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 // Copyright (c) 1991-1999 Matra Datavision
 // Copyright (c) 1999-2014 OPEN CASCADE SAS
 //
 // This file is part of Open CASCADE Technology software library.
 //
 // This library is free software; you can redistribute it and/or modify it under
 // the terms of the GNU Lesser General Public License version 2.1 as published
 // by the Free Software Foundation, with special exception defined in the file
 // OCCT_LGPL_EXCEPTION.txt. Consult the file LICENSE_LGPL_21.txt included in OCCT
 // distribution for complete text of the license and disclaimer of any warranty.
 //
 // Alternatively, this file may be used under the terms of Open CASCADE
 // commercial license or contractual agreement.
 
 #ifndef _gp_Hypr2d_HeaderFile
 #define _gp_Hypr2d_HeaderFile
 
 #include <gp.hxx>
 #include <gp_Ax22d.hxx>
 #include <gp_Ax2d.hxx>
 #include <gp_Pnt2d.hxx>
 #include <Standard_DomainError.hxx>
 #include <Standard_ConstructionError.hxx>
 
 //! 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:
 //! -   the origin is the center of the hyperbola,
 //! -   the "X Direction" defines the major axis of the hyperbola, and
 //! -   the "Y Direction" defines the minor axis of the hyperbola.
 //! This coordinate system is the "local coordinate system"
 //! of the hyperbola. The orientation of this coordinate
 //! system (direct or indirect) gives an implicit orientation to
 //! the hyperbola. In this coordinate system, the equation of
 //! the hyperbola is:
 //! X*X/(MajorRadius**2)-Y*Y/(MinorRadius**2) = 1.0
 //! The branch of the hyperbola described is the one located
 //! on the positive side of the major axis.
 //! The following schema shows the plane of the hyperbola,
 //! and in it, the respective positions of the three branches of
 //! hyperbolas constructed with the functions OtherBranch,
 //! ConjugateBranch1, and ConjugateBranch2:
 //! @code
 //! ^YAxis
 //! |
 //! FirstConjugateBranch
 //! |
 //! Other            |                Main
 //! --------------------- C ------------------------------>XAxis
 //! Branch           |                Branch
 //! |
 //! |
 //! SecondConjugateBranch
 //! |
 //! @endcode
 //! 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
 class gp_Hypr2d 
 {
 public:
 
   DEFINE_STANDARD_ALLOC
 
   //! Creates of an indefinite hyperbola.
   gp_Hypr2d()
   : majorRadius (RealLast()),
     minorRadius (RealLast())
   {}
 
   //! Creates a hyperbola with radii theMajorRadius and
   //! theMinorRadius, centered on the origin of theMajorAxis
   //! and where the unit vector of theMajorAxis is the "X
   //! Direction" of the local coordinate system of the
   //! hyperbola. This coordinate system is direct if theIsSense
   //! is true (the default value), and indirect if theIsSense is false.
   //! Warnings :
   //! It is yet  possible to create an Hyperbola with
   //! theMajorRadius <= theMinorRadius.
   //! Raises ConstructionError if theMajorRadius < 0.0 or theMinorRadius < 0.0
   gp_Hypr2d (const gp_Ax2d& theMajorAxis, const Standard_Real theMajorRadius,
             const Standard_Real theMinorRadius, const Standard_Boolean theIsSense = Standard_True)
   : majorRadius (theMajorRadius),
     minorRadius (theMinorRadius)
   {
     pos = gp_Ax22d (theMajorAxis, theIsSense);
     Standard_ConstructionError_Raise_if (theMinorRadius < 0.0 || theMajorRadius < 0.0,
       "gp_Hypr2d() - invalid construction parameters");
   }
 
   //! a hyperbola with radii theMajorRadius and
   //! theMinorRadius, positioned in the plane by coordinate system theA where:
   //! -   the origin of theA is the center of the hyperbola,
   //! -   the "X Direction" of theA defines the major axis of
   //! the hyperbola, that is, the major radius
   //! theMajorRadius is measured along this axis, and
   //! -   the "Y Direction" of theA defines the minor axis of
   //! the hyperbola, that is, the minor radius
   //! theMinorRadius is measured along this axis, and
   //! -   the orientation (direct or indirect sense) of theA
   //! gives the implicit orientation of the hyperbola.
   //! Warnings :
   //! It is yet  possible to create an Hyperbola with
   //! theMajorRadius <= theMinorRadius.
   //! Raises ConstructionError if theMajorRadius < 0.0 or theMinorRadius < 0.0
   gp_Hypr2d (const gp_Ax22d& theA, const Standard_Real theMajorRadius, const Standard_Real theMinorRadius)
   : pos (theA),
     majorRadius (theMajorRadius),
     minorRadius (theMinorRadius)
   {
     Standard_ConstructionError_Raise_if (theMinorRadius < 0.0 || theMajorRadius < 0.0,
                                          "gp_Hypr2d() - invalid construction parameters");
   }
 
   //! Modifies this hyperbola, by redefining its local
   //! coordinate system so that its origin becomes theP.
   void SetLocation (const gp_Pnt2d& theP) { pos.SetLocation (theP); }
 
   //! Modifies the major or minor radius of this hyperbola.
   //! Exceptions
   //! Standard_ConstructionError if theMajorRadius or
   //! MinorRadius is negative.
   void SetMajorRadius (const Standard_Real theMajorRadius)
   {
     Standard_ConstructionError_Raise_if (theMajorRadius < 0.0,
                                          "gp_Hypr2d::SetMajorRadius() - major radius should be greater or equal zero");
     majorRadius = theMajorRadius;
   }
 
   //! Modifies the major or minor radius of this hyperbola.
   //! Exceptions
   //! Standard_ConstructionError if MajorRadius or
   //! theMinorRadius is negative.
   void SetMinorRadius (const Standard_Real theMinorRadius)
   {
     Standard_ConstructionError_Raise_if (theMinorRadius < 0.0,
                                          "gp_Hypr2d::SetMinorRadius() - minor radius should be greater or equal zero");
     minorRadius = theMinorRadius;
   }
 
   //! Modifies this hyperbola, by redefining its local
   //! coordinate system so that it becomes theA.
   void SetAxis (const gp_Ax22d& theA) { pos.SetAxis (theA); }
 
   //! Changes the major axis of the hyperbola. The minor axis is
   //! recomputed and the location of the hyperbola too.
   void SetXAxis (const gp_Ax2d& theA) { pos.SetXAxis (theA); }
 
   //! Changes the minor axis of the hyperbola.The minor axis is
   //! recomputed and the location of the hyperbola too.
   void SetYAxis (const gp_Ax2d& theA) { pos.SetYAxis (theA); }
 
   //! 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 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 Asymptote2() const;
 
   //! Computes the coefficients of the implicit equation of
   //! the hyperbola :
   //! theA * (X**2) + theB * (Y**2) + 2*theC*(X*Y) + 2*theD*X + 2*theE*Y + theF = 0.
   Standard_EXPORT void Coefficients (Standard_Real& theA, Standard_Real& theB, Standard_Real& theC,
                                      Standard_Real& theD, Standard_Real& theE, Standard_Real& theF) const;
 
   //! Computes the branch of hyperbola which is on the positive side of the
   //! "YAxis" of <me>.
   gp_Hypr2d ConjugateBranch1() const
   {
     gp_Dir2d aV (pos.YDirection());
     Standard_Boolean isSign = (pos.XDirection().Crossed (pos.YDirection())) >= 0.0;
     return gp_Hypr2d (gp_Ax2d (pos.Location(), aV), minorRadius, majorRadius, isSign);
   }
 
   //! Computes the branch of hyperbola which is on the negative side of the
   //! "YAxis" of <me>.
   gp_Hypr2d ConjugateBranch2() const
   {
     gp_Dir2d aV (pos.YDirection().Reversed());
     Standard_Boolean isSign = (pos.XDirection().Crossed (pos.YDirection())) >= 0.0;
     return gp_Hypr2d (gp_Ax2d (pos.Location(), aV), minorRadius, majorRadius, isSign);
   }
 
   //! 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 Directrix1() const;
 
   //! This line is obtained by the symmetrical transformation
   //! of "Directrix1" with respect to the "YAxis" of the hyperbola.
   gp_Ax2d Directrix2() const;
 
   //! 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. Raises DomainError if MajorRadius = 0.0.
   Standard_Real Eccentricity() const
   {
     Standard_DomainError_Raise_if (majorRadius <= gp::Resolution(),
                                    "gp_Hypr2d::Eccentricity() - major radius is zero");
     return sqrt (majorRadius * majorRadius + minorRadius * minorRadius) / majorRadius;
   }
 
   //! Computes the focal distance. It is the distance between the
   //! "Location" of the hyperbola and "Focus1" or "Focus2".
   Standard_Real Focal() const
   {
     return 2.0 * sqrt (majorRadius * majorRadius + minorRadius * minorRadius);
   }
 
   //! Returns the first focus of the hyperbola. This focus is on the
   //! positive side of the "XAxis" of the hyperbola.
   gp_Pnt2d Focus1() const
   {
     Standard_Real aC = sqrt (majorRadius * majorRadius + minorRadius * minorRadius);
     return gp_Pnt2d (pos.Location().X() + aC * pos.XDirection().X(), pos.Location().Y() + aC * pos.XDirection().Y());
   }
 
   //! Returns the second focus of the hyperbola. This focus is on the
   //! negative side of the "XAxis" of the hyperbola.
   gp_Pnt2d Focus2() const
   {
     Standard_Real aC = sqrt(majorRadius * majorRadius + minorRadius * minorRadius);
     return gp_Pnt2d(pos.Location().X() - aC * pos.XDirection().X(), pos.Location().Y() - aC * pos.XDirection().Y());
   }
 
   //! Returns  the location point of the hyperbola.
   //! It is the intersection point between the "XAxis" and
   //! the "YAxis".
   const gp_Pnt2d& Location() const { return pos.Location(); }
 
   //! Returns the major radius of the hyperbola (it is the radius
   //! corresponding to the "XAxis" of the hyperbola).
   Standard_Real MajorRadius() const { return majorRadius; }
 
   //! Returns the minor radius of the hyperbola (it is the radius
   //! corresponding to the "YAxis" of the hyperbola).
   Standard_Real MinorRadius() const { return minorRadius; }
 
   //! Returns the branch of hyperbola obtained by doing the
   //! symmetrical transformation of <me> with respect to the
   //! "YAxis" of <me>.
   gp_Hypr2d OtherBranch() const
   {
     Standard_Boolean isSign = (pos.XDirection().Crossed (pos.YDirection())) >= 0.0;
     return gp_Hypr2d (gp_Ax2d (pos.Location(), pos.XDirection().Reversed()), majorRadius, minorRadius, isSign);
   }
 
   //! Returns p = (e * e - 1) * MajorRadius where e is the
   //! eccentricity of the hyperbola.
   //! Raises DomainError if MajorRadius = 0.0
   Standard_Real Parameter() const
   {
     Standard_DomainError_Raise_if (majorRadius <= gp::Resolution(),
                                    "gp_Hypr2d::Parameter() - major radius is zero");
     return (minorRadius * minorRadius) / majorRadius;
   }
 
   //! Returns the axisplacement of the hyperbola.
   const gp_Ax22d& Axis() const { return pos; }
 
   //! Computes an axis whose
   //! -   the origin is the center of this hyperbola, and
   //! -   the unit vector is the "X Direction" or "Y Direction"
   //! respectively of the local coordinate system of this hyperbola
   //! Returns the major axis of the hyperbola.
   gp_Ax2d XAxis() const { return pos.XAxis(); }
 
   //! Computes an axis whose
   //! -   the origin is the center of this hyperbola, and
   //! -   the unit vector is the "X Direction" or "Y Direction"
   //! respectively of the local coordinate system of this hyperbola
   //! Returns the minor axis of the hyperbola.
   gp_Ax2d YAxis() const { return pos.YAxis(); }
 
   void Reverse()
   {
     gp_Dir2d aTemp = pos.YDirection();
     aTemp.Reverse();
     pos.SetAxis (gp_Ax22d(pos.Location(), pos.XDirection(), aTemp));
   }
 
   //! 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:
   //! -   Reverse assigns the result to this hyperbola, while
   //! -   Reversed creates a new one.
   Standard_NODISCARD gp_Hypr2d Reversed() const;
 
   //! Returns true if the local coordinate system is direct
   //! and false in the other case.
   Standard_Boolean IsDirect() const
   {
     return (pos.XDirection().Crossed (pos.YDirection())) >= 0.0;
   }
 
   Standard_EXPORT void Mirror (const gp_Pnt2d& theP);
 
   //! Performs the symmetrical transformation of an hyperbola with
   //! respect  to the point theP which is the center of the symmetry.
   Standard_NODISCARD Standard_EXPORT gp_Hypr2d Mirrored (const gp_Pnt2d& theP) const;
 
   Standard_EXPORT void Mirror (const gp_Ax2d& theA);
 
   //! Performs the symmetrical transformation of an hyperbola with
   //! respect to an axis placement which is the axis of the symmetry.
   Standard_NODISCARD Standard_EXPORT gp_Hypr2d Mirrored (const gp_Ax2d& theA) const;
 
   void Rotate (const gp_Pnt2d& theP, const Standard_Real theAng) { pos.Rotate (theP, theAng); }
 
   //! Rotates an hyperbola. theP is the center of the rotation.
   //! theAng is the angular value of the rotation in radians.
   Standard_NODISCARD gp_Hypr2d Rotated (const gp_Pnt2d& theP, const Standard_Real theAng) const
   {
     gp_Hypr2d aH = *this;
     aH.pos.Rotate (theP, theAng);
     return aH;
   }
 
   void Scale (const gp_Pnt2d& theP, const Standard_Real theS);
 
   //! Scales an hyperbola. <theS> is the scaling value.
   //! If <theS> is positive only the location point is
   //! modified. But if <theS> is negative the "XAxis" is
   //! reversed and the "YAxis" too.
   Standard_NODISCARD gp_Hypr2d Scaled (const gp_Pnt2d& theP, const Standard_Real theS) const;
 
   void Transform (const gp_Trsf2d& theT);
 
   //! Transforms an hyperbola with the transformation theT from
   //! class Trsf2d.
   Standard_NODISCARD gp_Hypr2d Transformed (const gp_Trsf2d& theT) const;
 
   void Translate (const gp_Vec2d& theV) { pos.Translate (theV); }
 
   //! Translates an hyperbola in the direction of the vector theV.
   //! The magnitude of the translation is the vector's magnitude.
   Standard_NODISCARD gp_Hypr2d Translated (const gp_Vec2d& theV) const
   {
     gp_Hypr2d aH = *this;
     aH.pos.Translate (theV);
     return aH;
   }
 
   void Translate(const gp_Pnt2d& theP1, const gp_Pnt2d& theP2) { pos.Translate (theP1, theP2); }
 
   //! Translates an hyperbola from the point theP1 to the point theP2.
   Standard_NODISCARD gp_Hypr2d Translated (const gp_Pnt2d& theP1, const gp_Pnt2d& theP2) const
   {
     gp_Hypr2d aH = *this;
     aH.pos.Translate (theP1, theP2);
     return aH;
   }
 
 private:
 
   gp_Ax22d pos;
   Standard_Real majorRadius;
   Standard_Real minorRadius;
 
 };
 
 //=======================================================================
 //function : Asymptote1
 // purpose :
 //=======================================================================
 inline gp_Ax2d gp_Hypr2d::Asymptote1() const 
 {
   Standard_ConstructionError_Raise_if (majorRadius <= gp::Resolution(),
                                        "gp_Hypr2d::Asymptote1() - major radius is zero");
   gp_Dir2d aVdir = pos.XDirection();
   gp_XY aCoord1 (pos.YDirection().XY());
   gp_XY aCoord2 = aCoord1.Multiplied (minorRadius / majorRadius);
   aCoord1.Add (aCoord2);
   aVdir.SetXY (aCoord1);
   return gp_Ax2d (pos.Location(), aVdir);
 }
 
 //=======================================================================
 //function : Asymptote2
 // purpose :
 //=======================================================================
 inline gp_Ax2d gp_Hypr2d::Asymptote2() const
 {
   Standard_ConstructionError_Raise_if (majorRadius <= gp::Resolution(),
                                        "gp_Hypr2d::Asymptote2() - major radius is zero");
   gp_Vec2d aVdir = pos.XDirection();
   gp_XY  aCoord1 (pos.YDirection().XY());
   gp_XY  aCoord2 = aCoord1.Multiplied (-minorRadius / majorRadius);
   aCoord1.Add (aCoord2);
   aVdir.SetXY (aCoord1);
   return gp_Ax2d (pos.Location(), aVdir);
 }
 
 //=======================================================================
 //function : Directrix1
 // purpose :
 //=======================================================================
 inline gp_Ax2d gp_Hypr2d::Directrix1() const 
 {
   Standard_Real anE = Eccentricity();
   gp_XY anOrig = pos.XDirection().XY();
   anOrig.Multiply (majorRadius / anE);
   anOrig.Add (pos.Location().XY());
   return gp_Ax2d (gp_Pnt2d (anOrig), gp_Dir2d (pos.YDirection()));
 }
 
 //=======================================================================
 //function : Directrix2
 // purpose :
 //=======================================================================
 inline gp_Ax2d gp_Hypr2d::Directrix2() const
 {
   Standard_Real anE = Eccentricity();
   gp_XY anOrig = pos.XDirection().XY();
   anOrig.Multiply (Parameter() / anE);
   anOrig.Add (Focus1().XY());
   return gp_Ax2d (gp_Pnt2d (anOrig), gp_Dir2d (pos.YDirection()));
 }
 
 //=======================================================================
 //function : Reversed
 // purpose :
 //=======================================================================
 inline gp_Hypr2d gp_Hypr2d::Reversed() const
 {
   gp_Hypr2d aH = *this;
   gp_Dir2d aTemp = pos.YDirection();
   aTemp.Reverse ();
   aH.pos.SetAxis (gp_Ax22d (pos.Location(),pos.XDirection(), aTemp));
   return aH;
 }
 
 //=======================================================================
 //function : Scale
 // purpose :
 //=======================================================================
 inline void gp_Hypr2d::Scale (const gp_Pnt2d& theP, const Standard_Real theS)
 { 
   majorRadius *= theS;
   if (majorRadius < 0)
   {
     majorRadius = -majorRadius;
   }
   minorRadius *= theS;
   if (minorRadius < 0)
   {
     minorRadius = -minorRadius;
   }
   pos.Scale (theP, theS);
 }
 
 //=======================================================================
 //function : Scaled
 // purpose :
 //=======================================================================
 inline gp_Hypr2d gp_Hypr2d::Scaled (const gp_Pnt2d& theP, const Standard_Real theS) const
 {
   gp_Hypr2d aH = *this;
   aH.majorRadius *= theS;
   if (aH.majorRadius < 0)
   {
     aH.majorRadius = -aH.majorRadius;
   }
   aH.minorRadius *= theS;
   if (aH.minorRadius < 0)
   {
     aH.minorRadius = -aH.minorRadius;
   }
   aH.pos.Scale (theP, theS);
   return aH; 
 }
 
 //=======================================================================
 //function : Transform
 // purpose :
 //=======================================================================
 inline void gp_Hypr2d::Transform (const gp_Trsf2d& theT)
 {
   majorRadius *= theT.ScaleFactor();
   if (majorRadius < 0)
   {
     majorRadius = -majorRadius;
   }
   minorRadius *= theT.ScaleFactor();
   if (minorRadius < 0)
   {
     minorRadius = -minorRadius;
   }
   pos.Transform (theT);
 }
 
 //=======================================================================
 //function : Transformed
 // purpose :
 //=======================================================================
 inline gp_Hypr2d gp_Hypr2d::Transformed (const gp_Trsf2d& theT) const
 {
   gp_Hypr2d aH = *this;
   aH.majorRadius *= theT.ScaleFactor();
   if (aH.majorRadius < 0)
   {
     aH.majorRadius = -aH.majorRadius;
   }
   aH.minorRadius *= theT.ScaleFactor();
   if (aH.minorRadius < 0)
   {
     aH.minorRadius = -aH.minorRadius;
   }
   aH.pos.Transform (theT);
   return aH;
 }
 
 #endif // _gp_Hypr2d_HeaderFile

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