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

#include <Geom2d_Hyperbola.hxx>

Inheritance diagram for Geom2d_Hyperbola:

[legend]

Public Member Functions
	Geom2d_Hyperbola (const gp_Hypr2d &H)
	Creates an Hyperbola from a non persistent one from package gp More...

	Geom2d_Hyperbola (const gp_Ax2d &MajorAxis, const Standard_Real MajorRadius, const Standard_Real MinorRadius, const Standard_Boolean Sense=Standard_True)
	MajorAxis is the "XAxis" of the hyperbola. The YAxis is in the direct sense if "Sense" is True; The major radius of the hyperbola is on this "XAxis" and the minor radius is on the "YAxis" of the hyperbola. //! Raised if MajorRadius < 0.0 or if MinorRadius < 0.0 More...

	Geom2d_Hyperbola (const gp_Ax22d &Axis, const Standard_Real MajorRadius, const Standard_Real MinorRadius)
	The XDirection of "Axis" is the "XAxis" of the hyperbola and the YDirection of "Axis" is the "YAxis". The major radius of the hyperbola is on this "XAxis" and the minor radius is on the "YAxis" of the hyperbola. //! Raised if MajorRadius < 0.0 or if MinorRadius < 0.0 More...

void	SetHypr2d (const gp_Hypr2d &H)
	Converts the gp_Hypr2d hyperbola H into this hyperbola. More...

void	SetMajorRadius (const Standard_Real MajorRadius)
	Assigns a value to the major or minor radius of this hyperbola. <br> Exceptions Standard_ConstructionError if: More...

void	SetMinorRadius (const Standard_Real MinorRadius)
	Assigns a value to the major or minor radius of this hyperbola. <br> Exceptions Standard_ConstructionError if: More...

gp_Hypr2d	Hypr2d () const
	Converts this hyperbola into a gp_Hypr2d one. More...

Standard_Real	ReversedParameter (const Standard_Real U) const
	Computes the parameter on the reversed hyperbola, <br> for the point of parameter U on this hyperbola. For a hyperbola, the returned value is -U. More...

Standard_Real	FirstParameter () const
	Returns RealFirst from Standard. More...

Standard_Real	LastParameter () const
	returns RealLast from Standard. More...

Standard_Boolean	IsClosed () const
	Returns False. More...

Standard_Boolean	IsPeriodic () const
	return False for an hyperbola. 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 is the minor radius of the hyperbola. //! Raised 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 is the minor radius of the hyperbola. //! raised if MajorRadius = 0.0 More...

gp_Hypr2d	ConjugateBranch1 () const
	Computes the first conjugate branch relative to this hyperbola. <br> Note: The diagram given under the class purpose indicates where these two branches of hyperbola are positioned in relation to this branch of hyperbola. More...

gp_Hypr2d	ConjugateBranch2 () const
	Computes the second conjugate branch relative to this hyperbola. <br> Note: The diagram given under the class purpose indicates where these two branches of hyperbola are positioned in relation to this branch of hyperbola. More...

gp_Ax2d	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 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. //! raised if MajorRadius = 0.0 More...

Standard_Real	Focal () const
	Computes the focal distance. It is the distance between the two focus of the hyperbola. 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...

Standard_Real	MajorRadius () const
	Returns the major or minor radius of this hyperbola. <br> The major radius is also the distance between the center of the hyperbola and the apex of the main branch (located on the "X Axis" of the hyperbola). More...

Standard_Real	MinorRadius () const
	Returns the major or minor radius of this hyperbola. <br> The minor radius is also the distance between the center of the hyperbola and the apex of a conjugate branch (located on the "Y Axis" of the hyperbola). More...

gp_Hypr2d	OtherBranch () const
	Computes the "other" branch of this hyperbola. This <br> is a symmetrical branch with respect to the center of this hyperbola. Note: The diagram given under the class purpose indicates where the "other" branch is positioned in relation to this branch of the hyperbola. ^ YAxis \| FirstConjugateBranch \| Other \| Main -------------------------— C ---------------------------------------—&gtXAxis Branch \| Branch \| \| SecondConjugateBranch \| Warning The major radius can be less than the minor radius. More...

Standard_Real	Parameter () const
	Computes the parameter of this hyperbola. <br> The parameter is: p = (ee - 1) MajorRadius where e is the eccentricity of this hyperbola and MajorRadius its major radius. Exceptions Standard_DomainError if the major radius of this hyperbola is null. More...

void	D0 (const Standard_Real U, gp_Pnt2d &P) const
	Returns in P the point of parameter U. <br> P = C + MajorRadius * Cosh (U) * XDir + MinorRadius * Sinh (U) * YDir where C is the center of the hyperbola , XDir the XDirection and YDir the YDirection of the hyperbola's local coordinate system. More...

void	D1 (const Standard_Real U, gp_Pnt2d &P, gp_Vec2d &V1) const
	Returns the point P of parameter U and the first derivative V1. More...

void	D2 (const Standard_Real U, gp_Pnt2d &P, gp_Vec2d &V1, gp_Vec2d &V2) const
	Returns the point P of parameter U, the first and second derivatives V1 and V2. More...

void	D3 (const Standard_Real U, gp_Pnt2d &P, gp_Vec2d &V1, gp_Vec2d &V2, gp_Vec2d &V3) const
	Returns the point P of parameter U, the first second and third derivatives V1 V2 and V3. More...

gp_Vec2d	DN (const Standard_Real U, const Standard_Integer N) const
	For the point of parameter U of this hyperbola, <br> computes the vector corresponding to the Nth derivative. Exceptions Standard_RangeError if N is less than 1. More...

void	Transform (const gp_Trsf2d &T)
	Applies the transformation T to this hyperbola. More...

Handle_Geom2d_Geometry	Copy () const
	Creates a new object which is a copy of this hyperbola. More...

Public Member Functions inherited from Geom2d_Conic
void	SetAxis (const gp_Ax22d &A)
	Modifies this conic, redefining its local coordinate system <br> partially, by assigning P as its origin More...

void	SetXAxis (const gp_Ax2d &A)

void	SetYAxis (const gp_Ax2d &A)
	Assigns the origin and unit vector of axis A to the <br> origin of the local coordinate system of this conic and either: More...

void	SetLocation (const gp_Pnt2d &P)
	Modifies this conic, redefining its local coordinate <br> system fully, by assigning A as this coordinate system. More...

gp_Ax2d	XAxis () const
	Returns the "XAxis" of the conic. <br> This axis defines the origin of parametrization of the conic. This axis and the "Yaxis" define the local coordinate system of the conic. -C++: return const& More...

gp_Ax2d	YAxis () const
	Returns the "YAxis" of the conic. The "YAxis" is perpendicular to the "Xaxis". More...

gp_Pnt2d	Location () const
	Returns the location point of the conic. For the circle, the ellipse and the hyperbola it is the center of the conic. For the parabola it is the vertex of the parabola. More...

const gp_Ax22d &	Position () const
	Returns the local coordinates system of the conic. More...

void	Reverse ()
	Reverses the direction of parameterization of <me>. The local coordinate system of the conic is modified. More...

GeomAbs_Shape	Continuity () const
	Returns GeomAbs_CN which is the global continuity of any conic. More...

Standard_Boolean	IsCN (const Standard_Integer N) const
	Returns True, the order of continuity of a conic is infinite. More...

Public Member Functions inherited from Geom2d_Curve
virtual Standard_Real	TransformedParameter (const Standard_Real U, const gp_Trsf2d &T) const
	Computes the parameter on the curve transformed by <br> T for the point of parameter U on this curve. Note: this function generally returns U but it can be redefined (for example, on a line). More...

virtual Standard_Real	ParametricTransformation (const gp_Trsf2d &T) const
	Returns the coefficient required to compute the <br> parametric transformation of this curve when transformation T is applied. This coefficient is the ratio between the parameter of a point on this curve and the parameter of the transformed point on the new curve transformed by T. Note: this function generally returns 1. but it can be redefined (for example, on a line). More...

Handle_Geom2d_Curve	Reversed () const
	Creates a reversed duplicate Changes the orientation of this curve. The first and <br> last parameters are not changed, but the parametric direction of the curve is reversed. If the curve is bounded: More...

virtual Standard_Real	Period () const
	Returns thne period of this curve. //! raises if the curve is not periodic More...

gp_Pnt2d	Value (const Standard_Real U) const
	Computes the point of parameter U on <me>. <br> If the curve is periodic then the returned point is P(U) with U = Ustart + (U - Uend) where Ustart and Uend are the parametric bounds of the curve. it is implemented with D0. Raised only for the "OffsetCurve" if it is not possible to compute the current point. For example when the first derivative on the basis curve and the offset direction are parallel. More...

Public Member Functions inherited from Geom2d_Geometry
void	Mirror (const gp_Pnt2d &P)
	Performs the symmetrical transformation of a Geometry <br> with respect to the point P which is the center of the symmetry and assigns the result to this geometric object. More...

void	Mirror (const gp_Ax2d &A)
	Performs the symmetrical transformation of a Geometry <br> with respect to an axis placement which is the axis of the symmetry. More...

void	Rotate (const gp_Pnt2d &P, const Standard_Real Ang)
	Rotates a Geometry. P is the center of the rotation. <br> Ang is the angular value of the rotation in radians. More...

void	Scale (const gp_Pnt2d &P, const Standard_Real S)
	Scales a Geometry. S is the scaling value. More...

void	Translate (const gp_Vec2d &V)
	Translates a Geometry. V is the vector of the tanslation. More...

void	Translate (const gp_Pnt2d &P1, const gp_Pnt2d &P2)
	Translates a Geometry from the point P1 to the point P2. More...

Handle_Geom2d_Geometry	Mirrored (const gp_Pnt2d &P) const

Handle_Geom2d_Geometry	Mirrored (const gp_Ax2d &A) const

Handle_Geom2d_Geometry	Rotated (const gp_Pnt2d &P, const Standard_Real Ang) const

Handle_Geom2d_Geometry	Scaled (const gp_Pnt2d &P, const Standard_Real S) const

Handle_Geom2d_Geometry	Transformed (const gp_Trsf2d &T) const

Handle_Geom2d_Geometry	Translated (const gp_Vec2d &V) const

Handle_Geom2d_Geometry	Translated (const gp_Pnt2d &P1, const gp_Pnt2d &P2) const

Public Member Functions inherited from MMgt_TShared
virtual void	Delete () const
	Memory deallocator for transient classes. More...

Public Member Functions inherited from Standard_Transient
	Standard_Transient ()
	Empty constructor. More...

	Standard_Transient (const Standard_Transient &)
	Copy constructor – does nothing. More...

Standard_Transient &	operator= (const Standard_Transient &)
	Assignment operator, needed to avoid copying reference counter. More...

virtual	~Standard_Transient ()
	Destructor must be virtual. More...

virtual void	ShallowDump (Standard_OStream &) const

virtual const Handle_Standard_Type &	DynamicType () const
	Returns a type information object about this object. More...

Standard_Boolean	IsInstance (const Handle_Standard_Type &theType) const
	Returns a true value if this is an instance of Type. More...

Standard_Boolean	IsInstance (const Standard_CString theTypeName) const
	Returns a true value if this is an instance of TypeName. More...

Standard_Boolean	IsKind (const Handle_Standard_Type &theType) const
	Returns true if this is an instance of Type or an instance of any class that inherits from Type. Note that multiple inheritance is not supported by OCCT RTTI mechanism. More...

Standard_Boolean	IsKind (const Standard_CString theTypeName) const
	Returns true if this is an instance of TypeName or an instance of any class that inherits from TypeName. Note that multiple inheritance is not supported by OCCT RTTI mechanism. More...

virtual Handle_Standard_Transient	This () const
	Returns a Handle which references this object. Must never be called to objects created in stack. More...

Standard_Integer	GetRefCount () const
	Get the reference counter of this object. More...

Additional Inherited Members
Protected Attributes inherited from Geom2d_Conic
gp_Ax22d	pos

Detailed Description

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

the origin is the center of the hyperbola,
the "X Direction" defines the major axis, and
the "Y Direction" defines the minor axis.
This coordinate system is the local coordinate
system of the hyperbola.
The branch of the hyperbola described is the one
located on the positive side of the major axis.
The orientation (direct or indirect) of the local
coordinate system gives an explicit orientation to the
hyperbola, determining the direction in which the
parameter increases along the hyperbola.
The Geom2d_Hyperbola hyperbola is parameterized as follows:
P(U) = O + MajRad*Cosh(U)*XDir + MinRad*Sinh(U)*YDir
where:
P is the point of parameter U,
O, XDir and YDir are respectively the origin, "X <br> Direction" and "Y Direction" of its local coordinate system,
MajRad and MinRad are the major and minor radii of the hyperbola.
The "X Axis" of the local coordinate system therefore
defines the origin of the parameter of the hyperbola.
The parameter range is ] -infinite,+infinite [.
The following diagram illustrates the respective
positions, in the plane of the hyperbola, of the three
branches of hyperbolas constructed using the
functions OtherBranch, ConjugateBranch1 and
ConjugateBranch2:
^YAxis
|
FirstConjugateBranch
|
Other | Main
------------------— C
------------------—>XAxis
Branch |
Branch
|
SecondConjugateBranch
|
Warning
The value of the major radius (on the major axis) can
be less than the value of the minor radius (on the minor axis).
See Also
GCE2d_MakeHyperbola which provides functions for
more complex hyperbola constructions
gp_Ax22d
gp_Hypr2d for an equivalent, non-parameterized data structure

Constructor & Destructor Documentation

Geom2d_Hyperbola::Geom2d_Hyperbola ( const gp_Hypr2d & H )

Creates an Hyperbola from a non persistent one from package gp

Geom2d_Hyperbola::Geom2d_Hyperbola	(	const gp_Ax2d &	MajorAxis,
		const Standard_Real	MajorRadius,
		const Standard_Real	MinorRadius,
		const Standard_Boolean	Sense = `Standard_True`
	)

MajorAxis is the "XAxis" of the hyperbola.
The YAxis is in the direct sense if "Sense" is True;
The major radius of the hyperbola is on this "XAxis" and
the minor radius is on the "YAxis" of the hyperbola.
//! Raised if MajorRadius < 0.0 or if MinorRadius < 0.0

Geom2d_Hyperbola::Geom2d_Hyperbola	(	const gp_Ax22d &	Axis,
		const Standard_Real	MajorRadius,
		const Standard_Real	MinorRadius
	)

The XDirection of "Axis" is the "XAxis" of the hyperbola and
the YDirection of "Axis" is the "YAxis".
The major radius of the hyperbola is on this "XAxis" and
the minor radius is on the "YAxis" of the hyperbola.
//! Raised if MajorRadius < 0.0 or if MinorRadius < 0.0

Member Function Documentation

gp_Ax2d Geom2d_Hyperbola::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 is the
minor radius of the hyperbola.
//! Raised if MajorRadius = 0.0

gp_Ax2d Geom2d_Hyperbola::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 is the
minor radius of the hyperbola.
//! raised if MajorRadius = 0.0

gp_Hypr2d Geom2d_Hyperbola::ConjugateBranch1 ( ) const

 Computes the first conjugate branch relative to this hyperbola. <br>

Note: The diagram given under the class purpose
indicates where these two branches of hyperbola are
positioned in relation to this branch of hyperbola.

gp_Hypr2d Geom2d_Hyperbola::ConjugateBranch2 ( ) const

 Computes the second conjugate branch relative to this hyperbola. <br>

Note: The diagram given under the class purpose
indicates where these two branches of hyperbola are
positioned in relation to this branch of hyperbola.

Handle_Geom2d_Geometry Geom2d_Hyperbola::Copy ( ) const

virtual

Creates a new object which is a copy of this hyperbola.

Implements Geom2d_Geometry.

void Geom2d_Hyperbola::D0	(	const Standard_Real	U,
		gp_Pnt2d &	P
	)		const

virtual

Returns in P the point of parameter U. <br>

P = C + MajorRadius * Cosh (U) * XDir +
MinorRadius * Sinh (U) * YDir
where C is the center of the hyperbola , XDir the XDirection and
YDir the YDirection of the hyperbola's local coordinate system.

Implements Geom2d_Curve.

void Geom2d_Hyperbola::D1	(	const Standard_Real	U,
		gp_Pnt2d &	P,
		gp_Vec2d &	V1
	)		const

virtual

Returns the point P of parameter U and the first derivative V1.

Implements Geom2d_Curve.

void Geom2d_Hyperbola::D2	(	const Standard_Real	U,
		gp_Pnt2d &	P,
		gp_Vec2d &	V1,
		gp_Vec2d &	V2
	)		const

virtual

Returns the point P of parameter U, the first and second
derivatives V1 and V2.

Implements Geom2d_Curve.

void Geom2d_Hyperbola::D3	(	const Standard_Real	U,
		gp_Pnt2d &	P,
		gp_Vec2d &	V1,
		gp_Vec2d &	V2,
		gp_Vec2d &	V3
	)		const

virtual

Returns the point P of parameter U, the first second and
third derivatives V1 V2 and V3.

Implements Geom2d_Curve.

gp_Ax2d Geom2d_Hyperbola::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 directrix1 and the "XAxis" is the location point of the
directrix1. This point is on the positive side of the "XAxis".

gp_Ax2d Geom2d_Hyperbola::Directrix2 ( ) const

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

gp_Vec2d Geom2d_Hyperbola::DN	(	const Standard_Real	U,
		const Standard_Integer	N
	)		const

virtual

 For the point of parameter U of this hyperbola, <br>

computes the vector corresponding to the Nth derivative.
Exceptions Standard_RangeError if N is less than 1.

Implements Geom2d_Curve.

Standard_Real Geom2d_Hyperbola::Eccentricity ( ) const

virtual

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.
//! raised if MajorRadius = 0.0

Implements Geom2d_Conic.

Standard_Real Geom2d_Hyperbola::FirstParameter ( ) const

virtual

Returns RealFirst from Standard.

Implements Geom2d_Curve.

Standard_Real Geom2d_Hyperbola::Focal ( ) const

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

gp_Pnt2d Geom2d_Hyperbola::Focus1 ( ) const

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

gp_Pnt2d Geom2d_Hyperbola::Focus2 ( ) const

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

gp_Hypr2d Geom2d_Hyperbola::Hypr2d ( ) const

Converts this hyperbola into a gp_Hypr2d one.

Standard_Boolean Geom2d_Hyperbola::IsClosed ( ) const

virtual

Returns False.

Implements Geom2d_Curve.

Standard_Boolean Geom2d_Hyperbola::IsPeriodic ( ) const

virtual

return False for an hyperbola.

Implements Geom2d_Curve.

Standard_Real Geom2d_Hyperbola::LastParameter ( ) const

virtual

returns RealLast from Standard.

Implements Geom2d_Curve.

Standard_Real Geom2d_Hyperbola::MajorRadius ( ) const

 Returns the major or minor radius of this hyperbola. <br>

The major radius is also the distance between the
center of the hyperbola and the apex of the main
branch (located on the "X Axis" of the hyperbola).

Standard_Real Geom2d_Hyperbola::MinorRadius ( ) const

 Returns the major or minor radius of this hyperbola. <br>

The minor radius is also the distance between the
center of the hyperbola and the apex of a conjugate
branch (located on the "Y Axis" of the hyperbola).

gp_Hypr2d Geom2d_Hyperbola::OtherBranch ( ) const

Computes the "other" branch of this hyperbola. This <br>

is a symmetrical branch with respect to the center of this hyperbola.
Note: The diagram given under the class purpose
indicates where the "other" branch is positioned in
relation to this branch of the hyperbola.
^ YAxis
|
FirstConjugateBranch
|
Other | Main
-------------------------— C
---------------------------------------—&gtXAxis
Branch | Branch
|
|
SecondConjugateBranch
|
Warning
The major radius can be less than the minor radius.

Standard_Real Geom2d_Hyperbola::Parameter ( ) const

 Computes the parameter of this hyperbola. <br>

The parameter is:
p = (e*e - 1) * MajorRadius
where e is the eccentricity of this hyperbola and
MajorRadius its major radius.
Exceptions
Standard_DomainError if the major radius of this
hyperbola is null.

Standard_Real Geom2d_Hyperbola::ReversedParameter ( const Standard_Real U ) const

virtual

 Computes the parameter on the reversed hyperbola, <br>

for the point of parameter U on this hyperbola.
For a hyperbola, the returned value is -U.

Implements Geom2d_Conic.

void Geom2d_Hyperbola::SetHypr2d ( const gp_Hypr2d & H )

Converts the gp_Hypr2d hyperbola H into this hyperbola.

void Geom2d_Hyperbola::SetMajorRadius ( const Standard_Real MajorRadius )

 Assigns a value to the major or minor radius of this hyperbola. <br>

Exceptions
Standard_ConstructionError if:

MajorRadius is less than 0.0,
MinorRadius is less than 0.0.

void Geom2d_Hyperbola::SetMinorRadius ( const Standard_Real MinorRadius )

 Assigns a value to the major or minor radius of this hyperbola. <br>

Exceptions
Standard_ConstructionError if:

MajorRadius is less than 0.0,
MinorRadius is less than 0.0.

void Geom2d_Hyperbola::Transform ( const gp_Trsf2d & T )

virtual

Applies the transformation T to this hyperbola.

Implements Geom2d_Geometry.

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

Geom2d_Hyperbola.hxx

Public Member Functions

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation