gp_Ax2 Class Reference

Describes a right-handed coordinate system in 3D space. A coordinate system is defined by: More...

#include <gp_Ax2.hxx>

Public Member Functions
constexpr	gp_Ax2 () noexcept
	Creates an object corresponding to the reference coordinate system (OXYZ).
	gp_Ax2 (const gp_Pnt &P, const gp_Dir &N, const gp_Dir &Vx)
	Creates an axis placement with an origin P such that:
constexpr	gp_Ax2 (const gp_Pnt &theP, const gp_Dir::D theN, const gp_Dir::D theVx) noexcept
	Creates an axis placement with standard directions.
	gp_Ax2 (const gp_Pnt &P, const gp_Dir &V)
	Creates a coordinate system with an origin P, where V gives the "main Direction" (here, "X Direction" and "Y Direction" are defined automatically).
constexpr	gp_Ax2 (const gp_Pnt &theP, const gp_Dir::D theV) noexcept
	Creates a coordinate system with an origin P and standard main direction.
constexpr	gp_Ax2 (const gp_Dir::D theV) noexcept
	Creates a coordinate system at the origin with the given standard main direction. Replaces gp::XOY(), gp::YOZ(), gp::ZOX() static functions.
void	SetAxis (const gp_Ax1 &A1)
	Assigns the origin and "main Direction" of the axis A1 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 A1. Exceptions Standard_ConstructionError if A1 is parallel to the "X Direction" of this coordinate system.
void	SetDirection (const gp_Dir &V)
	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" = V ^ (previous "X Direction" ^ V) Exceptions Standard_ConstructionError if V is parallel to the "X Direction" of this coordinate system.
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 <Vx> is not normal to the main direction then <XDirection> is computed as follows XDirection = Direction ^ (Vx ^ Direction). Exceptions Standard_ConstructionError if Vx or Vy is parallel to the "main Direction" of this coordinate system.
void	SetYDirection (const gp_Dir &theVy)
	Changes the "Ydirection" of <me>. The main direction is not modified but the "Xdirection" is changed. If <Vy> is not normal to the main direction then "YDirection" is computed as follows YDirection = Direction ^ (<Vy> ^ Direction). Exceptions Standard_ConstructionError if Vx or Vy is parallel to the "main Direction" of this coordinate system.
double	Angle (const gp_Ax2 &theOther) const
	Computes the angular value, in radians, 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".
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>.
bool	IsCoplanar (const gp_Ax2 &Other, const double LinearTolerance, const double AngularTolerance) const
bool	IsCoplanar (const gp_Ax1 &A1, const double LinearTolerance, const double AngularTolerance) const
	Returns True if: . the distance between <me> and the "Location" point of A1 is lower of equal to LinearTolerance and . the main direction of <me> and the direction of A1 are normal. Note: the tolerance criterion for angular equality is given by AngularTolerance.
void	Mirror (const gp_Pnt &P) noexcept
	Performs a symmetrical transformation of this coordinate system with respect to:
gp_Ax2	Mirrored (const gp_Pnt &P) const noexcept
	Performs a symmetrical transformation of this coordinate system with respect to:
void	Mirror (const gp_Ax1 &A1)
	Performs a symmetrical transformation of this coordinate system with respect to:
gp_Ax2	Mirrored (const gp_Ax1 &A1) const
	Performs a symmetrical transformation of this coordinate system with respect to:
void	Mirror (const gp_Ax2 &A2)
	Performs a symmetrical transformation of this coordinate system with respect to:
gp_Ax2	Mirrored (const gp_Ax2 &A2) const
	Performs a symmetrical transformation of this coordinate system with respect to:
void	Rotate (const gp_Ax1 &theA1, const double theAng)
gp_Ax2	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.
constexpr void	Scale (const gp_Pnt &theP, const double theS) noexcept
constexpr gp_Ax2	Scaled (const gp_Pnt &theP, const double theS) const noexcept
	Applies a scaling transformation on the axis placement. The "Location" point of the axisplacement is modified. Warnings: If the scale 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_Ax2	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_Ax2	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_Ax2	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.

Static Protected Member Functions
static constexpr gp_Dir::D	getPerpendicularXDir (const gp_Dir::D theMainDir) noexcept
	Helper to compute perpendicular X direction for standard main directions.
static constexpr gp_Dir::D	getPerpendicularYDir (const gp_Dir::D theMainDir) noexcept
	Helper to compute Y direction (main x X) for standard directions.
static constexpr gp_Dir::D	crossStandardDir (const gp_Dir::D theA, const gp_Dir::D theB) noexcept
	Helper to compute cross product of two standard directions (right-handed: A x B)

Detailed Description

Describes a right-handed coordinate system in 3D space. A coordinate system is defined by:

• its origin (also referred to as its "Location point"), and
• three orthogonal unit vectors, termed respectively 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. The "main Direction" is also the "Z Direction". Since an Ax2 coordinate system is right-handed, its "main Direction" is always equal to the cross product of its "X Direction" and "Y Direction". (To define a left-handed coordinate system, use gp_Ax3.) 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 two axes", or
• to define geometric transformations. Note: we refer to the "X Axis", "Y Axis" and "Z Axis", respectively, as to 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".

Constructor & Destructor Documentation

gp_Ax2() [1/6]

constexpr gp_Ax2::gp_Ax2 ( )

inlineconstexprnoexcept

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

gp_Ax2() [2/6]

gp_Ax2::gp_Ax2 ( const gp_Pnt & P, const gp_Dir & N, const gp_Dir & Vx )

inline

Creates an axis placement with an origin P such that:

• N is the Direction, and
• the "X Direction" is normal to N, in the plane defined by the vectors (N, Vx): "X Direction" = (N ^ Vx) ^ N, Exception: raises ConstructionError if N and Vx are parallel (same or opposite orientation).

gp_Ax2() [3/6]

constexpr gp_Ax2::gp_Ax2 ( const gp_Pnt & theP, const gp_Dir::D theN, const gp_Dir::D theVx )

inlineconstexprnoexcept

Creates an axis placement with standard directions.

gp_Ax2() [4/6]

gp_Ax2::gp_Ax2	(	const gp_Pnt &	P,
		const gp_Dir &	V )

Creates a coordinate system with an origin P, where V gives the "main Direction" (here, "X Direction" and "Y Direction" are defined automatically).

gp_Ax2() [5/6]

constexpr gp_Ax2::gp_Ax2 ( const gp_Pnt & theP, const gp_Dir::D theV )

inlineconstexprnoexcept

Creates a coordinate system with an origin P and standard main direction.

gp_Ax2() [6/6]

constexpr gp_Ax2::gp_Ax2 ( const gp_Dir::D theV )

inlineexplicitconstexprnoexcept

Creates a coordinate system at the origin with the given standard main direction. Replaces gp::XOY(), gp::YOZ(), gp::ZOX() static functions.

Member Function Documentation

Angle()

double gp_Ax2::Angle ( const gp_Ax2 & theOther ) const

inline

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

Axis()

constexpr const gp_Ax1 & gp_Ax2::Axis ( ) const

inlineconstexprnoexcept

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

crossStandardDir()

constexpr gp_Dir::D gp_Ax2::crossStandardDir ( const gp_Dir::D theA, const gp_Dir::D theB )

inlinestaticconstexprprotectednoexcept

Helper to compute cross product of two standard directions (right-handed: A x B)

Direction()

constexpr const gp_Dir & gp_Ax2::Direction ( ) const

inlineconstexprnoexcept

Returns the main direction of <me>.

DumpJson()

void gp_Ax2::DumpJson	(	Standard_OStream &	theOStream,
		int	theDepth = -1 ) const

Dumps the content of me into the stream.

getPerpendicularXDir()

constexpr gp_Dir::D gp_Ax2::getPerpendicularXDir ( const gp_Dir::D theMainDir )

inlinestaticconstexprprotectednoexcept

Helper to compute perpendicular X direction for standard main directions.

getPerpendicularYDir()

constexpr gp_Dir::D gp_Ax2::getPerpendicularYDir ( const gp_Dir::D theMainDir )

inlinestaticconstexprprotectednoexcept

Helper to compute Y direction (main x X) for standard directions.

InitFromJson()

bool gp_Ax2::InitFromJson	(	const Standard_SStream &	theSStream,
		int &	theStreamPos )

Inits the content of me from the stream.

IsCoplanar() [1/2]

bool gp_Ax2::IsCoplanar ( const gp_Ax1 & A1, const double LinearTolerance, const double AngularTolerance ) const

inline

Returns True if: . the distance between <me> and the "Location" point of A1 is lower of equal to LinearTolerance and . the main direction of <me> and the direction of A1 are normal. Note: the tolerance criterion for angular equality is given by AngularTolerance.

IsCoplanar() [2/2]

bool gp_Ax2::IsCoplanar ( const gp_Ax2 & Other, const double LinearTolerance, const double AngularTolerance ) const

inline

Location()

constexpr const gp_Pnt & gp_Ax2::Location ( ) const

inlineconstexprnoexcept

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

Mirror() [1/3]

void gp_Ax2::Mirror

(

const gp_Ax1 &

A1

)

Performs a symmetrical transformation of this coordinate system with respect to:

• the axis A1, and assigns the result to this coordinate system. Warning This transformation is always performed on the origin. In case of a reflection with respect to a point:
• the main direction of the coordinate system is not changed, and
• the "X Direction" and the "Y Direction" are simply reversed In case of a reflection with respect to an axis or a plane:
• the transformation is applied to the "X Direction" and the "Y Direction", then
• the "main Direction" is recomputed as the cross product "X Direction" ^ "Y Direction". This maintains the right-handed property of the coordinate system.

Mirror() [2/3]

void gp_Ax2::Mirror

(

const gp_Ax2 &

A2

)

Performs a symmetrical transformation of this coordinate system with respect to:

• the plane defined by the origin, "X Direction" and "Y Direction" of coordinate system A2 and assigns the result to this coordinate system. Warning This transformation is always performed on the origin. In case of a reflection with respect to a point:
• the main direction of the coordinate system is not changed, and
• the "X Direction" and the "Y Direction" are simply reversed In case of a reflection with respect to an axis or a plane:
• the transformation is applied to the "X Direction" and the "Y Direction", then
• the "main Direction" is recomputed as the cross product "X Direction" ^ "Y Direction". This maintains the right-handed property of the coordinate system.

Mirror() [3/3]

void gp_Ax2::Mirror ( const gp_Pnt & P )

noexcept

Performs a symmetrical transformation of this coordinate system with respect to:

• the point P, and assigns the result to this coordinate system. Warning This transformation is always performed on the origin. In case of a reflection with respect to a point:
• the main direction of the coordinate system is not changed, and
• the "X Direction" and the "Y Direction" are simply reversed In case of a reflection with respect to an axis or a plane:
• the transformation is applied to the "X Direction" and the "Y Direction", then
• the "main Direction" is recomputed as the cross product "X Direction" ^ "Y Direction". This maintains the right-handed property of the coordinate system.

Mirrored() [1/3]

gp_Ax2 gp_Ax2::Mirrored

(

const gp_Ax1 &

A1

)

const

Performs a symmetrical transformation of this coordinate system with respect to:

• the axis A1, and creates a new one. Warning This transformation is always performed on the origin. In case of a reflection with respect to a point:
• the main direction of the coordinate system is not changed, and
• the "X Direction" and the "Y Direction" are simply reversed In case of a reflection with respect to an axis or a plane:
• the transformation is applied to the "X Direction" and the "Y Direction", then
• the "main Direction" is recomputed as the cross product "X Direction" ^ "Y Direction". This maintains the right-handed property of the coordinate system.

Mirrored() [2/3]

gp_Ax2 gp_Ax2::Mirrored

(

const gp_Ax2 &

A2

)

const

Performs a symmetrical transformation of this coordinate system with respect to:

• the plane defined by the origin, "X Direction" and "Y Direction" of coordinate system A2 and creates a new one. Warning This transformation is always performed on the origin. In case of a reflection with respect to a point:
• the main direction of the coordinate system is not changed, and
• the "X Direction" and the "Y Direction" are simply reversed In case of a reflection with respect to an axis or a plane:
• the transformation is applied to the "X Direction" and the "Y Direction", then
• the "main Direction" is recomputed as the cross product "X Direction" ^ "Y Direction". This maintains the right-handed property of the coordinate system.

Mirrored() [3/3]

gp_Ax2 gp_Ax2::Mirrored ( const gp_Pnt & P ) const

noexcept

Performs a symmetrical transformation of this coordinate system with respect to:

• the point P, and creates a new one. Warning This transformation is always performed on the origin. In case of a reflection with respect to a point:
• the main direction of the coordinate system is not changed, and
• the "X Direction" and the "Y Direction" are simply reversed In case of a reflection with respect to an axis or a plane:
• the transformation is applied to the "X Direction" and the "Y Direction", then
• the "main Direction" is recomputed as the cross product "X Direction" ^ "Y Direction". This maintains the right-handed property of the coordinate system.

Rotate()

void gp_Ax2::Rotate ( const gp_Ax1 & theA1, const double theAng )

inline

Rotated()

gp_Ax2 gp_Ax2::Rotated ( const gp_Ax1 & theA1, const double theAng ) const

inline

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

Scale()

constexpr void gp_Ax2::Scale ( const gp_Pnt & theP, const double theS )

inlineconstexprnoexcept

Scaled()

constexpr gp_Ax2 gp_Ax2::Scaled ( const gp_Pnt & theP, const double theS ) const

inlineconstexprnoexcept

Applies a scaling transformation on the axis placement. The "Location" point of the axisplacement is modified. Warnings: If the scale 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_Ax2::SetAxis ( const gp_Ax1 & A1 )

inline

Assigns the origin and "main Direction" of the axis A1 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 A1. Exceptions Standard_ConstructionError if A1 is parallel to the "X Direction" of this coordinate system.

SetDirection()

void gp_Ax2::SetDirection ( const gp_Dir & V )

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" = V ^ (previous "X Direction" ^ V) Exceptions Standard_ConstructionError if V is parallel to the "X Direction" of this coordinate system.

SetLocation()

constexpr void gp_Ax2::SetLocation ( const gp_Pnt & theP )

inlineconstexprnoexcept

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

SetXDirection()

void gp_Ax2::SetXDirection ( const gp_Dir & theVx )

inline

Changes the "Xdirection" of <me>. The main direction "Direction" is not modified, the "Ydirection" is modified. If <Vx> is not normal to the main direction then <XDirection> is computed as follows XDirection = Direction ^ (Vx ^ Direction). Exceptions Standard_ConstructionError if Vx or Vy is parallel to the "main Direction" of this coordinate system.

SetYDirection()

void gp_Ax2::SetYDirection ( const gp_Dir & theVy )

inline

Changes the "Ydirection" of <me>. The main direction is not modified but the "Xdirection" is changed. If <Vy> is not normal to the main direction then "YDirection" is computed as follows YDirection = Direction ^ (<Vy> ^ Direction). Exceptions Standard_ConstructionError if Vx or Vy is parallel to the "main Direction" of this coordinate system.

Transform()

void gp_Ax2::Transform ( const gp_Trsf & theT )

inline

Transformed()

gp_Ax2 gp_Ax2::Transformed ( const gp_Trsf & theT ) const

inline

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]

constexpr void gp_Ax2::Translate ( const gp_Pnt & theP1, const gp_Pnt & theP2 )

inlineconstexprnoexcept

Translate() [2/2]

constexpr void gp_Ax2::Translate ( const gp_Vec & theV )

inlineconstexprnoexcept

Translated() [1/2]

constexpr gp_Ax2 gp_Ax2::Translated ( const gp_Pnt & theP1, const gp_Pnt & theP2 ) const

inlineconstexprnoexcept

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

Translated() [2/2]

constexpr gp_Ax2 gp_Ax2::Translated ( const gp_Vec & theV ) const

inlineconstexprnoexcept

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

XDirection()

constexpr const gp_Dir & gp_Ax2::XDirection ( ) const

inlineconstexprnoexcept

Returns the "XDirection" of <me>.

YDirection()

constexpr const gp_Dir & gp_Ax2::YDirection ( ) const

inlineconstexprnoexcept

Returns the "YDirection" of <me>.

---

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

• gp_Ax2.hxx