Open CASCADE Technology
6.5.4
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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:
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#include <Geom_Parabola.hxx>
Public Member Functions | |
Geom_Parabola (const gp_Parab &Prb) | |
Creates a parabola from a non transient one. | |
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 | |
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. | |
void | SetFocal (const Standard_Real Focal) |
Assigns the value Focal to the focal distance of this parabola. Exceptions Standard_ConstructionError if Focal is negative. | |
void | SetParab (const gp_Parab &Prb) |
Converts the gp_Parab parabola Prb into this parabola. | |
gp_Parab | Parab () const |
Returns the non transient 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 the value of the first or last parameter of this parabola. This is, respectively: | |
Standard_Real | LastParameter () const |
Returns the value of the first or last parameter of this parabola. This is, respectively: | |
Standard_Boolean | IsClosed () const |
Returns False | |
Standard_Boolean | IsPeriodic () const |
Returns False | |
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_Real | Eccentricity () const |
Returns 1. (which is the eccentricity of any parabola). | |
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_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_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_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. | |
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. | |
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. | |
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. | |
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. | |
void | Transform (const gp_Trsf &T) |
Applies the transformation T to this parabola. | |
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_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() | |
Handle_Geom_Geometry | Copy () const |
Creates a new object which is a copy of this parabola. |
Geom_Parabola::Geom_Parabola | ( | const gp_Parab & | Prb | ) |
Geom_Parabola::Geom_Parabola | ( | const gp_Ax2 & | A2, |
const Standard_Real | Focal | ||
) |
Geom_Parabola::Geom_Parabola | ( | const gp_Ax1 & | D, |
const gp_Pnt & | F | ||
) |
Handle_Geom_Geometry Geom_Parabola::Copy | ( | ) | const [virtual] |
Implements Geom_Geometry.
void Geom_Parabola::D0 | ( | const Standard_Real | U, |
gp_Pnt & | P | ||
) | const [virtual] |
Implements Geom_Curve.
void Geom_Parabola::D1 | ( | const Standard_Real | U, |
gp_Pnt & | P, | ||
gp_Vec & | V1 | ||
) | const [virtual] |
Implements Geom_Curve.
void Geom_Parabola::D2 | ( | const Standard_Real | U, |
gp_Pnt & | P, | ||
gp_Vec & | V1, | ||
gp_Vec & | V2 | ||
) | const [virtual] |
Implements Geom_Curve.
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.
gp_Ax1 Geom_Parabola::Directrix | ( | ) | const |
gp_Vec Geom_Parabola::DN | ( | const Standard_Real | U, |
const Standard_Integer | N | ||
) | const [virtual] |
Implements Geom_Curve.
Standard_Real Geom_Parabola::Eccentricity | ( | ) | const [virtual] |
Implements Geom_Conic.
Standard_Real Geom_Parabola::FirstParameter | ( | ) | const [virtual] |
Implements Geom_Curve.
Standard_Real Geom_Parabola::Focal | ( | ) | const |
gp_Pnt Geom_Parabola::Focus | ( | ) | const |
Standard_Boolean Geom_Parabola::IsClosed | ( | ) | const [virtual] |
Implements Geom_Curve.
Standard_Boolean Geom_Parabola::IsPeriodic | ( | ) | const [virtual] |
Implements Geom_Curve.
Standard_Real Geom_Parabola::LastParameter | ( | ) | const [virtual] |
Implements Geom_Curve.
gp_Parab Geom_Parabola::Parab | ( | ) | const |
Standard_Real Geom_Parabola::Parameter | ( | ) | const |
Standard_Real Geom_Parabola::ParametricTransformation | ( | const gp_Trsf & | T | ) | const [virtual] |
Reimplemented from Geom_Curve.
Standard_Real Geom_Parabola::ReversedParameter | ( | const Standard_Real | U | ) | const [virtual] |
Implements Geom_Conic.
void Geom_Parabola::SetFocal | ( | const Standard_Real | Focal | ) |
void Geom_Parabola::SetParab | ( | const gp_Parab & | Prb | ) |
void Geom_Parabola::Transform | ( | const gp_Trsf & | T | ) | [virtual] |
Implements Geom_Geometry.
Standard_Real Geom_Parabola::TransformedParameter | ( | const Standard_Real | U, |
const gp_Trsf & | T | ||
) | const [virtual] |
Reimplemented from Geom_Curve.