Describes an ellipse in the plane (2D space). An ellipse is defined by its major and minor radii and positioned in the plane with a coordinate system (a gp_Ax22d object) as follows: More...

#include <gp_Elips2d.hxx>

Public Member Functions
	gp_Elips2d ()
	Creates an indefinite ellipse. More...

	gp_Elips2d (const gp_Ax2d &MajorAxis, const Standard_Real MajorRadius, const Standard_Real MinorRadius, const Standard_Boolean Sense=Standard_True)
	Creates an ellipse with the major axis, the major and the minor radius. The location of the MajorAxis is the center of the ellipse. The sense of parametrization is given by Sense. Warnings : It is possible to create an ellipse with MajorRadius = MinorRadius. Raises ConstructionError if MajorRadius < MinorRadius or MinorRadius < 0.0. More...

	gp_Elips2d (const gp_Ax22d &A, const Standard_Real MajorRadius, const Standard_Real MinorRadius)
	Creates an ellipse with radii MajorRadius and MinorRadius, positioned in the plane by coordinate system A where: More...

void	SetLocation (const gp_Pnt2d &P)
	Modifies this ellipse, by redefining its local coordinate system so that. More...

void	SetMajorRadius (const Standard_Real MajorRadius)
	Changes the value of the major radius. Raises ConstructionError if MajorRadius < MinorRadius. More...

void	SetMinorRadius (const Standard_Real MinorRadius)
	Changes the value of the minor radius. Raises ConstructionError if MajorRadius < MinorRadius or MinorRadius < 0.0. More...

void	SetAxis (const gp_Ax22d &A)
	Modifies this ellipse, by redefining its local coordinate system so that it becomes A. More...

void	SetXAxis (const gp_Ax2d &A)
	Modifies this ellipse, by redefining its local coordinate system so that its origin and its "X Direction" become those of the axis A. The "Y Direction" is then recomputed. The orientation of the local coordinate system is not modified. More...

void	SetYAxis (const gp_Ax2d &A)
	Modifies this ellipse, by redefining its local coordinate system so that its origin and its "Y Direction" become those of the axis A. The "X Direction" is then recomputed. The orientation of the local coordinate system is not modified. More...

Standard_Real	Area () const
	Computes the area of the ellipse. More...

void	Coefficients (Standard_Real &A, Standard_Real &B, Standard_Real &C, Standard_Real &D, Standard_Real &E, Standard_Real &F) const
	Returns the coefficients of the implicit equation of the ellipse. A * (X*2) + B (Y*2) + 2C(XY) + 2DX + 2EY + F = 0. More...

gp_Ax2d	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". More...

gp_Ax2d	Directrix2 () const
	This line is obtained by the symmetrical transformation of "Directrix1" with respect to the minor axis 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
	Returns the distance between the center of the ellipse and focus1 or focus2. More...

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

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

const gp_Pnt2d &	Location () const
	Returns the center of the ellipse. More...

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

Standard_Real	MinorRadius () const
	Returns the minor radius of the 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...

const gp_Ax22d &	Axis () const
	Returns the major axis of the ellipse. More...

gp_Ax2d	XAxis () const
	Returns the major axis of the ellipse. More...

gp_Ax2d	YAxis () const
	Returns the minor axis of the ellipse. Reverses the direction of the circle. More...

void	Reverse ()

gp_Elips2d	Reversed () const

Standard_Boolean	IsDirect () const
	Returns true if the local coordinate system is direct and false in the other case. More...

void	Mirror (const gp_Pnt2d &P)

gp_Elips2d	Mirrored (const gp_Pnt2d &P) const
	Performs the symmetrical transformation of a ellipse with respect to the point P which is the center of the symmetry. More...

void	Mirror (const gp_Ax2d &A)

gp_Elips2d	Mirrored (const gp_Ax2d &A) const
	Performs the symmetrical transformation of a ellipse with respect to an axis placement which is the axis of the symmetry. More...

void	Rotate (const gp_Pnt2d &P, const Standard_Real Ang)

gp_Elips2d	Rotated (const gp_Pnt2d &P, const Standard_Real Ang) const

void	Scale (const gp_Pnt2d &P, const Standard_Real S)

gp_Elips2d	Scaled (const gp_Pnt2d &P, const Standard_Real S) const
	Scales a ellipse. S is the scaling value. More...

void	Transform (const gp_Trsf2d &T)

gp_Elips2d	Transformed (const gp_Trsf2d &T) const
	Transforms an ellipse with the transformation T from class Trsf2d. More...

void	Translate (const gp_Vec2d &V)

gp_Elips2d	Translated (const gp_Vec2d &V) const
	Translates a ellipse in the direction of the vector V. The magnitude of the translation is the vector's magnitude. More...

void	Translate (const gp_Pnt2d &P1, const gp_Pnt2d &P2)

gp_Elips2d	Translated (const gp_Pnt2d &P1, const gp_Pnt2d &P2) const
	Translates a ellipse from the point P1 to the point P2. More...

Detailed Description

Describes an ellipse in the plane (2D space). An ellipse is defined by its major and minor radii and positioned in the plane with a coordinate system (a gp_Ax22d object) as follows:

the origin of the coordinate system is the center of the ellipse,
its "X Direction" defines the major axis of the ellipse, and
its "Y Direction" defines the minor axis of the ellipse. This coordinate system is the "local coordinate system" of the ellipse. Its orientation (direct or indirect) gives an implicit orientation to the ellipse. In this coordinate system, the equation of the ellipse is: X*X / (MajorRadius**2) + Y*Y / (MinorRadius**2) = 1.0 See Also gce_MakeElips2d which provides functions for more complex ellipse constructions Geom2d_Ellipse which provides additional functions for constructing ellipses and works, in particular, with the parametric equations of ellipses

Constructor & Destructor Documentation

◆ gp_Elips2d() [1/3]

gp_Elips2d::gp_Elips2d ( )

Creates an indefinite ellipse.

◆ gp_Elips2d() [2/3]

gp_Elips2d::gp_Elips2d	(	const gp_Ax2d &	MajorAxis,
		const Standard_Real	MajorRadius,
		const Standard_Real	MinorRadius,
		const Standard_Boolean	Sense = `Standard_True`
	)

Creates an ellipse with the major axis, the major and the minor radius. The location of the MajorAxis is the center of the ellipse. The sense of parametrization is given by Sense. Warnings : It is possible to create an ellipse with MajorRadius = MinorRadius. Raises ConstructionError if MajorRadius < MinorRadius or MinorRadius < 0.0.

◆ gp_Elips2d() [3/3]

gp_Elips2d::gp_Elips2d	(	const gp_Ax22d &	A,
		const Standard_Real	MajorRadius,
		const Standard_Real	MinorRadius
	)

Creates an ellipse with radii MajorRadius and MinorRadius, positioned in the plane by coordinate system A where:

the origin of A is the center of the ellipse,
the "X Direction" of A defines the major axis of the ellipse, that is, the major radius MajorRadius is measured along this axis, and
the "Y Direction" of A defines the minor axis of the ellipse, that is, the minor radius MinorRadius is measured along this axis, and
the orientation (direct or indirect sense) of A gives the orientation of the ellipse. Warnings : It is possible to create an ellipse with MajorRadius = MinorRadius. Raises ConstructionError if MajorRadius < MinorRadius or MinorRadius < 0.0

Member Function Documentation

◆ Area()

Standard_Real gp_Elips2d::Area ( ) const

Computes the area of the ellipse.

◆ Axis()

const gp_Ax22d& gp_Elips2d::Axis ( ) const

Returns the major axis of the ellipse.

◆ Coefficients()

void gp_Elips2d::Coefficients	(	Standard_Real &	A,
		Standard_Real &	B,
		Standard_Real &	C,
		Standard_Real &	D,
		Standard_Real &	E,
		Standard_Real &	F
	)		const

Returns the coefficients of the implicit equation of the ellipse. A * (X**2) + B * (Y**2) + 2*C*(X*Y) + 2*D*X + 2*E*Y + F = 0.

◆ Directrix1()

gp_Ax2d gp_Elips2d::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)

◆ Directrix2()

gp_Ax2d gp_Elips2d::Directrix2 ( ) const

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

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

◆ Eccentricity()

Standard_Real gp_Elips2d::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.

◆ Focal()

Standard_Real gp_Elips2d::Focal ( ) const

Returns the distance between the center of the ellipse and focus1 or focus2.

◆ Focus1()

gp_Pnt2d gp_Elips2d::Focus1 ( ) const

Returns the first focus of the ellipse. This focus is on the positive side of the major axis of the ellipse.

◆ Focus2()

gp_Pnt2d gp_Elips2d::Focus2 ( ) const

Returns the second focus of the ellipse. This focus is on the negative side of the major axis of the ellipse.

◆ IsDirect()

Standard_Boolean gp_Elips2d::IsDirect ( ) const

Returns true if the local coordinate system is direct and false in the other case.

◆ Location()

const gp_Pnt2d& gp_Elips2d::Location ( ) const

Returns the center of the ellipse.

◆ MajorRadius()

Standard_Real gp_Elips2d::MajorRadius ( ) const

Returns the major radius of the Ellipse.

◆ MinorRadius()

Standard_Real gp_Elips2d::MinorRadius ( ) const

Returns the minor radius of the Ellipse.

◆ Mirror() [1/2]

void gp_Elips2d::Mirror ( const gp_Pnt2d & P )

◆ Mirror() [2/2]

void gp_Elips2d::Mirror ( const gp_Ax2d & A )

◆ Mirrored() [1/2]

gp_Elips2d gp_Elips2d::Mirrored ( const gp_Pnt2d & P ) const

Performs the symmetrical transformation of a ellipse with respect to the point P which is the center of the symmetry.

◆ Mirrored() [2/2]

gp_Elips2d gp_Elips2d::Mirrored ( const gp_Ax2d & A ) const

Performs the symmetrical transformation of a ellipse with respect to an axis placement which is the axis of the symmetry.

◆ Parameter()

Standard_Real gp_Elips2d::Parameter ( ) const

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

◆ Reverse()

void gp_Elips2d::Reverse ( )

◆ Reversed()

gp_Elips2d gp_Elips2d::Reversed ( ) const

◆ Rotate()

void gp_Elips2d::Rotate	(	const gp_Pnt2d &	P,
		const Standard_Real	Ang
	)

◆ Rotated()

gp_Elips2d gp_Elips2d::Rotated	(	const gp_Pnt2d &	P,
		const Standard_Real	Ang
	)		const

◆ Scale()

void gp_Elips2d::Scale	(	const gp_Pnt2d &	P,
		const Standard_Real	S
	)

◆ Scaled()

gp_Elips2d gp_Elips2d::Scaled	(	const gp_Pnt2d &	P,
		const Standard_Real	S
	)		const

Scales a ellipse. S is the scaling value.

◆ SetAxis()

void gp_Elips2d::SetAxis ( const gp_Ax22d & A )

Modifies this ellipse, by redefining its local coordinate system so that it becomes A.

◆ SetLocation()

void gp_Elips2d::SetLocation ( const gp_Pnt2d & P )

Modifies this ellipse, by redefining its local coordinate system so that.

its origin becomes P.

◆ SetMajorRadius()

void gp_Elips2d::SetMajorRadius ( const Standard_Real MajorRadius )

Changes the value of the major radius. Raises ConstructionError if MajorRadius < MinorRadius.

◆ SetMinorRadius()

void gp_Elips2d::SetMinorRadius ( const Standard_Real MinorRadius )

Changes the value of the minor radius. Raises ConstructionError if MajorRadius < MinorRadius or MinorRadius < 0.0.

◆ SetXAxis()

void gp_Elips2d::SetXAxis ( const gp_Ax2d & A )

Modifies this ellipse, by redefining its local coordinate system so that its origin and its "X Direction" become those of the axis A. The "Y Direction" is then recomputed. The orientation of the local coordinate system is not modified.

◆ SetYAxis()

void gp_Elips2d::SetYAxis ( const gp_Ax2d & A )

Modifies this ellipse, by redefining its local coordinate system so that its origin and its "Y Direction" become those of the axis A. The "X Direction" is then recomputed. The orientation of the local coordinate system is not modified.

◆ Transform()

void gp_Elips2d::Transform ( const gp_Trsf2d & T )

◆ Transformed()

gp_Elips2d gp_Elips2d::Transformed ( const gp_Trsf2d & T ) const

Transforms an ellipse with the transformation T from class Trsf2d.

◆ Translate() [1/2]

void gp_Elips2d::Translate ( const gp_Vec2d & V )

◆ Translate() [2/2]

void gp_Elips2d::Translate	(	const gp_Pnt2d &	P1,
		const gp_Pnt2d &	P2
	)

◆ Translated() [1/2]

gp_Elips2d gp_Elips2d::Translated ( const gp_Vec2d & V ) const

Translates a ellipse in the direction of the vector V. The magnitude of the translation is the vector's magnitude.

◆ Translated() [2/2]

gp_Elips2d gp_Elips2d::Translated	(	const gp_Pnt2d &	P1,
		const gp_Pnt2d &	P2
	)		const

Translates a ellipse from the point P1 to the point P2.

◆ XAxis()

gp_Ax2d gp_Elips2d::XAxis ( ) const