Open CASCADE Technology  7.0.0
Geom2d_Ellipse Class Reference

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: More...

`#include <Geom2d_Ellipse.hxx>`

Inheritance diagram for Geom2d_Ellipse:
[legend]

## Public Member Functions

Geom2d_Ellipse (const gp_Elips2d &E)
Creates an ellipse by conversion of the gp_Elips2d ellipse E. More...

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 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: More...

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: More...

void SetElips2d (const gp_Elips2d &E)
Converts the gp_Elips2d ellipse E into this ellipse. More...

Assigns a value to the major radius of this ellipse. Exceptions Standard_ConstructionError if: More...

Assigns a value to the minor radius of this ellipse. Exceptions Standard_ConstructionError if: More...

gp_Elips2d Elips2d () const
Converts this ellipse into a gp_Elips2d ellipse. More...

Standard_Real ReversedParameter (const Standard_Real U) const override
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. More...

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) More...

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). More...

Standard_Real Eccentricity () const override
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. More...

Standard_Real Focal () const
Computes the focal distance. The focal distance is the distance between the center and a focus of the ellipse. More...

gp_Pnt2d Focus1 () const
Returns the first focus of the ellipse. This focus is on the positive side of the "XAxis" of the ellipse. More...

gp_Pnt2d Focus2 () const
Returns the second focus of the ellipse. This focus is on the negative side of the "XAxis" of the ellipse. More...

Standard_Real MajorRadius () const
Returns the major radius of this ellipse. More...

Standard_Real MinorRadius () const
Returns the minor radius of this ellipse. More...

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. More...

Standard_Real FirstParameter () const override
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. More...

Standard_Real LastParameter () const override
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. More...

Standard_Boolean IsClosed () const override
return True. More...

Standard_Boolean IsPeriodic () const override
return True. More...

void D0 (const Standard_Real U, gp_Pnt2d &P) const override
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. More...

void D1 (const Standard_Real U, gp_Pnt2d &P, gp_Vec2d &V1) const override
Returns the point P of parameter U and the first derivative V1. Raised if the continuity of the curve is not C1. More...

void D2 (const Standard_Real U, gp_Pnt2d &P, gp_Vec2d &V1, gp_Vec2d &V2) const override
Returns the point P of parameter U. The vectors V1 and V2 are the first and second derivatives at this point. More...

void D3 (const Standard_Real U, gp_Pnt2d &P, gp_Vec2d &V1, gp_Vec2d &V2, gp_Vec2d &V3) const override
Returns the point P of parameter U, the first second and third derivatives V1 V2 and V3. More...

gp_Vec2d DN (const Standard_Real U, const Standard_Integer N) const override
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. More...

void Transform (const gp_Trsf2d &T) override
Applies the transformation T to this ellipse. More...

Handle< Geom2d_GeometryCopy () const override
Creates a new object which is a copy of this ellipse. More...

Public Member Functions inherited from Geom2d_Conic
void SetAxis (const gp_Ax22d &A)
Modifies this conic, redefining its local coordinate system partially, by assigning P as its origin. More...

void SetXAxis (const gp_Ax2d &A)

void SetYAxis (const gp_Ax2d &A)
Assigns the origin and unit vector of axis A to the origin of the local coordinate system of this conic and either: More...

void SetLocation (const gp_Pnt2d &P)
Modifies this conic, redefining its local coordinate system fully, by assigning A as this coordinate system. More...

gp_Ax2d XAxis () const
Returns the "XAxis" of the conic. This axis defines the origin of parametrization of the conic. This axis and the "Yaxis" define the local coordinate system of the conic. -C++: return const&. More...

gp_Ax2d YAxis () const
Returns the "YAxis" of the conic. The "YAxis" is perpendicular to the "Xaxis". More...

gp_Pnt2d Location () const
Returns the location point of the conic. For the circle, the ellipse and the hyperbola it is the center of the conic. For the parabola it is the vertex of the parabola. More...

const gp_Ax22dPosition () const
Returns the local coordinates system of the conic. More...

void Reverse () override
Reverses the direction of parameterization of <me>. The local coordinate system of the conic is modified. More...

GeomAbs_Shape Continuity () const override
Returns GeomAbs_CN which is the global continuity of any conic. More...

Standard_Boolean IsCN (const Standard_Integer N) const override
Returns True, the order of continuity of a conic is infinite. More...

Public Member Functions inherited from Geom2d_Curve
virtual Standard_Real TransformedParameter (const Standard_Real U, const gp_Trsf2d &T) const
Computes the parameter on the curve transformed by T for the point of parameter U on this curve. Note: this function generally returns U but it can be redefined (for example, on a line). More...

virtual Standard_Real ParametricTransformation (const gp_Trsf2d &T) const
Returns the coefficient required to compute the parametric transformation of this curve when transformation T is applied. This coefficient is the ratio between the parameter of a point on this curve and the parameter of the transformed point on the new curve transformed by T. Note: this function generally returns 1. but it can be redefined (for example, on a line). More...

Handle< Geom2d_CurveReversed () const
Creates a reversed duplicate Changes the orientation of this curve. The first and last parameters are not changed, but the parametric direction of the curve is reversed. If the curve is bounded: More...

virtual Standard_Real Period () const
Returns thne period of this curve. raises if the curve is not periodic. More...

gp_Pnt2d Value (const Standard_Real U) const
Computes the point of parameter U on <me>. If the curve is periodic then the returned point is P(U) with U = Ustart + (U - Uend) where Ustart and Uend are the parametric bounds of the curve. More...

Public Member Functions inherited from Geom2d_Geometry
void Mirror (const gp_Pnt2d &P)
Performs the symmetrical transformation of a Geometry with respect to the point P which is the center of the symmetry and assigns the result to this geometric object. More...

void Mirror (const gp_Ax2d &A)
Performs the symmetrical transformation of a Geometry with respect to an axis placement which is the axis of the symmetry. More...

void Rotate (const gp_Pnt2d &P, const Standard_Real Ang)
Rotates a Geometry. P is the center of the rotation. Ang is the angular value of the rotation in radians. More...

void Scale (const gp_Pnt2d &P, const Standard_Real S)
Scales a Geometry. S is the scaling value. More...

void Translate (const gp_Vec2d &V)
Translates a Geometry. V is the vector of the tanslation. More...

void Translate (const gp_Pnt2d &P1, const gp_Pnt2d &P2)
Translates a Geometry from the point P1 to the point P2. More...

Handle< Geom2d_GeometryMirrored (const gp_Pnt2d &P) const

Handle< Geom2d_GeometryMirrored (const gp_Ax2d &A) const

Handle< Geom2d_GeometryRotated (const gp_Pnt2d &P, const Standard_Real Ang) const

Handle< Geom2d_GeometryScaled (const gp_Pnt2d &P, const Standard_Real S) const

Handle< Geom2d_GeometryTransformed (const gp_Trsf2d &T) const

Handle< Geom2d_GeometryTranslated (const gp_Vec2d &V) const

Handle< Geom2d_GeometryTranslated (const gp_Pnt2d &P1, const gp_Pnt2d &P2) const

Public Member Functions inherited from MMgt_TShared
virtual void Delete () const override
Memory deallocator for transient classes. More...

Public Member Functions inherited from Standard_Transient
Standard_Transient ()
Empty constructor. More...

Standard_Transient (const Standard_Transient &)
Copy constructor – does nothing. More...

Standard_Transientoperator= (const Standard_Transient &)
Assignment operator, needed to avoid copying reference counter. More...

virtual ~Standard_Transient ()
Destructor must be virtual. More...

virtual const opencascade::handle< Standard_Type > & DynamicType () const

Standard_Boolean IsInstance (const opencascade::handle< Standard_Type > &theType) const
Returns a true value if this is an instance of Type. More...

Standard_Boolean IsInstance (const Standard_CString theTypeName) const
Returns a true value if this is an instance of TypeName. More...

Standard_Boolean IsKind (const opencascade::handle< Standard_Type > &theType) const
Returns true if this is an instance of Type or an instance of any class that inherits from Type. Note that multiple inheritance is not supported by OCCT RTTI mechanism. More...

Standard_Boolean IsKind (const Standard_CString theTypeName) const
Returns true if this is an instance of TypeName or an instance of any class that inherits from TypeName. Note that multiple inheritance is not supported by OCCT RTTI mechanism. More...

Standard_TransientThis () const
Returns non-const pointer to this object (like const_cast). For protection against creating handle to objects allocated in stack or call from constructor, it will raise exception Standard_ProgramError if reference counter is zero. More...

Standard_Integer GetRefCount () const
Get the reference counter of this object. More...

void IncrementRefCounter () const
Increments the reference counter of this object. More...

Standard_Integer DecrementRefCounter () const
Decrements the reference counter of this object; returns the decremented value. More...

## Additional Inherited Members

Public Types inherited from Standard_Transient
typedef void base_type

Static Public Member Functions inherited from Standard_Transient
static const char * get_type_name ()

static const opencascade::handle< Standard_Type > & get_type_descriptor ()
Returns type descriptor of Standard_Transient class. More...

Protected Attributes inherited from Geom2d_Conic
gp_Ax22d pos

## Detailed Description

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:

• the origin is the center of the ellipse,
• the "X Direction" defines the major axis, and
• the "Y Direction" defines the minor axis. This coordinate system is the local coordinate system of the ellipse. The orientation (direct or indirect) of the local coordinate system gives an explicit orientation to the ellipse, determining the direction in which the parameter increases along the ellipse. The Geom2d_Ellipse ellipse is parameterized by an angle: P(U) = O + MajorRad*Cos(U)*XDir + MinorRad*Sin(U)*YDir where:
• P is the point of parameter U,
• O, XDir and YDir are respectively the origin, "X Direction" and "Y Direction" of its local coordinate system,
• MajorRad and MinorRad are the major and minor radii of the ellipse. The "X Axis" of the local coordinate system therefore defines the origin of the parameter of the ellipse. An ellipse is a closed and periodic curve. The period is 2.*Pi and the parameter range is [ 0,2.*Pi [. See Also GCE2d_MakeEllipse which provides functions for more complex ellipse constructions gp_Ax22d gp_Elips2d for an equivalent, non-parameterized data structure

## Constructor & Destructor Documentation

 Geom2d_Ellipse::Geom2d_Ellipse ( const gp_Elips2d & E )

Creates an ellipse by conversion of the gp_Elips2d ellipse E.

 Geom2d_Ellipse::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 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:

• MajorRadius is less than MinorRadius, or
• MinorRadius is less than 0.
 Geom2d_Ellipse::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:

• the center of the ellipse is the origin of Axis,
• the "X Direction" of Axis defines the major axis of the ellipse,
• the "Y Direction" of Axis defines the minor axis of the ellipse,
• the orientation of Axis (direct or indirect) gives the orientation of the ellipse. Warnings : It is not forbidden to create an ellipse with MajorRadius = MinorRadius. Exceptions Standard_ConstructionError if:
• MajorRadius is less than MinorRadius, or
• MinorRadius is less than 0.

## Member Function Documentation

 Handle< Geom2d_Geometry > Geom2d_Ellipse::Copy ( ) const
overridevirtual

Creates a new object which is a copy of this ellipse.

Implements Geom2d_Geometry.

 void Geom2d_Ellipse::D0 ( const Standard_Real U, gp_Pnt2d & P ) const
overridevirtual

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.

Implements Geom2d_Curve.

 void Geom2d_Ellipse::D1 ( const Standard_Real U, gp_Pnt2d & P, gp_Vec2d & V1 ) const
overridevirtual

Returns the point P of parameter U and the first derivative V1. Raised if the continuity of the curve is not C1.

Implements Geom2d_Curve.

 void Geom2d_Ellipse::D2 ( const Standard_Real U, gp_Pnt2d & P, gp_Vec2d & V1, gp_Vec2d & V2 ) const
overridevirtual

Returns the point P of parameter U. The vectors V1 and V2 are the first and second derivatives at this point.

Implements Geom2d_Curve.

 void Geom2d_Ellipse::D3 ( const Standard_Real U, gp_Pnt2d & P, gp_Vec2d & V1, gp_Vec2d & V2, gp_Vec2d & V3 ) const
overridevirtual

Returns the point P of parameter U, the first second and third derivatives V1 V2 and V3.

Implements Geom2d_Curve.

 gp_Ax2d Geom2d_Ellipse::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 Geom2d_Ellipse::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).

 gp_Vec2d Geom2d_Ellipse::DN ( const Standard_Real U, const Standard_Integer N ) const
overridevirtual

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.

Implements Geom2d_Curve.

 Standard_Real Geom2d_Ellipse::Eccentricity ( ) const
overridevirtual

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.

Implements Geom2d_Conic.

 gp_Elips2d Geom2d_Ellipse::Elips2d ( ) const

Converts this ellipse into a gp_Elips2d ellipse.

 Standard_Real Geom2d_Ellipse::FirstParameter ( ) const
overridevirtual

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.

Implements Geom2d_Curve.

 Standard_Real Geom2d_Ellipse::Focal ( ) const

Computes the focal distance. The focal distance is the distance between the center and a focus of the ellipse.

 gp_Pnt2d Geom2d_Ellipse::Focus1 ( ) const

Returns the first focus of the ellipse. This focus is on the positive side of the "XAxis" of the ellipse.

 gp_Pnt2d Geom2d_Ellipse::Focus2 ( ) const

Returns the second focus of the ellipse. This focus is on the negative side of the "XAxis" of the ellipse.

 Standard_Boolean Geom2d_Ellipse::IsClosed ( ) const
overridevirtual

return True.

Implements Geom2d_Curve.

 Standard_Boolean Geom2d_Ellipse::IsPeriodic ( ) const
overridevirtual

return True.

Implements Geom2d_Curve.

 Standard_Real Geom2d_Ellipse::LastParameter ( ) const
overridevirtual

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.

Implements Geom2d_Curve.

 Standard_Real Geom2d_Ellipse::MajorRadius ( ) const

Returns the major radius of this ellipse.

 Standard_Real Geom2d_Ellipse::MinorRadius ( ) const

Returns the minor radius of this ellipse.

 Standard_Real Geom2d_Ellipse::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 Geom2d_Ellipse::ReversedParameter ( const Standard_Real U ) const
overridevirtual

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.

Implements Geom2d_Conic.

 void Geom2d_Ellipse::SetElips2d ( const gp_Elips2d & E )

Converts the gp_Elips2d ellipse E into this ellipse.

 void Geom2d_Ellipse::SetMajorRadius ( const Standard_Real MajorRadius )

Assigns a value to the major radius of this ellipse. Exceptions Standard_ConstructionError if:

• the major radius of this ellipse becomes less than the minor radius, or
• MinorRadius is less than 0.
 void Geom2d_Ellipse::SetMinorRadius ( const Standard_Real MinorRadius )

Assigns a value to the minor radius of this ellipse. Exceptions Standard_ConstructionError if:

• the major radius of this ellipse becomes less than the minor radius, or
• MinorRadius is less than 0.
 void Geom2d_Ellipse::Transform ( const gp_Trsf2d & T )
overridevirtual

Applies the transformation T to this ellipse.

Implements Geom2d_Geometry.

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