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 // Created on: 1993-03-10
 // Created by: JCV
 // Copyright (c) 1993-1999 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 _Geom_SphericalSurface_HeaderFile
 #define _Geom_SphericalSurface_HeaderFile
 
 #include <Standard.hxx>
 #include <Standard_Type.hxx>
 
 #include <Geom_ElementarySurface.hxx>
 #include <Standard_Integer.hxx>
 class gp_Ax3;
 class gp_Sphere;
 class Geom_Curve;
 class gp_Pnt;
 class gp_Vec;
 class gp_Trsf;
 class Geom_Geometry;
 
 class Geom_SphericalSurface;
 DEFINE_STANDARD_HANDLE(Geom_SphericalSurface, Geom_ElementarySurface)
 
 //! Describes a sphere.
 //! A sphere is defined by its radius, and is positioned in
 //! space by a coordinate system (a gp_Ax3 object), the
 //! origin of which is the center of the sphere.
 //! This coordinate system is the "local coordinate
 //! system" of the sphere. The following apply:
 //! - Rotation around its "main Axis", in the trigonometric
 //! sense given by the "X Direction" and the "Y
 //! Direction", defines the u parametric direction.
 //! - Its "X Axis" gives the origin for the u parameter.
 //! - The "reference meridian" of the sphere is a
 //! half-circle, of radius equal to the radius of the
 //! sphere. It is located in the plane defined by the
 //! origin, "X Direction" and "main Direction", centered
 //! on the origin, and positioned on the positive side of the "X Axis".
 //! - Rotation around the "Y Axis" gives the v parameter
 //! on the reference meridian.
 //! - The "X Axis" gives the origin of the v parameter on
 //! the reference meridian.
 //! - The v parametric direction is oriented by the "main
 //! Direction", i.e. when v increases, the Z coordinate
 //! increases. (This implies that the "Y Direction"
 //! orients the reference meridian only when the local
 //! coordinate system is indirect.)
 //! - The u isoparametric curve is a half-circle obtained
 //! by rotating the reference meridian of the sphere
 //! through an angle u around the "main Axis", in the
 //! trigonometric sense defined by the "X Direction"
 //! and the "Y Direction".
 //! The parametric equation of the sphere is:
 //! P(u,v) = O + R*cos(v)*(cos(u)*XDir + sin(u)*YDir)+R*sin(v)*ZDir
 //! 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
 //! - R is the radius of the sphere.
 //! The parametric range of the two parameters is:
 //! - [ 0, 2.*Pi ] for u, and
 //! - [ - Pi/2., + Pi/2. ] for v.
 class Geom_SphericalSurface : public Geom_ElementarySurface
 {
 
 public:
   //! A3 is the local coordinate system of the surface.
   //! At the creation the parametrization of the surface is defined
   //! such as the normal Vector (N = D1U ^ D1V) is directed away from
   //! the center of the sphere.
   //! The direction of increasing parametric value V is defined by the
   //! rotation around the "YDirection" of A2 in the trigonometric sense
   //! and the orientation of increasing parametric value U is defined
   //! by the rotation around the main direction of A2 in the
   //! trigonometric sense.
   //! Warnings :
   //! It is not forbidden to create a spherical surface with
   //! Radius = 0.0
   //! Raised if Radius < 0.0.
   Standard_EXPORT Geom_SphericalSurface(const gp_Ax3& A3, const Standard_Real Radius);
 
   //! Creates a SphericalSurface from a non persistent Sphere from
   //! package gp.
   Standard_EXPORT Geom_SphericalSurface(const gp_Sphere& S);
 
   //! Assigns the value R to the radius of this sphere.
   //! Exceptions Standard_ConstructionError if R is less than 0.0.
   Standard_EXPORT void SetRadius(const Standard_Real R);
 
   //! Converts the gp_Sphere S into this sphere.
   Standard_EXPORT void SetSphere(const gp_Sphere& S);
 
   //! Returns a non persistent sphere with the same geometric
   //! properties as <me>.
   Standard_EXPORT gp_Sphere Sphere() const;
 
   //! Computes the u parameter on the modified
   //! surface, when reversing its u  parametric
   //! direction, for any point of u parameter U on this sphere.
   //! In the case of a sphere, these functions returns 2.PI - U.
   Standard_EXPORT Standard_Real UReversedParameter(const Standard_Real U) const Standard_OVERRIDE;
 
   //! Computes the v parameter on the modified
   //! surface, when reversing its v parametric
   //! direction, for any point of v parameter V on this sphere.
   //! In the case of a sphere, these functions returns   -U.
   Standard_EXPORT Standard_Real VReversedParameter(const Standard_Real V) const Standard_OVERRIDE;
 
   //! Computes the aera of the spherical surface.
   Standard_EXPORT Standard_Real Area() const;
 
   //! Returns the parametric bounds U1, U2, V1 and V2 of this sphere.
   //! For a sphere: U1 = 0, U2 = 2*PI, V1 = -PI/2, V2 = PI/2.
   Standard_EXPORT void Bounds(Standard_Real& U1,
                               Standard_Real& U2,
                               Standard_Real& V1,
                               Standard_Real& V2) const Standard_OVERRIDE;
 
   //! Returns the coefficients of the implicit equation of the
   //! quadric in the absolute cartesian coordinates system :
   //! These coefficients are normalized.
   //! 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 = 0.0
   Standard_EXPORT void Coefficients(Standard_Real& A1,
                                     Standard_Real& A2,
                                     Standard_Real& A3,
                                     Standard_Real& B1,
                                     Standard_Real& B2,
                                     Standard_Real& B3,
                                     Standard_Real& C1,
                                     Standard_Real& C2,
                                     Standard_Real& C3,
                                     Standard_Real& D) const;
 
   //! Computes the coefficients of the implicit equation of
   //! this quadric in the absolute Cartesian coordinate system:
   //! 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 = 0.0
   //! An implicit normalization is applied (i.e. A1 = A2 = 1.
   //! in the local coordinate system of this sphere).
   Standard_EXPORT Standard_Real Radius() const;
 
   //! Computes the volume of the spherical surface.
   Standard_EXPORT Standard_Real Volume() const;
 
   //! Returns True.
   Standard_EXPORT Standard_Boolean IsUClosed() const Standard_OVERRIDE;
 
   //! Returns False.
   Standard_EXPORT Standard_Boolean IsVClosed() const Standard_OVERRIDE;
 
   //! Returns True.
   Standard_EXPORT Standard_Boolean IsUPeriodic() const Standard_OVERRIDE;
 
   //! Returns False.
   Standard_EXPORT Standard_Boolean IsVPeriodic() const Standard_OVERRIDE;
 
   //! Computes the U isoparametric curve.
   //! The U isoparametric curves of the surface are defined by the
   //! section of the spherical surface with plane obtained by rotation
   //! of the plane (Location, XAxis, ZAxis) around ZAxis. This plane
   //! defines the origin of parametrization u.
   //! For a SphericalSurface the UIso curve is a Circle.
   //! Warnings : The radius of this circle can be zero.
   Standard_EXPORT Handle(Geom_Curve) UIso(const Standard_Real U) const Standard_OVERRIDE;
 
   //! Computes the V isoparametric curve.
   //! The V isoparametric curves of the surface  are defined by
   //! the section of the spherical surface with plane parallel to the
   //! plane (Location, XAxis, YAxis). This plane defines the origin of
   //! parametrization V.
   //! Be careful if  V is close to PI/2 or 3*PI/2 the radius of the
   //! circle becomes tiny. It is not forbidden in this toolkit to
   //! create circle with radius = 0.0
   //! For a SphericalSurface the VIso curve is a Circle.
   //! Warnings : The radius of this circle can be zero.
   Standard_EXPORT Handle(Geom_Curve) VIso(const Standard_Real V) const Standard_OVERRIDE;
 
   //! Computes the  point P (U, V) on the surface.
   //! P (U, V) = Loc + Radius * Sin (V) * Zdir +
   //! Radius * Cos (V) * (cos (U) * XDir + sin (U) * YDir)
   //! where Loc is the origin of the placement plane (XAxis, YAxis)
   //! XDir is the direction of the XAxis and YDir the direction of
   //! the YAxis and ZDir the direction of the ZAxis.
   Standard_EXPORT void D0(const Standard_Real U,
                           const Standard_Real V,
                           gp_Pnt&             P) const Standard_OVERRIDE;
 
   //! Computes the current point and the first derivatives in the
   //! directions U and V.
   Standard_EXPORT void D1(const Standard_Real U,
                           const Standard_Real V,
                           gp_Pnt&             P,
                           gp_Vec&             D1U,
                           gp_Vec&             D1V) const Standard_OVERRIDE;
 
   //! Computes the current point, the first and the second derivatives
   //! in the directions U and V.
   Standard_EXPORT void D2(const Standard_Real U,
                           const Standard_Real V,
                           gp_Pnt&             P,
                           gp_Vec&             D1U,
                           gp_Vec&             D1V,
                           gp_Vec&             D2U,
                           gp_Vec&             D2V,
                           gp_Vec&             D2UV) const Standard_OVERRIDE;
 
   //! Computes the current point, the first,the second and the third
   //! derivatives in the directions U and V.
   Standard_EXPORT void D3(const Standard_Real U,
                           const Standard_Real V,
                           gp_Pnt&             P,
                           gp_Vec&             D1U,
                           gp_Vec&             D1V,
                           gp_Vec&             D2U,
                           gp_Vec&             D2V,
                           gp_Vec&             D2UV,
                           gp_Vec&             D3U,
                           gp_Vec&             D3V,
                           gp_Vec&             D3UUV,
                           gp_Vec&             D3UVV) const Standard_OVERRIDE;
 
   //! Computes the derivative of order Nu in the direction u
   //! and Nv in the direction v.
   //! Raised if Nu + Nv < 1 or Nu < 0 or Nv < 0.
   Standard_EXPORT gp_Vec DN(const Standard_Real    U,
                             const Standard_Real    V,
                             const Standard_Integer Nu,
                             const Standard_Integer Nv) const Standard_OVERRIDE;
 
   //! Applies the transformation T to this sphere.
   Standard_EXPORT void Transform(const gp_Trsf& T) Standard_OVERRIDE;
 
   //! Creates a new object which is a copy of this sphere.
   Standard_EXPORT Handle(Geom_Geometry) Copy() const Standard_OVERRIDE;
 
   //! Dumps the content of me into the stream
   Standard_EXPORT virtual void DumpJson(Standard_OStream& theOStream,
                                         Standard_Integer  theDepth = -1) const Standard_OVERRIDE;
 
   DEFINE_STANDARD_RTTIEXT(Geom_SphericalSurface, Geom_ElementarySurface)
 
 protected:
 private:
   Standard_Real radius;
 };
 
 #endif // _Geom_SphericalSurface_HeaderFile

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