gp_Elips Class Reference

Describes an ellipse in 3D space. An ellipse is defined by its major and minor radii and positioned in space with a coordinate system (a gp_Ax2 object) as follows: More...

#include <gp_Elips.hxx>

Public Member Functions
constexpr	gp_Elips () noexcept
	Creates an indefinite ellipse.
constexpr	gp_Elips (const gp_Ax2 &theA2, const double theMajorRadius, const double theMinorRadius)
	The major radius of the ellipse is on the "XAxis" and the minor radius is on the "YAxis" of the ellipse. The "XAxis" is defined with the "XDirection" of theA2 and the "YAxis" is defined with the "YDirection" of theA2. Warnings : It is not forbidden to create an ellipse with theMajorRadius = theMinorRadius. Raises ConstructionError if theMajorRadius < theMinorRadius or theMinorRadius < 0.
void	SetAxis (const gp_Ax1 &theA1)
	Changes the axis normal to the plane of the ellipse. It modifies the definition of this plane. The "XAxis" and the "YAxis" are recomputed. The local coordinate system is redefined so that:
constexpr void	SetLocation (const gp_Pnt &theP) noexcept
	Modifies this ellipse, by redefining its local coordinate so that its origin becomes theP.
void	SetMajorRadius (const double theMajorRadius)
	The major radius of the ellipse is on the "XAxis" (major axis) of the ellipse. Raises ConstructionError if theMajorRadius < MinorRadius.
void	SetMinorRadius (const double theMinorRadius)
	The minor radius of the ellipse is on the "YAxis" (minor axis) of the ellipse. Raises ConstructionError if theMinorRadius > MajorRadius or MinorRadius < 0.
constexpr void	SetPosition (const gp_Ax2 &theA2) noexcept
	Modifies this ellipse, by redefining its local coordinate so that it becomes theA2.
constexpr double	Area () const noexcept
	Computes the area of the Ellipse.
constexpr const gp_Ax1 &	Axis () const noexcept
	Computes the axis normal to the plane of the ellipse.
gp_Ax1	Directrix1 () const
	Computes the first or second directrix of this ellipse. These are the lines, in the plane of the ellipse, normal to the major axis, at a distance equal to MajorRadius/e from the center of the ellipse, where e is the eccentricity of the ellipse. The first directrix (Directrix1) is on the positive side of the major axis. The second directrix (Directrix2) is on the negative side. The directrix is returned as an axis (gp_Ax1 object), the origin of which is situated on the "X Axis" of the local coordinate system of this ellipse. Exceptions Standard_ConstructionError if the eccentricity is null (the ellipse has degenerated into a circle).
gp_Ax1	Directrix2 () const
	This line is obtained by the symmetrical transformation of "Directrix1" with respect to the "YAxis" of the ellipse. Exceptions Standard_ConstructionError if the eccentricity is null (the ellipse has degenerated into a circle).
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. Raises ConstructionError if MajorRadius = 0.0.
double	Focal () const
	Computes the focal distance. It is the distance between the two focus focus1 and focus2 of the ellipse.
gp_Pnt	Focus1 () const
	Returns the first focus of the ellipse. This focus is on the positive side of the "XAxis" of the ellipse.
gp_Pnt	Focus2 () const
	Returns the second focus of the ellipse. This focus is on the negative side of the "XAxis" of the ellipse.
constexpr const gp_Pnt &	Location () const noexcept
	Returns the center of the ellipse. It is the "Location" point of the coordinate system 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.
double	Parameter () const
	Returns p = (1 - e * e) * MajorRadius where e is the eccentricity of the ellipse. Returns 0 if MajorRadius = 0.
constexpr const gp_Ax2 &	Position () const noexcept
	Returns the coordinate system of the ellipse.
constexpr gp_Ax1	XAxis () const noexcept
	Returns the "XAxis" of the ellipse whose origin is the center of this ellipse. It is the major axis of the ellipse.
constexpr gp_Ax1	YAxis () const noexcept
	Returns the "YAxis" of the ellipse whose unit vector is the "X Direction" or the "Y Direction" of the local coordinate system of this ellipse. This is the minor axis of the ellipse.
void	Mirror (const gp_Pnt &theP) noexcept
gp_Elips	Mirrored (const gp_Pnt &theP) const noexcept
	Performs the symmetrical transformation of an ellipse with respect to the point theP which is the center of the symmetry.
void	Mirror (const gp_Ax1 &theA1)
gp_Elips	Mirrored (const gp_Ax1 &theA1) const
	Performs the symmetrical transformation of an ellipse with respect to an axis placement which is the axis of the symmetry.
void	Mirror (const gp_Ax2 &theA2)
gp_Elips	Mirrored (const gp_Ax2 &theA2) const
	Performs the symmetrical transformation of an ellipse with respect to a plane. The axis placement theA2 locates the plane of the symmetry (Location, XDirection, YDirection).
void	Rotate (const gp_Ax1 &theA1, const double theAng)
gp_Elips	Rotated (const gp_Ax1 &theA1, const double theAng) const
	Rotates an ellipse. theA1 is the axis of the rotation. theAng is the angular value of the rotation in radians.
void	Scale (const gp_Pnt &theP, const double theS)
gp_Elips	Scaled (const gp_Pnt &theP, const double theS) const
	Scales an ellipse. theS is the scaling value.
void	Transform (const gp_Trsf &theT)
gp_Elips	Transformed (const gp_Trsf &theT) const
	Transforms an ellipse with the transformation theT from class Trsf.
constexpr void	Translate (const gp_Vec &theV) noexcept
constexpr gp_Elips	Translated (const gp_Vec &theV) const noexcept
	Translates an ellipse in the direction of the vector theV. The magnitude of the translation is the vector's magnitude.
constexpr void	Translate (const gp_Pnt &theP1, const gp_Pnt &theP2) noexcept
constexpr gp_Elips	Translated (const gp_Pnt &theP1, const gp_Pnt &theP2) const noexcept
	Translates an ellipse from the point theP1 to the point theP2.

Detailed Description

Describes an ellipse in 3D space. An ellipse is defined by its major and minor radii and positioned in space with a coordinate system (a gp_Ax2 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. Together, the origin, "X Direction" and "Y Direction" of this coordinate system define the plane of the ellipse. This coordinate system is the "local coordinate system" of the ellipse. In this coordinate system, the equation of the ellipse is:

  X*X / (MajorRadius**2) + Y*Y / (MinorRadius**2) = 1.0

  The "main Direction" of the local coordinate system gives the normal vector to the plane of the ellipse. This vector gives an implicit orientation to the ellipse (definition of the trigonometric sense). We refer to the "main Axis" of the local coordinate system as the "Axis" of the ellipse. See Also gce_MakeElips which provides functions for more complex ellipse constructions Geom_Ellipse which provides additional functions for constructing ellipses and works, in particular, with the parametric equations of ellipses

Constructor & Destructor Documentation

gp_Elips() [1/2]

gp_Elips::gp_Elips ( )

inlineconstexprnoexcept

Creates an indefinite ellipse.

gp_Elips() [2/2]

gp_Elips::gp_Elips ( const gp_Ax2 & theA2, const double theMajorRadius, const double theMinorRadius )

inlineconstexpr

The major radius of the ellipse is on the "XAxis" and the minor radius is on the "YAxis" of the ellipse. The "XAxis" is defined with the "XDirection" of theA2 and the "YAxis" is defined with the "YDirection" of theA2. Warnings : It is not forbidden to create an ellipse with theMajorRadius = theMinorRadius. Raises ConstructionError if theMajorRadius < theMinorRadius or theMinorRadius < 0.

Member Function Documentation

Area()

double gp_Elips::Area ( ) const

inlineconstexprnoexcept

Computes the area of the Ellipse.

Axis()

const gp_Ax1 & gp_Elips::Axis ( ) const

inlineconstexprnoexcept

Computes the axis normal to the plane of the ellipse.

Directrix1()

gp_Ax1 gp_Elips::Directrix1 ( ) const

inline

Computes the first or second directrix of this ellipse. These are the lines, in the plane of the ellipse, normal to the major axis, at a distance equal to MajorRadius/e from the center of the ellipse, where e is the eccentricity of the ellipse. The first directrix (Directrix1) is on the positive side of the major axis. The second directrix (Directrix2) is on the negative side. The directrix is returned as an axis (gp_Ax1 object), the origin of which is situated on the "X Axis" of the local coordinate system of this ellipse. Exceptions Standard_ConstructionError if the eccentricity is null (the ellipse has degenerated into a circle).

Directrix2()

gp_Ax1 gp_Elips::Directrix2 ( ) const

inline

This line is obtained by the symmetrical transformation of "Directrix1" with respect to the "YAxis" of the ellipse. Exceptions Standard_ConstructionError if the eccentricity is null (the ellipse has degenerated into a circle).

Eccentricity()

double gp_Elips::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. Raises ConstructionError if MajorRadius = 0.0.

Focal()

double gp_Elips::Focal ( ) const

inline

Computes the focal distance. It is the distance between the two focus focus1 and focus2 of the ellipse.

Focus1()

gp_Pnt gp_Elips::Focus1 ( ) const

inline

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

Focus2()

gp_Pnt gp_Elips::Focus2 ( ) const

inline

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

Location()

const gp_Pnt & gp_Elips::Location ( ) const

inlineconstexprnoexcept

Returns the center of the ellipse. It is the "Location" point of the coordinate system of the ellipse.

MajorRadius()

double gp_Elips::MajorRadius ( ) const

inlineconstexprnoexcept

Returns the major radius of the ellipse.

MinorRadius()

double gp_Elips::MinorRadius ( ) const

inlineconstexprnoexcept

Returns the minor radius of the ellipse.

Mirror() [1/3]

void gp_Elips::Mirror

(

const gp_Ax1 &

theA1

)

Mirror() [2/3]

void gp_Elips::Mirror

(

const gp_Ax2 &

theA2

)

Mirror() [3/3]

void gp_Elips::Mirror ( const gp_Pnt & theP )

noexcept

Mirrored() [1/3]

gp_Elips gp_Elips::Mirrored ( const gp_Ax1 & theA1 ) const

nodiscard

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

Mirrored() [2/3]

gp_Elips gp_Elips::Mirrored ( const gp_Ax2 & theA2 ) const

nodiscard

Performs the symmetrical transformation of an ellipse with respect to a plane. The axis placement theA2 locates the plane of the symmetry (Location, XDirection, YDirection).

Mirrored() [3/3]

gp_Elips gp_Elips::Mirrored ( const gp_Pnt & theP ) const

nodiscardnoexcept

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

Parameter()

double gp_Elips::Parameter ( ) const

inline

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

Position()

const gp_Ax2 & gp_Elips::Position ( ) const

inlineconstexprnoexcept

Returns the coordinate system of the ellipse.

Rotate()

void gp_Elips::Rotate ( const gp_Ax1 & theA1, const double theAng )

inline

Rotated()

gp_Elips gp_Elips::Rotated ( const gp_Ax1 & theA1, const double theAng ) const

inlinenodiscard

Rotates an ellipse. theA1 is the axis of the rotation. theAng is the angular value of the rotation in radians.

Scale()

void gp_Elips::Scale ( const gp_Pnt & theP, const double theS )

inline

Scaled()

gp_Elips gp_Elips::Scaled ( const gp_Pnt & theP, const double theS ) const

inlinenodiscard

Scales an ellipse. theS is the scaling value.

SetAxis()

void gp_Elips::SetAxis ( const gp_Ax1 & theA1 )

inline

Changes the axis normal to the plane of the ellipse. It modifies the definition of this plane. The "XAxis" and the "YAxis" are recomputed. The local coordinate system is redefined so that:

• its origin and "main Direction" become those of the axis theA1 (the "X Direction" and "Y Direction" are then recomputed in the same way as for any gp_Ax2), or Raises ConstructionError if the direction of theA1 is parallel to the direction of the "XAxis" of the ellipse.

SetLocation()

void gp_Elips::SetLocation ( const gp_Pnt & theP )

inlineconstexprnoexcept

Modifies this ellipse, by redefining its local coordinate so that its origin becomes theP.

SetMajorRadius()

void gp_Elips::SetMajorRadius ( const double theMajorRadius )

inline

The major radius of the ellipse is on the "XAxis" (major axis) of the ellipse. Raises ConstructionError if theMajorRadius < MinorRadius.

SetMinorRadius()

void gp_Elips::SetMinorRadius ( const double theMinorRadius )

inline

The minor radius of the ellipse is on the "YAxis" (minor axis) of the ellipse. Raises ConstructionError if theMinorRadius > MajorRadius or MinorRadius < 0.

SetPosition()

void gp_Elips::SetPosition ( const gp_Ax2 & theA2 )

inlineconstexprnoexcept

Modifies this ellipse, by redefining its local coordinate so that it becomes theA2.

Transform()

void gp_Elips::Transform ( const gp_Trsf & theT )

inline

Transformed()

gp_Elips gp_Elips::Transformed ( const gp_Trsf & theT ) const

inlinenodiscard

Transforms an ellipse with the transformation theT from class Trsf.

Translate() [1/2]

void gp_Elips::Translate ( const gp_Pnt & theP1, const gp_Pnt & theP2 )

inlineconstexprnoexcept

Translate() [2/2]

void gp_Elips::Translate ( const gp_Vec & theV )

inlineconstexprnoexcept

Translated() [1/2]

gp_Elips gp_Elips::Translated ( const gp_Pnt & theP1, const gp_Pnt & theP2 ) const

inlinenodiscardconstexprnoexcept

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

Translated() [2/2]

gp_Elips gp_Elips::Translated ( const gp_Vec & theV ) const

inlinenodiscardconstexprnoexcept

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

XAxis()

gp_Ax1 gp_Elips::XAxis ( ) const

inlineconstexprnoexcept

Returns the "XAxis" of the ellipse whose origin is the center of this ellipse. It is the major axis of the ellipse.

YAxis()

gp_Ax1 gp_Elips::YAxis ( ) const

inlineconstexprnoexcept

Returns the "YAxis" of the ellipse whose unit vector is the "X Direction" or the "Y Direction" of the local coordinate system of this ellipse. This is the minor axis of the ellipse.

---

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

• gp_Elips.hxx