// 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.
  constexpr gp_Hypr2d() noexcept
      : 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
  constexpr gp_Hypr2d(const gp_Ax2d& theMajorAxis,
                      const double   theMajorRadius,
                      const double   theMinorRadius,
                      const bool     theIsSense = true)
      : pos(theMajorAxis, theIsSense),
        majorRadius(theMajorRadius),
        minorRadius(theMinorRadius)
  {
    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
  constexpr gp_Hypr2d(const gp_Ax22d& theA,
                      const double    theMajorRadius,
                      const double    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.
  constexpr void SetLocation(const gp_Pnt2d& theP) noexcept { pos.SetLocation(theP); }

  //! Modifies the major or minor radius of this hyperbola.
  //! Exceptions
  //! Standard_ConstructionError if theMajorRadius or
  //! MinorRadius is negative.
  void SetMajorRadius(const double 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 double 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.
  constexpr void SetAxis(const gp_Ax22d& theA) noexcept { pos.SetAxis(theA); }

  //! Changes the major axis of the hyperbola. The minor axis is
  //! recomputed and the location of the hyperbola too.
  constexpr 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.
  constexpr 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(double& theA,
                                    double& theB,
                                    double& theC,
                                    double& theD,
                                    double& theE,
                                    double& theF) const;

  //! Computes the branch of hyperbola which is on the positive side of the
  //! "YAxis" of <me>.
  gp_Hypr2d ConjugateBranch1() const noexcept
  {
    gp_Dir2d aV(pos.YDirection());
    bool     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 noexcept
  {
    gp_Dir2d aV(pos.YDirection().Reversed());
    bool     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.
  double 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".
  double Focal() const noexcept
  {
    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 noexcept
  {
    double 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 noexcept
  {
    double 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".
  constexpr const gp_Pnt2d& Location() const noexcept { return pos.Location(); }

  //! Returns the major radius of the hyperbola (it is the radius
  //! corresponding to the "XAxis" of the hyperbola).
  constexpr double MajorRadius() const noexcept { return majorRadius; }

  //! Returns the minor radius of the hyperbola (it is the radius
  //! corresponding to the "YAxis" of the hyperbola).
  constexpr double MinorRadius() const noexcept { 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 noexcept
  {
    bool 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
  double 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.
  constexpr const gp_Ax22d& Axis() const noexcept { 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 noexcept { 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 noexcept { return pos.YAxis(); }

  void Reverse() noexcept
  {
    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.
  [[nodiscard]] gp_Hypr2d Reversed() const noexcept;

  //! Returns true if the local coordinate system is direct
  //! and false in the other case.
  constexpr bool IsDirect() const noexcept
  {
    return (pos.XDirection().Crossed(pos.YDirection())) >= 0.0;
  }

  Standard_EXPORT void Mirror(const gp_Pnt2d& theP) noexcept;

  //! Performs the symmetrical transformation of an hyperbola with
  //! respect to the point theP which is the center of the symmetry.
  [[nodiscard]] Standard_EXPORT gp_Hypr2d Mirrored(const gp_Pnt2d& theP) const noexcept;

  Standard_EXPORT void Mirror(const gp_Ax2d& theA) noexcept;

  //! Performs the symmetrical transformation of an hyperbola with
  //! respect to an axis placement which is the axis of the symmetry.
  [[nodiscard]] Standard_EXPORT gp_Hypr2d Mirrored(const gp_Ax2d& theA) const noexcept;

  void Rotate(const gp_Pnt2d& theP, const double 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.
  [[nodiscard]] gp_Hypr2d Rotated(const gp_Pnt2d& theP, const double theAng) const
  {
    gp_Hypr2d aH = *this;
    aH.pos.Rotate(theP, theAng);
    return aH;
  }

  void Scale(const gp_Pnt2d& theP, const double 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.
  [[nodiscard]] gp_Hypr2d Scaled(const gp_Pnt2d& theP, const double theS) const;

  void Transform(const gp_Trsf2d& theT);

  //! Transforms an hyperbola with the transformation theT from
  //! class Trsf2d.
  [[nodiscard]] gp_Hypr2d Transformed(const gp_Trsf2d& theT) const;

  constexpr void Translate(const gp_Vec2d& theV) noexcept { pos.Translate(theV); }

  //! Translates an hyperbola in the direction of the vector theV.
  //! The magnitude of the translation is the vector's magnitude.
  [[nodiscard]] constexpr gp_Hypr2d Translated(const gp_Vec2d& theV) const noexcept
  {
    gp_Hypr2d aH = *this;
    aH.pos.Translate(theV);
    return aH;
  }

  constexpr void Translate(const gp_Pnt2d& theP1, const gp_Pnt2d& theP2) noexcept
  {
    pos.Translate(theP1, theP2);
  }

  //! Translates an hyperbola from the point theP1 to the point theP2.
  [[nodiscard]] constexpr gp_Hypr2d Translated(const gp_Pnt2d& theP1,
                                               const gp_Pnt2d& theP2) const noexcept
  {
    gp_Hypr2d aH = *this;
    aH.pos.Translate(theP1, theP2);
    return aH;
  }

private:
  gp_Ax22d pos;
  double   majorRadius;
  double   minorRadius;
};

//=================================================================================================

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);
}

//=================================================================================================

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);
}

//=================================================================================================

inline gp_Ax2d gp_Hypr2d::Directrix1() const
{
  double 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()));
}

//=================================================================================================

inline gp_Ax2d gp_Hypr2d::Directrix2() const
{
  double 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()));
}

//=================================================================================================

inline gp_Hypr2d gp_Hypr2d::Reversed() const noexcept
{
  gp_Hypr2d aH    = *this;
  gp_Dir2d  aTemp = pos.YDirection();
  aTemp.Reverse();
  aH.pos.SetAxis(gp_Ax22d(pos.Location(), pos.XDirection(), aTemp));
  return aH;
}

//=================================================================================================

inline void gp_Hypr2d::Scale(const gp_Pnt2d& theP, const double theS)
{
  majorRadius *= theS;
  if (majorRadius < 0)
  {
    majorRadius = -majorRadius;
  }
  minorRadius *= theS;
  if (minorRadius < 0)
  {
    minorRadius = -minorRadius;
  }
  pos.Scale(theP, theS);
}

//=================================================================================================

inline gp_Hypr2d gp_Hypr2d::Scaled(const gp_Pnt2d& theP, const double 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;
}

//=================================================================================================

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);
}

//=================================================================================================

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