Describes a branch of a hyperbola in the plane (2D space). A hyperbola is defined by its major and minor radii, and positioned in the plane with a coordinate system (a gp_Ax22d object) of which: More...

#include <gp_Hypr2d.hxx>

Public Member Functions
constexpr	gp_Hypr2d () noexcept
	Creates of an indefinite hyperbola.
constexpr	gp_Hypr2d (const gp_Ax2d &theMajorAxis, const double theMajorRadius, const double theMinorRadius, const bool theIsSense=true)
	Creates a hyperbola with radii theMajorRadius and theMinorRadius, centered on the origin of theMajorAxis and where the unit vector of theMajorAxis is the "X Direction" of the local coordinate system of the hyperbola. This coordinate system is direct if theIsSense is true (the default value), and indirect if theIsSense is false. Warnings: It is yet possible to create an Hyperbola with theMajorRadius <= theMinorRadius. Raises ConstructionError if theMajorRadius < 0.0 or theMinorRadius < 0.0.
constexpr	gp_Hypr2d (const gp_Ax22d &theA, const double theMajorRadius, const double theMinorRadius)
	a hyperbola with radii theMajorRadius and theMinorRadius, positioned in the plane by coordinate system theA where:
constexpr void	SetLocation (const gp_Pnt2d &theP) noexcept
	Modifies this hyperbola, by redefining its local coordinate system so that its origin becomes theP.
void	SetMajorRadius (const double theMajorRadius)
	Modifies the major or minor radius of this hyperbola. Exceptions Standard_ConstructionError if theMajorRadius or MinorRadius is negative.
void	SetMinorRadius (const double theMinorRadius)
	Modifies the major or minor radius of this hyperbola. Exceptions Standard_ConstructionError if MajorRadius or theMinorRadius is negative.
constexpr void	SetAxis (const gp_Ax22d &theA) noexcept
	Modifies this hyperbola, by redefining its local coordinate system so that it becomes theA.
constexpr void	SetXAxis (const gp_Ax2d &theA)
	Changes the major axis of the hyperbola. The minor axis is recomputed and the location of the hyperbola too.
constexpr void	SetYAxis (const gp_Ax2d &theA)
	Changes the minor axis of the hyperbola.The minor axis is recomputed and the location of the hyperbola too.
gp_Ax2d	Asymptote1 () const
	In the local coordinate system of the hyperbola the equation of the hyperbola is (XX)/(AA) - (YY)/(BB) = 1.0 and the equation of the first asymptote is Y = (B/A)*X where A is the major radius of the hyperbola and B the minor radius of the hyperbola. Raises ConstructionError if MajorRadius = 0.0.
gp_Ax2d	Asymptote2 () const
	In the local coordinate system of the hyperbola the equation of the hyperbola is (XX)/(AA) - (YY)/(BB) = 1.0 and the equation of the first asymptote is Y = -(B/A)*X where A is the major radius of the hyperbola and B the minor radius of the hyperbola. Raises ConstructionError if MajorRadius = 0.0.
void	Coefficients (double &theA, double &theB, double &theC, double &theD, double &theE, double &theF) const
	Computes the coefficients of the implicit equation of the hyperbola : theA * (X*2) + theB (Y*2) + 2theC(XY) + 2theDX + 2theEY + theF = 0.
gp_Hypr2d	ConjugateBranch1 () const noexcept
	Computes the branch of hyperbola which is on the positive side of the "YAxis" of <me>.
gp_Hypr2d	ConjugateBranch2 () const noexcept
	Computes the branch of hyperbola which is on the negative side of the "YAxis" of <me>.
gp_Ax2d	Directrix1 () const
	Computes the directrix which is the line normal to the XAxis of the hyperbola in the local plane (Z = 0) at a distance d = MajorRadius / e from the center of the hyperbola, where e is the eccentricity of the hyperbola. This line is parallel to the "YAxis". The intersection point between the "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 "YAxis" of the hyperbola.
double	Eccentricity () const
	Returns the eccentricity of the hyperbola (e > 1). If f is the distance between the location of the hyperbola and the Focus1 then the eccentricity e = f / MajorRadius. Raises DomainError if MajorRadius = 0.0.
double	Focal () const noexcept
	Computes the focal distance. It is the distance between the "Location" of the hyperbola and "Focus1" or "Focus2".
gp_Pnt2d	Focus1 () const noexcept
	Returns the first focus of the hyperbola. This focus is on the positive side of the "XAxis" of the hyperbola.
gp_Pnt2d	Focus2 () const noexcept
	Returns the second focus of the hyperbola. This focus is on the negative side of the "XAxis" of the hyperbola.
constexpr const gp_Pnt2d &	Location () const noexcept
	Returns the location point of the hyperbola. It is the intersection point between the "XAxis" and the "YAxis".
constexpr double	MajorRadius () const noexcept
	Returns the major radius of the hyperbola (it is the radius corresponding to the "XAxis" of the hyperbola).
constexpr double	MinorRadius () const noexcept
	Returns the minor radius of the hyperbola (it is the radius corresponding to the "YAxis" of the hyperbola).
gp_Hypr2d	OtherBranch () const noexcept
	Returns the branch of hyperbola obtained by doing the symmetrical transformation of <me> with respect to the "YAxis" of <me>.
double	Parameter () const
	Returns p = (e * e - 1) * MajorRadius where e is the eccentricity of the hyperbola. Raises DomainError if MajorRadius = 0.0.
constexpr const gp_Ax22d &	Axis () const noexcept
	Returns the axisplacement of the hyperbola.
gp_Ax2d	XAxis () const noexcept
	Computes an axis whose.
gp_Ax2d	YAxis () const noexcept
	Computes an axis whose.
void	Reverse () noexcept
gp_Hypr2d	Reversed () const noexcept
	Reverses the orientation of the local coordinate system of this hyperbola (the "Y Axis" is reversed). Therefore, the implicit orientation of this hyperbola is reversed. Note:
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_Hypr2d	Mirrored (const gp_Pnt2d &theP) const noexcept
	Performs the symmetrical transformation of an hyperbola with respect to the point theP which is the center of the symmetry.
void	Mirror (const gp_Ax2d &theA) noexcept
gp_Hypr2d	Mirrored (const gp_Ax2d &theA) const noexcept
	Performs the symmetrical transformation of an hyperbola with respect to an axis placement which is the axis of the symmetry.
void	Rotate (const gp_Pnt2d &theP, const double theAng)
gp_Hypr2d	Rotated (const gp_Pnt2d &theP, const double theAng) const
	Rotates an hyperbola. theP is the center of the rotation. theAng is the angular value of the rotation in radians.
void	Scale (const gp_Pnt2d &theP, const double theS)
gp_Hypr2d	Scaled (const gp_Pnt2d &theP, const double theS) const
	Scales an hyperbola. <theS> is the scaling value. If <theS> is positive only the location point is modified. But if <theS> is negative the "XAxis" is reversed and the "YAxis" too.
void	Transform (const gp_Trsf2d &theT)
gp_Hypr2d	Transformed (const gp_Trsf2d &theT) const
	Transforms an hyperbola with the transformation theT from class Trsf2d.
constexpr void	Translate (const gp_Vec2d &theV) noexcept
constexpr gp_Hypr2d	Translated (const gp_Vec2d &theV) const noexcept
	Translates an hyperbola 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_Hypr2d	Translated (const gp_Pnt2d &theP1, const gp_Pnt2d &theP2) const noexcept
	Translates an hyperbola from the point theP1 to the point theP2.

Detailed Description

Describes a branch of a hyperbola in the plane (2D space). A hyperbola is defined by its major and minor radii, and positioned in the plane with a coordinate system (a gp_Ax22d object) of which:

the origin is the center of the hyperbola,
the "X Direction" defines the major axis of the hyperbola, and
the "Y Direction" defines the minor axis of the hyperbola. This coordinate system is the "local coordinate system" of the hyperbola. The orientation of this coordinate system (direct or indirect) gives an implicit orientation to the hyperbola. In this coordinate system, the equation of the hyperbola is: X*X/(MajorRadius**2)-Y*Y/(MinorRadius**2) = 1.0 The branch of the hyperbola described is the one located on the positive side of the major axis. The following schema shows the plane of the hyperbola, and in it, the respective positions of the three branches of hyperbolas constructed with the functions OtherBranch, ConjugateBranch1, and ConjugateBranch2:
^YAxis

|

FirstConjugateBranch

|

Other | Main

--------------------- C ------------------------------>XAxis

Branch | Branch

|

|

SecondConjugateBranch

|

gp_Hypr2d::YAxis
gp_Ax2d YAxis() const noexcept
Computes an axis whose.
Definition gp_Hypr2d.hxx:309

Warning The major radius can be less than the minor radius. See Also gce_MakeHypr2d which provides functions for more complex hyperbola constructions Geom2d_Hyperbola which provides additional functions for constructing hyperbolas and works, in particular, with the parametric equations of hyperbolas

Constructor & Destructor Documentation

◆ gp_Hypr2d() [1/3]

gp_Hypr2d::gp_Hypr2d ( )

inlineconstexprnoexcept

Creates of an indefinite hyperbola.

◆ gp_Hypr2d() [2/3]

gp_Hypr2d::gp_Hypr2d	(	const gp_Ax2d &	theMajorAxis,
		const double	theMajorRadius,
		const double	theMinorRadius,
		const bool	theIsSense = true )

inlineconstexpr

Creates a hyperbola with radii theMajorRadius and theMinorRadius, centered on the origin of theMajorAxis and where the unit vector of theMajorAxis is the "X Direction" of the local coordinate system of the hyperbola. This coordinate system is direct if theIsSense is true (the default value), and indirect if theIsSense is false. Warnings: It is yet possible to create an Hyperbola with theMajorRadius <= theMinorRadius. Raises ConstructionError if theMajorRadius < 0.0 or theMinorRadius < 0.0.

◆ gp_Hypr2d() [3/3]

gp_Hypr2d::gp_Hypr2d	(	const gp_Ax22d &	theA,
		const double	theMajorRadius,
		const double	theMinorRadius )

inlineconstexpr

a hyperbola with radii theMajorRadius and theMinorRadius, positioned in the plane by coordinate system theA where:

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

Member Function Documentation

◆ Asymptote1()

gp_Ax2d gp_Hypr2d::Asymptote1 ( ) const

inline

In the local coordinate system of the hyperbola the equation of the hyperbola is (X*X)/(A*A) - (Y*Y)/(B*B) = 1.0 and the equation of the first asymptote is Y = (B/A)*X where A is the major radius of the hyperbola and B the minor radius of the hyperbola. Raises ConstructionError if MajorRadius = 0.0.

◆ Asymptote2()

gp_Ax2d gp_Hypr2d::Asymptote2 ( ) const

inline

In the local coordinate system of the hyperbola the equation of the hyperbola is (X*X)/(A*A) - (Y*Y)/(B*B) = 1.0 and the equation of the first asymptote is Y = -(B/A)*X where A is the major radius of the hyperbola and B the minor radius of the hyperbola. Raises ConstructionError if MajorRadius = 0.0.

◆ Axis()

const gp_Ax22d & gp_Hypr2d::Axis ( ) const

inlineconstexprnoexcept

Returns the axisplacement of the hyperbola.

◆ Coefficients()

void gp_Hypr2d::Coefficients	(	double &	theA,
		double &	theB,
		double &	theC,
		double &	theD,
		double &	theE,
		double &	theF ) const

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

◆ ConjugateBranch1()

gp_Hypr2d gp_Hypr2d::ConjugateBranch1 ( ) const

inlinenoexcept

Computes the branch of hyperbola which is on the positive side of the "YAxis" of <me>.

◆ ConjugateBranch2()

gp_Hypr2d gp_Hypr2d::ConjugateBranch2 ( ) const

inlinenoexcept

Computes the branch of hyperbola which is on the negative side of the "YAxis" of <me>.

◆ Directrix1()

gp_Ax2d gp_Hypr2d::Directrix1 ( ) const

inline

Computes the directrix which is the line normal to the XAxis of the hyperbola in the local plane (Z = 0) at a distance d = MajorRadius / e from the center of the hyperbola, where e is the eccentricity of the hyperbola. This line is parallel to the "YAxis". The intersection point between the "Directrix1" and the "XAxis" is the "Location" point of the "Directrix1". This point is on the positive side of the "XAxis".

◆ Directrix2()

gp_Ax2d gp_Hypr2d::Directrix2 ( ) const

inline

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

◆ Eccentricity()

double gp_Hypr2d::Eccentricity ( ) const

inline

Returns the eccentricity of the hyperbola (e > 1). If f is the distance between the location of the hyperbola and the Focus1 then the eccentricity e = f / MajorRadius. Raises DomainError if MajorRadius = 0.0.

◆ Focal()

double gp_Hypr2d::Focal ( ) const

inlinenoexcept

Computes the focal distance. It is the distance between the "Location" of the hyperbola and "Focus1" or "Focus2".

◆ Focus1()

gp_Pnt2d gp_Hypr2d::Focus1 ( ) const

inlinenoexcept

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

◆ Focus2()

gp_Pnt2d gp_Hypr2d::Focus2 ( ) const

inlinenoexcept

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

◆ IsDirect()

bool gp_Hypr2d::IsDirect ( ) const

inlineconstexprnoexcept

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

◆ Location()

const gp_Pnt2d & gp_Hypr2d::Location ( ) const

inlineconstexprnoexcept

Returns the location point of the hyperbola. It is the intersection point between the "XAxis" and the "YAxis".

◆ MajorRadius()

double gp_Hypr2d::MajorRadius ( ) const

inlineconstexprnoexcept

Returns the major radius of the hyperbola (it is the radius corresponding to the "XAxis" of the hyperbola).

◆ MinorRadius()

double gp_Hypr2d::MinorRadius ( ) const

inlineconstexprnoexcept

Returns the minor radius of the hyperbola (it is the radius corresponding to the "YAxis" of the hyperbola).

◆ Mirror() [1/2]

void gp_Hypr2d::Mirror ( const gp_Ax2d & theA )

noexcept

◆ Mirror() [2/2]

void gp_Hypr2d::Mirror ( const gp_Pnt2d & theP )

noexcept

◆ Mirrored() [1/2]

gp_Hypr2d gp_Hypr2d::Mirrored ( const gp_Ax2d & theA ) const

nodiscardnoexcept

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

◆ Mirrored() [2/2]

gp_Hypr2d gp_Hypr2d::Mirrored ( const gp_Pnt2d & theP ) const

nodiscardnoexcept

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

◆ OtherBranch()

gp_Hypr2d gp_Hypr2d::OtherBranch ( ) const

inlinenoexcept

Returns the branch of hyperbola obtained by doing the symmetrical transformation of <me> with respect to the "YAxis" of <me>.

◆ Parameter()

double gp_Hypr2d::Parameter ( ) const

inline

Returns p = (e * e - 1) * MajorRadius where e is the eccentricity of the hyperbola. Raises DomainError if MajorRadius = 0.0.

◆ Reverse()

void gp_Hypr2d::Reverse ( )

inlinenoexcept

◆ Reversed()

gp_Hypr2d gp_Hypr2d::Reversed ( ) const

inlinenodiscardnoexcept

Reverses the orientation of the local coordinate system of this hyperbola (the "Y Axis" is reversed). Therefore, the implicit orientation of this hyperbola is reversed. Note:

Reverse assigns the result to this hyperbola, while
Reversed creates a new one.

◆ Rotate()

void gp_Hypr2d::Rotate	(	const gp_Pnt2d &	theP,
		const double	theAng )

inline

◆ Rotated()

gp_Hypr2d gp_Hypr2d::Rotated	(	const gp_Pnt2d &	theP,
		const double	theAng ) const

inlinenodiscard

Rotates an hyperbola. theP is the center of the rotation. theAng is the angular value of the rotation in radians.

◆ Scale()

void gp_Hypr2d::Scale	(	const gp_Pnt2d &	theP,
		const double	theS )

inline

◆ Scaled()

gp_Hypr2d gp_Hypr2d::Scaled	(	const gp_Pnt2d &	theP,
		const double	theS ) const

inlinenodiscard

Scales an hyperbola. <theS> is the scaling value. If <theS> is positive only the location point is modified. But if <theS> is negative the "XAxis" is reversed and the "YAxis" too.

◆ SetAxis()

void gp_Hypr2d::SetAxis ( const gp_Ax22d & theA )

inlineconstexprnoexcept

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

◆ SetLocation()

void gp_Hypr2d::SetLocation ( const gp_Pnt2d & theP )

inlineconstexprnoexcept

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

◆ SetMajorRadius()

void gp_Hypr2d::SetMajorRadius ( const double theMajorRadius )

inline

Modifies the major or minor radius of this hyperbola. Exceptions Standard_ConstructionError if theMajorRadius or MinorRadius is negative.

◆ SetMinorRadius()

void gp_Hypr2d::SetMinorRadius ( const double theMinorRadius )

inline

Modifies the major or minor radius of this hyperbola. Exceptions Standard_ConstructionError if MajorRadius or theMinorRadius is negative.

◆ SetXAxis()

void gp_Hypr2d::SetXAxis ( const gp_Ax2d & theA )

inlineconstexpr

Changes the major axis of the hyperbola. The minor axis is recomputed and the location of the hyperbola too.

◆ SetYAxis()

void gp_Hypr2d::SetYAxis ( const gp_Ax2d & theA )

inlineconstexpr

Changes the minor axis of the hyperbola.The minor axis is recomputed and the location of the hyperbola too.

◆ Transform()

void gp_Hypr2d::Transform ( const gp_Trsf2d & theT )

inline

◆ Transformed()

gp_Hypr2d gp_Hypr2d::Transformed ( const gp_Trsf2d & theT ) const

inlinenodiscard

Transforms an hyperbola with the transformation theT from class Trsf2d.

◆ Translate() [1/2]

void gp_Hypr2d::Translate	(	const gp_Pnt2d &	theP1,
		const gp_Pnt2d &	theP2 )

inlineconstexprnoexcept

◆ Translate() [2/2]

void gp_Hypr2d::Translate ( const gp_Vec2d & theV )

inlineconstexprnoexcept

◆ Translated() [1/2]

gp_Hypr2d gp_Hypr2d::Translated	(	const gp_Pnt2d &	theP1,
		const gp_Pnt2d &	theP2 ) const

inlinenodiscardconstexprnoexcept

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

◆ Translated() [2/2]

gp_Hypr2d gp_Hypr2d::Translated ( const gp_Vec2d & theV ) const

inlinenodiscardconstexprnoexcept

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

◆ XAxis()

gp_Ax2d gp_Hypr2d::XAxis ( ) const

inlinenoexcept

Computes an axis whose.

the origin is the center of this hyperbola, and
the unit vector is the "X Direction" or "Y Direction" respectively of the local coordinate system of this hyperbola Returns the major axis of the hyperbola.

◆ YAxis()

gp_Ax2d gp_Hypr2d::YAxis ( ) const

inlinenoexcept

Computes an axis whose.

the origin is the center of this hyperbola, and
the unit vector is the "X Direction" or "Y Direction" respectively of the local coordinate system of this hyperbola Returns the minor axis of the hyperbola.

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

gp_Hypr2d.hxx

Public Member Functions

Detailed Description

Constructor & Destructor Documentation

◆ gp_Hypr2d() [1/3]

◆ gp_Hypr2d() [2/3]

◆ gp_Hypr2d() [3/3]

Member Function Documentation

◆ Asymptote1()

◆ Asymptote2()

◆ Axis()

◆ Coefficients()

◆ ConjugateBranch1()

◆ ConjugateBranch2()

◆ Directrix1()

◆ Directrix2()

◆ Eccentricity()

◆ Focal()

◆ Focus1()

◆ Focus2()

◆ IsDirect()

◆ Location()

◆ MajorRadius()

◆ MinorRadius()

◆ Mirror() [1/2]

◆ Mirror() [2/2]

◆ Mirrored() [1/2]

◆ Mirrored() [2/2]

◆ OtherBranch()

◆ Parameter()

◆ Reverse()

◆ Reversed()

◆ Rotate()

◆ Rotated()

◆ Scale()

◆ Scaled()

◆ SetAxis()

◆ SetLocation()

◆ SetMajorRadius()

◆ SetMinorRadius()

◆ SetXAxis()

◆ SetYAxis()

◆ Transform()

◆ Transformed()

◆ Translate() [1/2]

◆ Translate() [2/2]

◆ Translated() [1/2]

◆ Translated() [2/2]

◆ XAxis()

◆ YAxis()