// 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 #include #include #include #include #include #include #include #include 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. //! 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 if iSolution == -1. //! 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. //! is end parameter of the segment void FillPoint(FilletPoint*, const Standard_Real theLimit); //! Computes the derivative value of the function in the current point. //! is small step for approximate derivative computation //! 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_