// 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 #include #include #include #include #include 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 so that 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 . 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 . //! @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