3::Direction ( ) const

inlineconstexprnoexcept

Returns the main direction of <me>.

◆ DumpJson()

void gp_Ax3::DumpJson	(	Standard_OStream &	theOStream,
		int	theDepth = -1 ) const

Dumps the content of me into the stream.

◆ InitFromJson()

bool gp_Ax3::InitFromJson	(	const Standard_SStream &	theSStream,
		int &	theStreamPos )

Inits the content of me from the stream.

◆ IsCoplanar() [1/2]

bool gp_Ax3::IsCoplanar	(	const gp_Ax1 &	theA1,
		const double	theLinearTolerance,
		const double	theAngularTolerance ) const

inline

Returns True if . the distance between <me> and the "Location" point of theA1 is lower of equal to theLinearTolerance and . the distance between theA1 and the "Location" point of <me> is lower or equal to theLinearTolerance and . the main direction of <me> and the direction of theA1 are normal.

◆ IsCoplanar() [2/2]

bool gp_Ax3::IsCoplanar	(	const gp_Ax3 &	theOther,
		const double	theLinearTolerance,
		const double	theAngularTolerance ) const

inline

Returns True if . the distance between the "Location" point of <me> and <theOther> is lower or equal to theLinearTolerance and . the distance between the "Location" point of <theOther> and <me> is lower or equal to theLinearTolerance and . the main direction of <me> and the main direction of <theOther> are parallel (same or opposite orientation).

◆ Location()

const gp_Pnt & gp_Ax3::Location ( ) const

inlineconstexprnoexcept

Returns the "Location" point (origin) of <me>.

◆ Mirror() [1/3]

void gp_Ax3::Mirror ( const gp_Ax1 & theA1 )

noexcept

◆ Mirror() [2/3]

void gp_Ax3::Mirror ( const gp_Ax2 & theA2 )

noexcept

◆ Mirror() [3/3]

void gp_Ax3::Mirror ( const gp_Pnt & theP )

noexcept

◆ Mirrored() [1/3]

gp_Ax3 gp_Ax3::Mirrored ( const gp_Ax1 & theA1 ) const

nodiscardnoexcept

Performs the symmetrical transformation of an axis placement with respect to an axis placement which is the axis of the symmetry. The transformation is performed on the "Location" point, on the "XDirection" and "YDirection". The resulting main "Direction" is the cross product between the "XDirection" and the "YDirection" after transformation.

◆ Mirrored() [2/3]

gp_Ax3 gp_Ax3::Mirrored ( const gp_Ax2 & theA2 ) const

nodiscardnoexcept

Performs the symmetrical transformation of an axis placement with respect to a plane. The axis placement <theA2> locates the plane of the symmetry: (Location, XDirection, YDirection). The transformation is performed on the "Location" point, on the "XDirection" and "YDirection". The resulting main "Direction" is the cross product between the "XDirection" and the "YDirection" after transformation.

◆ Mirrored() [3/3]

gp_Ax3 gp_Ax3::Mirrored ( const gp_Pnt & theP ) const

nodiscardnoexcept

Performs the symmetrical transformation of an axis placement with respect to the point theP which is the center of the symmetry. Warnings : The main direction of the axis placement is not changed. The "XDirection" and the "YDirection" are reversed. So the axis placement stay right handed.

◆ Rotate()

void gp_Ax3::Rotate	(	const gp_Ax1 &	theA1,
		const double	theAng )

inline

◆ Rotated()

gp_Ax3 gp_Ax3::Rotated	(	const gp_Ax1 &	theA1,
		const double	theAng ) const

inlinenodiscard

Rotates an axis placement. <theA1> is the axis of the rotation. theAng is the angular value of the rotation in radians.

◆ Scale()

void gp_Ax3::Scale	(	const gp_Pnt &	theP,
		const double	theS )

inline

◆ Scaled()

gp_Ax3 gp_Ax3::Scaled	(	const gp_Pnt &	theP,
		const double	theS ) const

inlinenodiscard

Applies a scaling transformation on the axis placement. The "Location" point of the axisplacement is modified. Warnings: If the scale <theS> is negative : . the main direction of the axis placement is not changed. . The "XDirection" and the "YDirection" are reversed. So the axis placement stay right handed.

◆ SetAxis()

void gp_Ax3::SetAxis ( const gp_Ax1 & theA1 )

inline

Assigns the origin and "main Direction" of the axis theA1 to this coordinate system, then recomputes its "X Direction" and "Y Direction". Note:

The new "X Direction" is computed as follows: new "X Direction" = V1 ^(previous "X Direction" ^ V) where V is the "Direction" of theA1.
The orientation of this coordinate system (right-handed or left-handed) is not modified. Raises ConstructionError if the "Direction" of <theA1> and the "XDirection" of <me> are parallel (same or opposite orientation) because it is impossible to calculate the new "XDirection" and the new "YDirection".

◆ SetDirection()

void gp_Ax3::SetDirection ( const gp_Dir & theV )

inline

Changes the main direction of this coordinate system, then recomputes its "X Direction" and "Y Direction". Note:

The new "X Direction" is computed as follows: new "X Direction" = theV ^ (previous "X Direction" ^ theV).
The orientation of this coordinate system (left- or right-handed) is not modified. Raises ConstructionError if <theV> and the previous "XDirection" are parallel because it is impossible to calculate the new "XDirection" and the new "YDirection".

◆ SetLocation()

void gp_Ax3::SetLocation ( const gp_Pnt & theP )

inlineconstexprnoexcept

Changes the "Location" point (origin) of <me>.

◆ SetXDirection()

void gp_Ax3::SetXDirection ( const gp_Dir & theVx )

inline

Changes the "Xdirection" of <me>. The main direction "Direction" is not modified, the "Ydirection" is modified. If <theVx> is not normal to the main direction then <XDirection> is computed as follows XDirection = Direction ^ (theVx ^ Direction). Raises ConstructionError if <theVx> is parallel (same or opposite orientation) to the main direction of <me>.

◆ SetYDirection()

void gp_Ax3::SetYDirection ( const gp_Dir & theVy )

inline

Changes the "Ydirection" of <me>. The main direction is not modified but the "Xdirection" is changed. If <theVy> is not normal to the main direction then "YDirection" is computed as follows YDirection = Direction ^ (<theVy> ^ Direction). Raises ConstructionError if <theVy> is parallel to the main direction of <me>.

◆ Transform()

void gp_Ax3::Transform ( const gp_Trsf & theT )

inline

◆ Transformed()

gp_Ax3 gp_Ax3::Transformed ( const gp_Trsf & theT ) const

inlinenodiscard

Transforms an axis placement with a Trsf. The "Location" point, the "XDirection" and the "YDirection" are transformed with theT. The resulting main "Direction" of <me> is the cross product between the "XDirection" and the "YDirection" after transformation.

◆ Translate() [1/2]

void gp_Ax3::Translate	(	const gp_Pnt &	theP1,
		const gp_Pnt &	theP2 )

inlineconstexprnoexcept

◆ Translate() [2/2]

void gp_Ax3::Translate ( const gp_Vec & theV )

inlineconstexprnoexcept

◆ Translated() [1/2]

gp_Ax3 gp_Ax3::Translated	(	const gp_Pnt &	theP1,
		const gp_Pnt &	theP2 ) const

inlinenodiscardconstexprnoexcept

Translates an axis placement from the point <theP1> to the point <theP2>.

◆ Translated() [2/2]

gp_Ax3 gp_Ax3::Translated ( const gp_Vec & theV ) const

inlinenodiscardconstexprnoexcept

Translates an axis plaxement in the direction of the vector <theV>. The magnitude of the translation is the vector's magnitude.

◆ XDirection()

const gp_Dir & gp_Ax3::XDirection ( ) const

inlineconstexprnoexcept

Returns the "XDirection" of <me>.

◆ XReverse()

void gp_Ax3::XReverse ( )

inlineconstexprnoexcept

Reverses the X direction of <me>.

◆ YDirection()

const gp_Dir & gp_Ax3::YDirection ( ) const

inlineconstexprnoexcept

Returns the "YDirection" of <me>.

◆ YReverse()

void gp_Ax3::YReverse ( )

inlineconstexprnoexcept

Reverses the Y direction of <me>.

◆ ZReverse()

void gp_Ax3::ZReverse ( )

inlineconstexprnoexcept

Reverses the Z direction of <me>.

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

gp_Ax3.hxx

Public Member Functions

Detailed Description

Constructor & Destructor Documentation

◆ gp_Ax3() [1/7]

◆ gp_Ax3() [2/7]

◆ gp_Ax3() [3/7]

◆ gp_Ax3() [4/7]

◆ gp_Ax3() [5/7]

◆ gp_Ax3() [6/7]

◆ gp_Ax3() [7/7]

Member Function Documentation

◆ Angle()

◆ Ax2()

◆ Axis()

◆ Direct()

◆ Direction()

◆ DumpJson()

◆ InitFromJson()

◆ IsCoplanar() [1/2]

◆ IsCoplanar() [2/2]

◆ Location()

◆ Mirror() [1/3]

◆ Mirror() [2/3]

◆ Mirror() [3/3]

◆ Mirrored() [1/3]

◆ Mirrored() [2/3]

◆ Mirrored() [3/3]

◆ Rotate()

◆ Rotated()

◆ Scale()

◆ Scaled()

◆ SetAxis()

◆ SetDirection()

◆ SetLocation()

◆ SetXDirection()

◆ SetYDirection()

◆ Transform()

◆ Transformed()

◆ Translate() [1/2]

◆ Translate() [2/2]

◆ Translated() [1/2]

◆ Translated() [2/2]

◆ XDirection()

◆ XReverse()

◆ YDirection()

◆ YReverse()

◆ ZReverse()