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Public Member Functions
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:
Inheritance graph
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Public Member Functions

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

 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 (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 (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.

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

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

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

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.

Standard_Real FirstParameter () const
 Returns RealFirst from Standard.

Standard_Real LastParameter () const
 Returns RealLast from Standard.

Standard_Boolean IsClosed () const
 Returns False

Standard_Boolean IsPeriodic () const
 Returns False

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.

Standard_Real Eccentricity () const
 Returns the eccentricity e = 1.0

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.

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.

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.

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.

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.

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.

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.

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.

void Transform (const gp_Trsf2d &T)
 Applies the transformation T to this parabola.

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.

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>.

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

is the same point as

Value(U).Transformed(T)

This methods returns T.ScaleFactor()

Handle_Geom2d_Geometry Copy () const
 Creates a new object, which is a copy of this parabola.


Detailed Description


Constructor & Destructor Documentation


Member Function Documentation

Handle_Geom2d_Geometry Geom2d_Parabola::Copy ( ) const [virtual]

Implements Geom2d_Geometry.

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

Implements Geom2d_Curve.

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

Implements Geom2d_Curve.

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

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]

Implements Geom2d_Curve.

Implements Geom2d_Curve.

Implements Geom2d_Conic.

Implements Geom2d_Curve.

Implements Geom2d_Curve.

Implements Geom2d_Curve.

Implements Geom2d_Curve.

Reimplemented from Geom2d_Curve.

Implements Geom2d_Conic.

Implements Geom2d_Geometry.

Reimplemented from Geom2d_Curve.


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