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 // Copyright (c) 2025 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 _ExtremaPC_Parabola_HeaderFile
 #define _ExtremaPC_Parabola_HeaderFile
 
 #include <ElCLib.hxx>
 #include <ExtremaPC.hxx>
 #include <gp_Parab.hxx>
 #include <gp_Pnt.hxx>
 #include <gp_Vec.hxx>
 #include <MathPoly_Cubic.hxx>
 #include <Precision.hxx>
 #include <Standard_DefineAlloc.hxx>
 
 #include <cmath>
 #include <optional>
 
 //! @brief Point-Parabola extrema computation.
 //!
 //! Computes the extrema between a 3D point and a parabola.
 //! Uses cubic polynomial solving via MathPoly::Cubic.
 //!
 //! The algorithm:
 //! 1. Projects point P onto the parabola plane -> Pp
 //! 2. For parabola C(u) = ((u^2)/(4F), u) with focal length F,
 //!    solves: (1/(4F)) * u^3 + (2F - X) * u - 2F*Y = 0
 //!    where (X, Y) are coordinates of Pp in parabola local frame.
 //!
 //! @note A parabola can have up to 3 extrema.
 //!
 //! The domain is fixed at construction time for optimal performance.
 //! For infinite parabola, construct without domain or with nullopt.
 class ExtremaPC_Parabola
 {
 public:
   DEFINE_STANDARD_ALLOC
 
   //! Constructor with parabola geometry (infinite).
   //! @param[in] theParabola the parabola to compute extrema for
   explicit ExtremaPC_Parabola(const gp_Parab& theParabola)
       : myParabola(theParabola),
         myDomain(std::nullopt)
   {
     cacheGeometry();
   }
 
   //! Constructor with parabola geometry and parameter domain.
   //! @param[in] theParabola the parabola to compute extrema for
   //! @param[in] theDomain parameter domain (fixed for all queries)
   ExtremaPC_Parabola(const gp_Parab& theParabola, const ExtremaPC::Domain1D& theDomain)
       : myParabola(theParabola),
         myDomain(theDomain.IsFinite() ? std::optional<ExtremaPC::Domain1D>(theDomain)
                                       : std::nullopt)
   {
     cacheGeometry();
   }
 
   //! Copy constructor is deleted.
   ExtremaPC_Parabola(const ExtremaPC_Parabola&) = delete;
 
   //! Copy assignment operator is deleted.
   ExtremaPC_Parabola& operator=(const ExtremaPC_Parabola&) = delete;
 
   //! Move constructor.
   ExtremaPC_Parabola(ExtremaPC_Parabola&&) = default;
 
   //! Move assignment operator.
   ExtremaPC_Parabola& operator=(ExtremaPC_Parabola&&) = default;
 
   //! Evaluates point on parabola at parameter using cached geometry.
   //! @param theU parameter
   //! @return point on parabola
   gp_Pnt Value(double theU) const
   {
     // Parabola: P(u) = Vertex + (u^2/4F)*XDir + u*YDir
     const double aX = theU * theU * my1Over4F;
     return gp_Pnt(myVertexX + aX * myXDirX + theU * myYDirX,
                   myVertexY + aX * myXDirY + theU * myYDirY,
                   myVertexZ + aX * myXDirZ + theU * myYDirZ);
   }
 
   //! Returns true if domain is bounded.
   bool IsBounded() const { return myDomain.has_value(); }
 
   //! Returns the domain (only valid if IsBounded() is true).
   const ExtremaPC::Domain1D& Domain() const { return *myDomain; }
 
   //! Compute extrema between point P and the parabola.
   //! Uses domain specified at construction time.
   //! @param theP query point
   //! @param theTol tolerance for duplicate detection
   //! @param theMode search mode (MinMax, Min, or Max)
   //! @return const reference to result containing extrema
   [[nodiscard]] const ExtremaPC::Result& Perform(
     const gp_Pnt&         theP,
     double                theTol,
     ExtremaPC::SearchMode theMode = ExtremaPC::SearchMode::MinMax) const
   {
     performCore(theP, myDomain, theTol, theMode);
     return myResult;
   }
 
   //! Compute extrema between point P and the parabola arc including endpoints.
   //! Uses domain specified at construction time.
   //! @param theP query point
   //! @param theTol tolerance for duplicate detection
   //! @param theMode search mode (MinMax, Min, or Max)
   //! @return const reference to result containing interior + endpoint extrema
   [[nodiscard]] const ExtremaPC::Result& PerformWithEndpoints(
     const gp_Pnt&         theP,
     double                theTol,
     ExtremaPC::SearchMode theMode = ExtremaPC::SearchMode::MinMax) const
   {
     (void)Perform(theP, theTol, theMode);
 
     // Add endpoints if interior computation succeeded and domain is bounded
     if (myResult.Status == ExtremaPC::Status::OK && myDomain.has_value())
     {
       ExtremaPC::AddEndpointExtrema(myResult, theP, *myDomain, *this, theTol, theMode);
     }
 
     return myResult;
   }
 
   //! Returns the parabola geometry.
   const gp_Parab& Parabola() const { return myParabola; }
 
 private:
   //! Cache geometry components for fast computation.
   void cacheGeometry()
   {
     const gp_Pnt& aVertex = myParabola.Location();
     myVertexX             = aVertex.X();
     myVertexY             = aVertex.Y();
     myVertexZ             = aVertex.Z();
 
     const gp_Dir aXDir = myParabola.XAxis().Direction();
     myXDirX            = aXDir.X();
     myXDirY            = aXDir.Y();
     myXDirZ            = aXDir.Z();
 
     const gp_Dir aYDir = myParabola.YAxis().Direction();
     myYDirX            = aYDir.X();
     myYDirY            = aYDir.Y();
     myYDirZ            = aYDir.Z();
 
     const gp_Dir& aAxis = myParabola.Axis().Direction();
     myAxisX             = aAxis.X();
     myAxisY             = aAxis.Y();
     myAxisZ             = aAxis.Z();
 
     myFocal   = myParabola.Focal();
     my1Over4F = 1.0 / (4.0 * myFocal);
     my2F      = 2.0 * myFocal;
   }
 
   //! Solve the cubic equation and return polynomial result using cached geometry.
   MathPoly::PolyResult solveCubic(const gp_Pnt& theP) const
   {
     // Vector from vertex to point
     const double aDx = theP.X() - myVertexX;
     const double aDy = theP.Y() - myVertexY;
     const double aDz = theP.Z() - myVertexZ;
 
     // Project point P onto the parabola plane
     // Height = (P - Vertex) . Axis
     const double aHeight = aDx * myAxisX + aDy * myAxisY + aDz * myAxisZ;
 
     // Projected point Pp = P - Height * Axis
     const double aPpX = theP.X() - aHeight * myAxisX;
     const double aPpY = theP.Y() - aHeight * myAxisY;
     const double aPpZ = theP.Z() - aHeight * myAxisZ;
 
     // Vector from vertex to projected point
     const double aOPpX = aPpX - myVertexX;
     const double aOPpY = aPpY - myVertexY;
     const double aOPpZ = aPpZ - myVertexZ;
 
     // Local coordinates in parabola frame
     const double aX = aOPpX * myXDirX + aOPpY * myXDirY + aOPpZ * myXDirZ;
     const double aY = aOPpX * myYDirX + aOPpY * myYDirY + aOPpZ * myYDirZ;
 
     // Solve cubic equation: (1/(4F)) * u^3 + (2F - X) * u - 2F*Y = 0
     return MathPoly::Cubic(my1Over4F, 0.0, my2F - aX, -my2F * aY);
   }
 
   //! Core algorithm - finds extrema with optional bounds checking.
   //! Stores results in myResult.
   //! @param theP query point
   //! @param theDomain optional parameter domain (nullopt for unbounded)
   //! @param theTol tolerance for duplicate detection
   //! @param theMode search mode
   void performCore(const gp_Pnt&                             theP,
                    const std::optional<ExtremaPC::Domain1D>& theDomain,
                    double                                    theTol,
                    ExtremaPC::SearchMode                     theMode) const
   {
     (void)theTol; // Tolerance used for endpoint detection
 
     myResult.Clear();
 
     MathPoly::PolyResult aPolyRes = solveCubic(theP);
 
     if (!aPolyRes.IsDone())
     {
       if (aPolyRes.Status == MathUtils::Status::InfiniteSolutions)
       {
         myResult.Status                 = ExtremaPC::Status::InfiniteSolutions;
         gp_Pnt aPtOnCurve               = Value(0.0);
         myResult.InfiniteSquareDistance = theP.SquareDistance(aPtOnCurve);
       }
       else
       {
         myResult.Status = ExtremaPC::Status::NumericalError;
       }
       return;
     }
 
     double aTol2 = Precision::SquareConfusion();
 
     // Process all roots
     for (size_t i = 0; i < aPolyRes.NbRoots; ++i)
     {
       double aU = aPolyRes.Roots[i];
 
       // Check bounds if domain is specified
       if (theDomain.has_value())
       {
         if (aU < theDomain->Min || aU > theDomain->Max)
           continue;
       }
 
       gp_Pnt aCurvePt = Value(aU);
 
       // Check for duplicates
       bool aDuplicate = false;
       for (int j = 0; j < myResult.Extrema.Length(); ++j)
       {
         if (aCurvePt.SquareDistance(myResult.Extrema.Value(j).Point) < aTol2)
         {
           aDuplicate = true;
           break;
         }
       }
       if (aDuplicate)
         continue;
 
       // Determine if minimum or maximum using neighbor comparison
       double aSqDist = theP.SquareDistance(aCurvePt);
       double aNeighborU;
       if (theDomain.has_value())
       {
         // For bounded case, choose neighbor direction based on position in domain
         aNeighborU = aU + (aU < (theDomain->Min + theDomain->Max) * 0.5 ? 1.0 : -1.0);
         aNeighborU = std::max(theDomain->Min, std::min(theDomain->Max, aNeighborU));
       }
       else
       {
         // For unbounded case, just use +1.0
         aNeighborU = aU + 1.0;
       }
       gp_Pnt aNeighborPt   = Value(aNeighborU);
       double aNeighborDist = theP.SquareDistance(aNeighborPt);
       bool   aIsMin        = aSqDist <= aNeighborDist;
 
       // Filter by search mode
       if (theMode == ExtremaPC::SearchMode::Min && !aIsMin)
         continue;
       if (theMode == ExtremaPC::SearchMode::Max && aIsMin)
         continue;
 
       ExtremaPC::ExtremumResult anExt;
       anExt.Parameter      = aU;
       anExt.Point          = aCurvePt;
       anExt.SquareDistance = aSqDist;
       anExt.IsMinimum      = aIsMin;
 
       myResult.Extrema.Append(anExt);
     }
 
     myResult.Status = ExtremaPC::Status::OK;
   }
 
   gp_Parab                           myParabola; //!< Parabola geometry
   std::optional<ExtremaPC::Domain1D> myDomain;   //!< Parameter domain (nullopt for infinite)
   mutable ExtremaPC::Result          myResult;   //!< Reusable result storage
 
   // Cached geometry components for fast computation
   double myVertexX, myVertexY, myVertexZ; //!< Vertex location
   double myXDirX, myXDirY, myXDirZ;       //!< X-axis direction
   double myYDirX, myYDirY, myYDirZ;       //!< Y-axis direction
   double myAxisX, myAxisY, myAxisZ;       //!< Main axis direction
   double myFocal;                         //!< Focal length
   double my1Over4F;                       //!< Precomputed 1/(4*F)
   double my2F;                            //!< Precomputed 2*F
 };
 
 #endif // _ExtremaPC_Parabola_HeaderFile

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