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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 _GeomEval_TBezierCurve_HeaderFile
 #define _GeomEval_TBezierCurve_HeaderFile
 
 #include <Geom_BoundedCurve.hxx>
 #include <NCollection_Array1.hxx>
 #include <gp_Pnt.hxx>
 
 class gp_Trsf;
 class Geom_Geometry;
 
 //! 3D Trigonometric Bezier curve.
 //! Uses a trigonometric Bernstein-like basis over the space
 //! {1, sin(alpha*t), cos(alpha*t), ..., sin(n*alpha*t), cos(n*alpha*t)}.
 //!
 //! The parameter domain is [0, Pi/alpha].
 //! The number of control points is 2*n + 1 for order n.
 //!
 //! The alpha parameter controls the frequency of the trigonometric basis.
 //! A T-Bezier curve of order n with poles P_0, P_1, ..., P_{2n} is:
 //! @code
 //!   C(t) = P_0 * T_0(t) + P_1 * T_1(t) + ... + P_{2n} * T_{2n}(t)
 //! @endcode
 //! where:
 //! - T_0(t) = 1
 //! - T_{2k-1}(t) = sin(k * alpha * t), for k = 1..n
 //! - T_{2k}(t) = cos(k * alpha * t), for k = 1..n
 //!
 //! For rational curves, each pole is weighted:
 //! @code
 //!   C(t) = sum(w_i * P_i * T_i(t)) / sum(w_i * T_i(t))
 //! @endcode
 class GeomEval_TBezierCurve : public Geom_BoundedCurve
 {
 public:
   //! Constructs a non-rational T-Bezier curve from poles and alpha.
   //! @param[in] thePoles control points (1-based, size must be odd >= 3)
   //! @param[in] theAlpha frequency parameter (must be > 0)
   //! @throw Standard_ConstructionError if NbPoles is not odd or < 3 or theAlpha <= 0
   Standard_EXPORT GeomEval_TBezierCurve(const NCollection_Array1<gp_Pnt>& thePoles,
                                         double                            theAlpha);
 
   //! Constructs a rational T-Bezier curve.
   //! @param[in] thePoles control points (1-based, size must be odd >= 3)
   //! @param[in] theWeights weights (same size as poles, all > 0)
   //! @param[in] theAlpha frequency parameter (must be > 0)
   //! @throw Standard_ConstructionError if validation fails
   Standard_EXPORT GeomEval_TBezierCurve(const NCollection_Array1<gp_Pnt>& thePoles,
                                         const NCollection_Array1<double>& theWeights,
                                         double                            theAlpha);
 
   //! Returns the poles array.
   Standard_EXPORT const NCollection_Array1<gp_Pnt>& Poles() const;
 
   //! Returns the weights array (empty if non-rational).
   Standard_EXPORT const NCollection_Array1<double>& Weights() const;
 
   //! Returns the frequency parameter alpha.
   Standard_EXPORT double Alpha() const;
 
   //! Returns the number of poles.
   Standard_EXPORT int NbPoles() const;
 
   //! Returns the trigonometric order n (NbPoles = 2*n + 1).
   Standard_EXPORT int Order() const;
 
   //! Returns true if the curve is rational.
   Standard_EXPORT bool IsRational() const;
 
   // -- Geom_BoundedCurve interface --
 
   //! Returns the start point C(0).
   Standard_EXPORT gp_Pnt StartPoint() const final;
 
   //! Returns the end point C(Pi/alpha).
   Standard_EXPORT gp_Pnt EndPoint() const final;
 
   // -- Geom_Curve interface --
 
   //! Reversal is not supported for this eval curve.
   //! @throw Standard_NotImplemented
   Standard_EXPORT void Reverse() final;
 
   //! Reversal is not supported for this eval curve.
   //! @throw Standard_NotImplemented
   Standard_EXPORT double ReversedParameter(const double U) const final;
 
   //! Returns the first parameter value: 0.0.
   Standard_EXPORT double FirstParameter() const final;
 
   //! Returns the last parameter value: Pi/alpha.
   Standard_EXPORT double LastParameter() const final;
 
   //! Returns true if StartPoint and EndPoint coincide.
   Standard_EXPORT bool IsClosed() const final;
 
   //! Returns false. T-Bezier curves are not periodic.
   Standard_EXPORT bool IsPeriodic() const final;
 
   //! Returns GeomAbs_CN. T-Bezier curves are infinitely differentiable.
   Standard_EXPORT GeomAbs_Shape Continuity() const final;
 
   //! Returns true for all N. T-Bezier curves are infinitely differentiable.
   Standard_EXPORT bool IsCN(const int N) const final;
 
   //! Computes the point C(U).
   Standard_EXPORT gp_Pnt EvalD0(const double U) const final;
 
   //! Computes the point and first derivative at U.
   Standard_EXPORT Geom_Curve::ResD1 EvalD1(const double U) const final;
 
   //! Computes the point and first two derivatives at U.
   Standard_EXPORT Geom_Curve::ResD2 EvalD2(const double U) const final;
 
   //! Computes the point and first three derivatives at U.
   Standard_EXPORT Geom_Curve::ResD3 EvalD3(const double U) const final;
 
   //! Computes the N-th derivative at U.
   //! @param[in] U parameter value
   //! @param[in] N derivative order (must be >= 1)
   //! @return the N-th derivative vector
   //! @throw Standard_RangeError if N < 1
   Standard_EXPORT gp_Vec EvalDN(const double U, const int N) const final;
 
   //! Transformation is not supported for this eval geometry.
   //! @throw Standard_NotImplemented
   Standard_EXPORT void Transform(const gp_Trsf& T) final;
 
   //! Creates a new object which is a copy of this T-Bezier curve.
   Standard_EXPORT occ::handle<Geom_Geometry> Copy() const final;
 
   //! Dumps the content of me into the stream.
   Standard_EXPORT void DumpJson(Standard_OStream& theOStream, int theDepth = -1) const final;
 
   DEFINE_STANDARD_RTTIEXT(GeomEval_TBezierCurve, Geom_BoundedCurve)
 
 private:
   //! Evaluate trigonometric basis functions at parameter theT.
   //! Returns array of size 2*n+1:
   //! {T_0(t), T_1(t), ..., T_{2n}(t)}
   //! where T_0=1, T_{2k-1}=sin(k*alpha*t), T_{2k}=cos(k*alpha*t).
   void evalBasis(double theT, NCollection_Array1<double>& theBasis) const;
 
   //! Evaluate derivatives of basis functions of order theDerivOrder.
   //! @param[in] theT parameter value
   //! @param[in] theDerivOrder derivative order (1, 2, 3, ...)
   //! @param[out] theBasisDeriv array of derivatives of size 2*n+1
   void evalBasisDeriv(double                      theT,
                       int                         theDerivOrder,
                       NCollection_Array1<double>& theBasisDeriv) const;
 
   //! Evaluate point on a non-rational curve: sum(P_i * B_i(t)).
   gp_Pnt evalNonRationalPoint(const NCollection_Array1<double>& theBasis) const;
 
   //! Evaluate derivative vector on a non-rational curve: sum(P_i * B_i'(t)).
   gp_Vec evalNonRationalDeriv(const NCollection_Array1<double>& theBasisDeriv) const;
 
   NCollection_Array1<gp_Pnt> myPoles;    //!< Control points
   NCollection_Array1<double> myWeights;  //!< Weights (empty if non-rational)
   double                     myAlpha;    //!< Frequency parameter
   bool                       myRational; //!< True if curve is rational
 };
 
 #endif // _GeomEval_TBezierCurve_HeaderFile

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