OCCT

// Copyright (c) 1994-1999 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 _GeomLProp_NumericCurInf2d_HeaderFile
#define _GeomLProp_NumericCurInf2d_HeaderFile

#include <Geom2d_Curve.hxx>
#include <GeomLProp_FuncCurExt2d.pxx>
#include <GeomLProp_FuncCurNul2d.pxx>
#include <LProp_CurAndInf.hxx>
#include <math_BracketedRoot.hxx>
#include <math_FunctionRoots.hxx>
#include <Precision.hxx>

//! Computes the local extremas of curvature and the inflection points
//! of a bounded 2D curve using numeric root-finding methods.
//! Uses GeomLProp_FuncCurExt2d for curvature extrema and
//! GeomLProp_FuncCurNul2d for inflection points.
class GeomLProp_NumericCurInf2d
{
public:
  GeomLProp_NumericCurInf2d()
      : myIsDone(false)
  {
  }

  //! Computes the local extremas of curvature over the full parameter range.
  //! @param theCurve [in] the 2D curve to analyze
  //! @param theResult [in,out] container for curvature extrema parameters
  void PerformCurExt(const occ::handle<Geom2d_Curve>& theCurve, LProp_CurAndInf& theResult)
  {
    PerformCurExt(theCurve, theCurve->FirstParameter(), theCurve->LastParameter(), theResult);
  }

  //! Computes the local extremas of curvature in [theUMin, theUMax].
  //! Roots of dKC/dU are found using math_FunctionRoots (sampling + bisection),
  //! then refined with math_BracketedRoot.
  //! @param theCurve [in] the 2D curve to analyze
  //! @param theUMin [in] the start of the parameter interval
  //! @param theUMax [in] the end of the parameter interval
  //! @param theResult [in,out] container for curvature extrema parameters
  void PerformCurExt(const occ::handle<Geom2d_Curve>& theCurve,
                     const double                     theUMin,
                     const double                     theUMax,
                     LProp_CurAndInf&                 theResult)
  {
    myIsDone = true;

    const double     anEpsH     = 1.e-4 * (theUMax - theUMin);
    constexpr double aTol       = Precision::PConfusion();
    constexpr int    aNbSamples = 100;

    GeomLProp_FuncCurExt2d aFunc(theCurve, anEpsH);
    math_FunctionRoots     aRootFinder(aFunc, theUMin, theUMax, aNbSamples, anEpsH, anEpsH, anEpsH);

    if (aRootFinder.IsDone())
    {
      for (int j = 1; j <= aRootFinder.NbSolutions(); j++)
      {
        double aParam = aRootFinder.Value(j);
        // Refine the root with bracketed bisection.
        math_BracketedRoot aRefinement(aFunc, aParam - anEpsH, aParam + anEpsH, aTol);
        if (aRefinement.IsDone())
        {
          aParam = aRefinement.Root();
        }
        const bool isMinRadius = aFunc.IsMinKC(aParam);
        theResult.AddExtCur(aParam, isMinRadius);
      }
    }
    else
    {
      myIsDone = false;
    }
  }

  //! Computes the inflection points over the full parameter range.
  //! @param theCurve [in] the 2D curve to analyze
  //! @param theResult [in,out] container for inflection point parameters
  void PerformInf(const occ::handle<Geom2d_Curve>& theCurve, LProp_CurAndInf& theResult)
  {
    PerformInf(theCurve, theCurve->FirstParameter(), theCurve->LastParameter(), theResult);
  }

  //! Computes the inflection points in [theUMin, theUMax].
  //! Inflection points are roots of the normalized curvature function.
  //! @param theCurve [in] the 2D curve to analyze
  //! @param theUMin [in] the start of the parameter interval
  //! @param theUMax [in] the end of the parameter interval
  //! @param theResult [in,out] container for inflection point parameters
  void PerformInf(const occ::handle<Geom2d_Curve>& theCurve,
                  const double                     theUMin,
                  const double                     theUMax,
                  LProp_CurAndInf&                 theResult)
  {
    myIsDone = true;
    GeomLProp_FuncCurNul2d aFunc(theCurve);
    constexpr double       anEpsX     = 1.e-6;
    constexpr double       anEpsF     = 1.e-6;
    constexpr int          aNbSamples = 30;

    math_FunctionRoots aRootFinder(aFunc, theUMin, theUMax, aNbSamples, anEpsX, anEpsF, anEpsX);

    if (aRootFinder.IsDone())
    {
      for (int j = 1; j <= aRootFinder.NbSolutions(); j++)
      {
        theResult.AddInflection(aRootFinder.Value(j));
      }
    }
    else
    {
      myIsDone = false;
    }
  }

  //! Returns true if the last computation was successful.
  bool IsDone() const { return myIsDone; }

private:
  bool myIsDone; //!< Status of the last computation.
};

#endif // _GeomLProp_NumericCurInf2d_HeaderFile