Describes a branch of a hyperbola in 3D space. A hyperbola is defined by its major and minor radii and positioned in space with a coordinate system (a gp_Ax2 object) of which: More...

#include <gp_Hypr.hxx>

Public Member Functions
constexpr	gp_Hypr () noexcept
	Creates of an indefinite hyperbola.

constexpr	gp_Hypr (const gp_Ax2 &theA2, const double theMajorRadius, const double theMinorRadius)
	Creates a hyperbola with radius theMajorRadius and theMinorRadius, positioned in the space by the coordinate system theA2 such that:

void	SetAxis (const gp_Ax1 &theA1)
	Modifies this hyperbola, by redefining its local coordinate system so that:

void	SetLocation (const gp_Pnt &theP)
	Modifies this hyperbola, by redefining its local coordinate system so that its origin becomes theP.

void	SetMajorRadius (const double theMajorRadius)
	Modifies the major radius of this hyperbola. Exceptions Standard_ConstructionError if theMajorRadius is negative.

void	SetMinorRadius (const double theMinorRadius)
	Modifies the minor radius of this hyperbola. Exceptions Standard_ConstructionError if theMinorRadius is negative.

constexpr void	SetPosition (const gp_Ax2 &theA2) noexcept
	Modifies this hyperbola, by redefining its local coordinate system so that it becomes A2.

gp_Ax1	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 and B is the minor radius. Raises ConstructionError if MajorRadius = 0.0.

gp_Ax1	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 and B is the minor radius. Raises ConstructionError if MajorRadius = 0.0.

constexpr const gp_Ax1 &	Axis () const noexcept
	Returns the axis passing through the center, and normal to the plane of this hyperbola.

gp_Hypr	ConjugateBranch1 () const
	Computes the branch of hyperbola which is on the positive side of the "YAxis" of <me>.

gp_Hypr	ConjugateBranch2 () const
	Computes the branch of hyperbola which is on the negative side of the "YAxis" of <me>.

gp_Ax1	Directrix1 () const
	This directrix 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_Ax1	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 the two focus of the hyperbola.

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

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

constexpr const gp_Pnt &	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 on the "XAxis" of the hyperbola.

constexpr double	MinorRadius () const noexcept
	Returns the minor radius of the hyperbola. It is the radius on the "YAxis" of the hyperbola.

gp_Hypr	OtherBranch () const
	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_Ax2 &	Position () const noexcept
	Returns the coordinate system of the hyperbola.

constexpr gp_Ax1	XAxis () const noexcept
	Computes an axis, whose.

constexpr gp_Ax1	YAxis () const noexcept
	Computes an axis, whose.

void	Mirror (const gp_Pnt &theP) noexcept

gp_Hypr	Mirrored (const gp_Pnt &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_Ax1 &theA1)

gp_Hypr	Mirrored (const gp_Ax1 &theA1) const
	Performs the symmetrical transformation of an hyperbola with respect to an axis placement which is the axis of the symmetry.

void	Mirror (const gp_Ax2 &theA2)

gp_Hypr	Mirrored (const gp_Ax2 &theA2) const
	Performs the symmetrical transformation of an hyperbola 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_Hypr	Rotated (const gp_Ax1 &theA1, const double theAng) const
	Rotates an hyperbola. 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_Hypr	Scaled (const gp_Pnt &theP, const double theS) const
	Scales an hyperbola. theS is the scaling value.

void	Transform (const gp_Trsf &theT)

gp_Hypr	Transformed (const gp_Trsf &theT) const
	Transforms an hyperbola with the transformation theT from class Trsf.

constexpr void	Translate (const gp_Vec &theV) noexcept

constexpr gp_Hypr	Translated (const gp_Vec &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_Pnt &theP1, const gp_Pnt &theP2) noexcept

constexpr gp_Hypr	Translated (const gp_Pnt &theP1, const gp_Pnt &theP2) const noexcept
	Translates an hyperbola from the point theP1 to the point theP2.

Detailed Description

Describes a branch of a hyperbola in 3D space. A hyperbola is defined by its major and minor radii and positioned in space with a coordinate system (a gp_Ax2 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. The origin, "X Direction" and "Y Direction" of this coordinate system together define the plane of the hyperbola. This coordinate system is the "local coordinate system" of 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 "main Direction" of the local coordinate system is a normal vector to the plane of the hyperbola. This vector gives an implicit orientation to the hyperbola. We refer to the "main Axis" of the local coordinate system as the "Axis" of the hyperbola. 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

| ^YAxis

NCollection_ForwardRangeIterator
STL input iterator that wraps an OCCT More()/Next() iterator.
Definition NCollection_ForwardRange.hxx:142

gp_Hypr::YAxis
constexpr gp_Ax1 YAxis() const noexcept
Computes an axis, whose.
Definition gp_Hypr.hxx:273

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

Constructor & Destructor Documentation

◆ gp_Hypr() [1/2]

constexpr gp_Hypr::gp_Hypr ( )

inlineconstexprnoexcept

Creates of an indefinite hyperbola.

◆ gp_Hypr() [2/2]

constexpr gp_Hypr::gp_Hypr	(	const gp_Ax2 &	theA2,
		const double	theMajorRadius,
		const double	theMinorRadius )

inlineconstexpr

Creates a hyperbola with radius theMajorRadius and theMinorRadius, positioned in the space by the coordinate system theA2 such that:

the origin of theA2 is the center of the hyperbola,
the "X Direction" of theA2 defines the major axis of the hyperbola, that is, the major radius theMajorRadius is measured along this axis, and
the "Y Direction" of theA2 defines the minor axis of the hyperbola, that is, the minor radius theMinorRadius is measured along this axis. Note: This class does not prevent the creation of a hyperbola where:
theMajorAxis is equal to theMinorAxis, or
theMajorAxis is less than theMinorAxis. Exceptions Standard_ConstructionError if theMajorAxis or theMinorAxis is negative. Raises ConstructionError if theMajorRadius < 0.0 or theMinorRadius < 0.0 Raised if theMajorRadius < 0.0 or theMinorRadius < 0.0

Member Function Documentation

◆ Asymptote1()

gp_Ax1 gp_Hypr::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 and B is the minor radius. Raises ConstructionError if MajorRadius = 0.0.

◆ Asymptote2()

gp_Ax1 gp_Hypr::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 and B is the minor radius. Raises ConstructionError if MajorRadius = 0.0.

◆ Axis()

constexpr const gp_Ax1 & gp_Hypr::Axis ( ) const

inlineconstexprnoexcept

Returns the axis passing through the center, and normal to the plane of this hyperbola.

◆ ConjugateBranch1()

gp_Hypr gp_Hypr::ConjugateBranch1 ( ) const

inline

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

◆ ConjugateBranch2()

gp_Hypr gp_Hypr::ConjugateBranch2 ( ) const

inline

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

◆ Directrix1()

gp_Ax1 gp_Hypr::Directrix1 ( ) const

inline

This directrix 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_Ax1 gp_Hypr::Directrix2 ( ) const

inline

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

◆ Eccentricity()

double gp_Hypr::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_Hypr::Focal ( ) const

inlinenoexcept

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

◆ Focus1()

gp_Pnt gp_Hypr::Focus1 ( ) const

inline

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

◆ Focus2()

gp_Pnt gp_Hypr::Focus2 ( ) const

inline

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

◆ Location()

constexpr const gp_Pnt & gp_Hypr::Location ( ) const

inlineconstexprnoexcept

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

◆ MajorRadius()

constexpr double gp_Hypr::MajorRadius ( ) const

inlineconstexprnoexcept

Returns the major radius of the hyperbola. It is the radius on the "XAxis" of the hyperbola.

◆ MinorRadius()

constexpr double gp_Hypr::MinorRadius ( ) const

inlineconstexprnoexcept

Returns the minor radius of the hyperbola. It is the radius on the "YAxis" of the hyperbola.

◆ Mirror() [1/3]

void gp_Hypr::Mirror ( const gp_Ax1 & theA1 )

◆ Mirror() [2/3]

void gp_Hypr::Mirror ( const gp_Ax2 & theA2 )

◆ Mirror() [3/3]

void gp_Hypr::Mirror ( const gp_Pnt & theP )

noexcept

◆ Mirrored() [1/3]

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

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

◆ Mirrored() [2/3]

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

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

◆ Mirrored() [3/3]

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

noexcept

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

◆ OtherBranch()

gp_Hypr gp_Hypr::OtherBranch ( ) const

inline

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

◆ Parameter()

double gp_Hypr::Parameter ( ) const

inline

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

◆ Position()

constexpr const gp_Ax2 & gp_Hypr::Position ( ) const

inlineconstexprnoexcept

Returns the coordinate system of the hyperbola.

◆ Rotate()

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

inline

◆ Rotated()

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

inline

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

◆ Scale()

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

inline

◆ Scaled()

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

inline

Scales an hyperbola. theS is the scaling value.

◆ SetAxis()

void gp_Hypr::SetAxis ( const gp_Ax1 & theA1 )

inline

Modifies this hyperbola, by redefining its local coordinate system 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). Raises ConstructionError if the direction of theA1 is parallel to the direction of the "XAxis" of the hyperbola.

◆ SetLocation()

void gp_Hypr::SetLocation ( const gp_Pnt & theP )

inline

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

◆ SetMajorRadius()

void gp_Hypr::SetMajorRadius ( const double theMajorRadius )

inline

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

◆ SetMinorRadius()

void gp_Hypr::SetMinorRadius ( const double theMinorRadius )

inline

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

◆ SetPosition()

constexpr void gp_Hypr::SetPosition ( const gp_Ax2 & theA2 )

inlineconstexprnoexcept

Modifies this hyperbola, by redefining its local coordinate system so that it becomes A2.

◆ Transform()

void gp_Hypr::Transform ( const gp_Trsf & theT )

inline

◆ Transformed()

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

inline

Transforms an hyperbola with the transformation theT from class Trsf.

◆ Translate() [1/2]

constexpr void gp_Hypr::Translate	(	const gp_Pnt &	theP1,
		const gp_Pnt &	theP2 )

inlineconstexprnoexcept

◆ Translate() [2/2]

constexpr void gp_Hypr::Translate ( const gp_Vec & theV )

inlineconstexprnoexcept

◆ Translated() [1/2]

constexpr gp_Hypr gp_Hypr::Translated	(	const gp_Pnt &	theP1,
		const gp_Pnt &	theP2 ) const

inlineconstexprnoexcept

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

◆ Translated() [2/2]

constexpr gp_Hypr gp_Hypr::Translated ( const gp_Vec & theV ) const

inlineconstexprnoexcept

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

◆ XAxis()

constexpr gp_Ax1 gp_Hypr::XAxis ( ) const

inlineconstexprnoexcept

Computes an axis, whose.

the origin is the center of this hyperbola, and
the unit vector is the "X Direction" of the local coordinate system of this hyperbola. These axes are, the major axis (the "X Axis") and of this hyperboReturns the "XAxis" of the hyperbola.

◆ YAxis()

constexpr gp_Ax1 gp_Hypr::YAxis ( ) const

inlineconstexprnoexcept

Computes an axis, whose.

the origin is the center of this hyperbola, and
the unit vector is the "Y Direction" of the local coordinate system of this hyperbola. These axes are the minor axis (the "Y Axis") of this hyperbola

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

gp_Hypr.hxx

Public Member Functions

Detailed Description

Constructor & Destructor Documentation

◆ gp_Hypr() [1/2]

◆ gp_Hypr() [2/2]

Member Function Documentation

◆ Asymptote1()

◆ Asymptote2()

◆ Axis()

◆ ConjugateBranch1()

◆ ConjugateBranch2()

◆ Directrix1()

◆ Directrix2()

◆ Eccentricity()

◆ Focal()

◆ Focus1()

◆ Focus2()

◆ Location()

◆ MajorRadius()

◆ MinorRadius()

◆ Mirror() [1/3]

◆ Mirror() [2/3]

◆ Mirror() [3/3]

◆ Mirrored() [1/3]

◆ Mirrored() [2/3]

◆ Mirrored() [3/3]

◆ OtherBranch()

◆ Parameter()

◆ Position()

◆ Rotate()

◆ Rotated()

◆ Scale()

◆ Scaled()

◆ SetAxis()

◆ SetLocation()

◆ SetMajorRadius()

◆ SetMinorRadius()

◆ SetPosition()

◆ Transform()

◆ Transformed()

◆ Translate() [1/2]

◆ Translate() [2/2]

◆ Translated() [1/2]

◆ Translated() [2/2]

◆ XAxis()

◆ YAxis()