[occt.git] / src / ElSLib / ElSLib.hxx

// Created on: 1991-09-09
// Created by: Michel Chauvat
// Copyright (c) 1991-1999 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 _ElSLib_HeaderFile
#define _ElSLib_HeaderFile

#include <Standard.hxx>
#include <Standard_DefineAlloc.hxx>
#include <Standard_Handle.hxx>

#include <Standard_Real.hxx>
#include <gp_Pnt.hxx>
#include <Standard_Integer.hxx>
#include <gp_Vec.hxx>
class gp_Pnt;
class gp_Pln;
class gp_Cone;
class gp_Cylinder;
class gp_Sphere;
class gp_Torus;
class gp_Vec;
class gp_Ax3;
class gp_Lin;
class gp_Circ;


//! Provides functions for basic geometric computation on
//! elementary surfaces.
//! This includes:
//! -   calculation of a point or derived vector on a surface
//! where the surface is provided by the gp package, or
//! defined in canonical form (as in the gp package), and
//! the point is defined with a parameter,
//! -   evaluation of the parameters corresponding to a
//! point on an elementary surface from gp,
//! -   calculation of isoparametric curves on an elementary
//! surface defined in canonical form (as in the gp package).
//! Notes:
//! -   ElSLib stands for Elementary Surfaces Library.
//! -   If the surfaces provided by the gp package are not
//! explicitly parameterized, they still have an implicit
//! parameterization, similar to that which they infer on
//! the equivalent Geom surfaces.
//! Note: ElSLib stands for Elementary Surfaces Library.
class ElSLib 
{
public:

  DEFINE_STANDARD_ALLOC

  
  //! For elementary surfaces from the gp package (planes,
  //! cones, cylinders, spheres and tori), computes the point
  //! of parameters (U, V).
    static gp_Pnt Value (const Standard_Real U, const Standard_Real V, const gp_Pln& Pl);
  
    static gp_Pnt Value (const Standard_Real U, const Standard_Real V, const gp_Cone& C);
  
    static gp_Pnt Value (const Standard_Real U, const Standard_Real V, const gp_Cylinder& C);
  
    static gp_Pnt Value (const Standard_Real U, const Standard_Real V, const gp_Sphere& S);
  
    static gp_Pnt Value (const Standard_Real U, const Standard_Real V, const gp_Torus& T);
  
  //! For elementary surfaces from the gp package (planes,
  //! cones, cylinders, spheres and tori), computes the
  //! derivative vector of order Nu and Nv in the u and v
  //! parametric directions respectively, at the point of
  //! parameters (U, V).
    static gp_Vec DN (const Standard_Real U, const Standard_Real V, const gp_Pln& Pl, const Standard_Integer Nu, const Standard_Integer Nv);
  
    static gp_Vec DN (const Standard_Real U, const Standard_Real V, const gp_Cone& C, const Standard_Integer Nu, const Standard_Integer Nv);
  
    static gp_Vec DN (const Standard_Real U, const Standard_Real V, const gp_Cylinder& C, const Standard_Integer Nu, const Standard_Integer Nv);
  
    static gp_Vec DN (const Standard_Real U, const Standard_Real V, const gp_Sphere& S, const Standard_Integer Nu, const Standard_Integer Nv);
  
    static gp_Vec DN (const Standard_Real U, const Standard_Real V, const gp_Torus& T, const Standard_Integer Nu, const Standard_Integer Nv);
  
  //! For elementary surfaces from the gp package (planes,
  //! cones, cylinders, spheres and tori), computes the point P
  //! of parameters (U, V).inline
    static void D0 (const Standard_Real U, const Standard_Real V, const gp_Pln& Pl, gp_Pnt& P);
  
    static void D0 (const Standard_Real U, const Standard_Real V, const gp_Cone& C, gp_Pnt& P);
  
    static void D0 (const Standard_Real U, const Standard_Real V, const gp_Cylinder& C, gp_Pnt& P);
  
    static void D0 (const Standard_Real U, const Standard_Real V, const gp_Sphere& S, gp_Pnt& P);
  
    static void D0 (const Standard_Real U, const Standard_Real V, const gp_Torus& T, gp_Pnt& P);
  

  //! For elementary surfaces from the gp package (planes,
  //! cones, cylinders, spheres and tori), computes:
  //! -   the point P of parameters (U, V), and
  //! -   the first derivative vectors Vu and Vv at this point in
  //! the u and v parametric directions respectively.
    static void D1 (const Standard_Real U, const Standard_Real V, const gp_Pln& Pl, gp_Pnt& P, gp_Vec& Vu, gp_Vec& Vv);
  
    static void D1 (const Standard_Real U, const Standard_Real V, const gp_Cone& C, gp_Pnt& P, gp_Vec& Vu, gp_Vec& Vv);
  
    static void D1 (const Standard_Real U, const Standard_Real V, const gp_Cylinder& C, gp_Pnt& P, gp_Vec& Vu, gp_Vec& Vv);
  
    static void D1 (const Standard_Real U, const Standard_Real V, const gp_Sphere& S, gp_Pnt& P, gp_Vec& Vu, gp_Vec& Vv);
  
    static void D1 (const Standard_Real U, const Standard_Real V, const gp_Torus& T, gp_Pnt& P, gp_Vec& Vu, gp_Vec& Vv);
  

  //! For elementary surfaces from the gp package (cones,
  //! cylinders, spheres and tori), computes:
  //! -   the point P of parameters (U, V), and
  //! -   the first derivative vectors Vu and Vv at this point in
  //! the u and v parametric directions respectively, and
  //! -   the second derivative vectors Vuu, Vvv and Vuv at this point.
    static void D2 (const Standard_Real U, const Standard_Real V, const gp_Cone& C, gp_Pnt& P, gp_Vec& Vu, gp_Vec& Vv, gp_Vec& Vuu, gp_Vec& Vvv, gp_Vec& Vuv);
  
    static void D2 (const Standard_Real U, const Standard_Real V, const gp_Cylinder& C, gp_Pnt& P, gp_Vec& Vu, gp_Vec& Vv, gp_Vec& Vuu, gp_Vec& Vvv, gp_Vec& Vuv);
  
    static void D2 (const Standard_Real U, const Standard_Real V, const gp_Sphere& S, gp_Pnt& P, gp_Vec& Vu, gp_Vec& Vv, gp_Vec& Vuu, gp_Vec& Vvv, gp_Vec& Vuv);
  
    static void D2 (const Standard_Real U, const Standard_Real V, const gp_Torus& T, gp_Pnt& P, gp_Vec& Vu, gp_Vec& Vv, gp_Vec& Vuu, gp_Vec& Vvv, gp_Vec& Vuv);
  

  //! For elementary surfaces from the gp package (cones,
  //! cylinders, spheres and tori), computes:
  //! -   the point P of parameters (U,V), and
  //! -   the first derivative vectors Vu and Vv at this point in
  //! the u and v parametric directions respectively, and
  //! -   the second derivative vectors Vuu, Vvv and Vuv at
  //! this point, and
  //! -   the third derivative vectors Vuuu, Vvvv, Vuuv and
  //! Vuvv at this point.
    static void D3 (const Standard_Real U, const Standard_Real V, const gp_Cone& C, gp_Pnt& P, gp_Vec& Vu, gp_Vec& Vv, gp_Vec& Vuu, gp_Vec& Vvv, gp_Vec& Vuv, gp_Vec& Vuuu, gp_Vec& Vvvv, gp_Vec& Vuuv, gp_Vec& Vuvv);
  
    static void D3 (const Standard_Real U, const Standard_Real V, const gp_Cylinder& C, gp_Pnt& P, gp_Vec& Vu, gp_Vec& Vv, gp_Vec& Vuu, gp_Vec& Vvv, gp_Vec& Vuv, gp_Vec& Vuuu, gp_Vec& Vvvv, gp_Vec& Vuuv, gp_Vec& Vuvv);
  
    static void D3 (const Standard_Real U, const Standard_Real V, const gp_Sphere& S, gp_Pnt& P, gp_Vec& Vu, gp_Vec& Vv, gp_Vec& Vuu, gp_Vec& Vvv, gp_Vec& Vuv, gp_Vec& Vuuu, gp_Vec& Vvvv, gp_Vec& Vuuv, gp_Vec& Vuvv);
  
  //! Surface evaluation
  //! The following functions compute the point and the
  //! derivatives on elementary surfaces defined with their
  //! geometric characterisitics.
  //! You don't need to create the surface to use these functions.
  //! These functions are called by the previous  ones.
  //! Example :
  //! A cylinder is defined with its position and its radius.
    static void D3 (const Standard_Real U, const Standard_Real V, const gp_Torus& T, gp_Pnt& P, gp_Vec& Vu, gp_Vec& Vv, gp_Vec& Vuu, gp_Vec& Vvv, gp_Vec& Vuv, gp_Vec& Vuuu, gp_Vec& Vvvv, gp_Vec& Vuuv, gp_Vec& Vuvv);
  
  Standard_EXPORT static gp_Pnt PlaneValue (const Standard_Real U, const Standard_Real V, const gp_Ax3& Pos);
  
  Standard_EXPORT static gp_Pnt CylinderValue (const Standard_Real U, const Standard_Real V, const gp_Ax3& Pos, const Standard_Real Radius);
  
  Standard_EXPORT static gp_Pnt ConeValue (const Standard_Real U, const Standard_Real V, const gp_Ax3& Pos, const Standard_Real Radius, const Standard_Real SAngle);
  
  Standard_EXPORT static gp_Pnt SphereValue (const Standard_Real U, const Standard_Real V, const gp_Ax3& Pos, const Standard_Real Radius);
  
  Standard_EXPORT static gp_Pnt TorusValue (const Standard_Real U, const Standard_Real V, const gp_Ax3& Pos, const Standard_Real MajorRadius, const Standard_Real MinorRadius);
  
  Standard_EXPORT static gp_Vec PlaneDN (const Standard_Real U, const Standard_Real V, const gp_Ax3& Pos, const Standard_Integer Nu, const Standard_Integer Nv);
  
  Standard_EXPORT static gp_Vec CylinderDN (const Standard_Real U, const Standard_Real V, const gp_Ax3& Pos, const Standard_Real Radius, const Standard_Integer Nu, const Standard_Integer Nv);
  
  Standard_EXPORT static gp_Vec ConeDN (const Standard_Real U, const Standard_Real V, const gp_Ax3& Pos, const Standard_Real Radius, const Standard_Real SAngle, const Standard_Integer Nu, const Standard_Integer Nv);
  
  Standard_EXPORT static gp_Vec SphereDN (const Standard_Real U, const Standard_Real V, const gp_Ax3& Pos, const Standard_Real Radius, const Standard_Integer Nu, const Standard_Integer Nv);
  
  Standard_EXPORT static gp_Vec TorusDN (const Standard_Real U, const Standard_Real V, const gp_Ax3& Pos, const Standard_Real MajorRadius, const Standard_Real MinorRadius, const Standard_Integer Nu, const Standard_Integer Nv);
  
  Standard_EXPORT static void PlaneD0 (const Standard_Real U, const Standard_Real V, const gp_Ax3& Pos, gp_Pnt& P);
  
  Standard_EXPORT static void ConeD0 (const Standard_Real U, const Standard_Real V, const gp_Ax3& Pos, const Standard_Real Radius, const Standard_Real SAngle, gp_Pnt& P);
  
  Standard_EXPORT static void CylinderD0 (const Standard_Real U, const Standard_Real V, const gp_Ax3& Pos, const Standard_Real Radius, gp_Pnt& P);
  
  Standard_EXPORT static void SphereD0 (const Standard_Real U, const Standard_Real V, const gp_Ax3& Pos, const Standard_Real Radius, gp_Pnt& P);
  
  Standard_EXPORT static void TorusD0 (const Standard_Real U, const Standard_Real V, const gp_Ax3& Pos, const Standard_Real MajorRadius, const Standard_Real MinorRadius, gp_Pnt& P);
  
  Standard_EXPORT static void PlaneD1 (const Standard_Real U, const Standard_Real V, const gp_Ax3& Pos, gp_Pnt& P, gp_Vec& Vu, gp_Vec& Vv);
  
  Standard_EXPORT static void ConeD1 (const Standard_Real U, const Standard_Real V, const gp_Ax3& Pos, const Standard_Real Radius, const Standard_Real SAngle, gp_Pnt& P, gp_Vec& Vu, gp_Vec& Vv);
  
  Standard_EXPORT static void CylinderD1 (const Standard_Real U, const Standard_Real V, const gp_Ax3& Pos, const Standard_Real Radius, gp_Pnt& P, gp_Vec& Vu, gp_Vec& Vv);
  
  Standard_EXPORT static void SphereD1 (const Standard_Real U, const Standard_Real V, const gp_Ax3& Pos, const Standard_Real Radius, gp_Pnt& P, gp_Vec& Vu, gp_Vec& Vv);
  
  Standard_EXPORT static void TorusD1 (const Standard_Real U, const Standard_Real V, const gp_Ax3& Pos, const Standard_Real MajorRadius, const Standard_Real MinorRadius, gp_Pnt& P, gp_Vec& Vu, gp_Vec& Vv);
  
  Standard_EXPORT static void ConeD2 (const Standard_Real U, const Standard_Real V, const gp_Ax3& Pos, const Standard_Real Radius, const Standard_Real SAngle, gp_Pnt& P, gp_Vec& Vu, gp_Vec& Vv, gp_Vec& Vuu, gp_Vec& Vvv, gp_Vec& Vuv);
  
  Standard_EXPORT static void CylinderD2 (const Standard_Real U, const Standard_Real V, const gp_Ax3& Pos, const Standard_Real Radius, gp_Pnt& P, gp_Vec& Vu, gp_Vec& Vv, gp_Vec& Vuu, gp_Vec& Vvv, gp_Vec& Vuv);
  
  Standard_EXPORT static void SphereD2 (const Standard_Real U, const Standard_Real V, const gp_Ax3& Pos, const Standard_Real Radius, gp_Pnt& P, gp_Vec& Vu, gp_Vec& Vv, gp_Vec& Vuu, gp_Vec& Vvv, gp_Vec& Vuv);
  
  Standard_EXPORT static void TorusD2 (const Standard_Real U, const Standard_Real V, const gp_Ax3& Pos, const Standard_Real MajorRadius, const Standard_Real MinorRadius, gp_Pnt& P, gp_Vec& Vu, gp_Vec& Vv, gp_Vec& Vuu, gp_Vec& Vvv, gp_Vec& Vuv);
  
  Standard_EXPORT static void ConeD3 (const Standard_Real U, const Standard_Real V, const gp_Ax3& Pos, const Standard_Real Radius, const Standard_Real SAngle, gp_Pnt& P, gp_Vec& Vu, gp_Vec& Vv, gp_Vec& Vuu, gp_Vec& Vvv, gp_Vec& Vuv, gp_Vec& Vuuu, gp_Vec& Vvvv, gp_Vec& Vuuv, gp_Vec& Vuvv);
  
  Standard_EXPORT static void CylinderD3 (const Standard_Real U, const Standard_Real V, const gp_Ax3& Pos, const Standard_Real Radius, gp_Pnt& P, gp_Vec& Vu, gp_Vec& Vv, gp_Vec& Vuu, gp_Vec& Vvv, gp_Vec& Vuv, gp_Vec& Vuuu, gp_Vec& Vvvv, gp_Vec& Vuuv, gp_Vec& Vuvv);
  
  Standard_EXPORT static void SphereD3 (const Standard_Real U, const Standard_Real V, const gp_Ax3& Pos, const Standard_Real Radius, gp_Pnt& P, gp_Vec& Vu, gp_Vec& Vv, gp_Vec& Vuu, gp_Vec& Vvv, gp_Vec& Vuv, gp_Vec& Vuuu, gp_Vec& Vvvv, gp_Vec& Vuuv, gp_Vec& Vuvv);
  

  //! The following functions compute the parametric values
  //! corresponding to a given point on a elementary surface.
  //! The point should be on the surface.
  Standard_EXPORT static void TorusD3 (const Standard_Real U, const Standard_Real V, const gp_Ax3& Pos, const Standard_Real MajorRadius, const Standard_Real MinorRadius, gp_Pnt& P, gp_Vec& Vu, gp_Vec& Vv, gp_Vec& Vuu, gp_Vec& Vvv, gp_Vec& Vuv, gp_Vec& Vuuu, gp_Vec& Vvvv, gp_Vec& Vuuv, gp_Vec& Vuvv);
  
  //! parametrization
  //! P (U, V) =
  //! Pl.Location() + U * Pl.XDirection() + V * Pl.YDirection()
    static void Parameters (const gp_Pln& Pl, const gp_Pnt& P, Standard_Real& U, Standard_Real& V);
  
  //! parametrization
  //! P (U, V) = Location + V * ZDirection +
  //! Radius * (Cos(U) * XDirection + Sin (U) * YDirection)
    static void Parameters (const gp_Cylinder& C, const gp_Pnt& P, Standard_Real& U, Standard_Real& V);
  
  //! parametrization
  //! P (U, V) =  Location + V * ZDirection +
  //! (Radius + V * Tan (SemiAngle)) *
  //! (Cos(U) * XDirection + Sin(U) * YDirection)
    static void Parameters (const gp_Cone& C, const gp_Pnt& P, Standard_Real& U, Standard_Real& V);
  
  //! parametrization
  //! P (U, V) = Location +
  //! Radius * Cos (V) * (Cos (U) * XDirection + Sin (U) * YDirection) +
  //! Radius * Sin (V) * ZDirection
    static void Parameters (const gp_Sphere& S, const gp_Pnt& P, Standard_Real& U, Standard_Real& V);
  
  //! parametrization
  //! P (U, V) = Location +
  //! (MajorRadius + MinorRadius * Cos(U)) *
  //! (Cos(V) * XDirection - Sin(V) * YDirection) +
  //! MinorRadius * Sin(U) * ZDirection
    static void Parameters (const gp_Torus& T, const gp_Pnt& P, Standard_Real& U, Standard_Real& V);
  
  //! parametrization
  //! P (U, V) =
  //! Pl.Location() + U * Pl.XDirection() + V * Pl.YDirection()
  Standard_EXPORT static void PlaneParameters (const gp_Ax3& Pos, const gp_Pnt& P, Standard_Real& U, Standard_Real& V);
  
  //! parametrization
  //! P (U, V) = Location + V * ZDirection +
  //! Radius * (Cos(U) * XDirection + Sin (U) * YDirection)
  Standard_EXPORT static void CylinderParameters (const gp_Ax3& Pos, const Standard_Real Radius, const gp_Pnt& P, Standard_Real& U, Standard_Real& V);
  
  //! parametrization
  //! P (U, V) =  Location + V * ZDirection +
  //! (Radius + V * Tan (SemiAngle)) *
  //! (Cos(U) * XDirection + Sin(U) * YDirection)
  Standard_EXPORT static void ConeParameters (const gp_Ax3& Pos, const Standard_Real Radius, const Standard_Real SAngle, const gp_Pnt& P, Standard_Real& U, Standard_Real& V);
  
  //! parametrization
  //! P (U, V) = Location +
  //! Radius * Cos (V) * (Cos (U) * XDirection + Sin (U) * YDirection) +
  //! Radius * Sin (V) * ZDirection
  Standard_EXPORT static void SphereParameters (const gp_Ax3& Pos, const Standard_Real Radius, const gp_Pnt& P, Standard_Real& U, Standard_Real& V);
  
  //! parametrization
  //! P (U, V) = Location +
  //! (MajorRadius + MinorRadius * Cos(U)) *
  //! (Cos(V) * XDirection - Sin(V) * YDirection) +
  //! MinorRadius * Sin(U) * ZDirection
  Standard_EXPORT static void TorusParameters (const gp_Ax3& Pos, const Standard_Real MajorRadius, const Standard_Real MinorRadius, const gp_Pnt& P, Standard_Real& U, Standard_Real& V);
  
  //! compute the U Isoparametric gp_Lin of the plane.
  Standard_EXPORT static gp_Lin PlaneUIso (const gp_Ax3& Pos, const Standard_Real U);
  
  //! compute the U Isoparametric gp_Lin of the cylinder.
  Standard_EXPORT static gp_Lin CylinderUIso (const gp_Ax3& Pos, const Standard_Real Radius, const Standard_Real U);
  
  //! compute the U Isoparametric gp_Lin of the cone.
  Standard_EXPORT static gp_Lin ConeUIso (const gp_Ax3& Pos, const Standard_Real Radius, const Standard_Real SAngle, const Standard_Real U);
  
  //! compute the U Isoparametric gp_Circ of the sphere,
  //! (the meridian is not trimmed).
  Standard_EXPORT static gp_Circ SphereUIso (const gp_Ax3& Pos, const Standard_Real Radius, const Standard_Real U);
  
  //! compute the U Isoparametric gp_Circ of the torus.
  Standard_EXPORT static gp_Circ TorusUIso (const gp_Ax3& Pos, const Standard_Real MajorRadius, const Standard_Real MinorRadius, const Standard_Real U);
  
  //! compute the V Isoparametric gp_Lin of the plane.
  Standard_EXPORT static gp_Lin PlaneVIso (const gp_Ax3& Pos, const Standard_Real V);
  
  //! compute the V Isoparametric gp_Circ of the cylinder.
  Standard_EXPORT static gp_Circ CylinderVIso (const gp_Ax3& Pos, const Standard_Real Radius, const Standard_Real V);
  
  //! compute the V Isoparametric gp_Circ of the cone.
  Standard_EXPORT static gp_Circ ConeVIso (const gp_Ax3& Pos, const Standard_Real Radius, const Standard_Real SAngle, const Standard_Real V);
  
  //! compute the V Isoparametric gp_Circ of the sphere,
  //! (the meridian is not trimmed).
  Standard_EXPORT static gp_Circ SphereVIso (const gp_Ax3& Pos, const Standard_Real Radius, const Standard_Real V);
  
  //! compute the V Isoparametric gp_Circ of the torus.
  Standard_EXPORT static gp_Circ TorusVIso (const gp_Ax3& Pos, const Standard_Real MajorRadius, const Standard_Real MinorRadius, const Standard_Real V);


protected:


private:


};


#include <ElSLib.lxx>


#endif // _ElSLib_HeaderFile
Commit	Line	Data
42cf5bc1	1	// Created on: 1991-09-09
	2	// Created by: Michel Chauvat
	3	// Copyright (c) 1991-1999 Matra Datavision
	4	// Copyright (c) 1999-2014 OPEN CASCADE SAS
	5	//
	6	// This file is part of Open CASCADE Technology software library.
	7	//
	8	// This library is free software; you can redistribute it and/or modify it under
	9	// the terms of the GNU Lesser General Public License version 2.1 as published
	10	// by the Free Software Foundation, with special exception defined in the file
	11	// OCCT_LGPL_EXCEPTION.txt. Consult the file LICENSE_LGPL_21.txt included in OCCT
	12	// distribution for complete text of the license and disclaimer of any warranty.
	13	//
	14	// Alternatively, this file may be used under the terms of Open CASCADE
	15	// commercial license or contractual agreement.
	16
	17	#ifndef _ElSLib_HeaderFile
	18	#define _ElSLib_HeaderFile
	19
	20	#include <Standard.hxx>
	21	#include <Standard_DefineAlloc.hxx>
	22	#include <Standard_Handle.hxx>
	23
	24	#include <Standard_Real.hxx>
	25	#include <gp_Pnt.hxx>
	26	#include <Standard_Integer.hxx>
	27	#include <gp_Vec.hxx>
	28	class gp_Pnt;
	29	class gp_Pln;
	30	class gp_Cone;
	31	class gp_Cylinder;
	32	class gp_Sphere;
	33	class gp_Torus;
	34	class gp_Vec;
	35	class gp_Ax3;
	36	class gp_Lin;
	37	class gp_Circ;
	38
	39
	40	//! Provides functions for basic geometric computation on
	41	//! elementary surfaces.
	42	//! This includes:
	43	//! - calculation of a point or derived vector on a surface
	44	//! where the surface is provided by the gp package, or
	45	//! defined in canonical form (as in the gp package), and
	46	//! the point is defined with a parameter,
	47	//! - evaluation of the parameters corresponding to a
	48	//! point on an elementary surface from gp,
	49	//! - calculation of isoparametric curves on an elementary
	50	//! surface defined in canonical form (as in the gp package).
	51	//! Notes:
	52	//! - ElSLib stands for Elementary Surfaces Library.
	53	//! - If the surfaces provided by the gp package are not
	54	//! explicitly parameterized, they still have an implicit
	55	//! parameterization, similar to that which they infer on
	56	//! the equivalent Geom surfaces.
	57	//! Note: ElSLib stands for Elementary Surfaces Library.
	58	class ElSLib
	59	{
	60	public:
	61
	62	DEFINE_STANDARD_ALLOC
	63
	64
65	//! For elementary surfaces from the gp package (planes,
66	//! cones, cylinders, spheres and tori), computes the point
67	//! of parameters (U, V).
0f57ab75	68	static gp_Pnt Value (const Standard_Real U, const Standard_Real V, const gp_Pln& Pl);
42cf5bc1	69
	70	static gp_Pnt Value (const Standard_Real U, const Standard_Real V, const gp_Cone& C);
	71
	72	static gp_Pnt Value (const Standard_Real U, const Standard_Real V, const gp_Cylinder& C);
	73
	74	static gp_Pnt Value (const Standard_Real U, const Standard_Real V, const gp_Sphere& S);
	75
	76	static gp_Pnt Value (const Standard_Real U, const Standard_Real V, const gp_Torus& T);
	77
	78	//! For elementary surfaces from the gp package (planes,
	79	//! cones, cylinders, spheres and tori), computes the
	80	//! derivative vector of order Nu and Nv in the u and v
	81	//! parametric directions respectively, at the point of
	82	//! parameters (U, V).
0f57ab75	83	static gp_Vec DN (const Standard_Real U, const Standard_Real V, const gp_Pln& Pl, const Standard_Integer Nu, const Standard_Integer Nv);
42cf5bc1	84
	85	static gp_Vec DN (const Standard_Real U, const Standard_Real V, const gp_Cone& C, const Standard_Integer Nu, const Standard_Integer Nv);
	86
	87	static gp_Vec DN (const Standard_Real U, const Standard_Real V, const gp_Cylinder& C, const Standard_Integer Nu, const Standard_Integer Nv);
	88
	89	static gp_Vec DN (const Standard_Real U, const Standard_Real V, const gp_Sphere& S, const Standard_Integer Nu, const Standard_Integer Nv);
	90
	91	static gp_Vec DN (const Standard_Real U, const Standard_Real V, const gp_Torus& T, const Standard_Integer Nu, const Standard_Integer Nv);
	92
	93	//! For elementary surfaces from the gp package (planes,
	94	//! cones, cylinders, spheres and tori), computes the point P
	95	//! of parameters (U, V).inline
0f57ab75	96	static void D0 (const Standard_Real U, const Standard_Real V, const gp_Pln& Pl, gp_Pnt& P);
42cf5bc1	97
	98	static void D0 (const Standard_Real U, const Standard_Real V, const gp_Cone& C, gp_Pnt& P);
	99
	100	static void D0 (const Standard_Real U, const Standard_Real V, const gp_Cylinder& C, gp_Pnt& P);
	101
	102	static void D0 (const Standard_Real U, const Standard_Real V, const gp_Sphere& S, gp_Pnt& P);
	103
	104	static void D0 (const Standard_Real U, const Standard_Real V, const gp_Torus& T, gp_Pnt& P);
	105
	106
	107	//! For elementary surfaces from the gp package (planes,
	108	//! cones, cylinders, spheres and tori), computes:
	109	//! - the point P of parameters (U, V), and
	110	//! - the first derivative vectors Vu and Vv at this point in
	111	//! the u and v parametric directions respectively.
0f57ab75	112	static void D1 (const Standard_Real U, const Standard_Real V, const gp_Pln& Pl, gp_Pnt& P, gp_Vec& Vu, gp_Vec& Vv);
42cf5bc1	113
	114	static void D1 (const Standard_Real U, const Standard_Real V, const gp_Cone& C, gp_Pnt& P, gp_Vec& Vu, gp_Vec& Vv);
	115
	116	static void D1 (const Standard_Real U, const Standard_Real V, const gp_Cylinder& C, gp_Pnt& P, gp_Vec& Vu, gp_Vec& Vv);
	117
	118	static void D1 (const Standard_Real U, const Standard_Real V, const gp_Sphere& S, gp_Pnt& P, gp_Vec& Vu, gp_Vec& Vv);
	119
	120	static void D1 (const Standard_Real U, const Standard_Real V, const gp_Torus& T, gp_Pnt& P, gp_Vec& Vu, gp_Vec& Vv);
	121
	122
	123	//! For elementary surfaces from the gp package (cones,
	124	//! cylinders, spheres and tori), computes:
	125	//! - the point P of parameters (U, V), and
	126	//! - the first derivative vectors Vu and Vv at this point in
	127	//! the u and v parametric directions respectively, and
	128	//! - the second derivative vectors Vuu, Vvv and Vuv at this point.
0f57ab75	129	static void D2 (const Standard_Real U, const Standard_Real V, const gp_Cone& C, gp_Pnt& P, gp_Vec& Vu, gp_Vec& Vv, gp_Vec& Vuu, gp_Vec& Vvv, gp_Vec& Vuv);
42cf5bc1	130
	131	static void D2 (const Standard_Real U, const Standard_Real V, const gp_Cylinder& C, gp_Pnt& P, gp_Vec& Vu, gp_Vec& Vv, gp_Vec& Vuu, gp_Vec& Vvv, gp_Vec& Vuv);
	132
	133	static void D2 (const Standard_Real U, const Standard_Real V, const gp_Sphere& S, gp_Pnt& P, gp_Vec& Vu, gp_Vec& Vv, gp_Vec& Vuu, gp_Vec& Vvv, gp_Vec& Vuv);
	134
	135	static void D2 (const Standard_Real U, const Standard_Real V, const gp_Torus& T, gp_Pnt& P, gp_Vec& Vu, gp_Vec& Vv, gp_Vec& Vuu, gp_Vec& Vvv, gp_Vec& Vuv);
	136
	137
	138	//! For elementary surfaces from the gp package (cones,
	139	//! cylinders, spheres and tori), computes:
	140	//! - the point P of parameters (U,V), and
	141	//! - the first derivative vectors Vu and Vv at this point in
	142	//! the u and v parametric directions respectively, and
	143	//! - the second derivative vectors Vuu, Vvv and Vuv at
	144	//! this point, and
	145	//! - the third derivative vectors Vuuu, Vvvv, Vuuv and
	146	//! Vuvv at this point.
0f57ab75	147	static void D3 (const Standard_Real U, const Standard_Real V, const gp_Cone& C, gp_Pnt& P, gp_Vec& Vu, gp_Vec& Vv, gp_Vec& Vuu, gp_Vec& Vvv, gp_Vec& Vuv, gp_Vec& Vuuu, gp_Vec& Vvvv, gp_Vec& Vuuv, gp_Vec& Vuvv);
42cf5bc1	148
	149	static void D3 (const Standard_Real U, const Standard_Real V, const gp_Cylinder& C, gp_Pnt& P, gp_Vec& Vu, gp_Vec& Vv, gp_Vec& Vuu, gp_Vec& Vvv, gp_Vec& Vuv, gp_Vec& Vuuu, gp_Vec& Vvvv, gp_Vec& Vuuv, gp_Vec& Vuvv);
	150
	151	static void D3 (const Standard_Real U, const Standard_Real V, const gp_Sphere& S, gp_Pnt& P, gp_Vec& Vu, gp_Vec& Vv, gp_Vec& Vuu, gp_Vec& Vvv, gp_Vec& Vuv, gp_Vec& Vuuu, gp_Vec& Vvvv, gp_Vec& Vuuv, gp_Vec& Vuvv);
	152
	153	//! Surface evaluation
	154	//! The following functions compute the point and the
	155	//! derivatives on elementary surfaces defined with their
	156	//! geometric characterisitics.
	157	//! You don't need to create the surface to use these functions.
	158	//! These functions are called by the previous ones.
	159	//! Example :
	160	//! A cylinder is defined with its position and its radius.
	161	static void D3 (const Standard_Real U, const Standard_Real V, const gp_Torus& T, gp_Pnt& P, gp_Vec& Vu, gp_Vec& Vv, gp_Vec& Vuu, gp_Vec& Vvv, gp_Vec& Vuv, gp_Vec& Vuuu, gp_Vec& Vvvv, gp_Vec& Vuuv, gp_Vec& Vuvv);
	162
	163	Standard_EXPORT static gp_Pnt PlaneValue (const Standard_Real U, const Standard_Real V, const gp_Ax3& Pos);
	164
	165	Standard_EXPORT static gp_Pnt CylinderValue (const Standard_Real U, const Standard_Real V, const gp_Ax3& Pos, const Standard_Real Radius);
	166
	167	Standard_EXPORT static gp_Pnt ConeValue (const Standard_Real U, const Standard_Real V, const gp_Ax3& Pos, const Standard_Real Radius, const Standard_Real SAngle);
	168
	169	Standard_EXPORT static gp_Pnt SphereValue (const Standard_Real U, const Standard_Real V, const gp_Ax3& Pos, const Standard_Real Radius);
	170
	171	Standard_EXPORT static gp_Pnt TorusValue (const Standard_Real U, const Standard_Real V, const gp_Ax3& Pos, const Standard_Real MajorRadius, const Standard_Real MinorRadius);
	172
	173	Standard_EXPORT static gp_Vec PlaneDN (const Standard_Real U, const Standard_Real V, const gp_Ax3& Pos, const Standard_Integer Nu, const Standard_Integer Nv);
	174
	175	Standard_EXPORT static gp_Vec CylinderDN (const Standard_Real U, const Standard_Real V, const gp_Ax3& Pos, const Standard_Real Radius, const Standard_Integer Nu, const Standard_Integer Nv);
	176
	177	Standard_EXPORT static gp_Vec ConeDN (const Standard_Real U, const Standard_Real V, const gp_Ax3& Pos, const Standard_Real Radius, const Standard_Real SAngle, const Standard_Integer Nu, const Standard_Integer Nv);
	178
	179	Standard_EXPORT static gp_Vec SphereDN (const Standard_Real U, const Standard_Real V, const gp_Ax3& Pos, const Standard_Real Radius, const Standard_Integer Nu, const Standard_Integer Nv);
	180
	181	Standard_EXPORT static gp_Vec TorusDN (const Standard_Real U, const Standard_Real V, const gp_Ax3& Pos, const Standard_Real MajorRadius, const Standard_Real MinorRadius, const Standard_Integer Nu, const Standard_Integer Nv);
	182
	183	Standard_EXPORT static void PlaneD0 (const Standard_Real U, const Standard_Real V, const gp_Ax3& Pos, gp_Pnt& P);
	184
	185	Standard_EXPORT static void ConeD0 (const Standard_Real U, const Standard_Real V, const gp_Ax3& Pos, const Standard_Real Radius, const Standard_Real SAngle, gp_Pnt& P);
	186
	187	Standard_EXPORT static void CylinderD0 (const Standard_Real U, const Standard_Real V, const gp_Ax3& Pos, const Standard_Real Radius, gp_Pnt& P);
	188
	189	Standard_EXPORT static void SphereD0 (const Standard_Real U, const Standard_Real V, const gp_Ax3& Pos, const Standard_Real Radius, gp_Pnt& P);
	190
	191	Standard_EXPORT static void TorusD0 (const Standard_Real U, const Standard_Real V, const gp_Ax3& Pos, const Standard_Real MajorRadius, const Standard_Real MinorRadius, gp_Pnt& P);
	192
	193	Standard_EXPORT static void PlaneD1 (const Standard_Real U, const Standard_Real V, const gp_Ax3& Pos, gp_Pnt& P, gp_Vec& Vu, gp_Vec& Vv);
	194
	195	Standard_EXPORT static void ConeD1 (const Standard_Real U, const Standard_Real V, const gp_Ax3& Pos, const Standard_Real Radius, const Standard_Real SAngle, gp_Pnt& P, gp_Vec& Vu, gp_Vec& Vv);
	196
	197	Standard_EXPORT static void CylinderD1 (const Standard_Real U, const Standard_Real V, const gp_Ax3& Pos, const Standard_Real Radius, gp_Pnt& P, gp_Vec& Vu, gp_Vec& Vv);
	198
	199	Standard_EXPORT static void SphereD1 (const Standard_Real U, const Standard_Real V, const gp_Ax3& Pos, const Standard_Real Radius, gp_Pnt& P, gp_Vec& Vu, gp_Vec& Vv);
	200
	201	Standard_EXPORT static void TorusD1 (const Standard_Real U, const Standard_Real V, const gp_Ax3& Pos, const Standard_Real MajorRadius, const Standard_Real MinorRadius, gp_Pnt& P, gp_Vec& Vu, gp_Vec& Vv);
	202
	203	Standard_EXPORT static void ConeD2 (const Standard_Real U, const Standard_Real V, const gp_Ax3& Pos, const Standard_Real Radius, const Standard_Real SAngle, gp_Pnt& P, gp_Vec& Vu, gp_Vec& Vv, gp_Vec& Vuu, gp_Vec& Vvv, gp_Vec& Vuv);
	204
	205	Standard_EXPORT static void CylinderD2 (const Standard_Real U, const Standard_Real V, const gp_Ax3& Pos, const Standard_Real Radius, gp_Pnt& P, gp_Vec& Vu, gp_Vec& Vv, gp_Vec& Vuu, gp_Vec& Vvv, gp_Vec& Vuv);
	206
	207	Standard_EXPORT static void SphereD2 (const Standard_Real U, const Standard_Real V, const gp_Ax3& Pos, const Standard_Real Radius, gp_Pnt& P, gp_Vec& Vu, gp_Vec& Vv, gp_Vec& Vuu, gp_Vec& Vvv, gp_Vec& Vuv);
	208
	209	Standard_EXPORT static void TorusD2 (const Standard_Real U, const Standard_Real V, const gp_Ax3& Pos, const Standard_Real MajorRadius, const Standard_Real MinorRadius, gp_Pnt& P, gp_Vec& Vu, gp_Vec& Vv, gp_Vec& Vuu, gp_Vec& Vvv, gp_Vec& Vuv);
	210
	211	Standard_EXPORT static void ConeD3 (const Standard_Real U, const Standard_Real V, const gp_Ax3& Pos, const Standard_Real Radius, const Standard_Real SAngle, gp_Pnt& P, gp_Vec& Vu, gp_Vec& Vv, gp_Vec& Vuu, gp_Vec& Vvv, gp_Vec& Vuv, gp_Vec& Vuuu, gp_Vec& Vvvv, gp_Vec& Vuuv, gp_Vec& Vuvv);
212
213	Standard_EXPORT static void CylinderD3 (const Standard_Real U, const Standard_Real V, const gp_Ax3& Pos, const Standard_Real Radius, gp_Pnt& P, gp_Vec& Vu, gp_Vec& Vv, gp_Vec& Vuu, gp_Vec& Vvv, gp_Vec& Vuv, gp_Vec& Vuuu, gp_Vec& Vvvv, gp_Vec& Vuuv, gp_Vec& Vuvv);
214
215	Standard_EXPORT static void SphereD3 (const Standard_Real U, const Standard_Real V, const gp_Ax3& Pos, const Standard_Real Radius, gp_Pnt& P, gp_Vec& Vu, gp_Vec& Vv, gp_Vec& Vuu, gp_Vec& Vvv, gp_Vec& Vuv, gp_Vec& Vuuu, gp_Vec& Vvvv, gp_Vec& Vuuv, gp_Vec& Vuvv);
216
217
218	//! The following functions compute the parametric values
219	//! corresponding to a given point on a elementary surface.
220	//! The point should be on the surface.
221	Standard_EXPORT static void TorusD3 (const Standard_Real U, const Standard_Real V, const gp_Ax3& Pos, const Standard_Real MajorRadius, const Standard_Real MinorRadius, gp_Pnt& P, gp_Vec& Vu, gp_Vec& Vv, gp_Vec& Vuu, gp_Vec& Vvv, gp_Vec& Vuv, gp_Vec& Vuuu, gp_Vec& Vvvv, gp_Vec& Vuuv, gp_Vec& Vuvv);
222
223	//! parametrization
224	//! P (U, V) =
225	//! Pl.Location() + U * Pl.XDirection() + V * Pl.YDirection()
226	static void Parameters (const gp_Pln& Pl, const gp_Pnt& P, Standard_Real& U, Standard_Real& V);
227
228	//! parametrization
229	//! P (U, V) = Location + V * ZDirection +
230	//! Radius * (Cos(U) * XDirection + Sin (U) * YDirection)
231	static void Parameters (const gp_Cylinder& C, const gp_Pnt& P, Standard_Real& U, Standard_Real& V);
232
233	//! parametrization
234	//! P (U, V) = Location + V * ZDirection +
235	//! (Radius + V * Tan (SemiAngle)) *
236	//! (Cos(U) * XDirection + Sin(U) * YDirection)
237	static void Parameters (const gp_Cone& C, const gp_Pnt& P, Standard_Real& U, Standard_Real& V);
238
239	//! parametrization
240	//! P (U, V) = Location +
241	//! Radius * Cos (V) * (Cos (U) * XDirection + Sin (U) * YDirection) +
242	//! Radius * Sin (V) * ZDirection
243	static void Parameters (const gp_Sphere& S, const gp_Pnt& P, Standard_Real& U, Standard_Real& V);
244
245	//! parametrization
246	//! P (U, V) = Location +
247	//! (MajorRadius + MinorRadius * Cos(U)) *
248	//! (Cos(V) * XDirection - Sin(V) * YDirection) +
249	//! MinorRadius * Sin(U) * ZDirection
250	static void Parameters (const gp_Torus& T, const gp_Pnt& P, Standard_Real& U, Standard_Real& V);
251
252	//! parametrization
253	//! P (U, V) =
254	//! Pl.Location() + U * Pl.XDirection() + V * Pl.YDirection()
255	Standard_EXPORT static void PlaneParameters (const gp_Ax3& Pos, const gp_Pnt& P, Standard_Real& U, Standard_Real& V);
256
257	//! parametrization
258	//! P (U, V) = Location + V * ZDirection +
259	//! Radius * (Cos(U) * XDirection + Sin (U) * YDirection)
260	Standard_EXPORT static void CylinderParameters (const gp_Ax3& Pos, const Standard_Real Radius, const gp_Pnt& P, Standard_Real& U, Standard_Real& V);
261
262	//! parametrization
263	//! P (U, V) = Location + V * ZDirection +
264	//! (Radius + V * Tan (SemiAngle)) *
265	//! (Cos(U) * XDirection + Sin(U) * YDirection)
266	Standard_EXPORT static void ConeParameters (const gp_Ax3& Pos, const Standard_Real Radius, const Standard_Real SAngle, const gp_Pnt& P, Standard_Real& U, Standard_Real& V);
267
268	//! parametrization
269	//! P (U, V) = Location +
270	//! Radius * Cos (V) * (Cos (U) * XDirection + Sin (U) * YDirection) +
271	//! Radius * Sin (V) * ZDirection
272	Standard_EXPORT static void SphereParameters (const gp_Ax3& Pos, const Standard_Real Radius, const gp_Pnt& P, Standard_Real& U, Standard_Real& V);
273
274	//! parametrization
275	//! P (U, V) = Location +
276	//! (MajorRadius + MinorRadius * Cos(U)) *
277	//! (Cos(V) * XDirection - Sin(V) * YDirection) +
278	//! MinorRadius * Sin(U) * ZDirection
279	Standard_EXPORT static void TorusParameters (const gp_Ax3& Pos, const Standard_Real MajorRadius, const Standard_Real MinorRadius, const gp_Pnt& P, Standard_Real& U, Standard_Real& V);
280
281	//! compute the U Isoparametric gp_Lin of the plane.
282	Standard_EXPORT static gp_Lin PlaneUIso (const gp_Ax3& Pos, const Standard_Real U);
283
284	//! compute the U Isoparametric gp_Lin of the cylinder.
285	Standard_EXPORT static gp_Lin CylinderUIso (const gp_Ax3& Pos, const Standard_Real Radius, const Standard_Real U);
286
287	//! compute the U Isoparametric gp_Lin of the cone.
288	Standard_EXPORT static gp_Lin ConeUIso (const gp_Ax3& Pos, const Standard_Real Radius, const Standard_Real SAngle, const Standard_Real U);
289
290	//! compute the U Isoparametric gp_Circ of the sphere,
291	//! (the meridian is not trimmed).
292	Standard_EXPORT static gp_Circ SphereUIso (const gp_Ax3& Pos, const Standard_Real Radius, const Standard_Real U);
293
294	//! compute the U Isoparametric gp_Circ of the torus.
295	Standard_EXPORT static gp_Circ TorusUIso (const gp_Ax3& Pos, const Standard_Real MajorRadius, const Standard_Real MinorRadius, const Standard_Real U);
296
297	//! compute the V Isoparametric gp_Lin of the plane.
298	Standard_EXPORT static gp_Lin PlaneVIso (const gp_Ax3& Pos, const Standard_Real V);
299
300	//! compute the V Isoparametric gp_Circ of the cylinder.
301	Standard_EXPORT static gp_Circ CylinderVIso (const gp_Ax3& Pos, const Standard_Real Radius, const Standard_Real V);
302
303	//! compute the V Isoparametric gp_Circ of the cone.
304	Standard_EXPORT static gp_Circ ConeVIso (const gp_Ax3& Pos, const Standard_Real Radius, const Standard_Real SAngle, const Standard_Real V);
305
306	//! compute the V Isoparametric gp_Circ of the sphere,
307	//! (the meridian is not trimmed).
308	Standard_EXPORT static gp_Circ SphereVIso (const gp_Ax3& Pos, const Standard_Real Radius, const Standard_Real V);
309
310	//! compute the V Isoparametric gp_Circ of the torus.
311	Standard_EXPORT static gp_Circ TorusVIso (const gp_Ax3& Pos, const Standard_Real MajorRadius, const Standard_Real MinorRadius, const Standard_Real V);
312
313
314
315
316	protected:
317
318
319
320
321
322	private:
323
324
325
326
327
328	};
329
330
331	#include <ElSLib.lxx>
332
333
334
335
336
337	#endif // _ElSLib_HeaderFile