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>
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 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. Exceptions Standard_ConstructionError if: More... | |
| void | SetMinorRadius (const Standard_Real MinorRadius) |
| Assigns a value to the minor radius of this hyperbola. 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 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_Ax1 | 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. More... | |
| gp_Ax1 | 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. 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 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 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_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. 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_Hypr | OtherBranch () const |
| Computes the "other" branch of this hyperbola. This 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 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_Pnt &P, gp_Vec &V1) const override |
| 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 override |
| 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 override |
| 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 override |
| 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) override |
| Applies the transformation T to this hyperbola. More... | |
| Handle< Geom_Geometry > | Copy () const override |
| 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 axis to the plane is A1. The XAxis and the YAxis are recomputed. 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 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 () override |
| Reverses the direction of parameterization of <me>. The local coordinate system of the conic is modified. More... | |
| GeomAbs_Shape | Continuity () const override |
| The continuity of the conic is Cn. More... | |
| Standard_Boolean | IsCN (const Standard_Integer N) const override |
| 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 the transform of the point of parameter U on <me>. More... | |
| virtual Standard_Real | ParametricTransformation (const gp_Trsf &T) const |
| Returns a coefficient to compute the parameter on the transformed curve for the transform of the point on <me>. More... | |
| Handle< Geom_Curve > | Reversed () const |
| Returns a copy of <me> reversed. More... | |
| virtual Standard_Real | Period () const |
| Returns the period of this curve. 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>. 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. 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 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 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 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 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 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 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 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.
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Creates a new object which is a copy of this hyperbola.
Implements Geom_Geometry.
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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 Geom_Curve.
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Returns the point P of parameter U and the first derivative V1.
Implements Geom_Curve.
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Returns the point P of parameter U, the first and second derivatives V1 and V2.
Implements Geom_Curve.
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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.
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The returned vector gives the value of the derivative for the order of derivation N. Raised if N < 1.
Implements Geom_Curve.
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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.
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overridevirtual |
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>.
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Returns False.
Implements Geom_Curve.
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return False for an hyperbola.
Implements Geom_Curve.
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returns RealLast from Standard.
Implements Geom_Curve.
| Standard_Real Geom_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 Geom_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_Hypr Geom_Hyperbola::OtherBranch | ( | ) | const |
Computes the "other" branch of this hyperbola. This 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.
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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 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. 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. Exceptions Standard_ConstructionError if:
- MajorRadius is less than 0.0, or
- MinorRadius is less than 0.0.Raised if MajorRadius < 0.0
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overridevirtual |
Applies the transformation T to this hyperbola.
Implements Geom_Geometry.
The documentation for this class was generated from the following file:
