// 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_ToroidalSurface_HeaderFile #define _Geom_ToroidalSurface_HeaderFile #include #include #include #include #include #include #include class gp_Ax3; class gp_Torus; class Geom_Curve; class gp_Pnt; class gp_Vec; class gp_Trsf; class Geom_Geometry; class Geom_ToroidalSurface; DEFINE_STANDARD_HANDLE(Geom_ToroidalSurface, Geom_ElementarySurface) //! Describes a torus. //! A torus is defined by its major and minor radii, and //! positioned in space with a coordinate system (a //! gp_Ax3 object) as follows: //! - The origin is the center of the torus. //! - The surface is obtained by rotating a circle around //! the "main Direction". This circle has a radius equal //! to the minor radius, and is located in the plane //! defined by the origin, "X Direction" and "main //! Direction". It is centered on the "X Axis", on its //! positive side, and positioned at a distance from the //! origin equal to the major radius. This circle is the //! "reference circle" of the torus. //! - The plane defined by the origin, the "X Direction" //! and the "Y Direction" is called the "reference plane" of the torus. //! This coordinate system is the "local coordinate //! system" of the torus. The following apply: //! - Rotation around its "main Axis", in the trigonometric //! sense given by "X Direction" and "Y Direction", //! defines the u parametric direction. //! - The "X Axis" gives the origin for the u parameter. //! - Rotation around an axis parallel to the "Y Axis" and //! passing through the center of the "reference circle" //! gives the v parameter on the "reference circle". //! - The "X Axis" gives the origin of the v parameter on //! the "reference circle". //! - The v parametric direction is oriented by the //! inverse of the "main Direction", i.e. near 0, as v //! increases, the Z coordinate decreases. (This //! implies that the "Y Direction" orients the reference //! circle only when the local coordinate system is direct.) //! - The u isoparametric curve is a circle obtained by //! rotating the "reference circle" of the torus through //! an angle u about the "main Axis". //! The parametric equation of the torus is : //! P(u, v) = O + (R + 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 the local coordinate system, //! - r and R are, respectively, the minor and major radius. //! The parametric range of the two parameters is: //! - [ 0, 2.*Pi ] for u //! - [ 0, 2.*Pi ] for v class Geom_ToroidalSurface : public Geom_ElementarySurface { public: //! A3 is the local coordinate system of the surface. //! The orientation of increasing V parametric value is defined //! by the rotation around the main axis (ZAxis) in the //! trigonometric sense. The parametrization of the surface in the //! U direction is defined such as the normal Vector (N = D1U ^ D1V) //! is oriented towards the "outside region" of the surface. //! Warnings : //! It is not forbidden to create a toroidal surface with //! MajorRadius = MinorRadius = 0.0 //! //! Raised if MinorRadius < 0.0 or if MajorRadius < 0.0 Standard_EXPORT Geom_ToroidalSurface(const gp_Ax3& A3, const Standard_Real MajorRadius, const Standard_Real MinorRadius); //! Creates a ToroidalSurface from a non transient Torus from //! package gp. Standard_EXPORT Geom_ToroidalSurface(const gp_Torus& T); //! Modifies this torus by changing its major radius. //! Exceptions //! Standard_ConstructionError if: //! - MajorRadius is negative, or //! - MajorRadius - r is less than or equal to //! gp::Resolution(), where r is the minor radius of this torus. Standard_EXPORT void SetMajorRadius (const Standard_Real MajorRadius); //! Modifies this torus by changing its minor radius. //! Exceptions //! Standard_ConstructionError if: //! - MinorRadius is negative, or //! - R - MinorRadius is less than or equal to //! gp::Resolution(), where R is the major radius of this torus. Standard_EXPORT void SetMinorRadius (const Standard_Real MinorRadius); //! Converts the gp_Torus torus T into this torus. Standard_EXPORT void SetTorus (const gp_Torus& T); //! Returns the non transient torus with the same geometric //! properties as . Standard_EXPORT gp_Torus Torus() const; //! Return the parameter on the Ureversed surface for //! the point of parameter U on . //! Return 2.PI - U. Standard_EXPORT Standard_Real UReversedParameter (const Standard_Real U) const Standard_OVERRIDE; //! Return the parameter on the Ureversed surface for //! the point of parameter U on . //! Return 2.PI - U. Standard_EXPORT Standard_Real VReversedParameter (const Standard_Real U) const Standard_OVERRIDE; //! Computes the aera of the surface. Standard_EXPORT Standard_Real Area() const; //! Returns the parametric bounds U1, U2, V1 and V2 of this torus. //! For a torus: U1 = V1 = 0 and U2 = V2 = 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 surface //! in the absolute cartesian coordinate system : //! Coef(1) * X**4 + Coef(2) * Y**4 + Coef(3) * Z**4 + //! Coef(4) * X**3 * Y + Coef(5) * X**3 * Z + Coef(6) * Y**3 * X + //! Coef(7) * Y**3 * Z + Coef(8) * Z**3 * X + Coef(9) * Z**3 * Y + //! Coef(10) * X**2 * Y**2 + Coef(11) * X**2 * Z**2 + //! Coef(12) * Y**2 * Z**2 + Coef(13) * X**3 + Coef(14) * Y**3 + //! Coef(15) * Z**3 + Coef(16) * X**2 * Y + Coef(17) * X**2 * Z + //! Coef(18) * Y**2 * X + Coef(19) * Y**2 * Z + Coef(20) * Z**2 * X + //! Coef(21) * Z**2 * Y + Coef(22) * X**2 + Coef(23) * Y**2 + //! Coef(24) * Z**2 + Coef(25) * X * Y + Coef(26) * X * Z + //! Coef(27) * Y * Z + Coef(28) * X + Coef(29) * Y + Coef(30) * Z + //! Coef(31) = 0.0 //! Raised if the length of Coef is lower than 31. Standard_EXPORT void Coefficients (TColStd_Array1OfReal& Coef) const; //! Returns the major radius, or the minor radius, of this torus. Standard_EXPORT Standard_Real MajorRadius() const; //! Returns the major radius, or the minor radius, of this torus. Standard_EXPORT Standard_Real MinorRadius() const; //! Computes the volume. Standard_EXPORT Standard_Real Volume() const; //! Returns True. Standard_EXPORT Standard_Boolean IsUClosed() const Standard_OVERRIDE; //! Returns True. Standard_EXPORT Standard_Boolean IsVClosed() const Standard_OVERRIDE; //! Returns True. Standard_EXPORT Standard_Boolean IsUPeriodic() const Standard_OVERRIDE; //! Returns True. Standard_EXPORT Standard_Boolean IsVPeriodic() const Standard_OVERRIDE; //! Computes the U isoparametric curve. //! //! For a toroidal surface the UIso curve is a circle. //! The center of the Uiso circle is at the distance MajorRadius //! from the location point of the toroidal surface. //! Warnings : //! The radius of the circle can be zero if for the surface //! MinorRadius = 0.0 Standard_EXPORT Handle(Geom_Curve) UIso (const Standard_Real U) const Standard_OVERRIDE; //! Computes the V isoparametric curve. //! //! For a ToroidalSurface the VIso curve is a circle. //! The axis of the circle is the main axis (ZAxis) of the //! toroidal surface. //! Warnings : //! The radius of the circle can be zero if for the surface //! MajorRadius = MinorRadius 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 + MinorRadius * Sin (V) * Zdir + //! (MajorRadius + MinorRadius * 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 torus. Standard_EXPORT void Transform (const gp_Trsf& T) Standard_OVERRIDE; //! Creates a new object which is a copy of this torus. 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_ToroidalSurface,Geom_ElementarySurface) protected: private: Standard_Real majorRadius; Standard_Real minorRadius; }; #endif // _Geom_ToroidalSurface_HeaderFile