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 // Created on: 2013-05-20
 // Created by: Mikhail PONIKAROV
 // Copyright (c) 2003-2014 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 ChFi2d_FilletAlgo_HeaderFile
 #define ChFi2d_FilletAlgo_HeaderFile
 
 #include <TopoDS_Edge.hxx>
 #include <TopoDS_Wire.hxx>
 #include <Geom2d_Curve.hxx>
 #include <Geom_Plane.hxx>
 #include <TColStd_ListOfReal.hxx>
 #include <TColStd_SequenceOfReal.hxx>
 #include <TColStd_SequenceOfBoolean.hxx>
 #include <TColStd_SequenceOfInteger.hxx>
 
 class FilletPoint;
 
 //! Algorithm that creates fillet edge: arc tangent to two edges in the start
 //! and in the end vertices. Initial edges must be located on the plane and 
 //! must be connected by the end or start points (shared vertices are not 
 //! obligatory). Created fillet arc is created with the given radius, that is
 //! useful in sketcher applications.
 //! 
 //! The algorithm is iterative that allows to create fillet on any curves
 //! of initial edges, that supports projection of point and C2 continuous.
 //! Principles of algorithm can de reduced to the Newton method:
 //! 1. Splitting initial edge into N segments where probably only 1 root can be
 //!    found. N depends on the complexity of the underlying curve.
 //! 2. On each segment compute value and derivative of the function:
 //!    - argument of the function is the parameter on the curve
 //!    - take point on the curve by the parameter: point of tangency
 //!    - make center of fillet: perpendicular vector from the point of tagency
 //!    - make projection from the center to the second curve
 //!    - length of the projection minus radius of the fillet is result of the 
 //!      function
 //!    - derivative of this function in the point is computed by value in 
 //!      point with small shift
 //! 3. Using Newton search method take the point on the segment where function
 //!    value is most close to zero. If it is not enough close, step 2 and 3 are
 //!    repeated taking as start or end point the found point.
 //! 4. If solution is found, result is created on point on root of the function (as a start point),
 //!    point of the projection onto second curve (as an end point) and center of arc in found center.
 //!    Initial edges are cut by the start and end point of tangency.
 class ChFi2d_FilletAlgo 
 {
 public:
 
   //! An empty constructor of the fillet algorithm.
   //! Call a method Init() to initialize the algorithm
   //! before calling of a Perform() method.
   Standard_EXPORT ChFi2d_FilletAlgo();
 
   //! A constructor of a fillet algorithm: accepts a wire consisting of two edges in a plane.
   Standard_EXPORT ChFi2d_FilletAlgo(const TopoDS_Wire& theWire, 
                                     const gp_Pln& thePlane);
 
   //! A constructor of a fillet algorithm: accepts two edges in a plane.
   Standard_EXPORT ChFi2d_FilletAlgo(const TopoDS_Edge& theEdge1, 
                                     const TopoDS_Edge& theEdge2, 
                                     const gp_Pln& thePlane);
 
   //! Initializes a fillet algorithm: accepts a wire consisting of two edges in a plane.
   Standard_EXPORT void Init(const TopoDS_Wire& theWire, 
                             const gp_Pln& thePlane);
 
   //! Initializes a fillet algorithm: accepts two edges in a plane.
   Standard_EXPORT void Init(const TopoDS_Edge& theEdge1, 
                             const TopoDS_Edge& theEdge2, 
                             const gp_Pln& thePlane);
 
   //! Constructs a fillet edge.
   //! Returns true, if at least one result was found
   Standard_EXPORT Standard_Boolean Perform(const Standard_Real theRadius);
 
   //! Returns number of possible solutions.
   //! <thePoint> chooses a particular fillet in case of several fillets
   //! may be constructed (for example, a circle intersecting a segment in 2 points).
   //! Put the intersecting (or common) point of the edges.
   Standard_EXPORT Standard_Integer NbResults(const gp_Pnt& thePoint);
 
   //! Returns result (fillet edge, modified edge1, modified edge2),
   //! nearest to the given point <thePoint> if iSolution == -1.
   //! <thePoint> chooses a particular fillet in case of several fillets
   //! may be constructed (for example, a circle intersecting a segment in 2 points).
   //! Put the intersecting (or common) point of the edges.
   Standard_EXPORT TopoDS_Edge Result(const gp_Pnt& thePoint,
                                      TopoDS_Edge& theEdge1, TopoDS_Edge& theEdge2,
                                      const Standard_Integer iSolution = -1);
 
 private:
   //! Computes the value the function in the current point.
   //! <theLimit> is end parameter of the segment
   void FillPoint(FilletPoint*, const Standard_Real theLimit);
   //! Computes the derivative value of the function in the current point.
   //! <theDiffStep> is small step for approximate derivative computation
   //! <theFront> is direction of the step: from or reversed
   void FillDiff(FilletPoint*, Standard_Real theDiffStep, Standard_Boolean theFront);
   //! Using Newton methods computes optimal point, that can be root of the
   //! function taking into account two input points, functions value and derivatives.
   //! Performs iteration until root is found or failed to find root.
   //! Stores roots in myResultParams.
   void PerformNewton(FilletPoint*, FilletPoint*);
   //! Splits segment by the parameter and calls Newton method for both segments.
   //! It supplies recursive iterations of the Newton methods calls
   //! (PerformNewton calls this function and this calls Netwton two times).
   Standard_Boolean ProcessPoint(FilletPoint*, FilletPoint*, Standard_Real);
 
   //! Initial edges where the fillet must be computed.
   TopoDS_Edge myEdge1, myEdge2;
   //! Plane where fillet arc must be created.
   Handle(Geom_Plane) myPlane;
   //! Underlying curves of the initial edges
   Handle(Geom2d_Curve) myCurve1, myCurve2;
   //! Start and end parameters of curves of initial edges.
   Standard_Real myStart1, myEnd1, myStart2, myEnd2, myRadius;
   //! List of params where roots were found.
   TColStd_ListOfReal myResultParams;
   //! sequence of 0 or 1: position of the fillet relatively to the first curve
   TColStd_SequenceOfInteger myResultOrientation;
   //! position of the fillet relatively to the first curve
   Standard_Boolean myStartSide;
   //! are initial edges where exchanged in the beginning: to make first edge 
   //! more simple and minimize number of iterations
   Standard_Boolean myEdgesExchnged;
   //! Number to avoid infinity recursion: indicates how deep the recursion is performed.
   Standard_Integer myDegreeOfRecursion;
 };
 
 //! Private class. Corresponds to the point on the first curve, computed
 //! fillet function and derivative on it.
 class FilletPoint 
 {
 public:
   //! Creates a point on a first curve by parameter on this curve.
   FilletPoint(const Standard_Real theParam);
 
   //! Changes the point position by changing point parameter on the first curve.
   void setParam(Standard_Real theParam) {myParam = theParam;}
 
   //! Returns the point parameter on the first curve.
   Standard_Real getParam() const {return myParam;}
 
   //! Returns number of found values of function in this point.
   Standard_Integer getNBValues() {return myV.Length();}
 
   //! Returns value of function in this point.
   Standard_Real getValue(int theIndex) {return myV.Value(theIndex);}
 
   //! Returns derivatives of function in this point.
   Standard_Real getDiff(int theIndex) {return myD.Value(theIndex);}
 
   //! Returns true if function is valid (rediuses vectors of fillet do not intersect any curve).
   Standard_Boolean isValid(int theIndex) {return myValid.Value(theIndex);}
 
   //! Returns the index of the nearest value
   int getNear(int theIndex) {return myNear.Value(theIndex);}
 
   //! Defines the parameter of the projected point on the second curve.
   void setParam2(const Standard_Real theParam2) {myParam2 = theParam2;}
 
   //! Returns the parameter of the projected point on the second curve.
   Standard_Real getParam2() { return myParam2 ; }
 
   //! Center of the fillet.
   void setCenter(const gp_Pnt2d thePoint) {myCenter = thePoint;}
   //! Center of the fillet.
   const gp_Pnt2d getCenter() {return myCenter;}
 
   //! Appends value of the function.
   void appendValue(Standard_Real theValue, Standard_Boolean theValid);
 
   //! Computes difference between this point and the given. Stores difference in myD.
   Standard_Boolean calculateDiff(FilletPoint*);
 
   //! Filters out the values and leaves the most optimal one.
   void FilterPoints(FilletPoint*);
 
   //! Returns a pointer to created copy of the point
   //! warning: this is not the full copy! Copies only: myParam, myV, myD, myValid
   FilletPoint* Copy();
 
   //! Returns the index of the solution or zero if there is no solution
   Standard_Integer hasSolution(Standard_Real theRadius);
 
   //! For debug only
   Standard_Real LowerValue() 
   {
     Standard_Integer a, aResultIndex = 0;
     Standard_Real aValue;
     for(a = myV.Length(); a > 0; a--) 
     {
       if (aResultIndex == 0 || Abs(aValue) > Abs(myV.Value(a))) 
       {
         aResultIndex = a;
         aValue = myV.Value(a);
       }
     }
     return aValue;
   }
   //! Removes the found value by the given index.
   void remove(Standard_Integer theIndex);
 
 private:
   //! Parameter on the first curve (start fillet point).
   Standard_Real myParam;
   //! Parameter on the second curve (end fillet point).
   Standard_Real myParam2;
   //! Values and derivative values of the fillet function.
   //! May be several if there are many projections on the second curve.
   TColStd_SequenceOfReal myV, myD;
   //! Center of the fillet arc.
   gp_Pnt2d myCenter;
   //! Flags for storage the validity of solutions. Indexes corresponds to indexes
   //! in sequences myV, myD.
   TColStd_SequenceOfBoolean myValid;
   TColStd_SequenceOfInteger myNear;
 };
 
 #endif // _FILLETALGO_H_

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