Open CASCADE Technology 6.6.0
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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>
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. |
Geom2d_Parabola::Geom2d_Parabola | ( | const gp_Parab2d & | Prb | ) |
Geom2d_Parabola::Geom2d_Parabola | ( | const gp_Ax2d & | MirrorAxis, |
const Standard_Real | Focal, | ||
const Standard_Boolean | Sense = Standard_True |
||
) |
Geom2d_Parabola::Geom2d_Parabola | ( | const gp_Ax22d & | Axis, |
const Standard_Real | Focal | ||
) |
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.
gp_Ax2d Geom2d_Parabola::Directrix | ( | ) | const |
gp_Vec2d Geom2d_Parabola::DN | ( | const Standard_Real | U, |
const Standard_Integer | N | ||
) | const [virtual] |
Implements Geom2d_Curve.
Standard_Real Geom2d_Parabola::Eccentricity | ( | ) | const [virtual] |
Implements Geom2d_Conic.
Standard_Real Geom2d_Parabola::FirstParameter | ( | ) | const [virtual] |
Implements Geom2d_Curve.
Standard_Real Geom2d_Parabola::Focal | ( | ) | const |
gp_Pnt2d Geom2d_Parabola::Focus | ( | ) | const |
Standard_Boolean Geom2d_Parabola::IsClosed | ( | ) | const [virtual] |
Implements Geom2d_Curve.
Standard_Boolean Geom2d_Parabola::IsPeriodic | ( | ) | const [virtual] |
Implements Geom2d_Curve.
Standard_Real Geom2d_Parabola::LastParameter | ( | ) | const [virtual] |
Implements Geom2d_Curve.
gp_Parab2d Geom2d_Parabola::Parab2d | ( | ) | const |
Standard_Real Geom2d_Parabola::Parameter | ( | ) | const |
Standard_Real Geom2d_Parabola::ParametricTransformation | ( | const gp_Trsf2d & | T | ) | const [virtual] |
Reimplemented from Geom2d_Curve.
Standard_Real Geom2d_Parabola::ReversedParameter | ( | const Standard_Real | U | ) | const [virtual] |
Implements Geom2d_Conic.
void Geom2d_Parabola::SetFocal | ( | const Standard_Real | Focal | ) |
void Geom2d_Parabola::SetParab2d | ( | const gp_Parab2d & | Prb | ) |
void Geom2d_Parabola::Transform | ( | const gp_Trsf2d & | T | ) | [virtual] |
Implements Geom2d_Geometry.
Standard_Real Geom2d_Parabola::TransformedParameter | ( | const Standard_Real | U, |
const gp_Trsf2d & | T | ||
) | const [virtual] |
Reimplemented from Geom2d_Curve.