# Geom2d_Parabola Class Reference

Describes a parabola in the plane (2D space). A parabola is defined by its focal length (i.e. the distance between its focus and its apex) and is positioned in the plane with a coordinate system (gp_Ax22d object) where: More...

`#include <Geom2d_Parabola.hxx>`

Inheritance diagram for Geom2d_Parabola: [legend]

## Public Member Functions

Geom2d_Parabola (const gp_Parab2d &Prb)
Creates a parabola from a non persistent one. More...

Geom2d_Parabola (const gp_Ax2d &MirrorAxis, const Standard_Real Focal, const Standard_Boolean Sense=Standard_True)
Creates a parabola with its "MirrorAxis" and it's focal length "Focal". MirrorAxis is the axis of symmetry of the curve, it is the "XAxis". The "YAxis" is parallel to the directrix of the parabola and is in the direct sense if Sense is True. The "Location" point of "MirrorAxis" is the vertex of the parabola Raised if Focal < 0.0. More...

Geom2d_Parabola (const gp_Ax22d &Axis, const Standard_Real Focal)
Creates a parabola with its Axis and it's focal length "Focal". The XDirection of Axis is the axis of symmetry of the curve, it is the "XAxis". The "YAxis" is parallel to the directrix of the parabola. The "Location" point of "Axis" is the vertex of the parabola. Raised if Focal < 0.0. More...

Geom2d_Parabola (const gp_Ax2d &D, const gp_Pnt2d &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. More...

void SetFocal (const Standard_Real Focal)
Assigns the value Focal to the focal length of this parabola. Exceptions Standard_ConstructionError if Focal is negative. More...

void SetParab2d (const gp_Parab2d &Prb)
Converts the gp_Parab2d parabola Prb into this parabola. More...

gp_Parab2d Parab2d () const
Returns the non persistent parabola from gp with the same geometric properties as <me>. More...

Standard_Real ReversedParameter (const Standard_Real U) const
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
Returns RealFirst from Standard. More...

Standard_Real LastParameter () const
Returns RealLast from Standard. More...

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

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

gp_Ax2d Directrix () const
The directrix is parallel to the "YAxis" of the parabola. The "Location" point of the directrix is the intersection point between the directrix and the symmetry axis ("XAxis") of the parabola. More...

Standard_Real Eccentricity () const
Returns the eccentricity e = 1.0. More...

gp_Pnt2d 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 length of this parabola. The focal length 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_Pnt2d &P) const
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_Pnt2d &P, gp_Vec2d &V1) const
Returns the point P of parameter U and the first derivative V1. More...

void D2 (const Standard_Real U, gp_Pnt2d &P, gp_Vec2d &V1, gp_Vec2d &V2) const
Returns the point P of parameter U, the first and second derivatives V1 and V2. More...

void D3 (const Standard_Real U, gp_Pnt2d &P, gp_Vec2d &V1, gp_Vec2d &V2, gp_Vec2d &V3) const
Returns the point P of parameter U, the first second and third derivatives V1 V2 and V3. More...

gp_Vec2d DN (const Standard_Real U, const Standard_Integer N) const
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_Trsf2d &T)
Applies the transformation T to this parabola. More...

Standard_Real TransformedParameter (const Standard_Real U, const gp_Trsf2d &T) const
Computes the parameter on the transformed parabola, for the point of parameter U on this parabola. For a parabola, the returned value is equal to U multiplied by the scale factor of transformation T. More...

Standard_Real ParametricTransformation (const gp_Trsf2d &T) const
Returns a coefficient to compute the parameter on the transformed curve for the transform of the point on <me>. More...

Handle< Geom2d_GeometryCopy () const
Creates a new object, which is a copy of this parabola. More... Public Member Functions inherited from Geom2d_Conic
void SetAxis (const gp_Ax22d &A)
Modifies this conic, redefining its local coordinate system partially, by assigning P as its origin. More...

void SetXAxis (const gp_Ax2d &A)

void SetYAxis (const gp_Ax2d &A)
Assigns the origin and unit vector of axis A to the origin of the local coordinate system of this conic and either: More...

void SetLocation (const gp_Pnt2d &P)
Modifies this conic, redefining its local coordinate system fully, by assigning A as this coordinate system. More...

gp_Ax2d XAxis () const
Returns the "XAxis" of the conic. This axis defines the origin of parametrization of the conic. This axis and the "Yaxis" define the local coordinate system of the conic. -C++: return const&. More...

gp_Ax2d YAxis () const
Returns the "YAxis" of the conic. The "YAxis" is perpendicular to the "Xaxis". More...

gp_Pnt2d Location () 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 vertex of the parabola. More...

const gp_Ax22dPosition () const
Returns the local coordinates system of the conic. More...

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

GeomAbs_Shape Continuity () const
Returns GeomAbs_CN which is the global continuity of any conic. More...

Standard_Boolean IsCN (const Standard_Integer N) const
Returns True, the order of continuity of a conic is infinite. More... Public Member Functions inherited from Geom2d_Curve
Handle< Geom2d_CurveReversed () const
Creates a reversed duplicate Changes the orientation of this curve. The first and last parameters are not changed, but the parametric direction of the curve is reversed. If the curve is bounded: More...

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

gp_Pnt2d 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. More... Public Member Functions inherited from Geom2d_Geometry
void Mirror (const gp_Pnt2d &P)
Performs the symmetrical transformation of a Geometry with respect to the point P which is the center of the symmetry and assigns the result to this geometric object. More...

void Mirror (const gp_Ax2d &A)
Performs the symmetrical transformation of a Geometry with respect to an axis placement which is the axis of the symmetry. More...

void Rotate (const gp_Pnt2d &P, const Standard_Real Ang)
Rotates a Geometry. P is the center of the rotation. Ang is the angular value of the rotation in radians. More...

void Scale (const gp_Pnt2d &P, const Standard_Real S)
Scales a Geometry. S is the scaling value. More...

void Translate (const gp_Vec2d &V)
Translates a Geometry. V is the vector of the tanslation. More...

void Translate (const gp_Pnt2d &P1, const gp_Pnt2d &P2)
Translates a Geometry from the point P1 to the point P2. More...

Handle< Geom2d_GeometryMirrored (const gp_Pnt2d &P) const

Handle< Geom2d_GeometryMirrored (const gp_Ax2d &A) const

Handle< Geom2d_GeometryRotated (const gp_Pnt2d &P, const Standard_Real Ang) const

Handle< Geom2d_GeometryScaled (const gp_Pnt2d &P, const Standard_Real S) const

Handle< Geom2d_GeometryTransformed (const gp_Trsf2d &T) const

Handle< Geom2d_GeometryTranslated (const gp_Vec2d &V) const

Handle< Geom2d_GeometryTranslated (const gp_Pnt2d &P1, const gp_Pnt2d &P2) const Public Member Functions inherited from MMgt_TShared
virtual void Delete () const
Memory deallocator for transient classes. More... 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 const
Handle_Standard_Type &
DynamicType () const

Standard_Boolean IsInstance (const 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 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...

virtual Handle_Standard_Transient This () const
Returns a Handle which references this object. Must never be called to objects created in stack. More...

Standard_Integer GetRefCount () const
Get the reference counter of this object. More... Protected Attributes inherited from Geom2d_Conic
gp_Ax22d pos

## Detailed Description

Describes a parabola in the plane (2D space). A parabola is defined by its focal length (i.e. the distance between its focus and its apex) and is positioned in the plane with a coordinate system (gp_Ax22d object) where:

• the origin is the apex of the parabola, and
• the "X Axis" defines the axis of symmetry; the parabola is on the positive side of this axis. This coordinate system is the local coordinate system of the parabola. The orientation (direct or indirect) 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 [.

## Constructor & Destructor Documentation

 Geom2d_Parabola::Geom2d_Parabola ( const gp_Parab2d & Prb )

Creates a parabola from a non persistent one.

 Geom2d_Parabola::Geom2d_Parabola ( const gp_Ax2d & MirrorAxis, const Standard_Real Focal, const Standard_Boolean Sense = `Standard_True` )

Creates a parabola with its "MirrorAxis" and it's focal length "Focal". MirrorAxis is the axis of symmetry of the curve, it is the "XAxis". The "YAxis" is parallel to the directrix of the parabola and is in the direct sense if Sense is True. The "Location" point of "MirrorAxis" is the vertex of the parabola Raised if Focal < 0.0.

 Geom2d_Parabola::Geom2d_Parabola ( const gp_Ax22d & Axis, const Standard_Real Focal )

Creates a parabola with its Axis and it's focal length "Focal". The XDirection of Axis is the axis of symmetry of the curve, it is the "XAxis". The "YAxis" is parallel to the directrix of the parabola. The "Location" point of "Axis" is the vertex of the parabola. Raised if Focal < 0.0.

 Geom2d_Parabola::Geom2d_Parabola ( const gp_Ax2d & D, const gp_Pnt2d & 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.

## Member Function Documentation

 Handle< Geom2d_Geometry > Geom2d_Parabola::Copy ( ) const
virtual

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

Implements Geom2d_Geometry.

 void Geom2d_Parabola::D0 ( const Standard_Real U, gp_Pnt2d & P ) const
virtual

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 Geom2d_Curve.

 void Geom2d_Parabola::D1 ( const Standard_Real U, gp_Pnt2d & P, gp_Vec2d & V1 ) const
virtual

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

Implements Geom2d_Curve.

 void Geom2d_Parabola::D2 ( const Standard_Real U, gp_Pnt2d & P, gp_Vec2d & V1, gp_Vec2d & V2 ) const
virtual

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

Implements Geom2d_Curve.

 void Geom2d_Parabola::D3 ( const Standard_Real U, gp_Pnt2d & P, gp_Vec2d & V1, gp_Vec2d & V2, gp_Vec2d & V3 ) const
virtual

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

Implements Geom2d_Curve.

 gp_Ax2d Geom2d_Parabola::Directrix ( ) const

The directrix is parallel to the "YAxis" of the parabola. The "Location" point of the directrix is the intersection point between the directrix and the symmetry axis ("XAxis") of the parabola.

 gp_Vec2d Geom2d_Parabola::DN ( const Standard_Real U, const Standard_Integer N ) const
virtual

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 Geom2d_Curve.

 Standard_Real Geom2d_Parabola::Eccentricity ( ) const
virtual

Returns the eccentricity e = 1.0.

Implements Geom2d_Conic.

 Standard_Real Geom2d_Parabola::FirstParameter ( ) const
virtual

Returns RealFirst from Standard.

Implements Geom2d_Curve.

 Standard_Real Geom2d_Parabola::Focal ( ) const

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

 gp_Pnt2d Geom2d_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.

 Standard_Boolean Geom2d_Parabola::IsClosed ( ) const
virtual

Returns False.

Implements Geom2d_Curve.

 Standard_Boolean Geom2d_Parabola::IsPeriodic ( ) const
virtual

Returns False.

Implements Geom2d_Curve.

 Standard_Real Geom2d_Parabola::LastParameter ( ) const
virtual

Returns RealLast from Standard.

Implements Geom2d_Curve.

 gp_Parab2d Geom2d_Parabola::Parab2d ( ) const

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

 Standard_Real Geom2d_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.

 Standard_Real Geom2d_Parabola::ParametricTransformation ( const gp_Trsf2d & T ) const
virtual

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 Geom2d_Curve.

 Standard_Real Geom2d_Parabola::ReversedParameter ( const Standard_Real U ) const
virtual

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 Geom2d_Conic.

 void Geom2d_Parabola::SetFocal ( const Standard_Real Focal )

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

 void Geom2d_Parabola::SetParab2d ( const gp_Parab2d & Prb )

Converts the gp_Parab2d parabola Prb into this parabola.

 void Geom2d_Parabola::Transform ( const gp_Trsf2d & T )
virtual

Applies the transformation T to this parabola.

Implements Geom2d_Geometry.

 Standard_Real Geom2d_Parabola::TransformedParameter ( const Standard_Real U, const gp_Trsf2d & T ) const
virtual

Computes the parameter on the transformed parabola, for the point of parameter U on this parabola. For a parabola, the returned value is equal to U multiplied by the scale factor of transformation T.

Reimplemented from Geom2d_Curve.

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