Describes a branch of a hyperbola in 3D space.
A hyperbola is defined by its major and minor radii
and, as with any conic curve, is positioned in space
with a right-handed coordinate system (gp_Ax2 object) where:
More...

#include <Geom_Hyperbola.hxx>

Inheritance diagram for Geom_Hyperbola:

[legend]

Public Member Functions
	Geom_Hyperbola (const gp_Hypr &H)
	Constructs a hyperbola by conversion of the gp_Hypr hyperbola H. More...

	Geom_Hyperbola (const gp_Ax2 &A2, const Standard_Real MajorRadius, const Standard_Real MinorRadius)
	Constructs a hyperbola defined by its major and <br> minor radii, MajorRadius and MinorRadius, where A2 locates the hyperbola and defines its orientation in 3D space such that: More...

void	SetHypr (const gp_Hypr &H)
	Converts the gp_Hypr hyperbola H into this hyperbola. More...

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

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

gp_Hypr	Hypr () const
	returns the non transient parabola from gp with the same geometric properties as <me>. 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_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. Raises ConstructionError if MajorRadius = 0.0 More...

gp_Ax1	Asymptote2 () const
	In the local coordinate system of the hyperbola the equation of <br> the hyperbola is (XX)/(AA) - (YY)/(BB) = 1.0 and the equation of the first asymptote is Y = -(B/A)*X. Raises ConstructionError if MajorRadius = 0.0 More...

gp_Hypr	ConjugateBranch1 () const
	This branch of hyperbola is on the positive side of the YAxis of <me>. More...

gp_Hypr	ConjugateBranch2 () const
	This branch of hyperbola is on the negative side of the <br> YAxis of <me>. 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_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 directrix1 and the XAxis is the location point of the directrix1. This point is on the positive side of the XAxis. More...

gp_Ax1	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_Pnt	Focus1 () const
	Returns the first focus of the hyperbola. This focus is on the positive side of the XAxis of the hyperbola. More...

gp_Pnt	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_Hypr	OtherBranch () const
	Computes the "other" branch of this hyperbola. This <br> is the 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. More...

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

void	D0 (const Standard_Real U, gp_Pnt &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_Pnt &P, gp_Vec &V1) const
	Returns the point P of parameter U and the first derivative V1. More...

void	D2 (const Standard_Real U, gp_Pnt &P, gp_Vec &V1, gp_Vec &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_Pnt &P, gp_Vec &V1, gp_Vec &V2, gp_Vec &V3) const
	Returns the point P of parameter U, the first second and third derivatives V1 V2 and V3. More...

gp_Vec	DN (const Standard_Real U, const Standard_Integer N) const
	The returned vector gives the value of the derivative for the order of derivation N. //! Raised if N < 1. More...

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

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

Public Member Functions inherited from Geom_Conic
void	SetAxis (const gp_Ax1 &A1)
	Changes the orientation of the conic's plane. The normal <br> axis to the plane is A1. The XAxis and the YAxis are recomputed. raised if the A1 is parallel to the XAxis of the conic. More...

void	SetLocation (const gp_Pnt &P)
	changes the location point of the conic. More...

void	SetPosition (const gp_Ax2 &A2)
	changes the local coordinate system of the conic. More...

gp_Ax1	Axis () const
	Returns the "main Axis" of this conic. This axis is <br> normal to the plane of the conic. More...

gp_Pnt	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 Apex of the parabola. More...

const gp_Ax2 &	Position () const
	Returns the local coordinates system of the conic. The main direction of the Axis2Placement is normal to the plane of the conic. The X direction of the Axis2placement is in the plane of the conic and corresponds to the origin for the conic's parametric value u. More...

gp_Ax1	XAxis () const
	Returns the XAxis of the conic. This axis defines the origin of parametrization of the conic. This axis is perpendicular to the Axis of the conic. This axis and the Yaxis define the plane of the conic. More...

gp_Ax1	YAxis () const
	Returns the YAxis of the conic. The YAxis is perpendicular to the Xaxis. This axis and the Xaxis define the plane 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
	The continuity of the conic is Cn. More...

Standard_Boolean	IsCN (const Standard_Integer N) const
	Returns True. //! Raised if N < 0. More...

Public Member Functions inherited from Geom_Curve
virtual Standard_Real	TransformedParameter (const Standard_Real U, const gp_Trsf &T) const
	Returns the parameter on the transformed curve for <br> the transform of the point of parameter U on <me>. <br> me->Transformed(T)->Value(me->TransformedParameter(U,T)) is the same point as me->Value(U).Transformed(T) This methods returns <U> It can be redefined. For example on the Line. More...

virtual Standard_Real	ParametricTransformation (const gp_Trsf &T) const
	Returns a coefficient to compute the parameter on <br> the transformed curve for the transform of the <br> point on <me>. <br> Transformed(T)->Value(U * ParametricTransformation(T)) is the same point as Value(U).Transformed(T) This methods returns 1. It can be redefined. For example on the Line. More...

Handle_Geom_Curve	Reversed () const
	Returns a copy of <me> reversed. More...

virtual Standard_Real	Period () const
	Returns the period of this curve. <br> Exceptions Standard_NoSuchObject if this curve is not periodic. More...

gp_Pnt	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 Geom_Geometry
void	Mirror (const gp_Pnt &P)
	Performs the symmetrical transformation of a Geometry with respect to the point P which is the center of the symmetry. More...

void	Mirror (const gp_Ax1 &A1)
	Performs the symmetrical transformation of a Geometry with respect to an axis placement which is the axis of the symmetry. More...

void	Mirror (const gp_Ax2 &A2)
	Performs the symmetrical transformation of a Geometry with respect to a plane. The axis placement A2 locates the plane of the symmetry : (Location, XDirection, YDirection). More...

void	Rotate (const gp_Ax1 &A1, const Standard_Real Ang)
	Rotates a Geometry. A1 is the axis of the rotation. Ang is the angular value of the rotation in radians. More...

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

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

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

Handle_Geom_Geometry	Mirrored (const gp_Pnt &P) const

Handle_Geom_Geometry	Mirrored (const gp_Ax1 &A1) const

Handle_Geom_Geometry	Mirrored (const gp_Ax2 &A2) const

Handle_Geom_Geometry	Rotated (const gp_Ax1 &A1, const Standard_Real Ang) const

Handle_Geom_Geometry	Scaled (const gp_Pnt &P, const Standard_Real S) const

Handle_Geom_Geometry	Transformed (const gp_Trsf &T) const

Handle_Geom_Geometry	Translated (const gp_Vec &V) const

Handle_Geom_Geometry	Translated (const gp_Pnt &P1, const gp_Pnt &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 Geom_Conic
gp_Ax2	pos

Detailed Description

Describes a branch of a hyperbola in 3D space.
A hyperbola is defined by its major and minor radii
and, as with any conic curve, is positioned in space
with a right-handed coordinate system (gp_Ax2 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.
The origin, "X Direction" and "Y Direction" of this
coordinate system define the plane of the hyperbola.
The 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 "main Direction" of the local coordinate system is
a vector normal to the plane of the hyperbola. The
axis, of which the origin and unit vector are
respectively the origin and "main Direction" of the
local coordinate system, is termed the "Axis" or "main <br> Axis" of the hyperbola.
The "main Direction" of the local coordinate system
gives an explicit orientation to the hyperbola,
determining the direction in which the parameter
increases along the hyperbola.
The Geom_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: Defines the main branch of an hyperbola.
^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).

Constructor & Destructor Documentation

Geom_Hyperbola::Geom_Hyperbola ( const gp_Hypr & H )

Constructs a hyperbola by conversion of the gp_Hypr hyperbola H.

Geom_Hyperbola::Geom_Hyperbola	(	const gp_Ax2 &	A2,
		const Standard_Real	MajorRadius,
		const Standard_Real	MinorRadius
	)

 Constructs a hyperbola defined by its major and <br>

minor radii, MajorRadius and MinorRadius, where A2 locates the
hyperbola and defines its orientation in 3D space such that:

the center of the hyperbola is the origin of A2,
the "X Direction" of A2 defines the major axis
of the hyperbola, i.e. the major radius
MajorRadius is measured along this axis,
the "Y Direction" of A2 defines the minor axis
of the hyperbola, i.e. the minor radius
MinorRadius is measured along this axis,
A2 is the local coordinate system of the hyperbola.
Exceptions
Standard_ConstructionError if:

MajorRadius is less than 0.0,

MinorRadius is less than 0.0.

Member Function Documentation

gp_Ax1 Geom_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.
Raises ConstructionError if MajorRadius = 0.0

gp_Ax1 Geom_Hyperbola::Asymptote2 ( ) const

In the local coordinate system of the hyperbola the equation of <br>

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.
Raises ConstructionError if MajorRadius = 0.0

gp_Hypr Geom_Hyperbola::ConjugateBranch1 ( ) const

This branch of hyperbola is on the positive side of the
YAxis of <me>.

gp_Hypr Geom_Hyperbola::ConjugateBranch2 ( ) const

This branch of hyperbola is on the negative side of the <br>

YAxis of <me>.
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_Geom_Geometry Geom_Hyperbola::Copy ( ) const

virtual

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

Implements Geom_Geometry.

void Geom_Hyperbola::D0	(	const Standard_Real	U,
		gp_Pnt &	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 Geom_Curve.

void Geom_Hyperbola::D1	(	const Standard_Real	U,
		gp_Pnt &	P,
		gp_Vec &	V1
	)		const

virtual

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

Implements Geom_Curve.

void Geom_Hyperbola::D2	(	const Standard_Real	U,
		gp_Pnt &	P,
		gp_Vec &	V1,
		gp_Vec &	V2
	)		const

virtual

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

Implements Geom_Curve.

void Geom_Hyperbola::D3	(	const Standard_Real	U,
		gp_Pnt &	P,
		gp_Vec &	V1,
		gp_Vec &	V2,
		gp_Vec &	V3
	)		const

virtual

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

Implements Geom_Curve.

gp_Ax1 Geom_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_Ax1 Geom_Hyperbola::Directrix2 ( ) const

This line is obtained by the symmetrical transformation
of "directrix1" with respect to the YAxis of the hyperbola.

gp_Vec Geom_Hyperbola::DN	(	const Standard_Real	U,
		const Standard_Integer	N
	)		const

virtual

The returned vector gives the value of the derivative for the
order of derivation N.
//! Raised if N < 1.

Implements Geom_Curve.

Standard_Real Geom_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 Geom_Conic.

Standard_Real Geom_Hyperbola::FirstParameter ( ) const

virtual

Returns RealFirst from Standard.

Implements Geom_Curve.

Standard_Real Geom_Hyperbola::Focal ( ) const

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

gp_Pnt Geom_Hyperbola::Focus1 ( ) const

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

gp_Pnt Geom_Hyperbola::Focus2 ( ) const

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

gp_Hypr Geom_Hyperbola::Hypr ( ) const

returns the non transient parabola from gp with the same
geometric properties as <me>.

Standard_Boolean Geom_Hyperbola::IsClosed ( ) const

virtual

Returns False.

Implements Geom_Curve.

Standard_Boolean Geom_Hyperbola::IsPeriodic ( ) const

virtual

return False for an hyperbola.

Implements Geom_Curve.

Standard_Real Geom_Hyperbola::LastParameter ( ) const

virtual

returns RealLast from Standard.

Implements Geom_Curve.

Standard_Real Geom_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 Geom_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_Hypr Geom_Hyperbola::OtherBranch ( ) const

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

is the 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.

Standard_Real Geom_Hyperbola::Parameter ( ) const

Returns p = (e * e - 1) * MajorRadius where e is the
eccentricity of the hyperbola.
//! raised if MajorRadius = 0.0

Standard_Real Geom_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 Geom_Conic.

void Geom_Hyperbola::SetHypr ( const gp_Hypr & H )

Converts the gp_Hypr hyperbola H into this hyperbola.

void Geom_Hyperbola::SetMajorRadius ( const Standard_Real MajorRadius )

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

Exceptions
Standard_ConstructionError if:

MajorRadius is less than 0.0, or
MinorRadius is less than 0.0.Raised if MajorRadius < 0.0

void Geom_Hyperbola::SetMinorRadius ( const Standard_Real MinorRadius )

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

Exceptions
Standard_ConstructionError if:

MajorRadius is less than 0.0, or
MinorRadius is less than 0.0.Raised if MajorRadius < 0.0

void Geom_Hyperbola::Transform ( const gp_Trsf & T )

virtual

Applies the transformation T to this hyperbola.

Implements Geom_Geometry.

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

Geom_Hyperbola.hxx

Public Member Functions

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation