occt/src/Geom2d/Geom2d_BezierCurve.hxx

// 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 <Standard_Type.hxx>

#include <Standard_Boolean.hxx>
#include <TColgp_HArray1OfPnt2d.hxx>
#include <TColStd_HArray1OfReal.hxx>
#include <Standard_Integer.hxx>
#include <Standard_Real.hxx>
#include <Geom2d_BoundedCurve.hxx>
#include <TColgp_Array1OfPnt2d.hxx>
#include <TColStd_Array1OfReal.hxx>
#include <GeomAbs_Shape.hxx>
#include <BSplCLib.hxx>

class Standard_ConstructionError;
class Standard_DimensionError;
class Standard_RangeError;
class Standard_OutOfRange;
class gp_Pnt2d;
class gp_Vec2d;
class gp_Trsf2d;
class Geom2d_Geometry;


class Geom2d_BezierCurve;
DEFINE_STANDARD_HANDLE(Geom2d_BezierCurve, Geom2d_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_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 TColgp_Array1OfPnt2d& 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 TColgp_Array1OfPnt2d& 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 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 Standard_Integer Index, const gp_Pnt2d& P, const Standard_Real 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 Standard_Integer Index, const gp_Pnt2d& P, const Standard_Real 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 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_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 Standard_Integer Index, const gp_Pnt2d& 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 False. A BezierCurve cannot be periodic in this
  //! package
  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;
  
  //! Returns GeomAbs_CN, which is the continuity of any Bezier curve.
  Standard_EXPORT GeomAbs_Shape Continuity() const Standard_OVERRIDE;
  

  //! 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 Standard_Integer Degree() const;
  
  Standard_EXPORT void D0 (const Standard_Real U, gp_Pnt2d& P) const Standard_OVERRIDE;
  
  Standard_EXPORT void D1 (const Standard_Real U, gp_Pnt2d& P, gp_Vec2d& V1) const Standard_OVERRIDE;
  
  Standard_EXPORT void D2 (const Standard_Real U, gp_Pnt2d& P, gp_Vec2d& V1, gp_Vec2d& V2) const Standard_OVERRIDE;
  
  Standard_EXPORT void D3 (const Standard_Real U, gp_Pnt2d& P, gp_Vec2d& V1, gp_Vec2d& V2, gp_Vec2d& V3) 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.
  //! Raises RangeError if N < 1.
  Standard_EXPORT gp_Vec2d DN (const Standard_Real U, const Standard_Integer N) const Standard_OVERRIDE;
  
  //! Returns the end point or start point of this Bezier curve.
  Standard_EXPORT gp_Pnt2d 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 for 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_Pnt2d& 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_Array1OfPnt2d& P) const;
  
  //! Returns all the poles of the curve.
  const TColgp_Array1OfPnt2d& Poles() const
  {
    return poles->Array1();
  }

  //! Returns Value (U=1), it is the first control point
  //! of the curve.
  Standard_EXPORT gp_Pnt2d StartPoint() const Standard_OVERRIDE;
  
  //! 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_Trsf2d& T) Standard_OVERRIDE;
  

  //! Returns the value of the maximum polynomial degree of a
  //! BezierCurve. This value is 25.
  Standard_EXPORT static Standard_Integer 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 Standard_Real ToleranceUV, Standard_Real& UTolerance);
  
  //! Creates a new object which is a copy of this Bezier curve.
  Standard_EXPORT Handle(Geom2d_Geometry) Copy() const Standard_OVERRIDE;




  DEFINE_STANDARD_RTTIEXT(Geom2d_BezierCurve,Geom2d_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_HArray1OfPnt2d)& Poles, const Handle(TColStd_HArray1OfReal)& Weights);


  Standard_Boolean rational;
  Standard_Boolean closed;
  Handle(TColgp_HArray1OfPnt2d) poles;
  Handle(TColStd_HArray1OfReal) weights;
  Standard_Real maxderivinv;
  Standard_Boolean maxderivinvok;


};







#endif // _Geom2d_BezierCurve_HeaderFile