Open CASCADE Technology Reference Manual 8.0.0
Loading...
Searching...
No Matches
Public Member Functions
Geom2d_Hyperbola Class Reference

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:
Inheritance graph
[legend]

Public Member Functions

 Geom2d_Hyperbola (const gp_Hypr2d &H)
 Creates an Hyperbola from a non persistent one from package gp.
 
 Geom2d_Hyperbola (const gp_Ax2d &MajorAxis, const double MajorRadius, const double MinorRadius, const bool Sense=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 (const gp_Ax22d &Axis, const double MajorRadius, const double 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.
 
void SetHypr2d (const gp_Hypr2d &H)
 Converts the gp_Hypr2d hyperbola H into this hyperbola.
 
void SetMajorRadius (const double MajorRadius)
 Assigns a value to the major or minor radius of this hyperbola. Exceptions Standard_ConstructionError if:
 
void SetMinorRadius (const double MinorRadius)
 Assigns a value to the major or minor radius of this hyperbola. Exceptions Standard_ConstructionError if:
 
gp_Hypr2d Hypr2d () const
 Converts this hyperbola into a gp_Hypr2d one.
 
double ReversedParameter (const double U) const final
 Computes the parameter on the reversed hyperbola, for the point of parameter U on this hyperbola. For a hyperbola, the returned value is -U.
 
double FirstParameter () const final
 Returns RealFirst from Standard.
 
double LastParameter () const final
 returns RealLast from Standard.
 
bool IsClosed () const final
 Returns False.
 
bool IsPeriodic () const final
 return False for an hyperbola.
 
gp_Ax2d 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 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 ConjugateBranch1 () const
 Computes the first conjugate branch relative to this hyperbola. 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 ConjugateBranch2 () const
 Computes the second conjugate branch relative to this hyperbola. 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_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".
 
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 final
 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. raised if MajorRadius = 0.0.
 
double Focal () const
 Computes the focal distance. It is the distance between the two focus of the hyperbola.
 
gp_Pnt2d Focus1 () const
 Returns the first focus of the hyperbola. This focus is on the positive side of the "XAxis" of the hyperbola.
 
gp_Pnt2d Focus2 () const
 Returns the second focus of the hyperbola. This focus is on the negative side of the "XAxis" of the hyperbola.
 
double MajorRadius () const
 Returns the major or minor radius of this hyperbola. 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).
 
double MinorRadius () const
 Returns the major or minor radius of this hyperbola. 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 OtherBranch () const
 Computes the "other" branch of this hyperbola. This 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.
 
double Parameter () const
 Computes the parameter of this hyperbola. 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.
 
gp_Pnt2d EvalD0 (const double U) const final
 Returns in P the point of parameter U. P = C + MajorRadius * std::cosh(U) * XDir + MinorRadius * std::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.
 
Geom2d_Curve::ResD1 EvalD1 (const double U) const final
 Returns the point P of parameter U and the first derivative V1.
 
Geom2d_Curve::ResD2 EvalD2 (const double U) const final
 Returns the point P of parameter U, the first and second derivatives V1 and V2.
 
Geom2d_Curve::ResD3 EvalD3 (const double U) const final
 Returns the point P of parameter U, the first second and third derivatives V1 V2 and V3.
 
gp_Vec2d EvalDN (const double U, const int N) const final
 For the point of parameter U of this hyperbola, computes the vector corresponding to the Nth derivative. Exceptions Standard_RangeError if N is less than 1.
 
void Transform (const gp_Trsf2d &T) final
 Applies the transformation T to this hyperbola.
 
occ::handle< Geom2d_GeometryCopy () const final
 Creates a new object which is a copy of this hyperbola.
 
void DumpJson (Standard_OStream &theOStream, int theDepth=-1) const final
 Dumps the content of me into the stream.
 
- Public Member Functions inherited from Geom2d_Conic
void SetAxis (const gp_Ax22d &theA)
 Modifies this conic, redefining its local coordinate system partially, by assigning theA as its axis.
 
void SetXAxis (const gp_Ax2d &theAX)
 Assigns the origin and unit vector of axis theA to the origin of the local coordinate system of this conic and X Direction. The other unit vector of the local coordinate system of this conic is recomputed normal to theA, without changing the orientation of the local coordinate system (right-handed or left-handed).
 
void SetYAxis (const gp_Ax2d &theAY)
 Assigns the origin and unit vector of axis theA to the origin of the local coordinate system of this conic and Y Direction. The other unit vector of the local coordinate system of this conic is recomputed normal to theA, without changing the orientation of the local coordinate system (right-handed or left-handed).
 
void SetLocation (const gp_Pnt2d &theP)
 Modifies this conic, redefining its local coordinate system partially, by assigning theP as its origin.
 
gp_Ax2d XAxis () const
 Returns the "XAxis" of the conic. 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&.
 
gp_Ax2d YAxis () const
 Returns the "YAxis" of the conic. The "YAxis" is perpendicular to the "Xaxis".
 
const gp_Pnt2dLocation () 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.
 
const gp_Ax22dPosition () const
 Returns the local coordinates system of the conic.
 
void Reverse () override
 Reverses the direction of parameterization of <me>. The local coordinate system of the conic is modified.
 
GeomAbs_Shape Continuity () const override
 Returns GeomAbs_CN which is the global continuity of any conic.
 
bool IsCN (const int N) const override
 Returns True, the order of continuity of a conic is infinite.
 
- Public Member Functions inherited from Geom2d_Curve
virtual double TransformedParameter (const double U, const gp_Trsf2d &T) const
 Computes the parameter on the curve transformed by 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).
 
virtual double ParametricTransformation (const gp_Trsf2d &T) const
 Returns the coefficient required to compute the 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).
 
occ::handle< Geom2d_CurveReversed () const
 Creates a reversed duplicate Changes the orientation of this curve. The first and last parameters are not changed, but the parametric direction of the curve is reversed. If the curve is bounded:
 
virtual double Period () const
 Returns the period of this curve. raises if the curve is not periodic.
 
void D0 (const double U, gp_Pnt2d &P) const
 Returns in P the point of parameter U.
 
void D1 (const double U, gp_Pnt2d &P, gp_Vec2d &V1) const
 Returns the point P of parameter U and the first derivative V1.
 
void D2 (const double 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.
 
void D3 (const double U, gp_Pnt2d &P, gp_Vec2d &V1, gp_Vec2d &V2, gp_Vec2d &V3) const
 Returns the point P of parameter U, the first, the second and the third derivative.
 
gp_Vec2d DN (const double U, const int N) const
 Computes the Nth derivative vector.
 
gp_Pnt2d Value (const double U) const
 Computes the point of parameter U on <me>. Implemented with D0.
 
- Public Member Functions inherited from Geom2d_Geometry
void Mirror (const gp_Pnt2d &P)
 Performs the symmetrical transformation of a Geometry with respect to the point P which is the center of the symmetry and assigns the result to this geometric object.
 
void Mirror (const gp_Ax2d &A)
 Performs the symmetrical transformation of a Geometry with respect to an axis placement which is the axis of the symmetry.
 
void Rotate (const gp_Pnt2d &P, const double Ang)
 Rotates a Geometry. P is the center of the rotation. Ang is the angular value of the rotation in radians.
 
void Scale (const gp_Pnt2d &P, const double S)
 Scales a Geometry. S is the scaling value.
 
void Translate (const gp_Vec2d &V)
 Translates a Geometry. V is the vector of the translation.
 
void Translate (const gp_Pnt2d &P1, const gp_Pnt2d &P2)
 Translates a Geometry from the point P1 to the point P2.
 
occ::handle< Geom2d_GeometryMirrored (const gp_Pnt2d &P) const
 
occ::handle< Geom2d_GeometryMirrored (const gp_Ax2d &A) const
 
occ::handle< Geom2d_GeometryRotated (const gp_Pnt2d &P, const double Ang) const
 
occ::handle< Geom2d_GeometryScaled (const gp_Pnt2d &P, const double S) const
 
occ::handle< Geom2d_GeometryTransformed (const gp_Trsf2d &T) const
 
occ::handle< Geom2d_GeometryTranslated (const gp_Vec2d &V) const
 
occ::handle< Geom2d_GeometryTranslated (const gp_Pnt2d &P1, const gp_Pnt2d &P2) const
 
- Public Member Functions inherited from Standard_Transient
 Standard_Transient ()
 Empty constructor.
 
 Standard_Transient (const Standard_Transient &)
 Copy constructor – does nothing.
 
Standard_Transientoperator= (const Standard_Transient &)
 Assignment operator, needed to avoid copying reference counter.
 
virtual ~Standard_Transient ()=default
 Destructor must be virtual.
 
virtual const opencascade::handle< Standard_Type > & DynamicType () const
 Returns a type descriptor about this object.
 
bool IsInstance (const opencascade::handle< Standard_Type > &theType) const
 Returns a true value if this is an instance of Type.
 
bool IsInstance (const char *const theTypeName) const
 Returns a true value if this is an instance of TypeName.
 
bool IsKind (const opencascade::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.
 
bool IsKind (const char *const 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.
 
Standard_TransientThis () const
 Returns non-const pointer to this object (like const_cast). For protection against creating handle to objects allocated in stack or call from constructor, it will raise exception Standard_ProgramError if reference counter is zero.
 
int GetRefCount () const noexcept
 Get the reference counter of this object.
 
void IncrementRefCounter () noexcept
 Increments the reference counter of this object. Uses relaxed memory ordering since incrementing only requires atomicity, not synchronization with other memory operations.
 
int DecrementRefCounter () noexcept
 Decrements the reference counter of this object; returns the decremented value. Uses release ordering for the decrement to ensure all writes to the object are visible before the count reaches zero. An acquire fence is added only when the count reaches zero, ensuring proper synchronization before deletion. This is more efficient than using acq_rel for every decrement.
 
virtual void Delete () const
 Memory deallocator for transient classes.
 

Additional Inherited Members

- Public Types inherited from Standard_Transient
typedef void base_type
 Returns a type descriptor about this object.
 
- Static Public Member Functions inherited from Standard_Transient
static constexpr const charget_type_name ()
 Returns a type descriptor about this object.
 
static const opencascade::handle< Standard_Type > & get_type_descriptor ()
 Returns type descriptor of Standard_Transient class.
 
- 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:

Constructor & Destructor Documentation

◆ Geom2d_Hyperbola() [1/3]

Geom2d_Hyperbola::Geom2d_Hyperbola ( const gp_Hypr2d & H)

Creates an Hyperbola from a non persistent one from package gp.

◆ Geom2d_Hyperbola() [2/3]

Geom2d_Hyperbola::Geom2d_Hyperbola ( const gp_Ax2d & MajorAxis,
const double MajorRadius,
const double MinorRadius,
const bool Sense = 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() [3/3]

Geom2d_Hyperbola::Geom2d_Hyperbola ( const gp_Ax22d & Axis,
const double MajorRadius,
const double 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

◆ Asymptote1()

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.

◆ Asymptote2()

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.

◆ ConjugateBranch1()

gp_Hypr2d Geom2d_Hyperbola::ConjugateBranch1 ( ) const

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

◆ ConjugateBranch2()

gp_Hypr2d Geom2d_Hyperbola::ConjugateBranch2 ( ) const

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

◆ Copy()

occ::handle< Geom2d_Geometry > Geom2d_Hyperbola::Copy ( ) const
finalvirtual

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

Implements Geom2d_Geometry.

◆ Directrix1()

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".

◆ Directrix2()

gp_Ax2d Geom2d_Hyperbola::Directrix2 ( ) const

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

◆ DumpJson()

void Geom2d_Hyperbola::DumpJson ( Standard_OStream & theOStream,
int theDepth = -1 ) const
finalvirtual

Dumps the content of me into the stream.

Reimplemented from Geom2d_Conic.

◆ Eccentricity()

double Geom2d_Hyperbola::Eccentricity ( ) const
finalvirtual

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. raised if MajorRadius = 0.0.

Implements Geom2d_Conic.

◆ EvalD0()

gp_Pnt2d Geom2d_Hyperbola::EvalD0 ( const double U) const
finalvirtual

Returns in P the point of parameter U. P = C + MajorRadius * std::cosh(U) * XDir + MinorRadius * std::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.

◆ EvalD1()

Geom2d_Curve::ResD1 Geom2d_Hyperbola::EvalD1 ( const double U) const
finalvirtual

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

Implements Geom2d_Curve.

◆ EvalD2()

Geom2d_Curve::ResD2 Geom2d_Hyperbola::EvalD2 ( const double U) const
finalvirtual

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

Implements Geom2d_Curve.

◆ EvalD3()

Geom2d_Curve::ResD3 Geom2d_Hyperbola::EvalD3 ( const double U) const
finalvirtual

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

Implements Geom2d_Curve.

◆ EvalDN()

gp_Vec2d Geom2d_Hyperbola::EvalDN ( const double U,
const int N ) const
finalvirtual

For the point of parameter U of this hyperbola, computes the vector corresponding to the Nth derivative. Exceptions Standard_RangeError if N is less than 1.

Implements Geom2d_Curve.

◆ FirstParameter()

double Geom2d_Hyperbola::FirstParameter ( ) const
finalvirtual

Returns RealFirst from Standard.

Implements Geom2d_Curve.

◆ Focal()

double Geom2d_Hyperbola::Focal ( ) const

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

◆ Focus1()

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.

◆ Focus2()

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.

◆ Hypr2d()

gp_Hypr2d Geom2d_Hyperbola::Hypr2d ( ) const

Converts this hyperbola into a gp_Hypr2d one.

◆ IsClosed()

bool Geom2d_Hyperbola::IsClosed ( ) const
finalvirtual

Returns False.

Implements Geom2d_Curve.

◆ IsPeriodic()

bool Geom2d_Hyperbola::IsPeriodic ( ) const
finalvirtual

return False for an hyperbola.

Implements Geom2d_Curve.

◆ LastParameter()

double Geom2d_Hyperbola::LastParameter ( ) const
finalvirtual

returns RealLast from Standard.

Implements Geom2d_Curve.

◆ MajorRadius()

double Geom2d_Hyperbola::MajorRadius ( ) const

Returns the major or minor radius of this hyperbola. 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).

◆ MinorRadius()

double Geom2d_Hyperbola::MinorRadius ( ) const

Returns the major or minor radius of this hyperbola. 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).

◆ OtherBranch()

gp_Hypr2d Geom2d_Hyperbola::OtherBranch ( ) const

Computes the "other" branch of this hyperbola. This 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.

◆ Parameter()

double Geom2d_Hyperbola::Parameter ( ) const

Computes the parameter of this hyperbola. 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.

◆ ReversedParameter()

double Geom2d_Hyperbola::ReversedParameter ( const double U) const
finalvirtual

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

Implements Geom2d_Conic.

◆ SetHypr2d()

void Geom2d_Hyperbola::SetHypr2d ( const gp_Hypr2d & H)

Converts the gp_Hypr2d hyperbola H into this hyperbola.

◆ SetMajorRadius()

void Geom2d_Hyperbola::SetMajorRadius ( const double MajorRadius)

Assigns a value to the major or minor radius of this hyperbola. Exceptions Standard_ConstructionError if:

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

◆ SetMinorRadius()

void Geom2d_Hyperbola::SetMinorRadius ( const double MinorRadius)

Assigns a value to the major or minor radius of this hyperbola. Exceptions Standard_ConstructionError if:

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

◆ Transform()

void Geom2d_Hyperbola::Transform ( const gp_Trsf2d & T)
finalvirtual

Applies the transformation T to this hyperbola.

Implements Geom2d_Geometry.


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