Open CASCADE Technology
7.5.0

Describes a branch of a hyperbola in the plane (2D space). A hyperbola is defined by its major and minor radii, and positioned in the plane with a coordinate system (a gp_Ax22d object) of which: More...
#include <gp_Hypr2d.hxx>
Public Member Functions  
gp_Hypr2d ()  
Creates of an indefinite hyperbola. More...  
gp_Hypr2d (const gp_Ax2d &MajorAxis, const Standard_Real MajorRadius, const Standard_Real MinorRadius, const Standard_Boolean Sense=Standard_True)  
Creates a hyperbola with radii MajorRadius and MinorRadius, centered on the origin of MajorAxis and where the unit vector of MajorAxis is the "X
Direction" of the local coordinate system of the hyperbola. This coordinate system is direct if Sense is true (the default value), and indirect if Sense is false. Warnings : It is yet possible to create an Hyperbola with MajorRadius <= MinorRadius. Raises ConstructionError if MajorRadius < 0.0 or MinorRadius < 0.0. More...  
gp_Hypr2d (const gp_Ax22d &A, const Standard_Real MajorRadius, const Standard_Real MinorRadius)  
a hyperbola with radii MajorRadius and MinorRadius, positioned in the plane by coordinate system A where: More...  
void  SetLocation (const gp_Pnt2d &P) 
Modifies this hyperbola, by redefining its local coordinate system so that its origin becomes P. More...  
void  SetMajorRadius (const Standard_Real MajorRadius) 
Modifies the major or minor radius of this hyperbola. Exceptions Standard_ConstructionError if MajorRadius or MinorRadius is negative. More...  
void  SetMinorRadius (const Standard_Real MinorRadius) 
Modifies the major or minor radius of this hyperbola. Exceptions Standard_ConstructionError if MajorRadius or MinorRadius is negative. More...  
void  SetAxis (const gp_Ax22d &A) 
Modifies this hyperbola, by redefining its local coordinate system so that it becomes A. More...  
void  SetXAxis (const gp_Ax2d &A) 
Changes the major axis of the hyperbola. The minor axis is recomputed and the location of the hyperbola too. More...  
void  SetYAxis (const gp_Ax2d &A) 
Changes the minor axis of the hyperbola.The minor axis is recomputed and the location of the hyperbola too. 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 the minor radius of the hyperbola. Raises ConstructionError 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 the minor radius of the hyperbola. Raises ConstructionError if MajorRadius = 0.0. More...  
void  Coefficients (Standard_Real &A, Standard_Real &B, Standard_Real &C, Standard_Real &D, Standard_Real &E, Standard_Real &F) const 
Computes the coefficients of the implicit equation of the hyperbola : A * (X**2) + B * (Y**2) + 2*C*(X*Y) + 2*D*X + 2*E*Y + F = 0. More...  
gp_Hypr2d  ConjugateBranch1 () const 
Computes the branch of hyperbola which is on the positive side of the "YAxis" of <me>. More...  
gp_Hypr2d  ConjugateBranch2 () const 
Computes the branch of hyperbola which is on the negative side of the "YAxis" of <me>. More...  
gp_Ax2d  Directrix1 () const 
Computes the directrix which 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 the "Directrix1" and the "XAxis" is the "Location" point of the "Directrix1". This point is on the positive side of the "XAxis". More...  
gp_Ax2d  Directrix2 () const 
This line is obtained by the symmetrical transformation of "Directrix1" with respect to the "YAxis" of the hyperbola. More...  
Standard_Real  Eccentricity () const 
Returns the excentricity of the hyperbola (e > 1). If f is the distance between the location of the hyperbola and the Focus1 then the eccentricity e = f / MajorRadius. Raises DomainError if MajorRadius = 0.0. More...  
Standard_Real  Focal () const 
Computes the focal distance. It is the distance between the "Location" of the hyperbola and "Focus1" or "Focus2". 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...  
const gp_Pnt2d &  Location () const 
Returns the location point of the hyperbola. It is the intersection point between the "XAxis" and the "YAxis". More...  
Standard_Real  MajorRadius () const 
Returns the major radius of the hyperbola (it is the radius corresponding to the "XAxis" of the hyperbola). More...  
Standard_Real  MinorRadius () const 
Returns the minor radius of the hyperbola (it is the radius corresponding to the "YAxis" of the hyperbola). More...  
gp_Hypr2d  OtherBranch () const 
Returns the branch of hyperbola obtained by doing the symmetrical transformation of <me> with respect to the "YAxis" of <me>. More...  
Standard_Real  Parameter () const 
Returns p = (e * e  1) * MajorRadius where e is the eccentricity of the hyperbola. Raises DomainError if MajorRadius = 0.0. More...  
const gp_Ax22d &  Axis () const 
Returns the axisplacement of the hyperbola. More...  
gp_Ax2d  XAxis () const 
Computes an axis whose. More...  
gp_Ax2d  YAxis () const 
Computes an axis whose. More...  
void  Reverse () 
gp_Hypr2d  Reversed () const 
Reverses the orientation of the local coordinate system of this hyperbola (the "Y Axis" is reversed). Therefore, the implicit orientation of this hyperbola is reversed. Note: More...  
Standard_Boolean  IsDirect () const 
Returns true if the local coordinate system is direct and false in the other case. More...  
void  Mirror (const gp_Pnt2d &P) 
gp_Hypr2d  Mirrored (const gp_Pnt2d &P) const 
Performs the symmetrical transformation of an hyperbola with respect to the point P which is the center of the symmetry. More...  
void  Mirror (const gp_Ax2d &A) 
gp_Hypr2d  Mirrored (const gp_Ax2d &A) const 
Performs the symmetrical transformation of an hyperbola with respect to an axis placement which is the axis of the symmetry. More...  
void  Rotate (const gp_Pnt2d &P, const Standard_Real Ang) 
gp_Hypr2d  Rotated (const gp_Pnt2d &P, const Standard_Real Ang) const 
Rotates an hyperbola. 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) 
gp_Hypr2d  Scaled (const gp_Pnt2d &P, const Standard_Real S) const 
Scales an hyperbola. <S> is the scaling value. If <S> is positive only the location point is modified. But if <S> is negative the "XAxis" is reversed and the "YAxis" too. More...  
void  Transform (const gp_Trsf2d &T) 
gp_Hypr2d  Transformed (const gp_Trsf2d &T) const 
Transforms an hyperbola with the transformation T from class Trsf2d. More...  
void  Translate (const gp_Vec2d &V) 
gp_Hypr2d  Translated (const gp_Vec2d &V) const 
Translates an hyperbola in the direction of the vector V. The magnitude of the translation is the vector's magnitude. More...  
void  Translate (const gp_Pnt2d &P1, const gp_Pnt2d &P2) 
gp_Hypr2d  Translated (const gp_Pnt2d &P1, const gp_Pnt2d &P2) const 
Translates an hyperbola from the point P1 to the point P2. More...  
Describes a branch of a hyperbola in the plane (2D space). A hyperbola is defined by its major and minor radii, and positioned in the plane with a coordinate system (a gp_Ax22d object) of which:
Warning The major radius can be less than the minor radius. See Also gce_MakeHypr2d which provides functions for more complex hyperbola constructions Geom2d_Hyperbola which provides additional functions for constructing hyperbolas and works, in particular, with the parametric equations of hyperbolas
gp_Hypr2d::gp_Hypr2d  (  ) 
Creates of an indefinite hyperbola.
gp_Hypr2d::gp_Hypr2d  (  const gp_Ax2d &  MajorAxis, 
const Standard_Real  MajorRadius,  
const Standard_Real  MinorRadius,  
const Standard_Boolean  Sense = Standard_True 

) 
Creates a hyperbola with radii MajorRadius and MinorRadius, centered on the origin of MajorAxis and where the unit vector of MajorAxis is the "X Direction" of the local coordinate system of the hyperbola. This coordinate system is direct if Sense is true (the default value), and indirect if Sense is false. Warnings : It is yet possible to create an Hyperbola with MajorRadius <= MinorRadius. Raises ConstructionError if MajorRadius < 0.0 or MinorRadius < 0.0.
gp_Hypr2d::gp_Hypr2d  (  const gp_Ax22d &  A, 
const Standard_Real  MajorRadius,  
const Standard_Real  MinorRadius  
) 
a hyperbola with radii MajorRadius and MinorRadius, positioned in the plane by coordinate system A where:
gp_Ax2d gp_Hypr2d::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 the minor radius of the hyperbola. Raises ConstructionError if MajorRadius = 0.0.
gp_Ax2d gp_Hypr2d::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 the minor radius of the hyperbola. Raises ConstructionError if MajorRadius = 0.0.
const gp_Ax22d& gp_Hypr2d::Axis  (  )  const 
Returns the axisplacement of the hyperbola.
void gp_Hypr2d::Coefficients  (  Standard_Real &  A, 
Standard_Real &  B,  
Standard_Real &  C,  
Standard_Real &  D,  
Standard_Real &  E,  
Standard_Real &  F  
)  const 
Computes the coefficients of the implicit equation of the hyperbola : A * (X**2) + B * (Y**2) + 2*C*(X*Y) + 2*D*X + 2*E*Y + F = 0.
gp_Hypr2d gp_Hypr2d::ConjugateBranch1  (  )  const 
Computes the branch of hyperbola which is on the positive side of the "YAxis" of <me>.
gp_Hypr2d gp_Hypr2d::ConjugateBranch2  (  )  const 
Computes the branch of hyperbola which is on the negative side of the "YAxis" of <me>.
gp_Ax2d gp_Hypr2d::Directrix1  (  )  const 
Computes the directrix which 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 the "Directrix1" and the "XAxis" is the "Location" point of the "Directrix1". This point is on the positive side of the "XAxis".
gp_Ax2d gp_Hypr2d::Directrix2  (  )  const 
This line is obtained by the symmetrical transformation of "Directrix1" with respect to the "YAxis" of the hyperbola.
Standard_Real gp_Hypr2d::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. Raises DomainError if MajorRadius = 0.0.
Standard_Real gp_Hypr2d::Focal  (  )  const 
Computes the focal distance. It is the distance between the "Location" of the hyperbola and "Focus1" or "Focus2".
gp_Pnt2d gp_Hypr2d::Focus1  (  )  const 
Returns the first focus of the hyperbola. This focus is on the positive side of the "XAxis" of the hyperbola.
gp_Pnt2d gp_Hypr2d::Focus2  (  )  const 
Returns the second focus of the hyperbola. This focus is on the negative side of the "XAxis" of the hyperbola.
Standard_Boolean gp_Hypr2d::IsDirect  (  )  const 
Returns true if the local coordinate system is direct and false in the other case.
const gp_Pnt2d& gp_Hypr2d::Location  (  )  const 
Returns the location point of the hyperbola. It is the intersection point between the "XAxis" and the "YAxis".
Standard_Real gp_Hypr2d::MajorRadius  (  )  const 
Returns the major radius of the hyperbola (it is the radius corresponding to the "XAxis" of the hyperbola).
Standard_Real gp_Hypr2d::MinorRadius  (  )  const 
Returns the minor radius of the hyperbola (it is the radius corresponding to the "YAxis" of the hyperbola).
void gp_Hypr2d::Mirror  (  const gp_Pnt2d &  P  ) 
void gp_Hypr2d::Mirror  (  const gp_Ax2d &  A  ) 
Performs the symmetrical transformation of an hyperbola with respect to the point P which is the center of the symmetry.
Performs the symmetrical transformation of an hyperbola with respect to an axis placement which is the axis of the symmetry.
gp_Hypr2d gp_Hypr2d::OtherBranch  (  )  const 
Returns the branch of hyperbola obtained by doing the symmetrical transformation of <me> with respect to the "YAxis" of <me>.
Standard_Real gp_Hypr2d::Parameter  (  )  const 
Returns p = (e * e  1) * MajorRadius where e is the eccentricity of the hyperbola. Raises DomainError if MajorRadius = 0.0.
void gp_Hypr2d::Reverse  (  ) 
gp_Hypr2d gp_Hypr2d::Reversed  (  )  const 
Reverses the orientation of the local coordinate system of this hyperbola (the "Y Axis" is reversed). Therefore, the implicit orientation of this hyperbola is reversed. Note:
void gp_Hypr2d::Rotate  (  const gp_Pnt2d &  P, 
const Standard_Real  Ang  
) 
gp_Hypr2d gp_Hypr2d::Rotated  (  const gp_Pnt2d &  P, 
const Standard_Real  Ang  
)  const 
Rotates an hyperbola. P is the center of the rotation. Ang is the angular value of the rotation in radians.
void gp_Hypr2d::Scale  (  const gp_Pnt2d &  P, 
const Standard_Real  S  
) 
gp_Hypr2d gp_Hypr2d::Scaled  (  const gp_Pnt2d &  P, 
const Standard_Real  S  
)  const 
Scales an hyperbola. <S> is the scaling value. If <S> is positive only the location point is modified. But if <S> is negative the "XAxis" is reversed and the "YAxis" too.
void gp_Hypr2d::SetAxis  (  const gp_Ax22d &  A  ) 
Modifies this hyperbola, by redefining its local coordinate system so that it becomes A.
void gp_Hypr2d::SetLocation  (  const gp_Pnt2d &  P  ) 
Modifies this hyperbola, by redefining its local coordinate system so that its origin becomes P.
void gp_Hypr2d::SetMajorRadius  (  const Standard_Real  MajorRadius  ) 
Modifies the major or minor radius of this hyperbola. Exceptions Standard_ConstructionError if MajorRadius or MinorRadius is negative.
void gp_Hypr2d::SetMinorRadius  (  const Standard_Real  MinorRadius  ) 
Modifies the major or minor radius of this hyperbola. Exceptions Standard_ConstructionError if MajorRadius or MinorRadius is negative.
void gp_Hypr2d::SetXAxis  (  const gp_Ax2d &  A  ) 
Changes the major axis of the hyperbola. The minor axis is recomputed and the location of the hyperbola too.
void gp_Hypr2d::SetYAxis  (  const gp_Ax2d &  A  ) 
Changes the minor axis of the hyperbola.The minor axis is recomputed and the location of the hyperbola too.
void gp_Hypr2d::Transform  (  const gp_Trsf2d &  T  ) 
Transforms an hyperbola with the transformation T from class Trsf2d.
void gp_Hypr2d::Translate  (  const gp_Vec2d &  V  ) 
Translates an hyperbola in the direction of the vector V. The magnitude of the translation is the vector's magnitude.
Translates an hyperbola from the point P1 to the point P2.
gp_Ax2d gp_Hypr2d::XAxis  (  )  const 
Computes an axis whose.
gp_Ax2d gp_Hypr2d::YAxis  (  )  const 
Computes an axis whose.