Describes a parabola in 3D space. A parabola is defined by its focal length (that is, the distance between its focus and apex) and positioned in space with a coordinate system (a gp_Ax2 object) where: More...

#include <gp_Parab.hxx>

Public Member Functions
constexpr	gp_Parab () noexcept
	Creates an indefinite Parabola.

constexpr	gp_Parab (const gp_Ax2 &theA2, const double theFocal)
	Creates a parabola with its local coordinate system "theA2" and it's focal length "Focal". The XDirection of theA2 defines the axis of symmetry of the parabola. The YDirection of theA2 is parallel to the directrix of the parabola. The Location point of theA2 is the vertex of the parabola Raises ConstructionError if theFocal < 0.0 Raised if theFocal < 0.0.

	gp_Parab (const gp_Ax1 &theD, const gp_Pnt &theF)
	theD is the directrix of the parabola and theF the focus point. The symmetry axis (XAxis) of the parabola is normal to the directrix and pass through the focus point theF, but its location point is the vertex of the parabola. The YAxis of the parabola is parallel to theD and its location point is the vertex of the parabola. The normal to the plane of the parabola is the cross product between the XAxis and the YAxis.

void	SetAxis (const gp_Ax1 &theA1)
	Modifies this parabola by redefining its local coordinate system so that.

void	SetFocal (const double theFocal)
	Changes the focal distance of the parabola. Raises ConstructionError if theFocal < 0.0.

constexpr void	SetLocation (const gp_Pnt &theP) noexcept
	Changes the location of the parabola. It is the vertex of the parabola.

constexpr void	SetPosition (const gp_Ax2 &theA2) noexcept
	Changes the local coordinate system of the parabola.

constexpr const gp_Ax1 &	Axis () const noexcept
	Returns the main axis of the parabola. It is the axis normal to the plane of the parabola passing through the vertex of the parabola.

gp_Ax1	Directrix () const
	Computes the directrix of this parabola. The directrix is:

constexpr double	Focal () const noexcept
	Returns the distance between the vertex and the focus of the parabola.

gp_Pnt	Focus () const

constexpr const gp_Pnt &	Location () const noexcept
	Returns the vertex of the parabola. It is the "Location" point of the coordinate system of the parabola.

constexpr double	Parameter () const noexcept
	Computes the parameter of the parabola. It is the distance between the focus and the directrix of the parabola. This distance is twice the focal length.

constexpr const gp_Ax2 &	Position () const noexcept
	Returns the local coordinate system of the parabola.

constexpr gp_Ax1	XAxis () const noexcept
	Returns the symmetry axis of the parabola. The location point of the axis is the vertex of the parabola.

constexpr gp_Ax1	YAxis () const noexcept
	It is an axis parallel to the directrix of the parabola. The location point of this axis is the vertex of the parabola.

void	Mirror (const gp_Pnt &theP) noexcept

gp_Parab	Mirrored (const gp_Pnt &theP) const noexcept
	Performs the symmetrical transformation of a parabola with respect to the point theP which is the center of the symmetry.

void	Mirror (const gp_Ax1 &theA1)

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

void	Mirror (const gp_Ax2 &theA2)

gp_Parab	Mirrored (const gp_Ax2 &theA2) const
	Performs the symmetrical transformation of a parabola 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_Parab	Rotated (const gp_Ax1 &theA1, const double theAng) const
	Rotates a parabola. theA1 is the axis of the rotation. Ang is the angular value of the rotation in radians.

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

gp_Parab	Scaled (const gp_Pnt &theP, const double theS) const
	Scales a parabola. theS is the scaling value. If theS is negative the direction of the symmetry axis XAxis is reversed and the direction of the YAxis too.

void	Transform (const gp_Trsf &theT)

gp_Parab	Transformed (const gp_Trsf &theT) const
	Transforms a parabola with the transformation theT from class Trsf.

constexpr void	Translate (const gp_Vec &theV) noexcept

constexpr gp_Parab	Translated (const gp_Vec &theV) const noexcept
	Translates a parabola 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_Parab	Translated (const gp_Pnt &theP1, const gp_Pnt &theP2) const noexcept
	Translates a parabola from the point theP1 to the point theP2.

Detailed Description

Describes a parabola in 3D space. A parabola is defined by its focal length (that is, the distance between its focus and apex) and positioned in space with a coordinate system (a gp_Ax2 object) where:

the origin of the coordinate system is on the apex of the parabola,
the "X Axis" of the coordinate system is the axis of symmetry; the parabola is on the positive side of this axis, and
the origin, "X Direction" and "Y Direction" of the coordinate system define the plane of the parabola. The equation of the parabola in this coordinate system, which is the "local coordinate system" of the parabola, is:
Y**2 = (2*P) * X.

where P, referred to as the parameter of the parabola, is the distance between the focus and the directrix (P is twice the focal length). The "main Direction" of the local coordinate system gives the normal vector to the plane of the parabola. See Also gce_MakeParab which provides functions for more complex parabola constructions Geom_Parabola which provides additional functions for constructing parabolas and works, in particular, with the parametric equations of parabolas

Constructor & Destructor Documentation

◆ gp_Parab() [1/3]

constexpr gp_Parab::gp_Parab ( )

inlineconstexprnoexcept

Creates an indefinite Parabola.

◆ gp_Parab() [2/3]

constexpr gp_Parab::gp_Parab	(	const gp_Ax2 &	theA2,
		const double	theFocal )

inlineconstexpr

Creates a parabola with its local coordinate system "theA2" and it's focal length "Focal". The XDirection of theA2 defines the axis of symmetry of the parabola. The YDirection of theA2 is parallel to the directrix of the parabola. The Location point of theA2 is the vertex of the parabola Raises ConstructionError if theFocal < 0.0 Raised if theFocal < 0.0.

◆ gp_Parab() [3/3]

gp_Parab::gp_Parab	(	const gp_Ax1 &	theD,
		const gp_Pnt &	theF )

inline

theD is the directrix of the parabola and theF the focus point. The symmetry axis (XAxis) of the parabola is normal to the directrix and pass through the focus point theF, but its location point is the vertex of the parabola. The YAxis of the parabola is parallel to theD and its location point is the vertex of the parabola. The normal to the plane of the parabola is the cross product between the XAxis and the YAxis.

Member Function Documentation

◆ Axis()

constexpr const gp_Ax1 & gp_Parab::Axis ( ) const

inlineconstexprnoexcept

Returns the main axis of the parabola. It is the axis normal to the plane of the parabola passing through the vertex of the parabola.

◆ Directrix()

gp_Ax1 gp_Parab::Directrix ( ) const

inline

Computes the directrix of this parabola. The directrix is:

a line parallel to the "Y Direction" of the local coordinate system of this parabola, and
located on the negative side of the axis of symmetry, at a distance from the apex which is equal to the focal length of this parabola. The directrix is returned as an axis (a gp_Ax1 object), the origin of which is situated on the "X Axis" of this parabola.

◆ Focal()

constexpr double gp_Parab::Focal ( ) const

inlineconstexprnoexcept

Returns the distance between the vertex and the focus of the parabola.

◆ Focus()

gp_Pnt gp_Parab::Focus ( ) const

inline

Computes the focus of the parabola.

◆ Location()

constexpr const gp_Pnt & gp_Parab::Location ( ) const

inlineconstexprnoexcept

Returns the vertex of the parabola. It is the "Location" point of the coordinate system of the parabola.

◆ Mirror() [1/3]

void gp_Parab::Mirror ( const gp_Ax1 & theA1 )

◆ Mirror() [2/3]

void gp_Parab::Mirror ( const gp_Ax2 & theA2 )

◆ Mirror() [3/3]

void gp_Parab::Mirror ( const gp_Pnt & theP )

noexcept

◆ Mirrored() [1/3]

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

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

◆ Mirrored() [2/3]

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

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

◆ Mirrored() [3/3]

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

noexcept

Performs the symmetrical transformation of a parabola with respect to the point theP which is the center of the symmetry.

◆ Parameter()

constexpr double gp_Parab::Parameter ( ) const

inlineconstexprnoexcept

Computes the parameter of the parabola. It is the distance between the focus and the directrix of the parabola. This distance is twice the focal length.

◆ Position()

constexpr const gp_Ax2 & gp_Parab::Position ( ) const

inlineconstexprnoexcept

Returns the local coordinate system of the parabola.

◆ Rotate()

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

inline

◆ Rotated()

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

inline

Rotates a parabola. theA1 is the axis of the rotation. Ang is the angular value of the rotation in radians.

◆ Scale()

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

inline

◆ Scaled()

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

inline

Scales a parabola. theS is the scaling value. If theS is negative the direction of the symmetry axis XAxis is reversed and the direction of the YAxis too.

◆ SetAxis()

void gp_Parab::SetAxis ( const gp_Ax1 & theA1 )

inline

Modifies this parabola by redefining its local coordinate system so that.

its origin and "main Direction" become those of the axis theA1 (the "X Direction" and "Y Direction" are then recomputed in the same way as for any gp_Ax2) Raises ConstructionError if the direction of theA1 is parallel to the previous XAxis of the parabola.

◆ SetFocal()

void gp_Parab::SetFocal ( const double theFocal )

inline

Changes the focal distance of the parabola. Raises ConstructionError if theFocal < 0.0.

◆ SetLocation()

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

inlineconstexprnoexcept

Changes the location of the parabola. It is the vertex of the parabola.

◆ SetPosition()

constexpr void gp_Parab::SetPosition ( const gp_Ax2 & theA2 )

inlineconstexprnoexcept

Changes the local coordinate system of the parabola.

◆ Transform()

void gp_Parab::Transform ( const gp_Trsf & theT )

inline

◆ Transformed()

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

inline

Transforms a parabola with the transformation theT from class Trsf.

◆ Translate() [1/2]

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

inlineconstexprnoexcept

◆ Translate() [2/2]

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

inlineconstexprnoexcept

◆ Translated() [1/2]

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

inlineconstexprnoexcept

Translates a parabola from the point theP1 to the point theP2.

◆ Translated() [2/2]

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

inlineconstexprnoexcept

Translates a parabola in the direction of the vector theV. The magnitude of the translation is the vector's magnitude.

◆ XAxis()

constexpr gp_Ax1 gp_Parab::XAxis ( ) const

inlineconstexprnoexcept

Returns the symmetry axis of the parabola. The location point of the axis is the vertex of the parabola.

◆ YAxis()

constexpr gp_Ax1 gp_Parab::YAxis ( ) const

inlineconstexprnoexcept

It is an axis parallel to the directrix of the parabola. The location point of this axis is the vertex of the parabola.

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

gp_Parab.hxx

Public Member Functions

Detailed Description

Constructor & Destructor Documentation

◆ gp_Parab() [1/3]

◆ gp_Parab() [2/3]

◆ gp_Parab() [3/3]

Member Function Documentation

◆ Axis()

◆ Directrix()

◆ Focal()

◆ Focus()

◆ Location()

◆ Mirror() [1/3]

◆ Mirror() [2/3]

◆ Mirror() [3/3]

◆ Mirrored() [1/3]

◆ Mirrored() [2/3]

◆ Mirrored() [3/3]

◆ Parameter()

◆ Position()

◆ Rotate()

◆ Rotated()

◆ Scale()

◆ Scaled()

◆ SetAxis()

◆ SetFocal()

◆ SetLocation()

◆ SetPosition()

◆ Transform()

◆ Transformed()

◆ Translate() [1/2]

◆ Translate() [2/2]

◆ Translated() [1/2]

◆ Translated() [2/2]

◆ XAxis()

◆ YAxis()