// Created on: 1996-11-08
// Created by: Jean Claude VAUTHIER
// Copyright (c) 1996-1999 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 _GCPnts_TangentialDeflection_HeaderFile
#define _GCPnts_TangentialDeflection_HeaderFile

#include "TColgp_SequenceOfPnt.hxx"
#include "TColStd_SequenceOfReal.hxx"
#include "gp_Pnt.hxx"
#include "math_Function.hxx"
#include "math_MultipleVarFunction.hxx"
#include "Adaptor3d_Curve.hxx"
#include "Adaptor2d_Curve2d.hxx"

//! Computes a set of  points on a curve from package
//! Adaptor3d  such  as between  two successive   points
//! P1(u1)and P2(u2) :
//! @code
//! . ||P1P3^P3P2||/||P1P3||*||P3P2||<AngularDeflection
//! . ||P1P2^P1P3||/||P1P2||<CurvatureDeflection
//! @endcode
//! where P3 is the point of abscissa ((u1+u2)/2), with
//! u1 the abscissa of the point P1 and u2 the abscissa
//! of the point P2.
//!
//! ^ is the cross product of two vectors, and ||P1P2||
//! the magnitude of the vector P1P2.
//!
//! The conditions AngularDeflection > gp::Resolution()
//! and CurvatureDeflection > gp::Resolution() must be
//! satisfied at the construction time.
//!
//! A minimum number of points can be fixed for a linear or circular element.
//! Example:
//! @code
//! Handle(Geom_BezierCurve) aCurve = new Geom_BezierCurve (thePoles);
//! GeomAdaptor_Curve aCurveAdaptor (aCurve);
//! double aCDeflect  = 0.01; // Curvature deflection
//! double anADeflect = 0.09; // Angular   deflection
//!
//! GCPnts_TangentialDeflection aPointsOnCurve;
//! aPointsOnCurve.Initialize (aCurveAdaptor, anADeflect, aCDeflect);
//! for (int i = 1; i <= aPointsOnCurve.NbPoints(); ++i)
//! {
//!   double aU   = aPointsOnCurve.Parameter (i);
//!   gp_Pnt aPnt = aPointsOnCurve.Value (i);
//! }
//! @endcode
class GCPnts_TangentialDeflection
{
public:
  DEFINE_STANDARD_ALLOC

  //! Empty constructor.
  //! @sa Initialize()
  Standard_EXPORT GCPnts_TangentialDeflection();

  //! Constructor for 3D curve.
  //! @param[in] theC  3d curve
  //! @param[in] theAngularDeflection    angular deflection in radians
  //! @param[in] theCurvatureDeflection  linear deflection
  //! @param[in] theMinimumOfPoints  minimum number of points
  //! @param[in] theUTol    tolerance in curve parametric scope
  //! @param[in] theMinLen  minimal length
  Standard_EXPORT GCPnts_TangentialDeflection(const Adaptor3d_Curve& theC,
                                              const Standard_Real    theAngularDeflection,
                                              const Standard_Real    theCurvatureDeflection,
                                              const Standard_Integer theMinimumOfPoints = 2,
                                              const Standard_Real    theUTol            = 1.0e-9,
                                              const Standard_Real    theMinLen          = 1.0e-7);

  //! Constructor for 3D curve with restricted range.
  //! @param[in] theC  3d curve
  //! @param[in] theFirstParameter  first parameter on curve
  //! @param[in] theLastParameter   last  parameter on curve
  //! @param[in] theAngularDeflection    angular deflection in radians
  //! @param[in] theCurvatureDeflection  linear deflection
  //! @param[in] theMinimumOfPoints  minimum number of points
  //! @param theUTo  l[in]  tolerance in curve parametric scope
  //! @param[in] theMinLen  minimal length
  Standard_EXPORT GCPnts_TangentialDeflection(const Adaptor3d_Curve& theC,
                                              const Standard_Real    theFirstParameter,
                                              const Standard_Real    theLastParameter,
                                              const Standard_Real    theAngularDeflection,
                                              const Standard_Real    theCurvatureDeflection,
                                              const Standard_Integer theMinimumOfPoints = 2,
                                              const Standard_Real    theUTol            = 1.0e-9,
                                              const Standard_Real    theMinLen          = 1.0e-7);

  //! Constructor for 2D curve.
  //! @param[in] theC  2d curve
  //! @param[in] theAngularDeflection    angular deflection in radians
  //! @param[in] theCurvatureDeflection  linear deflection
  //! @param[in] theMinimumOfPoints  minimum number of points
  //! @param[in] theUTol    tolerance in curve parametric scope
  //! @param[in] theMinLen  minimal length
  Standard_EXPORT GCPnts_TangentialDeflection(const Adaptor2d_Curve2d& theC,
                                              const Standard_Real      theAngularDeflection,
                                              const Standard_Real      theCurvatureDeflection,
                                              const Standard_Integer   theMinimumOfPoints = 2,
                                              const Standard_Real      theUTol            = 1.0e-9,
                                              const Standard_Real      theMinLen          = 1.0e-7);

  //! Constructor for 2D curve with restricted range.
  //! @param[in] theC  2d curve
  //! @param[in] theFirstParameter  first parameter on curve
  //! @param[in] theLastParameter   last  parameter on curve
  //! @param[in] theAngularDeflection    angular deflection in radians
  //! @param[in] theCurvatureDeflection  linear deflection
  //! @param[in] theMinimumOfPoints  minimum number of points
  //! @param[in] theUTol    tolerance in curve parametric scope
  //! @param[in] theMinLen  minimal length
  Standard_EXPORT GCPnts_TangentialDeflection(const Adaptor2d_Curve2d& theC,
                                              const Standard_Real      theFirstParameter,
                                              const Standard_Real      theLastParameter,
                                              const Standard_Real      theAngularDeflection,
                                              const Standard_Real      theCurvatureDeflection,
                                              const Standard_Integer   theMinimumOfPoints = 2,
                                              const Standard_Real      theUTol            = 1.0e-9,
                                              const Standard_Real      theMinLen          = 1.0e-7);

  //! Initialize algorithm for 3D curve.
  //! @param[in] theC  3d curve
  //! @param[in] theAngularDeflection    angular deflection in radians
  //! @param[in] theCurvatureDeflection  linear deflection
  //! @param[in] theMinimumOfPoints  minimum number of points
  //! @param[in] theUTol    tolerance in curve parametric scope
  //! @param[in] theMinLen  minimal length
  Standard_EXPORT void Initialize(const Adaptor3d_Curve& theC,
                                  const Standard_Real    theAngularDeflection,
                                  const Standard_Real    theCurvatureDeflection,
                                  const Standard_Integer theMinimumOfPoints = 2,
                                  const Standard_Real    theUTol            = 1.0e-9,
                                  const Standard_Real    theMinLen          = 1.0e-7);

  //! Initialize algorithm for 3D curve with restricted range.
  //! @param[in] theC  3d curve
  //! @param[in] theFirstParameter  first parameter on curve
  //! @param[in] theLastParameter   last  parameter on curve
  //! @param[in] theAngularDeflection    angular deflection in radians
  //! @param[in] theCurvatureDeflection  linear deflection
  //! @param[in] theMinimumOfPoints  minimum number of points
  //! @param[in] theUTol    tolerance in curve parametric scope
  //! @param[in] theMinLen  minimal length
  Standard_EXPORT void Initialize(const Adaptor3d_Curve& theC,
                                  const Standard_Real    theFirstParameter,
                                  const Standard_Real    theLastParameter,
                                  const Standard_Real    theAngularDeflection,
                                  const Standard_Real    theCurvatureDeflection,
                                  const Standard_Integer theMinimumOfPoints = 2,
                                  const Standard_Real    theUTol            = 1.0e-9,
                                  const Standard_Real    theMinLen          = 1.0e-7);

  //! Initialize algorithm for 2D curve.
  //! @param[in] theC  2d curve
  //! @param[in] theAngularDeflection    angular deflection in radians
  //! @param[in] theCurvatureDeflection  linear deflection
  //! @param[in] theMinimumOfPoints  minimum number of points
  //! @param[in] theUTol    tolerance in curve parametric scope
  //! @param[in] theMinLen  minimal length
  Standard_EXPORT void Initialize(const Adaptor2d_Curve2d& theC,
                                  const Standard_Real      theAngularDeflection,
                                  const Standard_Real      theCurvatureDeflection,
                                  const Standard_Integer   theMinimumOfPoints = 2,
                                  const Standard_Real      theUTol            = 1.0e-9,
                                  const Standard_Real      theMinLen          = 1.0e-7);

  //! Initialize algorithm for 2D curve with restricted range.
  //! @param[in] theC  2d curve
  //! @param[in] theFirstParameter  first parameter on curve
  //! @param[in] theLastParameter   last  parameter on curve
  //! @param[in] theAngularDeflection    angular deflection in radians
  //! @param[in] theCurvatureDeflection  linear deflection
  //! @param[in] theMinimumOfPoints  minimum number of points
  //! @param[in] theUTol    tolerance in curve parametric scope
  //! @param[in] theMinLen  minimal length
  Standard_EXPORT void Initialize(const Adaptor2d_Curve2d& theC,
                                  const Standard_Real      theFirstParameter,
                                  const Standard_Real      theLastParameter,
                                  const Standard_Real      theAngularDeflection,
                                  const Standard_Real      theCurvatureDeflection,
                                  const Standard_Integer   theMinimumOfPoints = 2,
                                  const Standard_Real      theUTol            = 1.0e-9,
                                  const Standard_Real      theMinLen          = 1.0e-7);

  //! Add point to already calculated points (or replace existing)
  //! Returns index of new added point
  //! or founded with parametric tolerance (replaced if theIsReplace is true)
  Standard_EXPORT Standard_Integer AddPoint(const gp_Pnt&          thePnt,
                                            const Standard_Real    theParam,
                                            const Standard_Boolean theIsReplace = Standard_True);

  Standard_Integer NbPoints() const { return myParameters.Length(); }

  Standard_Real Parameter(const Standard_Integer I) const { return myParameters.Value(I); }

  gp_Pnt Value(const Standard_Integer I) const { return myPoints.Value(I); }

  //! Computes angular step for the arc using the given parameters.
  Standard_EXPORT static Standard_Real ArcAngularStep(const Standard_Real theRadius,
                                                      const Standard_Real theLinearDeflection,
                                                      const Standard_Real theAngularDeflection,
                                                      const Standard_Real theMinLength);

private:
  template <class TheCurve>
  void initialize(const TheCurve&        theC,
                  const Standard_Real    theFirstParameter,
                  const Standard_Real    theLastParameter,
                  const Standard_Real    theAngularDeflection,
                  const Standard_Real    theCurvatureDeflection,
                  const Standard_Integer theMinimumOfPoints,
                  const Standard_Real    theUTol,
                  const Standard_Real    theMinLen);

  template <class TheCurve>
  void PerformLinear(const TheCurve& theC);

  template <class TheCurve>
  void PerformCircular(const TheCurve& theC);

  //! Respecting the angle and the deflection,
  //! we impose a minimum number of points on a curve.
  template <class TheCurve>
  void PerformCurve(const TheCurve& theC);

  template <class TheCurve>
  void EvaluateDu(const TheCurve&     theC,
                  const Standard_Real theU,
                  gp_Pnt&             theP,
                  Standard_Real&      theDu,
                  Standard_Boolean&   theNotDone) const;

  //! Estimation of maximal deflection for interval [theU1, theU2]
  template <class TheCurve>
  void EstimDefl(const TheCurve&     theC,
                 const Standard_Real theU1,
                 const Standard_Real theU2,
                 Standard_Real&      theMaxDefl,
                 Standard_Real&      theUMax);

private:
  Standard_Real          myAngularDeflection;
  Standard_Real          myCurvatureDeflection;
  Standard_Real          myUTol;
  Standard_Integer       myMinNbPnts;
  Standard_Real          myMinLen;
  Standard_Real          myLastU;
  Standard_Real          myFirstu;
  TColgp_SequenceOfPnt   myPoints;
  TColStd_SequenceOfReal myParameters;
};

#endif // _GCPnts_TangentialDeflection_HeaderFile