occt/src/Geom2d/Geom2d_Curve.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_Curve_HeaderFile
#define _Geom2d_Curve_HeaderFile

#include <Standard.hxx>
#include <Standard_Type.hxx>

#include <Geom2d_Geometry.hxx>
#include <Standard_Real.hxx>
#include <Standard_Boolean.hxx>
#include <GeomAbs_Shape.hxx>
#include <Standard_Integer.hxx>
class Standard_RangeError;
class Standard_NoSuchObject;
class Geom2d_UndefinedDerivative;
class Geom2d_UndefinedValue;
class gp_Trsf2d;
class gp_Pnt2d;
class gp_Vec2d;


class Geom2d_Curve;
DEFINE_STANDARD_HANDLE(Geom2d_Curve, Geom2d_Geometry)

//! The abstract class Curve describes the common
//! behavior of curves in 2D space. The Geom2d
//! package provides numerous concrete classes of
//! derived curves, including lines, circles, conics, Bezier
//! or BSpline curves, etc.
//! The main characteristic of these curves is that they
//! are parameterized. The Geom2d_Curve class shows:
//! - how to work with the parametric equation of a
//! curve in order to calculate the point of parameter
//! u, together with the vector tangent and the
//! derivative vectors of order 2, 3,..., N at this point;
//! - how to obtain general information about the curve
//! (for example, level of continuity, closed
//! characteristics, periodicity, bounds of the parameter field);
//! - how the parameter changes when a geometric
//! transformation is applied to the curve or when the
//! orientation of the curve is inverted.
//! All curves must have a geometric continuity: a curve is
//! at least "C0". Generally, this property is checked at
//! the time of construction or when the curve is edited.
//! Where this is not the case, the documentation
//! explicitly states so.
//! Warning
//! The Geom2d package does not prevent the
//! construction of curves with null length or curves which
//! self-intersect.
class Geom2d_Curve : public Geom2d_Geometry
{

public:

  

  //! Changes the direction of parametrization of <me>.
  //! The "FirstParameter" and the "LastParameter" are not changed
  //! but the orientation  of the curve is modified. If the curve
  //! is bounded the StartPoint of the initial curve becomes the
  //! EndPoint of the reversed curve  and the EndPoint of the initial
  //! curve becomes the StartPoint of the reversed curve.
  Standard_EXPORT virtual void Reverse() = 0;
  
  //! Computes the parameter on the reversed curve for
  //! the point of parameter U on this curve.
  //! Note: The point of parameter U on this curve is
  //! identical to the point of parameter
  //! ReversedParameter(U) on the reversed curve.
  Standard_EXPORT virtual Standard_Real ReversedParameter (const Standard_Real U) const = 0;
  
  //! Computes the parameter on the curve transformed by
  //! T for the point of parameter U on this curve.
  //! Note: this function generally returns U but it can be
  //! redefined (for example, on a line).
  Standard_EXPORT virtual Standard_Real TransformedParameter (const Standard_Real U, const gp_Trsf2d& T) const;
  
  //! Returns the coefficient required to compute the
  //! parametric transformation of this curve when
  //! transformation T is applied. This coefficient is the
  //! ratio between the parameter of a point on this curve
  //! and the parameter of the transformed point on the
  //! new curve transformed by T.
  //! Note: this function generally returns 1. but it can be
  //! redefined (for example, on a line).
  Standard_EXPORT virtual Standard_Real ParametricTransformation (const gp_Trsf2d& T) const;
  
  //! Creates a reversed duplicate Changes the orientation of this curve. The first and
  //! last parameters are not changed, but the parametric
  //! direction of the curve is reversed.
  //! If the curve is bounded:
  //! - the start point of the initial curve becomes the end
  //! point of the reversed curve, and
  //! - the end point of the initial curve becomes the start
  //! point of the reversed curve.
  //! - Reversed creates a new curve.
  Standard_EXPORT Standard_NODISCARD Handle(Geom2d_Curve) Reversed() const;
  
  //! Returns the value of the first parameter.
  //! Warnings :
  //! It can be RealFirst or RealLast from package Standard
  //! if the curve is infinite
  Standard_EXPORT virtual Standard_Real FirstParameter() const = 0;
  
  //! Value of the last parameter.
  //! Warnings :
  //! It can be RealFirst or RealLast from package Standard
  //! if the curve is infinite
  Standard_EXPORT virtual Standard_Real LastParameter() const = 0;
  
  //! Returns true if the curve is closed.
  //! Examples :
  //! Some curves such as circle are always closed, others such as line
  //! are never closed (by definition).
  //! Some Curves such as OffsetCurve can be closed or not. These curves
  //! are considered as closed if the distance between the first point
  //! and the last point of the curve is lower or equal to the Resolution
  //! from package gp wich is a fixed criterion independant of the
  //! application.
  Standard_EXPORT virtual Standard_Boolean IsClosed() const = 0;
  

  //! Returns true if the parameter of the curve is periodic.
  //! It is possible only if the curve is closed and if the
  //! following relation is satisfied :
  //! for each parametric value U the distance between the point
  //! P(u) and the point P (u + T) is lower or equal to Resolution
  //! from package gp, T is the period and must be a constant.
  //! There are three possibilities :
  //! . the curve is never periodic by definition (SegmentLine)
  //! . the curve is always periodic by definition (Circle)
  //! . the curve can be defined as periodic (BSpline). In this case
  //! a function SetPeriodic allows you to give the shape of the
  //! curve.  The general rule for this case is : if a curve can be
  //! periodic or not the default periodicity set is non periodic
  //! and you have to turn (explicitly) the curve into a periodic
  //! curve  if you want the curve to be periodic.
  Standard_EXPORT virtual Standard_Boolean IsPeriodic() const = 0;
  
  //! Returns thne period of this curve.
  //! raises if the curve is not periodic
  Standard_EXPORT virtual Standard_Real Period() const;
  

  //! It is the global continuity of the curve :
  //! C0 : only geometric continuity,
  //! C1 : continuity of the first derivative all along the Curve,
  //! C2 : continuity of the second derivative all along the Curve,
  //! C3 : continuity of the third derivative all along the Curve,
  //! G1 : tangency continuity all along the Curve,
  //! G2 : curvature continuity all along the Curve,
  //! CN : the order of continuity is infinite.
  Standard_EXPORT virtual GeomAbs_Shape Continuity() const = 0;
  
  //! Returns true if the degree of continuity of this curve is at least N.
  //! Exceptions Standard_RangeError if N is less than 0.
  Standard_EXPORT virtual Standard_Boolean IsCN (const Standard_Integer N) const = 0;
  
  //! Returns in P the point of parameter U.
  //! If the curve is periodic  then the returned point is P(U) with
  //! U = Ustart + (U - Uend)  where Ustart and Uend are the
  //! parametric bounds of the curve.
  //!
  //! Raised only for the "OffsetCurve" if it is not possible to
  //! compute the current point. For example when the first
  //! derivative on the basis curve and the offset direction
  //! are parallel.
  Standard_EXPORT virtual void D0 (const Standard_Real U, gp_Pnt2d& P) const = 0;
  

  //! Returns the point P of parameter U and the first derivative V1.
  //! Raised if the continuity of the curve is not C1.
  Standard_EXPORT virtual void D1 (const Standard_Real U, gp_Pnt2d& P, gp_Vec2d& V1) const = 0;
  

  //! Returns the point P of parameter U, the first and second
  //! derivatives V1 and V2.
  //! Raised if the continuity of the curve is not C2.
  Standard_EXPORT virtual void D2 (const Standard_Real U, gp_Pnt2d& P, gp_Vec2d& V1, gp_Vec2d& V2) const = 0;
  

  //! Returns the point P of parameter U, the first, the second
  //! and the third derivative.
  //! Raised if the continuity of the curve is not C3.
  Standard_EXPORT virtual void D3 (const Standard_Real U, gp_Pnt2d& P, gp_Vec2d& V1, gp_Vec2d& V2, gp_Vec2d& V3) const = 0;
  
  //! For the point of parameter U of this curve, computes
  //! the vector corresponding to the Nth derivative.
  //! Exceptions
  //! StdFail_UndefinedDerivative if:
  //! - the continuity of the curve is not "CN", or
  //! - the derivative vector cannot be computed easily;
  //! this is the case with specific types of curve (for
  //! example, a rational BSpline curve where N is greater than 3).
  //! Standard_RangeError if N is less than 1.
  Standard_EXPORT virtual gp_Vec2d DN (const Standard_Real U, const Standard_Integer N) const = 0;
  
  //! Computes the point of parameter U on <me>.
  //! If the curve is periodic  then the returned point is P(U) with
  //! U = Ustart + (U - Uend)  where Ustart and Uend are the
  //! parametric bounds of the curve.
  //!
  //! it is implemented with D0.
  //!
  //! Raised only for the "OffsetCurve" if it is not possible to
  //! compute the current point. For example when the first
  //! derivative on the basis curve and the offset direction
  //! are parallel.
  Standard_EXPORT gp_Pnt2d Value (const Standard_Real U) const;




  DEFINE_STANDARD_RTTIEXT(Geom2d_Curve,Geom2d_Geometry)

protected:




private:




};







#endif // _Geom2d_Curve_HeaderFile