// 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_EllipsoidSurface_HeaderFile #define _GeomEval_EllipsoidSurface_HeaderFile #include "Geom_ElementarySurface.hxx" //! Describes a triaxial ellipsoid surface. //! An ellipsoid is defined by three semi-axes A, B, C (all > 0) //! and is positioned in space by a coordinate system (a gp_Ax3 object), //! the origin of which is the center of the ellipsoid. //! //! The parametric equation of the ellipsoid is: //! @code //! P(u,v) = O + A*cos(v)*cos(u)*XDir + B*cos(v)*sin(u)*YDir + C*sin(v)*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, B, C are the three semi-axes. //! //! The parametric range is: //! - [0, 2*Pi] for u, and //! - [-Pi/2, Pi/2] for v. //! //! When A == B the surface degenerates to a spheroid (ellipsoid of revolution). //! //! The implicit equation in local coordinates is: //! @code //! X^2/A^2 + Y^2/B^2 + Z^2/C^2 - 1 = 0 //! @endcode class GeomEval_EllipsoidSurface : public Geom_ElementarySurface { public: //! Creates a triaxial ellipsoid surface with the given local coordinate system //! and three semi-axes. //! @param[in] thePosition the local coordinate system //! @param[in] theA the semi-axis along XDir (must be > 0) //! @param[in] theB the semi-axis along YDir (must be > 0) //! @param[in] theC the semi-axis along ZDir (must be > 0) //! @throw Standard_ConstructionError if any semi-axis <= 0 Standard_EXPORT GeomEval_EllipsoidSurface(const gp_Ax3& thePosition, double theA, double theB, double theC); //! Returns the semi-axis A (along XDir). Standard_EXPORT double SemiAxisA() const; //! Returns the semi-axis B (along YDir). Standard_EXPORT double SemiAxisB() const; //! Returns the semi-axis C (along ZDir). Standard_EXPORT double SemiAxisC() const; //! Assigns the value theA to the semi-axis A. //! @param[in] theA the new semi-axis value (must be > 0) //! @throw Standard_ConstructionError if theA <= 0 Standard_EXPORT void SetSemiAxisA(double theA); //! Assigns the value theB to the semi-axis B. //! @param[in] theB the new semi-axis value (must be > 0) //! @throw Standard_ConstructionError if theB <= 0 Standard_EXPORT void SetSemiAxisB(double theB); //! Assigns the value theC to the semi-axis C. //! @param[in] theC the new semi-axis value (must be > 0) //! @throw Standard_ConstructionError if theC <= 0 Standard_EXPORT void SetSemiAxisC(double theC); //! 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 ellipsoid. //! @param[out] U1 lower U bound (0) //! @param[out] U2 upper U bound (2*Pi) //! @param[out] V1 lower V bound (-Pi/2) //! @param[out] V2 upper V bound (Pi/2) Standard_EXPORT void Bounds(double& U1, double& U2, double& V1, double& V2) const final; //! Returns True. The ellipsoid is closed in U (period 2*Pi). Standard_EXPORT bool IsUClosed() const final; //! Returns False. Standard_EXPORT bool IsVClosed() const final; //! Returns True. The ellipsoid is periodic in U (period 2*Pi). Standard_EXPORT bool IsUPeriodic() const final; //! Returns False. Standard_EXPORT bool IsVPeriodic() const final; //! Computes the U isoparametric curve. //! For a triaxial ellipsoid, the U isoparametric curve is not //! a standard Geom_Curve type. //! @throw Standard_NotImplemented Standard_EXPORT occ::handle UIso(const double U) const final; //! Computes the V isoparametric curve. //! For a triaxial ellipsoid, the V isoparametric curve is not //! a standard Geom_Curve type (it is an ellipse only when A == B). //! @throw Standard_NotImplemented Standard_EXPORT occ::handle VIso(const double V) const final; //! Computes the point P(U, V) on the surface. //! @code //! P(U, V) = O + A*cos(V)*cos(U)*XDir + B*cos(V)*sin(U)*YDir + C*sin(V)*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 ellipsoid. Standard_EXPORT occ::handle 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^2/C^2 - 1 = 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_EllipsoidSurface, Geom_ElementarySurface) private: double myA; //!< Semi-axis along XDir double myB; //!< Semi-axis along YDir double myC; //!< Semi-axis along ZDir }; #endif // _GeomEval_EllipsoidSurface_HeaderFile