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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_ConicalSurface_HeaderFile
 #define _Geom_ConicalSurface_HeaderFile
 
 #include <Standard.hxx>
 #include <Standard_Type.hxx>
 
 #include <Geom_ElementarySurface.hxx>
 #include <Standard_Integer.hxx>
 class gp_Ax3;
 class gp_Cone;
 class gp_Trsf;
 class gp_GTrsf2d;
 class gp_Pnt;
 class Geom_Curve;
 class gp_Vec;
 class Geom_Geometry;
 
 
 class Geom_ConicalSurface;
 DEFINE_STANDARD_HANDLE(Geom_ConicalSurface, Geom_ElementarySurface)
 
 //! Describes a cone.
 //! A cone is defined by the half-angle (can be negative) at its apex, and
 //! is positioned in space by a coordinate system (a
 //! gp_Ax3 object) and a reference radius as follows:
 //! - The "main Axis" of the coordinate system is the
 //! axis of revolution of the cone.
 //! - The plane defined by the origin, the "X Direction"
 //! and the "Y Direction" of the coordinate system is
 //! the reference plane of the cone. The intersection
 //! of the cone with this reference plane is a circle of
 //! radius equal to the reference radius.
 //! - The apex of the cone is on the negative side of
 //! the "main Axis" of the coordinate system if the
 //! half-angle is positive, and on the positive side if
 //! the half-angle is negative.
 //! This coordinate system is the "local coordinate
 //! system" of the cone. 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.
 //! - Its "main Direction" is the v parametric direction of the cone.
 //! - Its origin is the origin of the v parameter.
 //! The parametric range of the two parameters is:
 //! @code
 //!  - [ 0, 2.*Pi ] for u, and
 //!  - ] -infinity, +infinity [ for v
 //! @endcode
 //! The parametric equation of the cone is:
 //! @code
 //! P(u, v) = O + (R + v*sin(Ang)) * (cos(u)*XDir + sin(u)*YDir) + v*cos(Ang)*ZDir
 //! @endcode
 //! where:
 //! - O, XDir, YDir and ZDir are respectively
 //! the origin, the "X Direction", the "Y Direction" and
 //! the "Z Direction" of the cone's local coordinate system,
 //! - Ang is the half-angle at the apex of the cone,   and
 //! - R is the reference radius.
 class Geom_ConicalSurface : public Geom_ElementarySurface
 {
 
 public:
 
   
 
   //! A3 defines the local coordinate system of the conical surface.
   //! Ang is the conical surface semi-angle. Its absolute value is in range
   //! ]0, PI/2[.
   //! Radius is the radius of the circle Viso in the placement plane
   //! of the conical surface defined with "XAxis" and "YAxis".
   //! The "ZDirection" of A3 defines the direction of the surface's
   //! axis of symmetry.
   //! If the location point of A3 is the apex of the surface
   //! Radius = 0 .
   //! At the creation the parametrization of the surface is defined
   //! such that the normal Vector (N = D1U ^ D1V) is oriented towards
   //! the "outside region" of the surface.
   //!
   //! Raised if Radius < 0.0 or Abs(Ang) < Resolution from gp or
   //! Abs(Ang) >= PI/2 - Resolution
   Standard_EXPORT Geom_ConicalSurface(const gp_Ax3& A3, const Standard_Real Ang, const Standard_Real Radius);
   
 
   //! Creates a ConicalSurface from a non transient gp_Cone.
   Standard_EXPORT Geom_ConicalSurface(const gp_Cone& C);
 
   //! Set <me> so that <me> has the same geometric properties as C.
   Standard_EXPORT void SetCone (const gp_Cone& C);
 
   //! Changes the radius of the conical surface in the placement plane (Z = 0, V = 0).
   //! The local coordinate system is not modified.
   //! Raised if R < 0.0
   Standard_EXPORT void SetRadius (const Standard_Real R);
 
   //! Changes the semi angle of the conical surface.
   //! Semi-angle can be negative. Its absolute value
   //! Abs(Ang) is in range ]0,PI/2[.
   //! Raises ConstructionError if Abs(Ang) < Resolution from gp or
   //! Abs(Ang) >= PI/2 - Resolution
   Standard_EXPORT void SetSemiAngle(const Standard_Real Ang);
 
   //! Returns a non transient cone with the same geometric properties as <me>.
   Standard_EXPORT gp_Cone Cone() const;
 
   //! Eeturn 2.PI - U.
   Standard_EXPORT Standard_Real UReversedParameter (const Standard_Real U) const Standard_OVERRIDE;
 
   //! Computes the u (or v) parameter on the modified surface,
   //! when reversing its u (or v) parametric direction,
   //! for any point of u parameter U (or of v parameter V) on this cone.
   //! In the case of a cone, these functions return respectively:
   //! - 2.*Pi - U, -V.
   Standard_EXPORT Standard_Real VReversedParameter (const Standard_Real V) const Standard_OVERRIDE;
   
   //! Changes the orientation of this cone in the v parametric direction.
   //! The bounds of the surface are not changed but the v parametric direction is reversed.
   //! As a consequence, for a cone:
   //! - the "main Direction" of the local coordinate system
   //! is reversed, and
   //! - the half-angle at the apex is inverted.
   Standard_EXPORT virtual void VReverse() Standard_OVERRIDE;
 
   //! Computes the parameters on the transformed surface for
   //! the transform of the point of parameters U,V on <me>.
   //! @code
   //!   me->Transformed(T)->Value(U',V')
   //! @endcode
   //! is the same point as
   //! @code
   //!   me->Value(U,V).Transformed(T)
   //! @endcode
   //! Where U',V' are the new values of U,V after calling
   //! @code
   //!   me->TransformParameters(U,V,T)
   //! @endcode
   //! This method multiplies V by T.ScaleFactor()
   Standard_EXPORT virtual void TransformParameters (Standard_Real& U, Standard_Real& V, const gp_Trsf& T) const Standard_OVERRIDE;
 
   //! Returns a 2d transformation used to find the new
   //! parameters of a point on the transformed surface.
   //! @code
   //!   me->Transformed(T)->Value(U',V')
   //! @endcode
   //! is the same point as
   //! @code
   //!   me->Value(U,V).Transformed(T)
   //! @endcode
   //! Where U',V' are obtained by transforming U,V with the 2d transformation returned by
   //! @code
   //!   me->ParametricTransformation(T)
   //! @endcode
   //! This method returns a scale centered on the U axis with T.ScaleFactor
   Standard_EXPORT virtual gp_GTrsf2d ParametricTransformation (const gp_Trsf& T) const Standard_OVERRIDE;
 
   //! Computes the apex of this cone. It is on the negative
   //! side of the axis of revolution of this cone if the
   //! half-angle at the apex is positive, and on the positive
   //! side of the "main Axis" if the half-angle is negative.
   Standard_EXPORT gp_Pnt Apex() const;
 
   //! The conical surface is infinite in the V direction so
   //! V1 = Realfirst from Standard and V2 = RealLast.
   //! U1 = 0 and U2 = 2*PI.
   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 coordinate system :
   //! These coefficients are normalized.
   //! @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 = 0.0
   //! @endcode
   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;
 
   //! Returns the reference radius of this cone.
   //! The reference radius is the radius of the circle formed
   //! by the intersection of this cone and its reference
   //! plane (i.e. the plane defined by the origin, "X
   //! Direction" and "Y Direction" of the local coordinate
   //! system of this cone).
   //! If the apex of this cone is on the origin of the local
   //! coordinate system of this cone, the returned value is 0.
   Standard_EXPORT Standard_Real RefRadius() const;
 
   //! Returns the semi-angle at the apex of this cone.
   //! Attention! Semi-angle can be negative.
   Standard_EXPORT Standard_Real SemiAngle() 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;
 
   //! Builds the U isoparametric line of this cone.
   //! The origin of this line is on the reference plane of this cone
   //! (i.e. the plane defined by the origin, "X Direction"
   //! and "Y Direction" of the local coordinate system of this cone).
   Standard_EXPORT Handle(Geom_Curve) UIso (const Standard_Real U) const Standard_OVERRIDE;
 
   //! Builds the V isoparametric circle of this cone.
   //! It is the circle on this cone, located in the plane of Z
   //! coordinate V*cos(Semi-Angle) in the local coordinate system of this cone.
   //! The "Axis" of this circle is the axis of revolution of this cone.
   //! Its starting point is defined by the "X Direction" of this cone.
   //! Warning
   //! If the V isoparametric circle is close to the apex of
   //! this cone, the radius of the circle becomes very small.
   //! It is possible to have a circle with radius equal to 0.0.
   Standard_EXPORT Handle(Geom_Curve) VIso (const Standard_Real V) const Standard_OVERRIDE;
 
   //! Computes the point P (U, V) on the surface.
   //! @code
   //!   P (U, V) = Loc +
   //!              (RefRadius + V * sin (Semi-Angle)) * (cos (U) * XDir + sin (U) * YDir) +
   //!              V * cos (Semi-Angle) * ZDir
   //! @endcode
   //! 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.
   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 u
   //! parametric direction, and Nv in the v parametric
   //! direction at the point of parameters (U, V) of this cone.
   //! Exceptions
   //! Standard_RangeError if:
   //! - Nu + Nv is less than 1,
   //! - Nu or Nv is negative.
   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 cone.
   Standard_EXPORT void Transform (const gp_Trsf& T) Standard_OVERRIDE;
 
   //! Creates a new object which is a copy of this cone.
   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_ConicalSurface,Geom_ElementarySurface)
 
 private:
 
   Standard_Real radius;
   Standard_Real semiAngle;
 
 };
 
 #endif // _Geom_ConicalSurface_HeaderFile

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