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 // Copyright (c) 2025 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 _GeomEval_HypParaboloidSurface_HeaderFile
 #define _GeomEval_HypParaboloidSurface_HeaderFile
 
 #include <Geom_ElementarySurface.hxx>
 
 //! Describes a hyperbolic paraboloid (saddle surface).
 //!
 //! A hyperbolic paraboloid is defined by two semi-axis lengths A and B,
 //! and is positioned in space by a coordinate system (a gp_Ax3 object),
 //! the origin of which is the saddle point.
 //!
 //! The parametric equation (rectangular parametrization) is:
 //! @code
 //!   P(u,v) = O + u*XDir + v*YDir + (u^2/A^2 - v^2/B^2)*ZDir
 //! @endcode
 //! where:
 //! - O, XDir, YDir and ZDir are respectively the origin,
 //!   the "X Direction", the "Y Direction" and the "Z Direction"
 //!   of its local coordinate system, and
 //! - A and B are the semi-axis lengths (both > 0).
 //!
 //! The parametric range is:
 //! - (-inf, +inf) for u, and
 //! - (-inf, +inf) for v.
 //!
 //! The surface is doubly ruled, not periodic, and not closed.
 //!
 //! The implicit equation in local coordinates is:
 //! @code
 //!   X^2/A^2 - Y^2/B^2 - Z = 0
 //! @endcode
 class GeomEval_HypParaboloidSurface : public Geom_ElementarySurface
 {
 public:
   //! Creates a hyperbolic paraboloid surface with the given local coordinate system
   //! and semi-axis lengths.
   //! @param[in] thePosition the local coordinate system
   //! @param[in] theA the first semi-axis length (must be > 0)
   //! @param[in] theB the second semi-axis length (must be > 0)
   //! @throw Standard_ConstructionError if theA <= 0 or theB <= 0
   Standard_EXPORT GeomEval_HypParaboloidSurface(const gp_Ax3& thePosition,
                                                 double        theA,
                                                 double        theB);
 
   //! Returns the first semi-axis length A.
   Standard_EXPORT double SemiAxisA() const;
 
   //! Returns the second semi-axis length B.
   Standard_EXPORT double SemiAxisB() const;
 
   //! Assigns the value theA to the first semi-axis length.
   //! @param[in] theA the new first semi-axis length (must be > 0)
   //! @throw Standard_ConstructionError if theA <= 0
   Standard_EXPORT void SetSemiAxisA(double theA);
 
   //! Assigns the value theB to the second semi-axis length.
   //! @param[in] theB the new second semi-axis length (must be > 0)
   //! @throw Standard_ConstructionError if theB <= 0
   Standard_EXPORT void SetSemiAxisB(double theB);
 
   //! Reversal is not supported for this eval surface.
   //! @throw Standard_NotImplemented
   Standard_EXPORT void UReverse() final;
 
   //! Reversal is not supported for this eval surface.
   //! @throw Standard_NotImplemented
   Standard_EXPORT void VReverse() final;
 
   //! Reversal is not supported for this eval surface.
   //! @throw Standard_NotImplemented
   Standard_EXPORT double UReversedParameter(const double U) const final;
 
   //! Reversal is not supported for this eval surface.
   //! @throw Standard_NotImplemented
   Standard_EXPORT double VReversedParameter(const double V) const final;
 
   //! Returns the parametric bounds U1, U2, V1 and V2 of this surface.
   //! @param[out] U1 lower U bound (-Precision::Infinite())
   //! @param[out] U2 upper U bound (Precision::Infinite())
   //! @param[out] V1 lower V bound (-Precision::Infinite())
   //! @param[out] V2 upper V bound (Precision::Infinite())
   Standard_EXPORT void Bounds(double& U1, double& U2, double& V1, double& V2) const final;
 
   //! Returns False. The hyperbolic paraboloid is not closed in U.
   Standard_EXPORT bool IsUClosed() const final;
 
   //! Returns False. The hyperbolic paraboloid is not closed in V.
   Standard_EXPORT bool IsVClosed() const final;
 
   //! Returns False. The hyperbolic paraboloid is not periodic in U.
   Standard_EXPORT bool IsUPeriodic() const final;
 
   //! Returns False. The hyperbolic paraboloid is not periodic in V.
   Standard_EXPORT bool IsVPeriodic() const final;
 
   //! Computes the U isoparametric curve.
   //! For a hyperbolic paraboloid, no standard Geom_Curve representation is available.
   //! @throw Standard_NotImplemented
   Standard_EXPORT occ::handle<Geom_Curve> UIso(const double U) const final;
 
   //! Computes the V isoparametric curve.
   //! For a hyperbolic paraboloid, no standard Geom_Curve representation is available.
   //! @throw Standard_NotImplemented
   Standard_EXPORT occ::handle<Geom_Curve> VIso(const double V) const final;
 
   //! Computes the point P(U, V) on the surface.
   //! @code
   //!   P(U, V) = O + U*XDir + V*YDir + (U^2/A^2 - V^2/B^2)*ZDir
   //! @endcode
   Standard_EXPORT gp_Pnt EvalD0(const double U, const double V) const final;
 
   //! Computes the point and the first partial derivatives at (U, V).
   Standard_EXPORT Geom_Surface::ResD1 EvalD1(const double U, const double V) const final;
 
   //! Computes the point and partial derivatives up to 2nd order at (U, V).
   Standard_EXPORT Geom_Surface::ResD2 EvalD2(const double U, const double V) const final;
 
   //! Computes the point and partial derivatives up to 3rd order at (U, V).
   Standard_EXPORT Geom_Surface::ResD3 EvalD3(const double U, const double V) const final;
 
   //! Computes the derivative of order Nu in the direction u
   //! and Nv in the direction v.
   //! @param[in] U the u parameter
   //! @param[in] V the v parameter
   //! @param[in] Nu derivative order in u (must be >= 0)
   //! @param[in] Nv derivative order in v (must be >= 0)
   //! @return the derivative vector
   //! @throw Geom_UndefinedDerivative if Nu + Nv < 1 or Nu < 0 or Nv < 0
   Standard_EXPORT gp_Vec EvalDN(const double U,
                                 const double V,
                                 const int    Nu,
                                 const int    Nv) const final;
 
   //! Transformation is not supported for this eval geometry.
   //! @throw Standard_NotImplemented
   Standard_EXPORT void Transform(const gp_Trsf& T) final;
 
   //! Creates a new object which is a copy of this hyperbolic paraboloid.
   Standard_EXPORT occ::handle<Geom_Geometry> Copy() const final;
 
   //! Dumps the content of me into the stream.
   Standard_EXPORT void DumpJson(Standard_OStream& theOStream, int theDepth = -1) const final;
 
   //! Returns the coefficients of the implicit equation of the
   //! quadric in the absolute Cartesian coordinate system:
   //! @code
   //!   A1*X^2 + A2*Y^2 + A3*Z^2 + 2*(B1*X*Y + B2*X*Z + B3*Y*Z) +
   //!   2*(C1*X + C2*Y + C3*Z) + D = 0
   //! @endcode
   //! In local coordinates the equation is: X^2/A^2 - Y^2/B^2 - Z = 0.
   Standard_EXPORT void Coefficients(double& A1,
                                     double& A2,
                                     double& A3,
                                     double& B1,
                                     double& B2,
                                     double& B3,
                                     double& C1,
                                     double& C2,
                                     double& C3,
                                     double& D) const;
 
   DEFINE_STANDARD_RTTIEXT(GeomEval_HypParaboloidSurface, Geom_ElementarySurface)
 
 private:
   double myA;
   double myB;
 };
 
 #endif // _GeomEval_HypParaboloidSurface_HeaderFile

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