# Geom_Parabola Class Reference

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

`#include <Geom_Parabola.hxx>`

Inheritance diagram for Geom_Parabola: [legend]

## Public Member Functions

Geom_Parabola (const gp_Parab &Prb)
Creates a parabola from a non transient one. More...

Geom_Parabola (const gp_Ax2 &A2, const Standard_Real Focal)
Creates a parabola with its local coordinate system "A2" and it's focal length "Focal". The XDirection of A2 defines the axis of symmetry of the parabola. The YDirection of A2 is parallel to the directrix of the parabola. The Location point of A2 is the vertex of the parabola Raised if Focal < 0.0. More...

Geom_Parabola (const gp_Ax1 &D, const gp_Pnt &F)
D is the directrix of the parabola and F the focus point. The symmetry axis (XAxis) of the parabola is normal to the directrix and pass through the focus point F, but its location point is the vertex of the parabola. The YAxis of the parabola is parallel to D 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 SetFocal (const Standard_Real Focal)
Assigns the value Focal to the focal distance of this parabola. Exceptions Standard_ConstructionError if Focal is negative. More...

void SetParab (const gp_Parab &Prb)
Converts the gp_Parab parabola Prb into this parabola. More...

gp_Parab Parab () const
Returns the non transient parabola from gp with the same geometric properties as <me>. More...

Standard_Real ReversedParameter (const Standard_Real U) const override
Computes the parameter on the reversed parabola, for the point of parameter U on this parabola. For a parabola, the returned value is: -U. More...

Standard_Real FirstParameter () const override
Returns the value of the first or last parameter of this parabola. This is, respectively: More...

Standard_Real LastParameter () const override
Returns the value of the first or last parameter of this parabola. This is, respectively: More...

Standard_Boolean IsClosed () const override
Returns False. More...

Standard_Boolean IsPeriodic () const override
Returns False. More...

gp_Ax1 Directrix () const
Computes the directrix of this parabola. This is a line normal to the axis of symmetry, in the plane of this parabola, located on the negative side of its axis of symmetry, at a distance from the apex equal to the focal length. The directrix is returned as an axis (gp_Ax1 object), where the origin is located on the "X Axis" of this parabola. More...

Standard_Real Eccentricity () const override
Returns 1. (which is the eccentricity of any parabola). More...

gp_Pnt Focus () const
Computes the focus of this parabola. The focus is on the positive side of the "X Axis" of the local coordinate system of the parabola. More...

Standard_Real Focal () const
Computes the focal distance of this parabola The focal distance is the distance between the apex and the focus of the parabola. More...

Standard_Real Parameter () const
Computes the parameter of this parabola which is the distance between its focus and its directrix. This distance is twice the focal length. If P is the parameter of the parabola, the equation of the parabola in its local coordinate system is: Y**2 = 2.*P*X. More...

void D0 (const Standard_Real U, gp_Pnt &P) const override
Returns in P the point of parameter U. If U = 0 the returned point is the origin of the XAxis and the YAxis of the parabola and it is the vertex of the parabola. P = S + F * (U * U * XDir + * U * YDir) where S is the vertex of the parabola, XDir the XDirection and YDir the YDirection of the parabola's local coordinate system. More...

void D1 (const Standard_Real U, gp_Pnt &P, gp_Vec &V1) const override
Returns the point P of parameter U and the first derivative V1. More...

void D2 (const Standard_Real U, gp_Pnt &P, gp_Vec &V1, gp_Vec &V2) const override
Returns the point P of parameter U, the first and second derivatives V1 and V2. More...

void D3 (const Standard_Real U, gp_Pnt &P, gp_Vec &V1, gp_Vec &V2, gp_Vec &V3) const override
Returns the point P of parameter U, the first second and third derivatives V1 V2 and V3. More...

gp_Vec DN (const Standard_Real U, const Standard_Integer N) const override
For the point of parameter U of this parabola, computes the vector corresponding to the Nth derivative. Exceptions Standard_RangeError if N is less than 1. More...

void Transform (const gp_Trsf &T) override
Applies the transformation T to this parabola. More...

Standard_Real TransformedParameter (const Standard_Real U, const gp_Trsf &T) const override
Returns the parameter on the transformed curve for the transform of the point of parameter U on <me>. More...

Standard_Real ParametricTransformation (const gp_Trsf &T) const override
Returns a coefficient to compute the parameter on the transformed curve for the transform of the point on <me>. More...

Handle< Geom_GeometryCopy () const override
Creates a new object which is a copy of this parabola. More...

virtual void DumpJson (Standard_OStream &theOStream, Standard_Integer theDepth=-1) const override
Dumps the content of me into the stream. More... Public Member Functions inherited from Geom_Conic
void SetAxis (const gp_Ax1 &theA1)
Changes the orientation of the conic's plane. The normal axis to the plane is A1. The XAxis and the YAxis are recomputed. More...

void SetLocation (const gp_Pnt &theP)
changes the location point of the conic. More...

void SetPosition (const gp_Ax2 &theA2)
changes the local coordinate system of the conic. More...

const gp_Ax1Axis () const
Returns the "main Axis" of this conic. This axis is normal to the plane of the conic. More...

const gp_PntLocation () const
Returns the location point of the conic. For the circle, the ellipse and the hyperbola it is the center of the conic. For the parabola it is the Apex of the parabola. More...

const gp_Ax2Position () const
Returns the local coordinates system of the conic. The main direction of the Axis2Placement is normal to the plane of the conic. The X direction of the Axis2placement is in the plane of the conic and corresponds to the origin for the conic's parametric value u. More...

gp_Ax1 XAxis () const
Returns the XAxis of the conic. This axis defines the origin of parametrization of the conic. This axis is perpendicular to the Axis of the conic. This axis and the Yaxis define the plane of the conic. More...

gp_Ax1 YAxis () const
Returns the YAxis of the conic. The YAxis is perpendicular to the Xaxis. This axis and the Xaxis define the plane of the conic. More...

void Reverse () override
Reverses the direction of parameterization of <me>. The local coordinate system of the conic is modified. More...

GeomAbs_Shape Continuity () const override
The continuity of the conic is Cn. More...

Standard_Boolean IsCN (const Standard_Integer N) const override
Returns True. Raised if N < 0. More... Public Member Functions inherited from Geom_Curve
Handle< Geom_CurveReversed () const
Returns a copy of <me> reversed. More...

virtual Standard_Real Period () const
Returns the period of this curve. Exceptions Standard_NoSuchObject if this curve is not periodic. More...

gp_Pnt Value (const Standard_Real U) const
Computes the point of parameter U on <me>. If the curve is periodic then the returned point is P(U) with U = Ustart + (U - Uend) where Ustart and Uend are the parametric bounds of the curve. it is implemented with D0. More... Public Member Functions inherited from Geom_Geometry
void Mirror (const gp_Pnt &P)
Performs the symmetrical transformation of a Geometry with respect to the point P which is the center of the symmetry. More...

void Mirror (const gp_Ax1 &A1)
Performs the symmetrical transformation of a Geometry with respect to an axis placement which is the axis of the symmetry. More...

void Mirror (const gp_Ax2 &A2)
Performs the symmetrical transformation of a Geometry with respect to a plane. The axis placement A2 locates the plane of the symmetry : (Location, XDirection, YDirection). More...

void Rotate (const gp_Ax1 &A1, const Standard_Real Ang)
Rotates a Geometry. A1 is the axis of the rotation. Ang is the angular value of the rotation in radians. More...

void Scale (const gp_Pnt &P, const Standard_Real S)
Scales a Geometry. S is the scaling value. More...

void Translate (const gp_Vec &V)
Translates a Geometry. V is the vector of the translation. More...

void Translate (const gp_Pnt &P1, const gp_Pnt &P2)
Translates a Geometry from the point P1 to the point P2. More...

Handle< Geom_GeometryMirrored (const gp_Pnt &P) const

Handle< Geom_GeometryMirrored (const gp_Ax1 &A1) const

Handle< Geom_GeometryMirrored (const gp_Ax2 &A2) const

Handle< Geom_GeometryRotated (const gp_Ax1 &A1, const Standard_Real Ang) const

Handle< Geom_GeometryScaled (const gp_Pnt &P, const Standard_Real S) const

Handle< Geom_GeometryTransformed (const gp_Trsf &T) const

Handle< Geom_GeometryTranslated (const gp_Vec &V) const

Handle< Geom_GeometryTranslated (const gp_Pnt &P1, const gp_Pnt &P2) const Public Member Functions inherited from Standard_Transient
Standard_Transient ()
Empty constructor. More...

Standard_Transient (const Standard_Transient &)
Copy constructor – does nothing. More...

Standard_Transientoperator= (const Standard_Transient &)
Assignment operator, needed to avoid copying reference counter. More...

virtual ~Standard_Transient ()
Destructor must be virtual. More...

virtual void Delete () const
Memory deallocator for transient classes. More...

virtual const opencascade::handle< Standard_Type > & DynamicType () const

Standard_Boolean IsInstance (const opencascade::handle< Standard_Type > &theType) const
Returns a true value if this is an instance of Type. More...

Standard_Boolean IsInstance (const Standard_CString theTypeName) const
Returns a true value if this is an instance of TypeName. More...

Standard_Boolean IsKind (const opencascade::handle< Standard_Type > &theType) const
Returns true if this is an instance of Type or an instance of any class that inherits from Type. Note that multiple inheritance is not supported by OCCT RTTI mechanism. More...

Standard_Boolean IsKind (const Standard_CString theTypeName) const
Returns true if this is an instance of TypeName or an instance of any class that inherits from TypeName. Note that multiple inheritance is not supported by OCCT RTTI mechanism. More...

Standard_TransientThis () const
Returns non-const pointer to this object (like const_cast). For protection against creating handle to objects allocated in stack or call from constructor, it will raise exception Standard_ProgramError if reference counter is zero. More...

Standard_Integer GetRefCount () const
Get the reference counter of this object. More...

void IncrementRefCounter () const
Increments the reference counter of this object. More...

Standard_Integer DecrementRefCounter () const
Decrements the reference counter of this object; returns the decremented value. More... Public Types inherited from Standard_Transient
typedef void base_type Static Public Member Functions inherited from Standard_Transient
static const char * get_type_name ()

static const opencascade::handle< Standard_Type > & get_type_descriptor ()
Returns type descriptor of Standard_Transient class. More... Protected Attributes inherited from Geom_Conic
gp_Ax2 pos

## Detailed Description

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

• the origin is the apex of the parabola,
• the "X Axis" defines the axis of symmetry; the parabola is on the positive side of this axis,
• the origin, "X Direction" and "Y Direction" define the plane of the parabola. This coordinate system is the local coordinate system of the parabola. The "main Direction" of this coordinate system is a vector normal to the plane of the parabola. The axis, of which the origin and unit vector are respectively the origin and "main Direction" of the local coordinate system, is termed the "Axis" or "main Axis" of the parabola. The "main Direction" of the local coordinate system gives an explicit orientation to the parabola, determining the direction in which the parameter increases along the parabola. The Geom_Parabola parabola is parameterized as follows: P(U) = O + U*U/(4.*F)*XDir + U*YDir where:
• P is the point of parameter U,
• O, XDir and YDir are respectively the origin, "X Direction" and "Y Direction" of its local coordinate system,
• F is the focal length of the parabola. The parameter of the parabola is therefore its Y coordinate in the local coordinate system, with the "X Axis" of the local coordinate system defining the origin of the parameter. The parameter range is ] -infinite, +infinite [.

## ◆ Geom_Parabola() [1/3]

 Geom_Parabola::Geom_Parabola ( const gp_Parab & Prb )

Creates a parabola from a non transient one.

## ◆ Geom_Parabola() [2/3]

 Geom_Parabola::Geom_Parabola ( const gp_Ax2 & A2, const Standard_Real Focal )

Creates a parabola with its local coordinate system "A2" and it's focal length "Focal". The XDirection of A2 defines the axis of symmetry of the parabola. The YDirection of A2 is parallel to the directrix of the parabola. The Location point of A2 is the vertex of the parabola Raised if Focal < 0.0.

## ◆ Geom_Parabola() [3/3]

 Geom_Parabola::Geom_Parabola ( const gp_Ax1 & D, const gp_Pnt & F )

D is the directrix of the parabola and F the focus point. The symmetry axis (XAxis) of the parabola is normal to the directrix and pass through the focus point F, but its location point is the vertex of the parabola. The YAxis of the parabola is parallel to D 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.

## ◆ Copy()

 Handle< Geom_Geometry > Geom_Parabola::Copy ( ) const
overridevirtual

Creates a new object which is a copy of this parabola.

Implements Geom_Geometry.

## ◆ D0()

 void Geom_Parabola::D0 ( const Standard_Real U, gp_Pnt & P ) const
overridevirtual

Returns in P the point of parameter U. If U = 0 the returned point is the origin of the XAxis and the YAxis of the parabola and it is the vertex of the parabola. P = S + F * (U * U * XDir + * U * YDir) where S is the vertex of the parabola, XDir the XDirection and YDir the YDirection of the parabola's local coordinate system.

Implements Geom_Curve.

## ◆ D1()

 void Geom_Parabola::D1 ( const Standard_Real U, gp_Pnt & P, gp_Vec & V1 ) const
overridevirtual

Returns the point P of parameter U and the first derivative V1.

Implements Geom_Curve.

## ◆ D2()

 void Geom_Parabola::D2 ( const Standard_Real U, gp_Pnt & P, gp_Vec & V1, gp_Vec & V2 ) const
overridevirtual

Returns the point P of parameter U, the first and second derivatives V1 and V2.

Implements Geom_Curve.

## ◆ D3()

 void Geom_Parabola::D3 ( const Standard_Real U, gp_Pnt & P, gp_Vec & V1, gp_Vec & V2, gp_Vec & V3 ) const
overridevirtual

Returns the point P of parameter U, the first second and third derivatives V1 V2 and V3.

Implements Geom_Curve.

## ◆ Directrix()

 gp_Ax1 Geom_Parabola::Directrix ( ) const

Computes the directrix of this parabola. This is a line normal to the axis of symmetry, in the plane of this parabola, located on the negative side of its axis of symmetry, at a distance from the apex equal to the focal length. The directrix is returned as an axis (gp_Ax1 object), where the origin is located on the "X Axis" of this parabola.

## ◆ DN()

 gp_Vec Geom_Parabola::DN ( const Standard_Real U, const Standard_Integer N ) const
overridevirtual

For the point of parameter U of this parabola, computes the vector corresponding to the Nth derivative. Exceptions Standard_RangeError if N is less than 1.

Implements Geom_Curve.

## ◆ DumpJson()

 virtual void Geom_Parabola::DumpJson ( Standard_OStream & theOStream, Standard_Integer theDepth = `-1` ) const
overridevirtual

Dumps the content of me into the stream.

Reimplemented from Geom_Conic.

## ◆ Eccentricity()

 Standard_Real Geom_Parabola::Eccentricity ( ) const
overridevirtual

Returns 1. (which is the eccentricity of any parabola).

Implements Geom_Conic.

## ◆ FirstParameter()

 Standard_Real Geom_Parabola::FirstParameter ( ) const
overridevirtual

Returns the value of the first or last parameter of this parabola. This is, respectively:

• Standard_Real::RealFirst(), or
• Standard_Real::RealLast().

Implements Geom_Curve.

## ◆ Focal()

 Standard_Real Geom_Parabola::Focal ( ) const

Computes the focal distance of this parabola The focal distance is the distance between the apex and the focus of the parabola.

## ◆ Focus()

 gp_Pnt Geom_Parabola::Focus ( ) const

Computes the focus of this parabola. The focus is on the positive side of the "X Axis" of the local coordinate system of the parabola.

## ◆ IsClosed()

 Standard_Boolean Geom_Parabola::IsClosed ( ) const
overridevirtual

Returns False.

Implements Geom_Curve.

## ◆ IsPeriodic()

 Standard_Boolean Geom_Parabola::IsPeriodic ( ) const
overridevirtual

Returns False.

Implements Geom_Curve.

## ◆ LastParameter()

 Standard_Real Geom_Parabola::LastParameter ( ) const
overridevirtual

Returns the value of the first or last parameter of this parabola. This is, respectively:

• Standard_Real::RealFirst(), or
• Standard_Real::RealLast().

Implements Geom_Curve.

## ◆ Parab()

 gp_Parab Geom_Parabola::Parab ( ) const

Returns the non transient parabola from gp with the same geometric properties as <me>.

## ◆ Parameter()

 Standard_Real Geom_Parabola::Parameter ( ) const

Computes the parameter of this parabola which is the distance between its focus and its directrix. This distance is twice the focal length. If P is the parameter of the parabola, the equation of the parabola in its local coordinate system is: Y**2 = 2.*P*X.

## ◆ ParametricTransformation()

 Standard_Real Geom_Parabola::ParametricTransformation ( const gp_Trsf & T ) const
overridevirtual

Returns a coefficient to compute the parameter on the transformed curve for the transform of the point on <me>.

Transformed(T)->Value(U * ParametricTransformation(T))

is the same point as

Value(U).Transformed(T)

This methods returns T.ScaleFactor()

Reimplemented from Geom_Curve.

## ◆ ReversedParameter()

 Standard_Real Geom_Parabola::ReversedParameter ( const Standard_Real U ) const
overridevirtual

Computes the parameter on the reversed parabola, for the point of parameter U on this parabola. For a parabola, the returned value is: -U.

Implements Geom_Conic.

## ◆ SetFocal()

 void Geom_Parabola::SetFocal ( const Standard_Real Focal )

Assigns the value Focal to the focal distance of this parabola. Exceptions Standard_ConstructionError if Focal is negative.

## ◆ SetParab()

 void Geom_Parabola::SetParab ( const gp_Parab & Prb )

Converts the gp_Parab parabola Prb into this parabola.

## ◆ Transform()

 void Geom_Parabola::Transform ( const gp_Trsf & T )
overridevirtual

Applies the transformation T to this parabola.

Implements Geom_Geometry.

## ◆ TransformedParameter()

 Standard_Real Geom_Parabola::TransformedParameter ( const Standard_Real U, const gp_Trsf & T ) const
overridevirtual

Returns the parameter on the transformed curve for the transform of the point of parameter U on <me>.

me->Transformed(T)->Value(me->TransformedParameter(U,T))

is the same point as

me->Value(U).Transformed(T)

This methods returns * T.ScaleFactor()

Reimplemented from Geom_Curve.

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