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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_Hypr_HeaderFile
 #define _gp_Hypr_HeaderFile
 
 #include <gp.hxx>
 #include <gp_Ax1.hxx>
 #include <gp_Ax2.hxx>
 #include <gp_Pnt.hxx>
 #include <Standard_DomainError.hxx>
 #include <Standard_ConstructionError.hxx>
 
 //! Describes a branch of a hyperbola in 3D space.
 //! A hyperbola is defined by its major and minor radii and
 //! positioned in space with a coordinate system (a gp_Ax2
 //! 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.
 //! The origin, "X Direction" and "Y Direction" of this
 //! coordinate system together define the plane of the
 //! hyperbola. This coordinate system is the "local
 //! coordinate system" of 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 "main Direction" of the local coordinate system is a
 //! normal vector to the plane of the hyperbola. This vector
 //! gives an implicit orientation to the hyperbola. We refer to
 //! the "main Axis" of the local coordinate system as the
 //! "Axis" of the hyperbola.
 //! 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
 //! |                  ^YAxis
 //! @endcode
 //! Warning
 //! The major radius can be less than the minor radius.
 //! See Also
 //! gce_MakeHypr which provides functions for more
 //! complex hyperbola constructions
 //! Geom_Hyperbola which provides additional functions for
 //! constructing hyperbolas and works, in particular, with the
 //! parametric equations of hyperbolas
 class gp_Hypr
 {
 public:
   DEFINE_STANDARD_ALLOC
 
   //! Creates of an indefinite hyperbola.
   gp_Hypr()
       : majorRadius(RealLast()),
         minorRadius(RealFirst())
   {
   }
 
   //! Creates a hyperbola with radius theMajorRadius and
   //! theMinorRadius, positioned in the space by the
   //! coordinate system theA2 such that:
   //! -   the origin of theA2 is the center of the hyperbola,
   //! -   the "X Direction" of theA2 defines the major axis of
   //! the hyperbola, that is, the major radius
   //! theMajorRadius is measured along this axis, and
   //! -   the "Y Direction" of theA2 defines the minor axis of
   //! the hyperbola, that is, the minor radius
   //! theMinorRadius is measured along this axis.
   //! Note: This class does not prevent the creation of a
   //! hyperbola where:
   //! -   theMajorAxis is equal to theMinorAxis, or
   //! -   theMajorAxis is less than theMinorAxis.
   //! Exceptions
   //! Standard_ConstructionError if theMajorAxis or theMinorAxis is negative.
   //! Raises ConstructionError if theMajorRadius < 0.0 or theMinorRadius < 0.0
   //! Raised if theMajorRadius < 0.0 or theMinorRadius < 0.0
   gp_Hypr(const gp_Ax2&       theA2,
           const Standard_Real theMajorRadius,
           const Standard_Real theMinorRadius)
       : pos(theA2),
         majorRadius(theMajorRadius),
         minorRadius(theMinorRadius)
   {
     Standard_ConstructionError_Raise_if(theMinorRadius < 0.0 || theMajorRadius < 0.0,
                                         "gp_Hypr() - invalid construction parameters");
   }
 
   //! Modifies this hyperbola, by redefining its local coordinate
   //! system so that:
   //! -   its origin and "main Direction" become those of the
   //! axis theA1 (the "X Direction" and "Y Direction" are then
   //! recomputed in the same way as for any gp_Ax2).
   //! Raises ConstructionError if the direction of theA1 is parallel to the direction of
   //! the "XAxis" of the hyperbola.
   void SetAxis(const gp_Ax1& theA1) { pos.SetAxis(theA1); }
 
   //! Modifies this hyperbola, by redefining its local coordinate
   //! system so that its origin becomes theP.
   void SetLocation(const gp_Pnt& theP) { pos = gp_Ax2(theP, pos.Direction(), pos.XDirection()); }
 
   //! Modifies the major  radius of this hyperbola.
   //! Exceptions
   //! Standard_ConstructionError if theMajorRadius is negative.
   void SetMajorRadius(const Standard_Real theMajorRadius)
   {
     Standard_ConstructionError_Raise_if(
       theMajorRadius < 0.0,
       "gp_Hypr::SetMajorRadius() - major radius should be greater or equal zero");
     majorRadius = theMajorRadius;
   }
 
   //! Modifies the minor  radius of this hyperbola.
   //! Exceptions
   //! Standard_ConstructionError if theMinorRadius is negative.
   void SetMinorRadius(const Standard_Real theMinorRadius)
   {
     Standard_ConstructionError_Raise_if(
       theMinorRadius < 0.0,
       "gp_Hypr::SetMinorRadius() - minor radius should be greater or equal zero");
     minorRadius = theMinorRadius;
   }
 
   //! Modifies this hyperbola, by redefining its local coordinate
   //! system so that it becomes A2.
   void SetPosition(const gp_Ax2& theA2) { pos = theA2; }
 
   //! 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 and B is the minor radius. Raises ConstructionError if MajorRadius
   //! = 0.0
   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.
   //! where A is the major radius and B is the minor radius. Raises ConstructionError if MajorRadius
   //! = 0.0
   gp_Ax1 Asymptote2() const;
 
   //! Returns the axis passing through the center,
   //! and normal to the plane of this hyperbola.
   const gp_Ax1& Axis() const { return pos.Axis(); }
 
   //! Computes the branch of hyperbola which is on the positive side of the
   //! "YAxis" of <me>.
   gp_Hypr ConjugateBranch1() const
   {
     return gp_Hypr(gp_Ax2(pos.Location(), pos.Direction(), pos.YDirection()),
                    minorRadius,
                    majorRadius);
   }
 
   //! Computes the branch of hyperbola which is on the negative side of the
   //! "YAxis" of <me>.
   gp_Hypr ConjugateBranch2() const
   {
     gp_Dir aD = pos.YDirection();
     aD.Reverse();
     return gp_Hypr(gp_Ax2(pos.Location(), pos.Direction(), aD), minorRadius, majorRadius);
   }
 
   //! 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 the directrix1 and the "XAxis" is the "Location" point
   //! of the directrix1. This point is on the positive side of the
   //! "XAxis".
   gp_Ax1 Directrix1() const;
 
   //! This line is obtained by the symmetrical transformation
   //! of "Directrix1" with respect to the "YAxis" of the hyperbola.
   gp_Ax1 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_Hypr::Eccentricity() - major radius is zero");
     return sqrt(majorRadius * majorRadius + minorRadius * minorRadius) / majorRadius;
   }
 
   //! Computes the focal distance. It is the distance between the
   //! the two focus of the hyperbola.
   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_Pnt Focus1() const;
 
   //! Returns the second focus of the hyperbola. This focus is on the
   //! negative side of the "XAxis" of the hyperbola.
   gp_Pnt Focus2() const;
 
   //! Returns  the location point of the hyperbola. It is the
   //! intersection point between the "XAxis" and the "YAxis".
   const gp_Pnt& Location() const { return pos.Location(); }
 
   //! Returns the major radius of the hyperbola. It is the radius
   //! on the "XAxis" of the hyperbola.
   Standard_Real MajorRadius() const { return majorRadius; }
 
   //! Returns the minor radius of the hyperbola. It is the radius
   //! on 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_Hypr OtherBranch() const
   {
     gp_Dir aD = pos.XDirection();
     aD.Reverse();
     return gp_Hypr(gp_Ax2(pos.Location(), pos.Direction(), aD), majorRadius, minorRadius);
   }
 
   //! 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_Hypr::Parameter() - major radius is zero");
     return (minorRadius * minorRadius) / majorRadius;
   }
 
   //! Returns the coordinate system of the hyperbola.
   const gp_Ax2& Position() const { return pos; }
 
   //! Computes an axis, whose
   //! -   the origin is the center of this hyperbola, and
   //! -   the unit vector is the "X Direction"
   //! of the local coordinate system of this hyperbola.
   //! These axes are, the major axis (the "X
   //! Axis") and  of this hyperboReturns the "XAxis" of the hyperbola.
   gp_Ax1 XAxis() const { return gp_Ax1(pos.Location(), pos.XDirection()); }
 
   //! Computes an axis, whose
   //! -   the origin is the center of this hyperbola, and
   //! -   the unit vector is the "Y Direction"
   //! of the local coordinate system of this hyperbola.
   //! These axes are the minor axis (the "Y Axis") of this hyperbola
   gp_Ax1 YAxis() const { return gp_Ax1(pos.Location(), pos.YDirection()); }
 
   Standard_EXPORT void Mirror(const gp_Pnt& 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_Hypr Mirrored(const gp_Pnt& theP) const;
 
   Standard_EXPORT void Mirror(const gp_Ax1& theA1);
 
   //! 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_Hypr Mirrored(const gp_Ax1& theA1) const;
 
   Standard_EXPORT void Mirror(const gp_Ax2& theA2);
 
   //! Performs the symmetrical transformation of an hyperbola with
   //! respect to a plane. The axis placement theA2 locates the plane
   //! of the symmetry (Location, XDirection, YDirection).
   Standard_NODISCARD Standard_EXPORT gp_Hypr Mirrored(const gp_Ax2& theA2) const;
 
   void Rotate(const gp_Ax1& theA1, const Standard_Real theAng) { pos.Rotate(theA1, theAng); }
 
   //! Rotates an hyperbola. theA1 is the axis of the rotation.
   //! theAng is the angular value of the rotation in radians.
   Standard_NODISCARD gp_Hypr Rotated(const gp_Ax1& theA1, const Standard_Real theAng) const
   {
     gp_Hypr aH = *this;
     aH.pos.Rotate(theA1, theAng);
     return aH;
   }
 
   void Scale(const gp_Pnt& theP, const Standard_Real theS);
 
   //! Scales an hyperbola. theS is the scaling value.
   Standard_NODISCARD gp_Hypr Scaled(const gp_Pnt& theP, const Standard_Real theS) const;
 
   void Transform(const gp_Trsf& theT);
 
   //! Transforms an hyperbola with the transformation theT from
   //! class Trsf.
   Standard_NODISCARD gp_Hypr Transformed(const gp_Trsf& theT) const;
 
   void Translate(const gp_Vec& 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_Hypr Translated(const gp_Vec& theV) const
   {
     gp_Hypr aH = *this;
     aH.pos.Translate(theV);
     return aH;
   }
 
   void Translate(const gp_Pnt& theP1, const gp_Pnt& theP2) { pos.Translate(theP1, theP2); }
 
   //! Translates an hyperbola from the point theP1 to the point theP2.
   Standard_NODISCARD gp_Hypr Translated(const gp_Pnt& theP1, const gp_Pnt& theP2) const
   {
     gp_Hypr aH = *this;
     aH.pos.Translate(theP1, theP2);
     return aH;
   }
 
 private:
   gp_Ax2        pos;
   Standard_Real majorRadius;
   Standard_Real minorRadius;
 };
 
 //=======================================================================
 // function : Asymptote1
 // purpose :
 //=======================================================================
 inline gp_Ax1 gp_Hypr::Asymptote1() const
 {
   Standard_ConstructionError_Raise_if(majorRadius <= gp::Resolution(),
                                       "gp_Hypr::Asymptote1() - major radius is zero");
   gp_Vec aV1 = gp_Vec(pos.YDirection());
   aV1.Multiply(minorRadius / majorRadius);
   gp_Vec aV = gp_Vec(pos.XDirection());
   aV.Add(aV1);
   return gp_Ax1(pos.Location(), gp_Dir(aV));
 }
 
 //=======================================================================
 // function : Asymptote2
 // purpose :
 //=======================================================================
 inline gp_Ax1 gp_Hypr::Asymptote2() const
 {
   Standard_ConstructionError_Raise_if(majorRadius <= gp::Resolution(),
                                       "gp_Hypr::Asymptote1() - major radius is zero");
   gp_Vec aV1 = gp_Vec(pos.YDirection());
   aV1.Multiply(-minorRadius / majorRadius);
   gp_Vec aV = gp_Vec(pos.XDirection());
   aV.Add(aV1);
   return gp_Ax1(pos.Location(), gp_Dir(aV));
 }
 
 //=======================================================================
 // function : Focus1
 // purpose :
 //=======================================================================
 inline gp_Pnt gp_Hypr::Focus1() const
 {
   Standard_Real aC  = sqrt(majorRadius * majorRadius + minorRadius * minorRadius);
   const gp_Pnt& aPP = pos.Location();
   const gp_Dir& aDD = pos.XDirection();
   return gp_Pnt(aPP.X() + aC * aDD.X(), aPP.Y() + aC * aDD.Y(), aPP.Z() + aC * aDD.Z());
 }
 
 //=======================================================================
 // function : Focus2
 // purpose :
 //=======================================================================
 inline gp_Pnt gp_Hypr::Focus2() const
 {
   Standard_Real aC  = sqrt(majorRadius * majorRadius + minorRadius * minorRadius);
   const gp_Pnt& aPP = pos.Location();
   const gp_Dir& aDD = pos.XDirection();
   return gp_Pnt(aPP.X() - aC * aDD.X(), aPP.Y() - aC * aDD.Y(), aPP.Z() - aC * aDD.Z());
 }
 
 //=======================================================================
 // function : Scale
 // purpose :
 //=======================================================================
 inline void gp_Hypr::Scale(const gp_Pnt& 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_Hypr gp_Hypr::Scaled(const gp_Pnt& theP, const Standard_Real theS) const
 {
   gp_Hypr 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_Hypr::Transform(const gp_Trsf& 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_Hypr gp_Hypr::Transformed(const gp_Trsf& theT) const
 {
   gp_Hypr 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;
 }
 
 //=======================================================================
 // function : Directrix1
 // purpose :
 //=======================================================================
 inline gp_Ax1 gp_Hypr::Directrix1() const
 {
   Standard_Real anE    = Eccentricity();
   gp_XYZ        anOrig = pos.XDirection().XYZ();
   anOrig.Multiply(majorRadius / anE);
   anOrig.Add(pos.Location().XYZ());
   return gp_Ax1(gp_Pnt(anOrig), pos.YDirection());
 }
 
 //=======================================================================
 // function : Directrix2
 // purpose :
 //=======================================================================
 inline gp_Ax1 gp_Hypr::Directrix2() const
 {
   Standard_Real anE    = Eccentricity();
   gp_XYZ        anOrig = pos.XDirection().XYZ();
   anOrig.Multiply(-majorRadius / anE);
   anOrig.Add(pos.Location().XYZ());
   return gp_Ax1(gp_Pnt(anOrig), pos.YDirection());
 }
 
 #endif // _gp_Hypr_HeaderFile

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