Open CASCADE Technology 6.6.0
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Describes an ellipse in the plane (2D space).
An ellipse is defined by its major and minor radii and,
as with any conic curve, is positioned in the plane
with a coordinate system (gp_Ax22d object) where:
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#include <Geom2d_Ellipse.hxx>
Public Member Functions | |
Geom2d_Ellipse (const gp_Elips2d &E) | |
Creates an ellipse by conversion of the gp_Elips2d ellipse E. | |
Geom2d_Ellipse (const gp_Ax2d &MajorAxis, const Standard_Real MajorRadius, const Standard_Real MinorRadius, const Standard_Boolean Sense=Standard_True) | |
Creates an ellipse defined by its major and minor radii, MajorRadius and MinorRadius, and positioned in the plane by its major axis MajorAxis; the center of the ellipse is the origin of MajorAxis and the unit vector of MajorAxis is the "X <br> Direction" of the local coordinate system of the ellipse; this coordinate system is direct if Sense is true (default value) or indirect if Sense is false. Warnings : It is not forbidden to create an ellipse with MajorRadius = MinorRadius. Exceptions Standard_ConstructionError if: | |
Geom2d_Ellipse (const gp_Ax22d &Axis, const Standard_Real MajorRadius, const Standard_Real MinorRadius) | |
Creates an ellipse defined by its major and minor radii, MajorRadius and MinorRadius, where the coordinate system Axis locates the ellipse and defines its orientation in the plane such that: | |
void | SetElips2d (const gp_Elips2d &E) |
Converts the gp_Elips2d ellipse E into this ellipse. | |
void | SetMajorRadius (const Standard_Real MajorRadius) |
Assigns a value to the major radius of this ellipse. Exceptions Standard_ConstructionError if: | |
void | SetMinorRadius (const Standard_Real MinorRadius) |
Assigns a value to the minor radius of this ellipse. Exceptions Standard_ConstructionError if: | |
gp_Elips2d | Elips2d () const |
Converts this ellipse into a gp_Elips2d ellipse. | |
Standard_Real | ReversedParameter (const Standard_Real U) const |
Computes the parameter on the reversed ellipse for the point of parameter U on this ellipse. For an ellipse, the returned value is: 2.*Pi - U. | |
gp_Ax2d | Directrix1 () const |
Computes the directrices of this ellipse. This directrix is the line normal to the XAxis of the ellipse in the local plane (Z = 0) at a distance d = MajorRadius / e from the center of the ellipse, where e is the eccentricity of the ellipse. This line is parallel to the "YAxis". The intersection point between directrix1 and the "XAxis" is the "Location" point of the directrix1. This point is on the positive side of the "XAxis". Raises ConstructionError if Eccentricity = 0.0. (The ellipse degenerates into a circle) | |
gp_Ax2d | Directrix2 () const |
This line is obtained by the symmetrical transformation of "Directrix1" with respect to the "YAxis" of the ellipse. Raises ConstructionError if Eccentricity = 0.0. (The ellipse degenerates into a circle). | |
Standard_Real | Eccentricity () const |
Returns the eccentricity of the ellipse between 0.0 and 1.0 If f is the distance between the center of the ellipse and the Focus1 then the eccentricity e = f / MajorRadius. Returns 0 if MajorRadius = 0 | |
Standard_Real | Focal () const |
Computes the focal distance. The focal distance is the distance between the center and a focus of the ellipse. | |
gp_Pnt2d | Focus1 () const |
Returns the first focus of the ellipse. This focus is on the positive side of the "XAxis" of the ellipse. | |
gp_Pnt2d | Focus2 () const |
Returns the second focus of the ellipse. This focus is on the negative side of the "XAxis" of the ellipse. | |
Standard_Real | MajorRadius () const |
Returns the major radius of this ellipse. | |
Standard_Real | MinorRadius () const |
Returns the minor radius of this ellipse. | |
Standard_Real | Parameter () const |
Computes the parameter of this ellipse. This value is given by the formula p = (1 - e * e) * MajorRadius where e is the eccentricity of the ellipse. Returns 0 if MajorRadius = 0 | |
Standard_Real | FirstParameter () const |
Returns the value of the first parameter of this ellipse. This is 0.0, which gives the start point of this ellipse. The start point and end point of an ellipse are coincident. | |
Standard_Real | LastParameter () const |
Returns the value of the last parameter of this ellipse. This is 2.*Pi, which gives the end point of this ellipse. The start point and end point of an ellipse are coincident. | |
Standard_Boolean | IsClosed () const |
return True. | |
Standard_Boolean | IsPeriodic () const |
return True. | |
void | D0 (const Standard_Real U, gp_Pnt2d &P) const |
Returns in P the point of parameter U. P = C + MajorRadius * Cos (U) * XDir + MinorRadius * Sin (U) * YDir where C is the center of the ellipse , XDir the direction of the "XAxis" and "YDir" the "YAxis" of the ellipse. | |
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. //! Raised if the continuity of the curve is not C1. | |
void | D2 (const Standard_Real U, gp_Pnt2d &P, gp_Vec2d &V1, gp_Vec2d &V2) const |
Returns the point P of parameter U. The vectors V1 and V2 are the first and second derivatives at this point. | |
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 ellipse, 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 ellipse. | |
Handle_Geom2d_Geometry | Copy () const |
Creates a new object which is a copy of this ellipse. |
Geom2d_Ellipse::Geom2d_Ellipse | ( | const gp_Elips2d & | E | ) |
Geom2d_Ellipse::Geom2d_Ellipse | ( | const gp_Ax2d & | MajorAxis, |
const Standard_Real | MajorRadius, | ||
const Standard_Real | MinorRadius, | ||
const Standard_Boolean | Sense = Standard_True |
||
) |
Geom2d_Ellipse::Geom2d_Ellipse | ( | const gp_Ax22d & | Axis, |
const Standard_Real | MajorRadius, | ||
const Standard_Real | MinorRadius | ||
) |
MajorRadius is less than MinorRadius, or
Handle_Geom2d_Geometry Geom2d_Ellipse::Copy | ( | ) | const [virtual] |
Implements Geom2d_Geometry.
void Geom2d_Ellipse::D0 | ( | const Standard_Real | U, |
gp_Pnt2d & | P | ||
) | const [virtual] |
Implements Geom2d_Curve.
void Geom2d_Ellipse::D1 | ( | const Standard_Real | U, |
gp_Pnt2d & | P, | ||
gp_Vec2d & | V1 | ||
) | const [virtual] |
Implements Geom2d_Curve.
void Geom2d_Ellipse::D2 | ( | const Standard_Real | U, |
gp_Pnt2d & | P, | ||
gp_Vec2d & | V1, | ||
gp_Vec2d & | V2 | ||
) | const [virtual] |
Implements Geom2d_Curve.
void Geom2d_Ellipse::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_Ellipse::Directrix1 | ( | ) | const |
gp_Ax2d Geom2d_Ellipse::Directrix2 | ( | ) | const |
gp_Vec2d Geom2d_Ellipse::DN | ( | const Standard_Real | U, |
const Standard_Integer | N | ||
) | const [virtual] |
Implements Geom2d_Curve.
Standard_Real Geom2d_Ellipse::Eccentricity | ( | ) | const [virtual] |
Implements Geom2d_Conic.
gp_Elips2d Geom2d_Ellipse::Elips2d | ( | ) | const |
Standard_Real Geom2d_Ellipse::FirstParameter | ( | ) | const [virtual] |
Implements Geom2d_Curve.
Standard_Real Geom2d_Ellipse::Focal | ( | ) | const |
gp_Pnt2d Geom2d_Ellipse::Focus1 | ( | ) | const |
gp_Pnt2d Geom2d_Ellipse::Focus2 | ( | ) | const |
Standard_Boolean Geom2d_Ellipse::IsClosed | ( | ) | const [virtual] |
Implements Geom2d_Curve.
Standard_Boolean Geom2d_Ellipse::IsPeriodic | ( | ) | const [virtual] |
Implements Geom2d_Curve.
Standard_Real Geom2d_Ellipse::LastParameter | ( | ) | const [virtual] |
Implements Geom2d_Curve.
Standard_Real Geom2d_Ellipse::MajorRadius | ( | ) | const |
Standard_Real Geom2d_Ellipse::MinorRadius | ( | ) | const |
Standard_Real Geom2d_Ellipse::Parameter | ( | ) | const |
Standard_Real Geom2d_Ellipse::ReversedParameter | ( | const Standard_Real | U | ) | const [virtual] |
Implements Geom2d_Conic.
void Geom2d_Ellipse::SetElips2d | ( | const gp_Elips2d & | E | ) |
void Geom2d_Ellipse::SetMajorRadius | ( | const Standard_Real | MajorRadius | ) |
void Geom2d_Ellipse::SetMinorRadius | ( | const Standard_Real | MinorRadius | ) |
void Geom2d_Ellipse::Transform | ( | const gp_Trsf2d & | T | ) | [virtual] |
Implements Geom2d_Geometry.