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>
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. Exceptions Standard_ConstructionError if: More... | |
| void | SetMinorRadius (const Standard_Real MinorRadius) |
| Assigns a value to the major or minor radius of this hyperbola. 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 override |
| Computes the parameter on the reversed hyperbola, for the point of parameter U on this hyperbola. For a hyperbola, the returned value is -U. More... | |
| Standard_Real | FirstParameter () const override |
| Returns RealFirst from Standard. More... | |
| Standard_Real | LastParameter () const override |
| returns RealLast from Standard. More... | |
| Standard_Boolean | IsClosed () const override |
| Returns False. More... | |
| Standard_Boolean | IsPeriodic () const override |
| return False for an hyperbola. More... | |
| 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. More... | |
| 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. More... | |
| 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. More... | |
| 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. 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 override |
| 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. 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. 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 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 ---------------------------------------—>XAxis 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. 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. More... | |
| void | D0 (const Standard_Real U, gp_Pnt2d &P) const override |
| Returns in P the point of parameter U. 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 override |
| 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 override |
| 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 override |
| 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 override |
| 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. More... | |
| void | Transform (const gp_Trsf2d &T) override |
| Applies the transformation T to this hyperbola. More... | |
| Handle< Geom2d_Geometry > | Copy () const override |
| 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 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 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 system fully, by assigning A as this coordinate system. More... | |
| 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&. 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 () override |
| Reverses the direction of parameterization of <me>. The local coordinate system of the conic is modified. More... | |
| GeomAbs_Shape | Continuity () const override |
| Returns GeomAbs_CN which is the global continuity of any conic. More... | |
| Standard_Boolean | IsCN (const Standard_Integer N) const override |
| 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 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 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 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>. 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. More... | |
| 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. More... | |
| 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. More... | |
| void | Rotate (const gp_Pnt2d &P, const Standard_Real Ang) |
| Rotates a Geometry. 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) |
| 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 override |
| 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 const opencascade::handle< Standard_Type > & | DynamicType () const |
| Returns a type descriptor about this object. More... | |
| Standard_Boolean | IsInstance (const opencascade::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 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. 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... | |
| Standard_Transient * | This () 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. More... | |
| Standard_Integer | GetRefCount () const |
| Get the reference counter of this object. More... | |
| void | IncrementRefCounter () const |
| Increments the reference counter of this object. More... | |
| Standard_Integer | DecrementRefCounter () const |
| Decrements the reference counter of this object; returns the decremented value. More... | |
Additional Inherited Members | |
| Public Types inherited from Standard_Transient | |
| typedef void | base_type |
| Returns a type descriptor about this object. More... | |
| Static Public Member Functions inherited from Standard_Transient | |
| static const char * | get_type_name () |
| Returns a type descriptor about this object. More... | |
| static const opencascade::handle< Standard_Type > & | get_type_descriptor () |
| Returns type descriptor of Standard_Transient class. More... | |
| 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 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. 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. Note: The diagram given under the class purpose indicates where these two branches of hyperbola are positioned in relation to this branch of hyperbola.
|
overridevirtual |
Creates a new object which is a copy of this hyperbola.
Implements Geom2d_Geometry.
|
overridevirtual |
Returns in P the point of parameter U. 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.
|
overridevirtual |
Returns the point P of parameter U and the first derivative V1.
Implements Geom2d_Curve.
|
overridevirtual |
Returns the point P of parameter U, the first and second derivatives V1 and V2.
Implements Geom2d_Curve.
|
overridevirtual |
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.
|
overridevirtual |
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.
|
overridevirtual |
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.
|
overridevirtual |
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.
|
overridevirtual |
Returns False.
Implements Geom2d_Curve.
|
overridevirtual |
return False for an hyperbola.
Implements Geom2d_Curve.
|
overridevirtual |
returns RealLast from Standard.
Implements Geom2d_Curve.
| Standard_Real 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).
| Standard_Real 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).
| 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 ---------------------------------------—>XAxis 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. 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.
|
overridevirtual |
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.
| 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. 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. Exceptions Standard_ConstructionError if:
- MajorRadius is less than 0.0,
- MinorRadius is less than 0.0.
|
overridevirtual |
Applies the transformation T to this hyperbola.
Implements Geom2d_Geometry.
The documentation for this class was generated from the following file:
