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Geom2d


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:
- 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 <br> 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 <br> Axis" of the local coordinate system defining the
origin of the parameter.
The parameter range is ] -infinite,+infinite [.
.

#include <Geom2d_Parabola.hxx>

Inheritance diagram for Geom2d_Parabola:

Inheritance graph
[legend]

Public Member Functions

Standard_EXPORT Geom2d_Parabola (const gp_Parab2d &Prb)
 Creates a parabola from a non persistent one.
.
Standard_EXPORT 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
.
Standard_EXPORT 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
.
Standard_EXPORT 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.
.
Standard_EXPORT void SetFocal (const Standard_Real Focal)
 Assigns the value Focal to the focal length of this parabola.
Exceptions Standard_ConstructionError if Focal is negative.
.
Standard_EXPORT void SetParab2d (const gp_Parab2d &Prb)
 Converts the gp_Parab2d parabola Prb into this parabola.
.
Standard_EXPORT gp_Parab2d Parab2d () const
 Returns the non persistent parabola from gp with the same
geometric properties as <me>.
.
Standard_EXPORT 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_EXPORT Standard_Real FirstParameter () const
 Returns RealFirst from Standard.
.
Standard_EXPORT Standard_Real LastParameter () const
 Returns RealLast from Standard.
.
Standard_EXPORT Standard_Boolean IsClosed () const
 Returns False
.
Standard_EXPORT Standard_Boolean IsPeriodic () const
 Returns False
.
Standard_EXPORT 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_EXPORT Standard_Real Eccentricity () const
 Returns the eccentricity e = 1.0
.
Standard_EXPORT 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_EXPORT 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_EXPORT 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.
.
Standard_EXPORT 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.
.
Standard_EXPORT 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.
.
Standard_EXPORT 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.
.
Standard_EXPORT 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.
.
Standard_EXPORT 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.
.
Standard_EXPORT void Transform (const gp_Trsf2d &T)
 Applies the transformation T to this parabola.
.
Standard_EXPORT 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_EXPORT 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()
.
Standard_EXPORT Handle_Geom2d_Geometry Copy () const
 Creates a new object, which is a copy of this parabola.
.
Standard_EXPORT const Handle (Standard_Type)&DynamicType() const

Private Attributes

Standard_Real focalLength

Constructor & Destructor Documentation

Standard_EXPORT Geom2d_Parabola::Geom2d_Parabola const gp_Parab2d &  Prb  ) 
 

Standard_EXPORT Geom2d_Parabola::Geom2d_Parabola const gp_Ax2d &  MirrorAxis,
const Standard_Real  Focal,
const Standard_Boolean  Sense = Standard_True
 

Standard_EXPORT Geom2d_Parabola::Geom2d_Parabola const gp_Ax22d &  Axis,
const Standard_Real  Focal
 

Standard_EXPORT Geom2d_Parabola::Geom2d_Parabola const gp_Ax2d &  D,
const gp_Pnt2d &  F
 


Member Function Documentation

Standard_EXPORT Handle_Geom2d_Geometry Geom2d_Parabola::Copy  )  const [virtual]
 

Implements Geom2d_Geometry.

Standard_EXPORT void Geom2d_Parabola::D0 const Standard_Real  U,
gp_Pnt2d &  P
const [virtual]
 

Implements Geom2d_Curve.

Standard_EXPORT void Geom2d_Parabola::D1 const Standard_Real  U,
gp_Pnt2d &  P,
gp_Vec2d &  V1
const [virtual]
 

Implements Geom2d_Curve.

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

Implements Geom2d_Curve.

Standard_EXPORT 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.

Standard_EXPORT gp_Ax2d Geom2d_Parabola::Directrix  )  const
 

Standard_EXPORT gp_Vec2d Geom2d_Parabola::DN const Standard_Real  U,
const Standard_Integer  N
const [virtual]
 

Implements Geom2d_Curve.

Standard_EXPORT Standard_Real Geom2d_Parabola::Eccentricity  )  const [virtual]
 

Implements Geom2d_Conic.

Standard_EXPORT Standard_Real Geom2d_Parabola::FirstParameter  )  const [virtual]
 

Implements Geom2d_Curve.

Standard_EXPORT Standard_Real Geom2d_Parabola::Focal  )  const
 

Standard_EXPORT gp_Pnt2d Geom2d_Parabola::Focus  )  const
 

Standard_EXPORT const Geom2d_Parabola::Handle Standard_Type   )  const
 

Reimplemented from Geom2d_Conic.

Standard_EXPORT Standard_Boolean Geom2d_Parabola::IsClosed  )  const [virtual]
 

Implements Geom2d_Curve.

Standard_EXPORT Standard_Boolean Geom2d_Parabola::IsPeriodic  )  const [virtual]
 

Implements Geom2d_Curve.

Standard_EXPORT Standard_Real Geom2d_Parabola::LastParameter  )  const [virtual]
 

Implements Geom2d_Curve.

Standard_EXPORT gp_Parab2d Geom2d_Parabola::Parab2d  )  const
 

Standard_EXPORT Standard_Real Geom2d_Parabola::Parameter  )  const
 

Standard_EXPORT Standard_Real Geom2d_Parabola::ParametricTransformation const gp_Trsf2d &  T  )  const [virtual]
 

Reimplemented from Geom2d_Curve.

Standard_EXPORT Standard_Real Geom2d_Parabola::ReversedParameter const Standard_Real  U  )  const [virtual]
 

Implements Geom2d_Conic.

Standard_EXPORT void Geom2d_Parabola::SetFocal const Standard_Real  Focal  ) 
 

Standard_EXPORT void Geom2d_Parabola::SetParab2d const gp_Parab2d &  Prb  ) 
 

Standard_EXPORT void Geom2d_Parabola::Transform const gp_Trsf2d &  T  )  [virtual]
 

Implements Geom2d_Geometry.

Standard_EXPORT Standard_Real Geom2d_Parabola::TransformedParameter const Standard_Real  U,
const gp_Trsf2d &  T
const [virtual]
 

Reimplemented from Geom2d_Curve.


Field Documentation

Standard_Real Geom2d_Parabola::focalLength [private]
 


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