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 // Created on: 1993-03-24
 // Created by: JCV
 // 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 _Geom2d_BezierCurve_HeaderFile
 #define _Geom2d_BezierCurve_HeaderFile
 
 #include <Standard.hxx>
 
 #include <gp_Pnt2d.hxx>
 #include <NCollection_Array1.hxx>
 #include <Geom2d_BoundedCurve.hxx>
 #include <GeomAbs_Shape.hxx>
 #include <BSplCLib.hxx>
 
 class gp_Trsf2d;
 class Geom2d_Geometry;
 
 namespace Geom2dEval_RepCurveDesc
 {
 class Base;
 }
 
 //! 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_Pnt2d 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
 //! which joins the first pole to the second pole is the
 //! tangent to the curve at its start point, and the
 //! segment which 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
 //! exact representations of the arcs of a circle or
 //! ellipse. Moreover, if the weights of all the 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 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
 //! Geom2d_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 a 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 Geom2d_BezierCurve : public Geom2d_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 Geom2d_BezierCurve(const NCollection_Array1<gp_Pnt2d>& 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 Geom2d_BezierCurve(const NCollection_Array1<gp_Pnt2d>& CurvePoles,
                                      const NCollection_Array1<double>&   PoleWeights);
 
   //! Copy constructor for optimized copying without validation.
   Standard_EXPORT Geom2d_BezierCurve(const Geom2d_BezierCurve& theOther);
 
   //! Returns true if an evaluation representation is attached.
   bool HasEvalRepresentation() const { return !myEvalRep.IsNull(); }
 
   //! Returns the current evaluation representation descriptor (may be null).
   const occ::handle<Geom2dEval_RepCurveDesc::Base>& EvalRepresentation() const { return myEvalRep; }
 
   //! Sets a new evaluation representation.
   //! Validates descriptor data and ensures no circular references.
   Standard_EXPORT void SetEvalRepresentation(
     const occ::handle<Geom2dEval_RepCurveDesc::Base>& theDesc);
 
   //! Removes the evaluation representation.
   void ClearEvalRepresentation() { myEvalRep.Nullify(); }
 
   //! 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 int Degree);
 
   //! 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 [0, NbPoles]
   //!
   //! Raised if the resulting number of poles is greater than
   //! MaxDegree + 1.
   Standard_EXPORT void InsertPoleAfter(const int       Index,
                                        const gp_Pnt2d& P,
                                        const double    Weight = 1.0);
 
   //! 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+1]
   //!
   //! Raised if the resulting number of poles is greater than
   //! MaxDegree + 1.
   Standard_EXPORT void InsertPoleBefore(const int       Index,
                                         const gp_Pnt2d& P,
                                         const double    Weight = 1.0);
 
   //! 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]
   Standard_EXPORT void RemovePole(const int Index);
 
   //! Reverses the direction of parametrization of <me>
   //! Value (NewU) = Value (1 - OldU)
   Standard_EXPORT void Reverse() final;
 
   //! Returns the parameter on the reversed curve for
   //! the point of parameter U on <me>.
   //!
   //! returns 1-U
   Standard_EXPORT double ReversedParameter(const double U) const final;
 
   //! 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 double U1, const double 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 int Index, const gp_Pnt2d& 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 int Index, const gp_Pnt2d& P, const double 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 int Index, const double 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 bool IsClosed() const final;
 
   //! Continuity of the curve, returns True.
   Standard_EXPORT bool IsCN(const int N) const final;
 
   //! Returns False. A BezierCurve cannot be periodic in this
   //! package
   Standard_EXPORT bool IsPeriodic() const final;
 
   //! Returns false if all the weights are identical. The tolerance
   //! criterion is Resolution from package gp.
   Standard_EXPORT bool IsRational() const;
 
   //! Returns GeomAbs_CN, which is the continuity of any Bezier curve.
   Standard_EXPORT GeomAbs_Shape Continuity() const final;
 
   //! Returns the polynomial degree of the curve. It is the number
   //! of poles less one. In this package the Degree of a Bezier
   //! curve cannot be greater than "MaxDegree".
   Standard_EXPORT int Degree() const;
 
   Standard_EXPORT gp_Pnt2d EvalD0(const double U) const final;
 
   Standard_EXPORT Geom2d_Curve::ResD1 EvalD1(const double U) const final;
 
   Standard_EXPORT Geom2d_Curve::ResD2 EvalD2(const double U) const final;
 
   Standard_EXPORT Geom2d_Curve::ResD3 EvalD3(const double U) const final;
 
   //! 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.
   //! Raises RangeError if N < 1.
   Standard_EXPORT gp_Vec2d EvalDN(const double U, const int N) const final;
 
   //! Returns the end point or start point of this Bezier curve.
   Standard_EXPORT gp_Pnt2d EndPoint() const final;
 
   //! 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 double FirstParameter() const final;
 
   //! 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 double LastParameter() const final;
 
   //! Returns the number of poles for this Bezier curve.
   Standard_EXPORT int NbPoles() const;
 
   //! Returns the pole of range Index.
   //! Raised if Index is not in the range [1, NbPoles]
   Standard_EXPORT const gp_Pnt2d& Pole(const int Index) const;
 
   //! Returns all the poles of the curve.
   //!
   //! Raised if the length of P is not equal to the number of poles.
   Standard_DEPRECATED("use Poles() returning const reference instead")
   Standard_EXPORT void Poles(NCollection_Array1<gp_Pnt2d>& P) const;
 
   //! Returns all the poles of the curve.
   const NCollection_Array1<gp_Pnt2d>& Poles() const { return myPoles; }
 
   //! Returns Value (U=1), it is the first control point
   //! of the curve.
   Standard_EXPORT gp_Pnt2d StartPoint() const final;
 
   //! Returns the weight of range Index.
   //! Raised if Index is not in the range [1, NbPoles]
   Standard_EXPORT double Weight(const int Index) const;
 
   //! Returns all the weights of the curve.
   //!
   //! Raised if the length of W is not equal to the number of poles.
   Standard_DEPRECATED("use Weights() returning const pointer instead")
   Standard_EXPORT void Weights(NCollection_Array1<double>& W) const;
 
   //! Returns all the weights of the curve.
   const NCollection_Array1<double>* Weights() const
   {
     return myRational ? &myWeights : BSplCLib::NoWeights();
   }
 
   //! Returns a const reference to the weights array.
   //! For rational curves: the internal owning weights array.
   //! For non-rational curves: a non-owning view of unit weights from BSplCLib.
   //! The array is always sized to match NbPoles().
   //! @warning Do NOT modify elements through the returned reference.
   const NCollection_Array1<double>& WeightsArray() const { return myWeights; }
 
   //! Applies the transformation T to this Bezier curve.
   Standard_EXPORT void Transform(const gp_Trsf2d& T) final;
 
   //! Returns the value of the maximum polynomial degree of a
   //! BezierCurve. This value is 25.
   Standard_EXPORT static int MaxDegree();
 
   //! Computes for this Bezier curve the parametric
   //! tolerance UTolerance for a given tolerance
   //! Tolerance3D (relative to dimensions in the plane).
   //! If f(t) is the equation of this Bezier curve,
   //! UTolerance ensures that
   //! | t1 - t0| < Utolerance ===>
   //! |f(t1) - f(t0)| < ToleranceUV
   Standard_EXPORT void Resolution(const double ToleranceUV, double& UTolerance);
 
   //! Creates a new object which is a copy of this Bezier curve.
   Standard_EXPORT occ::handle<Geom2d_Geometry> Copy() const final;
 
   //! Dumps the content of me into the stream
   Standard_EXPORT void DumpJson(Standard_OStream& theOStream, int theDepth = -1) const final;
 
   //! Returns Bezier knots {0.0, 1.0} as a static array.
   Standard_EXPORT const NCollection_Array1<double>& Knots() const;
 
   //! Returns Bezier multiplicities for the current degree.
   Standard_EXPORT const NCollection_Array1<int>& Multiplicities() const;
 
   //! Returns Bezier flat knots for the current degree.
   Standard_EXPORT const NCollection_Array1<double>& KnotSequence() const;
 
   DEFINE_STANDARD_RTTIEXT(Geom2d_BezierCurve, Geom2d_BoundedCurve)
 
 protected:
   //! Set poles to thePoles, weights to theWeights.
   //! If theWeights is null the curve is non rational.
   //! Update rational and closed.
   void init(const NCollection_Array1<gp_Pnt2d>& thePoles,
             const NCollection_Array1<double>*   theWeights);
 
 private:
   NCollection_Array1<gp_Pnt2d>               myPoles;
   NCollection_Array1<double>                 myWeights;
   occ::handle<Geom2dEval_RepCurveDesc::Base> myEvalRep;
   bool                                       myRational      = false;
   bool                                       myClosed        = false;
   double                                     myMaxDerivInv   = 0.0;
   bool                                       myMaxDerivInvOk = false;
 };
 
 #endif // _Geom2d_BezierCurve_HeaderFile

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