gp_Elips2d Class Reference

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
constexpr	gp_Elips2d () noexcept
	Creates an indefinite ellipse.
constexpr	gp_Elips2d (const gp_Ax2d &theMajorAxis, const double theMajorRadius, const double theMinorRadius, const bool theIsSense=true)
	Creates an ellipse with the major axis, the major and the minor radius. The location of the theMajorAxis is the center of the ellipse. The sense of parametrization is given by theIsSense. Warnings: It is possible to create an ellipse with theMajorRadius = theMinorRadius. Raises ConstructionError if theMajorRadius < theMinorRadius or theMinorRadius < 0.0.
constexpr	gp_Elips2d (const gp_Ax22d &theA, const double theMajorRadius, const double theMinorRadius)
	Creates an ellipse with radii MajorRadius and MinorRadius, positioned in the plane by coordinate system theA where:
constexpr void	SetLocation (const gp_Pnt2d &theP) noexcept
	Modifies this ellipse, by redefining its local coordinate system so that.
void	SetMajorRadius (const double theMajorRadius)
	Changes the value of the major radius. Raises ConstructionError if theMajorRadius < MinorRadius.
void	SetMinorRadius (const double theMinorRadius)
	Changes the value of the minor radius. Raises ConstructionError if MajorRadius < theMinorRadius or MinorRadius < 0.0.
constexpr void	SetAxis (const gp_Ax22d &theA) noexcept
	Modifies this ellipse, by redefining its local coordinate system so that it becomes theA.
constexpr void	SetXAxis (const gp_Ax2d &theA)
	Modifies this ellipse, by redefining its local coordinate system so that its origin and its "X Direction" become those of the axis theA. The "Y Direction" is then recomputed. The orientation of the local coordinate system is not modified.
constexpr void	SetYAxis (const gp_Ax2d &theA)
	Modifies this ellipse, by redefining its local coordinate system so that its origin and its "Y Direction" become those of the axis theA. The "X Direction" is then recomputed. The orientation of the local coordinate system is not modified.
constexpr double	Area () const noexcept
	Computes the area of the ellipse.
void	Coefficients (double &theA, double &theB, double &theC, double &theD, double &theE, double &theF) const
	Returns the coefficients of the implicit equation of the ellipse. theA * (X**2) + theB * (Y**2) + 2*theC*(X*Y) + 2*theD*X + 2*theE*Y + theF = 0.
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".
gp_Ax2d	Directrix2 () const
	This line is obtained by the symmetrical transformation of "Directrix1" with respect to the minor axis of the ellipse.
double	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.
double	Focal () const
	Returns the distance between the center of the ellipse and focus1 or focus2.
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.
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.
constexpr const gp_Pnt2d &	Location () const noexcept
	Returns the center of the ellipse.
constexpr double	MajorRadius () const noexcept
	Returns the major radius of the Ellipse.
constexpr double	MinorRadius () const noexcept
	Returns the minor radius of the Ellipse.
constexpr double	Parameter () const noexcept
	Returns p = (1 - e * e) * MajorRadius where e is the eccentricity of the ellipse. Returns 0 if MajorRadius = 0.
constexpr const gp_Ax22d &	Axis () const noexcept
	Returns the major axis of the ellipse.
gp_Ax2d	XAxis () const noexcept
	Returns the major axis of the ellipse.
gp_Ax2d	YAxis () const noexcept
	Returns the minor axis of the ellipse. Reverses the direction of the circle.
void	Reverse () noexcept
gp_Elips2d	Reversed () const noexcept
constexpr bool	IsDirect () const noexcept
	Returns true if the local coordinate system is direct and false in the other case.
void	Mirror (const gp_Pnt2d &theP) noexcept
gp_Elips2d	Mirrored (const gp_Pnt2d &theP) const noexcept
	Performs the symmetrical transformation of a ellipse with respect to the point theP which is the center of the symmetry.
void	Mirror (const gp_Ax2d &theA) noexcept
gp_Elips2d	Mirrored (const gp_Ax2d &theA) const noexcept
	Performs the symmetrical transformation of a ellipse with respect to an axis placement which is the axis of the symmetry.
void	Rotate (const gp_Pnt2d &theP, const double theAng)
gp_Elips2d	Rotated (const gp_Pnt2d &theP, const double theAng) const
void	Scale (const gp_Pnt2d &theP, const double theS)
gp_Elips2d	Scaled (const gp_Pnt2d &theP, const double theS) const
	Scales a ellipse. theS is the scaling value.
void	Transform (const gp_Trsf2d &theT)
gp_Elips2d	Transformed (const gp_Trsf2d &theT) const
	Transforms an ellipse with the transformation theT from class Trsf2d.
constexpr void	Translate (const gp_Vec2d &theV) noexcept
constexpr gp_Elips2d	Translated (const gp_Vec2d &theV) const noexcept
	Translates a ellipse in the direction of the vector theV. The magnitude of the translation is the vector's magnitude.
constexpr void	Translate (const gp_Pnt2d &theP1, const gp_Pnt2d &theP2) noexcept
constexpr gp_Elips2d	Translated (const gp_Pnt2d &theP1, const gp_Pnt2d &theP2) const noexcept
	Translates a ellipse from the point theP1 to the point theP2.

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 ( )

inlineconstexprnoexcept

Creates an indefinite ellipse.

gp_Elips2d() [2/3]

gp_Elips2d::gp_Elips2d ( const gp_Ax2d & theMajorAxis, const double theMajorRadius, const double theMinorRadius, const bool theIsSense = true )

inlineconstexpr

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

gp_Elips2d() [3/3]

gp_Elips2d::gp_Elips2d ( const gp_Ax22d & theA, const double theMajorRadius, const double theMinorRadius )

inlineconstexpr

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

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

Member Function Documentation

Area()

double gp_Elips2d::Area ( ) const

inlineconstexprnoexcept

Computes the area of the ellipse.

Axis()

const gp_Ax22d & gp_Elips2d::Axis ( ) const

inlineconstexprnoexcept

Returns the major axis of the ellipse.

Coefficients()

void gp_Elips2d::Coefficients	(	double &	theA,
		double &	theB,
		double &	theC,
		double &	theD,
		double &	theE,
		double &	theF ) const

Returns the coefficients of the implicit equation of the ellipse. theA * (X**2) + theB * (Y**2) + 2*theC*(X*Y) + 2*theD*X + 2*theE*Y + theF = 0.

Directrix1()

gp_Ax2d gp_Elips2d::Directrix1 ( ) const

inline

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

inline

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()

double gp_Elips2d::Eccentricity ( ) const

inline

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()

double gp_Elips2d::Focal ( ) const

inline

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

Focus1()

gp_Pnt2d gp_Elips2d::Focus1 ( ) const

inline

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

inline

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

IsDirect()

bool gp_Elips2d::IsDirect ( ) const

inlineconstexprnoexcept

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

Location()

const gp_Pnt2d & gp_Elips2d::Location ( ) const

inlineconstexprnoexcept

Returns the center of the ellipse.

MajorRadius()

double gp_Elips2d::MajorRadius ( ) const

inlineconstexprnoexcept

Returns the major radius of the Ellipse.

MinorRadius()

double gp_Elips2d::MinorRadius ( ) const

inlineconstexprnoexcept

Returns the minor radius of the Ellipse.

Mirror() [1/2]

void gp_Elips2d::Mirror ( const gp_Ax2d & theA )

noexcept

Mirror() [2/2]

void gp_Elips2d::Mirror ( const gp_Pnt2d & theP )

noexcept

Mirrored() [1/2]

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

nodiscardnoexcept

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

Mirrored() [2/2]

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

nodiscardnoexcept

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

Parameter()

double gp_Elips2d::Parameter ( ) const

inlineconstexprnoexcept

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

Reverse()

void gp_Elips2d::Reverse ( )

inlinenoexcept

Reversed()

gp_Elips2d gp_Elips2d::Reversed ( ) const

inlinenodiscardnoexcept

Rotate()

void gp_Elips2d::Rotate ( const gp_Pnt2d & theP, const double theAng )

inline

Rotated()

gp_Elips2d gp_Elips2d::Rotated ( const gp_Pnt2d & theP, const double theAng ) const

inlinenodiscard

Scale()

void gp_Elips2d::Scale ( const gp_Pnt2d & theP, const double theS )

inline

Scaled()

gp_Elips2d gp_Elips2d::Scaled ( const gp_Pnt2d & theP, const double theS ) const

inlinenodiscard

Scales a ellipse. theS is the scaling value.

SetAxis()

void gp_Elips2d::SetAxis ( const gp_Ax22d & theA )

inlineconstexprnoexcept

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

SetLocation()

void gp_Elips2d::SetLocation ( const gp_Pnt2d & theP )

inlineconstexprnoexcept

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

• its origin becomes theP.

SetMajorRadius()

void gp_Elips2d::SetMajorRadius ( const double theMajorRadius )

inline

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

SetMinorRadius()

void gp_Elips2d::SetMinorRadius ( const double theMinorRadius )

inline

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

SetXAxis()

void gp_Elips2d::SetXAxis ( const gp_Ax2d & theA )

inlineconstexpr

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

SetYAxis()

void gp_Elips2d::SetYAxis ( const gp_Ax2d & theA )

inlineconstexpr

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

Transform()

void gp_Elips2d::Transform ( const gp_Trsf2d & theT )

inline

Transformed()

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

inlinenodiscard

Transforms an ellipse with the transformation theT from class Trsf2d.

Translate() [1/2]

void gp_Elips2d::Translate ( const gp_Pnt2d & theP1, const gp_Pnt2d & theP2 )

inlineconstexprnoexcept

Translate() [2/2]

void gp_Elips2d::Translate ( const gp_Vec2d & theV )

inlineconstexprnoexcept

Translated() [1/2]

gp_Elips2d gp_Elips2d::Translated ( const gp_Pnt2d & theP1, const gp_Pnt2d & theP2 ) const

inlinenodiscardconstexprnoexcept

Translates a ellipse from the point theP1 to the point theP2.

Translated() [2/2]

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

inlinenodiscardconstexprnoexcept

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

XAxis()

gp_Ax2d gp_Elips2d::XAxis ( ) const

inlinenoexcept

Returns the major axis of the ellipse.

YAxis()

gp_Ax2d gp_Elips2d::YAxis ( ) const

inlinenoexcept

Returns the minor axis of the ellipse. Reverses the direction of the circle.

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

• gp_Elips2d.hxx