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 // Created on: 1993-03-09
 // Created by: Philippe DAUTRY
 // Copyright (c) 1993-1999 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 _Geom_BezierCurve_HeaderFile
 #define _Geom_BezierCurve_HeaderFile
 
 #include <Standard.hxx>
 
 #include <TColgp_HArray1OfPnt.hxx>
 #include <Standard_Integer.hxx>
 #include <Standard_Real.hxx>
 #include <Geom_BoundedCurve.hxx>
 #include <TColgp_Array1OfPnt.hxx>
 #include <GeomAbs_Shape.hxx>
 #include <BSplCLib.hxx>
 
 class gp_Pnt;
 class gp_Vec;
 class gp_Trsf;
 class Geom_Geometry;
 
 
 class Geom_BezierCurve;
 DEFINE_STANDARD_HANDLE(Geom_BezierCurve, Geom_BoundedCurve)
 
 //! Describes a rational or non-rational Bezier curve
 //! - a non-rational Bezier curve is defined by a table of
 //! poles (also called control points),
 //! - a rational Bezier curve is defined by a table of
 //! poles with varying weights.
 //! These data are manipulated by two parallel arrays:
 //! - the poles table, which is an array of gp_Pnt points, and
 //! - the weights table, which is an array of reals.
 //! The bounds of these arrays are 1 and "the number of "poles" of the curve.
 //! The poles of the curve are "control points" used to deform the curve.
 //! The first pole is the start point of the curve, and the
 //! last pole is the end point of the curve. The segment
 //! that joins the first pole to the second pole is the
 //! tangent to the curve at its start point, and the
 //! segment that joins the last pole to the
 //! second-from-last pole is the tangent to the curve at its end point.
 //! It is more difficult to give a geometric signification to
 //! the weights but they are useful for providing the exact
 //! representations of arcs of a circle or ellipse.
 //! Moreover, if the weights of all poles are equal, the
 //! curve is polynomial; it is therefore a non-rational
 //! curve. The non-rational curve is a special and
 //! frequently used case. The weights are defined and
 //! used only in the case of a rational curve.
 //! The degree of a Bezier curve is equal to the number
 //! of poles, minus 1. It must be greater than or equal to
 //! 1. However, the degree of a Geom_BezierCurve
 //! curve is limited to a value (25) which is defined and
 //! controlled by the system. This value is returned by the function MaxDegree.
 //! The parameter range for a Bezier curve is [ 0, 1 ].
 //! If the first and last control points of the Bezier curve
 //! are the same point then the curve is closed. For
 //! example, to create a closed Bezier curve with four
 //! control points, you have to give the set of control
 //! points P1, P2, P3 and P1.
 //! The continuity of a Bezier curve is infinite.
 //! It is not possible to build a Bezier curve with negative
 //! weights. We consider that a weight value is zero if it
 //! is less than or equal to gp::Resolution(). We
 //! also consider that two weight values W1 and W2 are equal if:
 //! |W2 - W1| <= gp::Resolution().
 //! Warning
 //! - When considering the continuity of a closed Bezier
 //! curve at the junction point, remember that a curve
 //! of this type is never periodic. This means that the
 //! derivatives for the parameter u = 0 have no
 //! reason to be the same as the derivatives for the
 //! parameter u = 1 even if the curve is closed.
 //! - The length of a Bezier curve can be null.
 class Geom_BezierCurve : public Geom_BoundedCurve
 {
 
 public:
 
   
   //! Creates a non rational Bezier curve with a set of poles
   //! CurvePoles.  The weights are defaulted to all being 1.
   //! Raises ConstructionError if the number of poles is greater than MaxDegree + 1
   //! or lower than 2.
   Standard_EXPORT Geom_BezierCurve(const TColgp_Array1OfPnt& CurvePoles);
   
   //! Creates a rational Bezier curve with the set of poles
   //! CurvePoles and the set of weights  PoleWeights .
   //! If all the weights are identical the curve is considered
   //! as non rational. Raises ConstructionError if
   //! the number of poles is greater than  MaxDegree + 1 or lower
   //! than 2 or CurvePoles and CurveWeights have not the same length
   //! or one weight value is lower or equal to Resolution from package gp.
   Standard_EXPORT Geom_BezierCurve(const TColgp_Array1OfPnt& CurvePoles, const TColStd_Array1OfReal& PoleWeights);
   
   //! Increases the degree of a bezier curve. Degree is the new
   //! degree of <me>. Raises ConstructionError
   //! if Degree is greater than MaxDegree or lower than 2
   //! or lower than the initial degree of <me>.
   Standard_EXPORT void Increase (const Standard_Integer Degree);
   
   //! Inserts a pole P after the pole of range Index.
   //! If the curve <me> is rational the weight value for the new
   //! pole of range Index is 1.0.
   //! raised if Index is not in the range [1, NbPoles]
   //!
   //! raised if the resulting number of poles is greater than
   //! MaxDegree + 1.
   Standard_EXPORT void InsertPoleAfter (const Standard_Integer Index, const gp_Pnt& P);
   
 
   //! Inserts a pole with its weight in the set of poles after the
   //! pole of range Index. If the curve was non rational it can
   //! become rational if all the weights are not identical.
   //! Raised if Index is not in the range [1, NbPoles]
   //!
   //! Raised if the resulting number of poles is greater than
   //! MaxDegree + 1.
   //! Raised if Weight is lower or equal to Resolution from package gp.
   Standard_EXPORT void InsertPoleAfter (const Standard_Integer Index, const gp_Pnt& P, const Standard_Real Weight);
   
   //! Inserts a pole P before the pole of range Index.
   //! If the curve <me> is rational the weight value for the new
   //! pole of range Index is 1.0.
   //! Raised if Index is not in the range [1, NbPoles]
   //!
   //! Raised if the resulting number of poles is greater than
   //! MaxDegree + 1.
   Standard_EXPORT void InsertPoleBefore (const Standard_Integer Index, const gp_Pnt& P);
   
 
   //! Inserts a pole with its weight in the set of poles after
   //! the pole of range Index. If the curve was non rational it
   //! can become rational if all the weights are not identical.
   //! Raised if Index is not in the range [1, NbPoles]
   //!
   //! Raised if the resulting number of poles is greater than
   //! MaxDegree + 1.
   //! Raised if Weight is lower or equal to Resolution from
   //! package gp.
   Standard_EXPORT void InsertPoleBefore (const Standard_Integer Index, const gp_Pnt& P, const Standard_Real Weight);
   
   //! Removes the pole of range Index.
   //! If the curve was rational it can become non rational.
   //! Raised if Index is not in the range [1, NbPoles]
   //! Raised if Degree is lower than 2.
   Standard_EXPORT void RemovePole (const Standard_Integer Index);
   
 
   //! Reverses the direction of parametrization of <me>
   //! Value (NewU) =  Value (1 - OldU)
   Standard_EXPORT void Reverse() Standard_OVERRIDE;
   
   //! Returns the  parameter on the  reversed  curve for
   //! the point of parameter U on <me>.
   //!
   //! returns 1-U
   Standard_EXPORT Standard_Real ReversedParameter (const Standard_Real U) const Standard_OVERRIDE;
   
 
   //! Segments the curve between U1 and U2 which can be out
   //! of the bounds of the curve. The curve is oriented from U1
   //! to U2.
   //! The control points are modified, the first and the last point
   //! are not the same but the parametrization range is [0, 1]
   //! else it could not be a Bezier curve.
   //! Warnings :
   //! Even if <me> is not closed it can become closed after the
   //! segmentation for example if U1 or U2 are out of the bounds
   //! of the curve <me> or if the curve makes loop.
   //! After the segmentation the length of a curve can be null.
   Standard_EXPORT void Segment (const Standard_Real U1, const Standard_Real U2);
   
 
   //! Substitutes the pole of range index with P.
   //! If the curve <me> is rational the weight of range Index
   //! is not modified.
   //! raiseD if Index is not in the range [1, NbPoles]
   Standard_EXPORT void SetPole (const Standard_Integer Index, const gp_Pnt& P);
   
 
   //! Substitutes the pole and the weights of range Index.
   //! If the curve <me> is not rational it can become rational
   //! if all the weights are not identical.
   //! If the curve was rational it can become non rational if
   //! all the weights are identical.
   //! Raised if Index is not in the range [1, NbPoles]
   //! Raised if Weight <= Resolution from package gp
   Standard_EXPORT void SetPole (const Standard_Integer Index, const gp_Pnt& P, const Standard_Real Weight);
   
 
   //! Changes the weight of the pole of range Index.
   //! If the curve <me> is not rational it can become rational
   //! if all the weights are not identical.
   //! If the curve was rational it can become non rational if
   //! all the weights are identical.
   //! Raised if Index is not in the range [1, NbPoles]
   //! Raised if Weight <= Resolution from package gp
   Standard_EXPORT void SetWeight (const Standard_Integer Index, const Standard_Real Weight);
   
 
   //! Returns True if the distance between the first point
   //! and the last point of the curve is lower or equal to
   //! the Resolution from package gp.
   Standard_EXPORT Standard_Boolean IsClosed() const Standard_OVERRIDE;
   
   //! Continuity of the curve, returns True.
   Standard_EXPORT Standard_Boolean IsCN (const Standard_Integer N) const Standard_OVERRIDE;
   
 
   //! Returns True if the parametrization of a curve is periodic.
   //! (P(u) = P(u + T) T = constante)
   Standard_EXPORT Standard_Boolean IsPeriodic() const Standard_OVERRIDE;
   
 
   //! Returns false if all the weights are identical. The tolerance
   //! criterion is Resolution from package gp.
   Standard_EXPORT Standard_Boolean IsRational() const;
   
   //! a Bezier curve is CN
   Standard_EXPORT GeomAbs_Shape Continuity() const Standard_OVERRIDE;
   
   //! Returns the polynomial degree of the curve.
   //! it is the number of poles - 1
   //! point P and derivatives (V1, V2, V3) computation
   //! The Bezier Curve has a Polynomial representation so the
   //! parameter U can be out of the bounds of the curve.
   Standard_EXPORT Standard_Integer Degree() const;
   
   Standard_EXPORT void D0 (const Standard_Real U, gp_Pnt& P) const Standard_OVERRIDE;
   
   Standard_EXPORT void D1 (const Standard_Real U, gp_Pnt& P, gp_Vec& V1) const Standard_OVERRIDE;
   
   Standard_EXPORT void D2 (const Standard_Real U, gp_Pnt& P, gp_Vec& V1, gp_Vec& V2) const Standard_OVERRIDE;
   
   //! For this Bezier curve, computes
   //! - the point P of parameter U, or
   //! - the point P and one or more of the following values:
   //! - V1, the first derivative vector,
   //! - V2, the second derivative vector,
   //! - V3, the third derivative vector.
   //! Note: the parameter U can be outside the bounds of the curve.
   Standard_EXPORT void D3 (const Standard_Real U, gp_Pnt& P, gp_Vec& V1, gp_Vec& V2, gp_Vec& V3) const Standard_OVERRIDE;
   
   //! For the point of parameter U of this Bezier curve,
   //! computes the vector corresponding to the Nth derivative.
   //! Note: the parameter U can be outside the bounds of the curve.
   //! Exceptions Standard_RangeError if N is less than 1.
   Standard_EXPORT gp_Vec DN (const Standard_Real U, const Standard_Integer N) const Standard_OVERRIDE;
   
   //! Returns Value (U=0.), it is the first control point of the curve.
   Standard_EXPORT gp_Pnt StartPoint() const Standard_OVERRIDE;
   
   //! Returns Value (U=1.), it is the last control point of the Bezier curve.
   Standard_EXPORT gp_Pnt EndPoint() const Standard_OVERRIDE;
   
   //! Returns the value of the first  parameter of this
   //! Bezier curve. This is 0.0, which gives the start point of this Bezier curve
   Standard_EXPORT Standard_Real FirstParameter() const Standard_OVERRIDE;
   
   //! Returns the value of the last parameter of this
   //! Bezier curve. This is  1.0, which gives the end point of this Bezier curve.
   Standard_EXPORT Standard_Real LastParameter() const Standard_OVERRIDE;
   
   //! Returns the number of poles of this Bezier curve.
   Standard_EXPORT Standard_Integer NbPoles() const;
   
   //! Returns the pole of range Index.
   //! Raised if Index is not in the range [1, NbPoles]
   Standard_EXPORT const gp_Pnt& Pole (const Standard_Integer Index) const;
   
   //! Returns all the poles of the curve.
   //!
   //! Raised if the length of P is not equal to the number of poles.
   Standard_EXPORT void Poles (TColgp_Array1OfPnt& P) const;
 
     //! Returns all the poles of the curve.
   Standard_EXPORT const TColgp_Array1OfPnt& Poles () const;
   
   //! Returns the weight of range Index.
   //! Raised if Index is not in the range [1, NbPoles]
   Standard_EXPORT Standard_Real Weight (const Standard_Integer Index) const;
   
   //! Returns all the weights of the curve.
   //!
   //! Raised if the length of W is not equal to the number of poles.
   Standard_EXPORT void Weights (TColStd_Array1OfReal& W) const;
 
   //! Returns all the weights of the curve.
   const TColStd_Array1OfReal* Weights() const
   {
     if (!weights.IsNull())
       return &weights->Array1();
     return BSplCLib::NoWeights();
   }
 
   //! Applies the transformation T to this Bezier curve.
   Standard_EXPORT void Transform (const gp_Trsf& T) Standard_OVERRIDE;
   
 
   //! Returns the value of the maximum polynomial degree
   //! of any Geom_BezierCurve curve. This value is 25.
   Standard_EXPORT static Standard_Integer MaxDegree();
   
   //! Computes for this Bezier curve the parametric
   //! tolerance UTolerance for a given 3D tolerance Tolerance3D.
   //! If f(t) is the equation of this Bezier curve,
   //! UTolerance ensures that:
   //! |t1-t0| < UTolerance ===> |f(t1)-f(t0)| < Tolerance3D
   Standard_EXPORT void Resolution (const Standard_Real Tolerance3D, Standard_Real& UTolerance);
   
   //! Creates a new object which is a copy of this Bezier curve.
   Standard_EXPORT Handle(Geom_Geometry) Copy() const Standard_OVERRIDE;
 
   //! Dumps the content of me into the stream
   Standard_EXPORT virtual void DumpJson (Standard_OStream& theOStream, Standard_Integer theDepth = -1) const Standard_OVERRIDE;
 
 
 
 
   DEFINE_STANDARD_RTTIEXT(Geom_BezierCurve,Geom_BoundedCurve)
 
 protected:
 
 
 
 
 private:
 
   
   //! Set  poles  to  Poles,  weights to  Weights  (not
   //! copied). If Weights is   null  the  curve is    non
   //! rational. Create the arrays of coefficients.  Poles
   //! and    Weights  are   assumed   to  have the  first
   //! coefficient 1.
   //! Update rational and closed.
   //!
   //! if nbpoles < 2 or nbboles > MaDegree + 1
   void Init (const Handle(TColgp_HArray1OfPnt)& Poles, const Handle(TColStd_HArray1OfReal)& Weights);
 
   Standard_Boolean rational;
   Standard_Boolean closed;
   Handle(TColgp_HArray1OfPnt) poles;
   Handle(TColStd_HArray1OfReal) weights;
   Standard_Real maxderivinv;
   Standard_Boolean maxderivinvok;
 
 
 };
 
 
 
 
 
 
 
 #endif // _Geom_BezierCurve_HeaderFile

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