// 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 #include #include #include #include #include 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 . 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