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
	gp_Hypr2d ()
	Creates of an indefinite hyperbola. More...

	gp_Hypr2d (const gp_Ax2d &MajorAxis, const Standard_Real MajorRadius, const Standard_Real MinorRadius, const Standard_Boolean Sense=Standard_True)
	Creates a hyperbola with radii MajorRadius and MinorRadius, centered on the origin of MajorAxis and where the unit vector of MajorAxis is the "X Direction" of the local coordinate system of the hyperbola. This coordinate system is direct if Sense is true (the default value), and indirect if Sense is false. Warnings : It is yet possible to create an Hyperbola with MajorRadius <= MinorRadius. Raises ConstructionError if MajorRadius < 0.0 or MinorRadius < 0.0. More...

	gp_Hypr2d (const gp_Ax22d &A, const Standard_Real MajorRadius, const Standard_Real MinorRadius)
	a hyperbola with radii MajorRadius and MinorRadius, positioned in the plane by coordinate system A where: More...

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

void	SetMajorRadius (const Standard_Real MajorRadius)
	Modifies the major or minor radius of this hyperbola. Exceptions Standard_ConstructionError if MajorRadius or MinorRadius is negative. More...

void	SetMinorRadius (const Standard_Real MinorRadius)
	Modifies the major or minor radius of this hyperbola. Exceptions Standard_ConstructionError if MajorRadius or MinorRadius is negative. More...

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

void	SetXAxis (const gp_Ax2d &A)
	Changes the major axis of the hyperbola. The minor axis is recomputed and the location of the hyperbola too. More...

void	SetYAxis (const gp_Ax2d &A)
	Changes the minor axis of the hyperbola.The minor axis is recomputed and the location of the hyperbola too. More...

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. More...

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. More...

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

gp_Hypr2d	ConjugateBranch1 () const
	Computes the branch of hyperbola which is on the positive side of the "YAxis" of <me>. More...

gp_Hypr2d	ConjugateBranch2 () const
	Computes the branch of hyperbola which is on the negative side of the "YAxis" of <me>. More...

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". More...

gp_Ax2d	Directrix2 () const
	This line is obtained by the symmetrical transformation of "Directrix1" with respect to the "YAxis" of the hyperbola. More...

Standard_Real	Eccentricity () const
	Returns the excentricity 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. More...

Standard_Real	Focal () const
	Computes the focal distance. It is the distance between the "Location" of the hyperbola and "Focus1" or "Focus2". More...

gp_Pnt2d	Focus1 () const
	Returns the first focus of the hyperbola. This focus is on the positive side of the "XAxis" of the hyperbola. More...

gp_Pnt2d	Focus2 () const
	Returns the second focus of the hyperbola. This focus is on the negative side of the "XAxis" of the hyperbola. More...

const gp_Pnt2d &	Location () const
	Returns the location point of the hyperbola. It is the intersection point between the "XAxis" and the "YAxis". More...

Standard_Real	MajorRadius () const
	Returns the major radius of the hyperbola (it is the radius corresponding to the "XAxis" of the hyperbola). More...

Standard_Real	MinorRadius () const
	Returns the minor radius of the hyperbola (it is the radius corresponding to the "YAxis" of the hyperbola). More...

gp_Hypr2d	OtherBranch () const
	Returns the branch of hyperbola obtained by doing the symmetrical transformation of <me> with respect to the "YAxis" of <me>. More...

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

const gp_Ax22d &	Axis () const
	Returns the axisplacement of the hyperbola. More...

gp_Ax2d	XAxis () const
	Computes an axis whose. More...

gp_Ax2d	YAxis () const
	Computes an axis whose. More...

void	Reverse ()

gp_Hypr2d	Reversed () const
	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: More...

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_Hypr2d	Mirrored (const gp_Pnt2d &P) const
	Performs the symmetrical transformation of an hyperbola with respect to the point P which is the center of the symmetry. More...

void	Mirror (const gp_Ax2d &A)

gp_Hypr2d	Mirrored (const gp_Ax2d &A) const
	Performs the symmetrical transformation of an hyperbola 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_Hypr2d	Rotated (const gp_Pnt2d &P, const Standard_Real Ang) const
	Rotates an hyperbola. P is the center of the rotation. Ang is the angular value of the rotation in radians. More...

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

gp_Hypr2d	Scaled (const gp_Pnt2d &P, const Standard_Real S) const
	Scales an hyperbola. <S> is the scaling value. If <S> is positive only the location point is modified. But if <S> is negative the "XAxis" is reversed and the "YAxis" too. More...

void	Transform (const gp_Trsf2d &T)

gp_Hypr2d	Transformed (const gp_Trsf2d &T) const
	Transforms an hyperbola with the transformation T from class Trsf2d. More...

void	Translate (const gp_Vec2d &V)

gp_Hypr2d	Translated (const gp_Vec2d &V) const
	Translates an hyperbola 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_Hypr2d	Translated (const gp_Pnt2d &P1, const gp_Pnt2d &P2) const
	Translates an hyperbola from the point P1 to the point P2. More...

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 |

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 ( )

Creates of an indefinite hyperbola.

◆ gp_Hypr2d() [2/3]

gp_Hypr2d::gp_Hypr2d	(	const gp_Ax2d &	MajorAxis,
		const Standard_Real	MajorRadius,
		const Standard_Real	MinorRadius,
		const Standard_Boolean	Sense = `Standard_True`
	)

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

◆ gp_Hypr2d() [3/3]

gp_Hypr2d::gp_Hypr2d	(	const gp_Ax22d &	A,
		const Standard_Real	MajorRadius,
		const Standard_Real	MinorRadius
	)

a hyperbola with radii MajorRadius and MinorRadius, positioned in the plane by coordinate system A where:

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

Member Function Documentation

◆ Asymptote1()

gp_Ax2d gp_Hypr2d::Asymptote1 ( ) const

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

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

Returns the axisplacement of the hyperbola.

◆ Coefficients()

void gp_Hypr2d::Coefficients	(	Standard_Real &	A,
		Standard_Real &	B,
		Standard_Real &	C,
		Standard_Real &	D,
		Standard_Real &	E,
		Standard_Real &	F
	)		const

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

◆ ConjugateBranch1()

gp_Hypr2d gp_Hypr2d::ConjugateBranch1 ( ) const

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

◆ ConjugateBranch2()

gp_Hypr2d gp_Hypr2d::ConjugateBranch2 ( ) const

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

◆ Directrix1()

gp_Ax2d gp_Hypr2d::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".

◆ Directrix2()

gp_Ax2d gp_Hypr2d::Directrix2 ( ) const

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

◆ Eccentricity()

Standard_Real gp_Hypr2d::Eccentricity ( ) const

Returns the excentricity 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()

Standard_Real gp_Hypr2d::Focal ( ) const

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

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

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

◆ IsDirect()

Standard_Boolean gp_Hypr2d::IsDirect ( ) const

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

◆ Location()

const gp_Pnt2d& gp_Hypr2d::Location ( ) const

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

◆ MajorRadius()

Standard_Real gp_Hypr2d::MajorRadius ( ) const

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

◆ MinorRadius()

Standard_Real gp_Hypr2d::MinorRadius ( ) const

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_Pnt2d & P )

◆ Mirror() [2/2]

void gp_Hypr2d::Mirror ( const gp_Ax2d & A )

◆ Mirrored() [1/2]

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

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

◆ Mirrored() [2/2]

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

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

◆ OtherBranch()

gp_Hypr2d gp_Hypr2d::OtherBranch ( ) const

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

◆ Parameter()

Standard_Real gp_Hypr2d::Parameter ( ) const

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 ( )

◆ Reversed()

gp_Hypr2d gp_Hypr2d::Reversed ( ) const

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 &	P,
		const Standard_Real	Ang
	)

◆ Rotated()

gp_Hypr2d gp_Hypr2d::Rotated	(	const gp_Pnt2d &	P,
		const Standard_Real	Ang
	)		const

Rotates an hyperbola. P is the center of the rotation. Ang is the angular value of the rotation in radians.

◆ Scale()

void gp_Hypr2d::Scale	(	const gp_Pnt2d &	P,
		const Standard_Real	S
	)

◆ Scaled()

gp_Hypr2d gp_Hypr2d::Scaled	(	const gp_Pnt2d &	P,
		const Standard_Real	S
	)		const

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

◆ SetAxis()

void gp_Hypr2d::SetAxis ( const gp_Ax22d & A )

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

◆ SetLocation()

void gp_Hypr2d::SetLocation ( const gp_Pnt2d & P )

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

◆ SetMajorRadius()

void gp_Hypr2d::SetMajorRadius ( const Standard_Real MajorRadius )

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

◆ SetMinorRadius()

void gp_Hypr2d::SetMinorRadius ( const Standard_Real MinorRadius )

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

◆ SetXAxis()

void gp_Hypr2d::SetXAxis ( const gp_Ax2d & A )

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 & A )

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 & T )

◆ Transformed()

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

Transforms an hyperbola with the transformation T from class Trsf2d.

◆ Translate() [1/2]

void gp_Hypr2d::Translate ( const gp_Vec2d & V )

◆ Translate() [2/2]

void gp_Hypr2d::Translate	(	const gp_Pnt2d &	P1,
		const gp_Pnt2d &	P2
	)

◆ Translated() [1/2]

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

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

◆ Translated() [2/2]

gp_Hypr2d gp_Hypr2d::Translated	(	const gp_Pnt2d &	P1,
		const gp_Pnt2d &	P2
	)		const

Translates an hyperbola from the point P1 to the point P2.

◆ XAxis()

gp_Ax2d gp_Hypr2d::XAxis ( ) const

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