# Geom_Ellipse Class Reference

Describes an ellipse in 3D space. An ellipse is defined by its major and minor radii and, as with any conic curve, is positioned in space with a right-handed coordinate system (gp_Ax2 object) where: More...

`#include <Geom_Ellipse.hxx>`

Inheritance diagram for Geom_Ellipse: [legend]

## Public Member Functions

Geom_Ellipse (const gp_Elips &E)
Constructs an ellipse by conversion of the gp_Elips ellipse E. More...

Constructs an ellipse defined by its major and minor radii, MajorRadius and MinorRadius, where A2 locates the ellipse and defines its orientation in 3D space such that: More...

void SetElips (const gp_Elips &E)
Converts the gp_Elips ellipse E into this ellipse. More...

Assigns a value to the major radius of this ellipse. ConstructionError raised if MajorRadius < MinorRadius. More...

gp_Elips Elips () const
returns the non transient ellipse from gp with the same More...

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. More...

gp_Ax1 Directrix1 () const
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". Raised if Eccentricity = 0.0. (The ellipse degenerates into a circle) More...

gp_Ax1 Directrix2 () const
This line is obtained by the symmetrical transformation of "Directrix1" with respect to the "YAxis" of the ellipse. More...

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. More...

Standard_Real Focal () const
Computes the focal distance. It is the distance between the the two focus of the ellipse. More...

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

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

Returns the major radius of this ellipse. More...

Returns the minor radius of this ellipse. More...

Standard_Real Parameter () const
Returns p = (1 - e * e) * MajorRadius where e is the eccentricity of the ellipse. Returns 0 if MajorRadius = 0. More...

Standard_Real FirstParameter () const
Returns the value of the first parameter of this ellipse. This is respectively: More...

Standard_Real LastParameter () const
Returns the value of the last parameter of this ellipse. This is respectively: More...

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

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

void D0 (const Standard_Real U, gp_Pnt &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. More...

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. Raised if the continuity of the curve is not C1. More...

void D2 (const Standard_Real U, gp_Pnt &P, gp_Vec &V1, gp_Vec &V2) const
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_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. More...

gp_Vec 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. More...

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

Handle< Geom_GeometryCopy () const
Creates a new object which is a copy of this ellipse. More... Public Member Functions inherited from Geom_Conic
void SetAxis (const gp_Ax1 &A1)
Changes the orientation of the conic's plane. The normal axis to the plane is A1. The XAxis and the YAxis are recomputed. More...

void SetLocation (const gp_Pnt &P)
changes the location point of the conic. More...

void SetPosition (const gp_Ax2 &A2)
changes the local coordinate system of the conic. More...

gp_Ax1 Axis () const
Returns the "main Axis" of this conic. This axis is normal to the plane of the conic. More...

gp_Pnt 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 Apex of the parabola. More...

const gp_Ax2Position () const
Returns the local coordinates system of the conic. The main direction of the Axis2Placement is normal to the plane of the conic. The X direction of the Axis2placement is in the plane of the conic and corresponds to the origin for the conic's parametric value u. More...

gp_Ax1 XAxis () const
Returns the XAxis of the conic. This axis defines the origin of parametrization of the conic. This axis is perpendicular to the Axis of the conic. This axis and the Yaxis define the plane of the conic. More...

gp_Ax1 YAxis () const
Returns the YAxis of the conic. The YAxis is perpendicular to the Xaxis. This axis and the Xaxis define the plane of the conic. More...

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

GeomAbs_Shape Continuity () const
The continuity of the conic is Cn. More...

Standard_Boolean IsCN (const Standard_Integer N) const
Returns True. Raised if N < 0. More... Public Member Functions inherited from Geom_Curve
virtual 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>. More...

virtual 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>. More...

Handle< Geom_CurveReversed () const
Returns a copy of <me> reversed. More...

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

gp_Pnt 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. it is implemented with D0. More... Public Member Functions inherited from Geom_Geometry
void Mirror (const gp_Pnt &P)
Performs the symmetrical transformation of a Geometry with respect to the point P which is the center of the symmetry. More...

void Mirror (const gp_Ax1 &A1)
Performs the symmetrical transformation of a Geometry with respect to an axis placement which is the axis of the symmetry. More...

void Mirror (const gp_Ax2 &A2)
Performs the symmetrical transformation of a Geometry with respect to a plane. The axis placement A2 locates the plane of the symmetry : (Location, XDirection, YDirection). More...

void Rotate (const gp_Ax1 &A1, const Standard_Real Ang)
Rotates a Geometry. A1 is the axis of the rotation. Ang is the angular value of the rotation in radians. More...

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

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

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

Handle< Geom_GeometryMirrored (const gp_Pnt &P) const

Handle< Geom_GeometryMirrored (const gp_Ax1 &A1) const

Handle< Geom_GeometryMirrored (const gp_Ax2 &A2) const

Handle< Geom_GeometryRotated (const gp_Ax1 &A1, const Standard_Real Ang) const

Handle< Geom_GeometryScaled (const gp_Pnt &P, const Standard_Real S) const

Handle< Geom_GeometryTransformed (const gp_Trsf &T) const

Handle< Geom_GeometryTranslated (const gp_Vec &V) const

Handle< Geom_GeometryTranslated (const gp_Pnt &P1, const gp_Pnt &P2) const Public Member Functions inherited from MMgt_TShared
virtual void Delete () const
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
Handle_Standard_Type &
DynamicType () const

Standard_Boolean IsInstance (const 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 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...

virtual Handle_Standard_Transient This () const
Returns a Handle which references this object. Must never be called to objects created in stack. More...

Standard_Integer GetRefCount () const
Get the reference counter of this object. More... Protected Attributes inherited from Geom_Conic
gp_Ax2 pos

## Detailed Description

Describes an ellipse in 3D space. An ellipse is defined by its major and minor radii and, as with any conic curve, is positioned in space with a right-handed coordinate system (gp_Ax2 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. The origin, "X Direction" and "Y Direction" of this coordinate system define the plane of the ellipse. The coordinate system is the local coordinate system of the ellipse. The "main Direction" of this coordinate system is the vector normal to the plane of the ellipse. 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 ellipse. The "main Direction" of the local coordinate system gives an explicit orientation to the ellipse (definition of the trigonometric sense), determining the direction in which the parameter increases along the ellipse. The Geom_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 [.

## Constructor & Destructor Documentation

 Geom_Ellipse::Geom_Ellipse ( const gp_Elips & E )

Constructs an ellipse by conversion of the gp_Elips ellipse E.

 Geom_Ellipse::Geom_Ellipse ( const gp_Ax2 & A2, const Standard_Real MajorRadius, const Standard_Real MinorRadius )

Constructs an ellipse defined by its major and minor radii, MajorRadius and MinorRadius, where A2 locates the ellipse and defines its orientation in 3D space such that:

• the center of the ellipse is the origin of A2,
• the "X Direction" of A2 defines the major axis of the ellipse, i.e. the major radius MajorRadius is measured along this axis,
• the "Y Direction" of A2 defines the minor axis of the ellipse, i.e. the minor radius MinorRadius is measured along this axis,
• A2 is the local coordinate system of the ellipse. Exceptions Standard_ConstructionError if:
• MinorRadius is less than 0. Warning The Geom package does not prevent the construction of an ellipse where MajorRadius and MinorRadius are equal.

## Member Function Documentation

 Handle< Geom_Geometry > Geom_Ellipse::Copy ( ) const
virtual

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

Implements Geom_Geometry.

 void Geom_Ellipse::D0 ( const Standard_Real U, gp_Pnt & P ) const
virtual

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 Geom_Curve.

 void Geom_Ellipse::D1 ( const Standard_Real U, gp_Pnt & P, gp_Vec & V1 ) const
virtual

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

Implements Geom_Curve.

 void Geom_Ellipse::D2 ( const Standard_Real U, gp_Pnt & P, gp_Vec & V1, gp_Vec & V2 ) const
virtual

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

Implements Geom_Curve.

 void Geom_Ellipse::D3 ( const Standard_Real U, gp_Pnt & P, gp_Vec & V1, gp_Vec & V2, gp_Vec & V3 ) const
virtual

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

Implements Geom_Curve.

 gp_Ax1 Geom_Ellipse::Directrix1 ( ) const

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". Raised if Eccentricity = 0.0. (The ellipse degenerates into a circle)

 gp_Ax1 Geom_Ellipse::Directrix2 ( ) const

This line is obtained by the symmetrical transformation of "Directrix1" with respect to the "YAxis" of the ellipse.

Raised if Eccentricity = 0.0. (The ellipse degenerates into a circle).

 gp_Vec Geom_Ellipse::DN ( const Standard_Real U, const Standard_Integer N ) const
virtual

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 Geom_Curve.

 Standard_Real Geom_Ellipse::Eccentricity ( ) const
virtual

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 Geom_Conic.

 gp_Elips Geom_Ellipse::Elips ( ) const

returns the non transient ellipse from gp with the same

 Standard_Real Geom_Ellipse::FirstParameter ( ) const
virtual

Returns the value of the first parameter of this ellipse. This is respectively:

• 0.0, which gives the start point of this ellipse, or The start point and end point of an ellipse are coincident.

Implements Geom_Curve.

 Standard_Real Geom_Ellipse::Focal ( ) const

Computes the focal distance. It is the distance between the the two focus of the ellipse.

 gp_Pnt Geom_Ellipse::Focus1 ( ) const

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

 gp_Pnt Geom_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 Geom_Ellipse::IsClosed ( ) const
virtual

return True.

Implements Geom_Curve.

 Standard_Boolean Geom_Ellipse::IsPeriodic ( ) const
virtual

return True.

Implements Geom_Curve.

 Standard_Real Geom_Ellipse::LastParameter ( ) const
virtual

Returns the value of the last parameter of this ellipse. This is respectively:

• 2.*Pi, which gives the end point of this ellipse. The start point and end point of an ellipse are coincident.

Implements Geom_Curve.

Returns the major radius of this ellipse.

Returns the minor radius of this ellipse.

 Standard_Real Geom_Ellipse::Parameter ( ) const

Returns p = (1 - e * e) * MajorRadius where e is the eccentricity of the ellipse. Returns 0 if MajorRadius = 0.

 Standard_Real Geom_Ellipse::ReversedParameter ( const Standard_Real U ) const
virtual

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 Geom_Conic.

 void Geom_Ellipse::SetElips ( const gp_Elips & E )

Converts the gp_Elips ellipse E into this ellipse.