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Geom


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:
- 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 <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 <Geom_Parabola.hxx>

Inheritance diagram for Geom_Parabola:

Inheritance graph
[legend]

Public Member Functions

Standard_EXPORT Geom_Parabola (const gp_Parab &Prb)
 Creates a parabola from a non transient one.
.
Standard_EXPORT 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
.
Standard_EXPORT 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.
.
Standard_EXPORT void SetFocal (const Standard_Real Focal)
 Assigns the value Focal to the focal distance of this parabola.
Exceptions Standard_ConstructionError if Focal is negative.
.
Standard_EXPORT void SetParab (const gp_Parab &Prb)
 Converts the gp_Parab parabola Prb into this parabola.
.
Standard_EXPORT gp_Parab Parab () const
 Returns the non transient 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 the value of the first or last parameter of this
parabola. This is, respectively:
- Standard_Real::RealFirst(), or
- Standard_Real::RealLast().
.
Standard_EXPORT Standard_Real LastParameter () const
 Returns the value of the first or last parameter of this
parabola. This is, respectively:
- Standard_Real::RealFirst(), or
- Standard_Real::RealLast().
.
Standard_EXPORT Standard_Boolean IsClosed () const
 Returns False
.
Standard_EXPORT Standard_Boolean IsPeriodic () const
 Returns False
.
Standard_EXPORT 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.
.
Standard_EXPORT Standard_Real Eccentricity () const
 Returns 1. (which is the eccentricity of any parabola).
.
Standard_EXPORT 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.
.
Standard_EXPORT 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.
.
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_Pnt &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_Pnt &P, gp_Vec &V1) const
 Returns the point P of parameter U and the first derivative V1.
.
Standard_EXPORT void D2 (const Standard_Real U, gp_Pnt &P, gp_Vec &V1, gp_Vec &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_Pnt &P, gp_Vec &V1, gp_Vec &V2, gp_Vec &V3) const
 Returns the point P of parameter U, the first second and third
derivatives V1 V2 and V3.
.
Standard_EXPORT gp_Vec 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_Trsf &T)
 Applies the transformation T to this parabola.
.
Standard_EXPORT Standard_Real TransformedParameter (const Standard_Real U, const gp_Trsf &T) const
 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 <u> * T.ScaleFactor()
.
Standard_EXPORT Standard_Real ParametricTransformation (const gp_Trsf &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_Geom_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 Geom_Parabola::Geom_Parabola const gp_Parab &  Prb  ) 
 

Standard_EXPORT Geom_Parabola::Geom_Parabola const gp_Ax2 &  A2,
const Standard_Real  Focal
 

Standard_EXPORT Geom_Parabola::Geom_Parabola const gp_Ax1 &  D,
const gp_Pnt &  F
 


Member Function Documentation

Standard_EXPORT Handle_Geom_Geometry Geom_Parabola::Copy  )  const [virtual]
 

Implements Geom_Geometry.

Standard_EXPORT void Geom_Parabola::D0 const Standard_Real  U,
gp_Pnt &  P
const [virtual]
 

Implements Geom_Curve.

Standard_EXPORT void Geom_Parabola::D1 const Standard_Real  U,
gp_Pnt &  P,
gp_Vec &  V1
const [virtual]
 

Implements Geom_Curve.

Standard_EXPORT void Geom_Parabola::D2 const Standard_Real  U,
gp_Pnt &  P,
gp_Vec &  V1,
gp_Vec &  V2
const [virtual]
 

Implements Geom_Curve.

Standard_EXPORT void Geom_Parabola::D3 const Standard_Real  U,
gp_Pnt &  P,
gp_Vec &  V1,
gp_Vec &  V2,
gp_Vec &  V3
const [virtual]
 

Implements Geom_Curve.

Standard_EXPORT gp_Ax1 Geom_Parabola::Directrix  )  const
 

Standard_EXPORT gp_Vec Geom_Parabola::DN const Standard_Real  U,
const Standard_Integer  N
const [virtual]
 

Implements Geom_Curve.

Standard_EXPORT Standard_Real Geom_Parabola::Eccentricity  )  const [virtual]
 

Implements Geom_Conic.

Standard_EXPORT Standard_Real Geom_Parabola::FirstParameter  )  const [virtual]
 

Implements Geom_Curve.

Standard_EXPORT Standard_Real Geom_Parabola::Focal  )  const
 

Standard_EXPORT gp_Pnt Geom_Parabola::Focus  )  const
 

Standard_EXPORT const Geom_Parabola::Handle Standard_Type   )  const
 

Reimplemented from Geom_Conic.

Standard_EXPORT Standard_Boolean Geom_Parabola::IsClosed  )  const [virtual]
 

Implements Geom_Curve.

Standard_EXPORT Standard_Boolean Geom_Parabola::IsPeriodic  )  const [virtual]
 

Implements Geom_Curve.

Standard_EXPORT Standard_Real Geom_Parabola::LastParameter  )  const [virtual]
 

Implements Geom_Curve.

Standard_EXPORT gp_Parab Geom_Parabola::Parab  )  const
 

Standard_EXPORT Standard_Real Geom_Parabola::Parameter  )  const
 

Standard_EXPORT Standard_Real Geom_Parabola::ParametricTransformation const gp_Trsf &  T  )  const [virtual]
 

Reimplemented from Geom_Curve.

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

Implements Geom_Conic.

Standard_EXPORT void Geom_Parabola::SetFocal const Standard_Real  Focal  ) 
 

Standard_EXPORT void Geom_Parabola::SetParab const gp_Parab &  Prb  ) 
 

Standard_EXPORT void Geom_Parabola::Transform const gp_Trsf &  T  )  [virtual]
 

Implements Geom_Geometry.

Standard_EXPORT Standard_Real Geom_Parabola::TransformedParameter const Standard_Real  U,
const gp_Trsf &  T
const [virtual]
 

Reimplemented from Geom_Curve.


Field Documentation

Standard_Real Geom_Parabola::focalLength [private]
 


The documentation for this class was generated from the following file:
Generated on Mon Aug 25 13:22:56 2008 for OpenCASCADE by  doxygen 1.4.1