# gp_Parab Class Reference

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

gp_Parab ()
Creates an indefinite Parabola. More...

gp_Parab (const gp_Ax2 &theA2, const Standard_Real 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. More...

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. More...

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

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

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

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

const gp_Ax1Axis () const
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. More...

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

Standard_Real Focal () const
Returns the distance between the vertex and the focus of the parabola. More...

gp_Pnt Focus () const

const gp_PntLocation () const
Returns the vertex of the parabola. It is the "Location" point of the coordinate system of the parabola. More...

Standard_Real Parameter () const
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. More...

const gp_Ax2Position () const
Returns the local coordinate system of the parabola. More...

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

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

void Mirror (const gp_Pnt &theP)

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

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. More...

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). More...

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

gp_Parab Rotated (const gp_Ax1 &theA1, const Standard_Real theAng) const
Rotates a parabola. theA1 is the axis of the rotation. Ang is the angular value of the rotation in radians. More...

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

gp_Parab Scaled (const gp_Pnt &theP, const Standard_Real 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. More...

void Transform (const gp_Trsf &theT)

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

void Translate (const gp_Vec &theV)

gp_Parab Translated (const gp_Vec &theV) const
Translates a parabola in the direction of the vector theV. The magnitude of the translation is the vector's magnitude. More...

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

gp_Parab Translated (const gp_Pnt &theP1, const gp_Pnt &theP2) const
Translates a parabola from the point theP1 to the point theP2. More...

## 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

## ◆ gp_Parab() [1/3]

 gp_Parab::gp_Parab ( )
inline

Creates an indefinite Parabola.

## ◆ gp_Parab() [2/3]

 gp_Parab::gp_Parab ( const gp_Ax2 & theA2, const Standard_Real theFocal )
inline

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.

## ◆ Axis()

 const gp_Ax1& gp_Parab::Axis ( ) const
inline

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()

 Standard_Real gp_Parab::Focal ( ) const
inline

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()

 const gp_Pnt& gp_Parab::Location ( ) const
inline

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 )

## ◆ 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

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

## ◆ Parameter()

 Standard_Real gp_Parab::Parameter ( ) const
inline

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()

 const gp_Ax2& gp_Parab::Position ( ) const
inline

Returns the local coordinate system of the parabola.

## ◆ Rotate()

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

## ◆ Rotated()

 gp_Parab gp_Parab::Rotated ( const gp_Ax1 & theA1, const Standard_Real 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 Standard_Real theS )
inline

## ◆ Scaled()

 gp_Parab gp_Parab::Scaled ( const gp_Pnt & theP, const Standard_Real 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 Standard_Real theFocal )
inline

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

## ◆ SetLocation()

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

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

## ◆ SetPosition()

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

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]

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

## ◆ Translate() [2/2]

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

## ◆ Translated() [1/2]

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

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

## ◆ Translated() [2/2]

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

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

## ◆ XAxis()

 gp_Ax1 gp_Parab::XAxis ( ) const
inline

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

## ◆ YAxis()

 gp_Ax1 gp_Parab::YAxis ( ) const
inline

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: