occt/src/Geom/Geom_Curve.hxx

// Created on: 1993-03-10
// 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 _Geom_Curve_HeaderFile
#define _Geom_Curve_HeaderFile

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

#include <Geom_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 Geom_UndefinedDerivative;
class Geom_UndefinedValue;
class gp_Trsf;
class gp_Pnt;
class gp_Vec;


class Geom_Curve;
DEFINE_STANDARD_HANDLE(Geom_Curve, Geom_Geometry)

//! The abstract class Curve describes the common
//! behavior of curves in 3D space. The Geom 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 Geom_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 states so explicitly.
//! Warning
//! The Geom package does not prevent the
//! construction of curves with null length or curves which
//! self-intersect.
class Geom_Curve : public Geom_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;
  
  //! Returns the  parameter on the  reversed  curve for
  //! the point of parameter U on <me>.
  //!
  //! me->Reversed()->Value(me->ReversedParameter(U))
  //!
  //! is the same point as
  //!
  //! me->Value(U)
  Standard_EXPORT virtual Standard_Real ReversedParameter (const Standard_Real U) const = 0;
  
  //! Returns the  parameter on the  transformed  curve for
  //! the transform of the point of parameter U on <me>.
  //!
  //! me->Transformed(T)->Value(me->TransformedParameter(U,T))
  //!
  //! is the same point as
  //!
  //! me->Value(U).Transformed(T)
  //!
  //! This methods returns <U>
  //!
  //! It can be redefined. For example on the Line.
  Standard_EXPORT virtual Standard_Real TransformedParameter (const Standard_Real U, const gp_Trsf& T) const;
  
  //! Returns a  coefficient to compute the parameter on
  //! the transformed  curve  for  the transform  of the
  //! point on <me>.
  //!
  //! Transformed(T)->Value(U * ParametricTransformation(T))
  //!
  //! is the same point as
  //!
  //! Value(U).Transformed(T)
  //!
  //! This methods returns 1.
  //!
  //! It can be redefined. For example on the Line.
  Standard_EXPORT virtual Standard_Real ParametricTransformation (const gp_Trsf& T) const;
  
  //! Returns a copy of <me> reversed.
  Standard_EXPORT Standard_NODISCARD Handle(Geom_Curve) Reversed() const;
  
  //! Returns the value of the first parameter.
  //! Warnings :
  //! It can be RealFirst from package Standard
  //! if the curve is infinite
  Standard_EXPORT virtual Standard_Real FirstParameter() const = 0;
  
  //! Returns the value of the last parameter.
  //! Warnings :
  //! It can be RealLast from package Standard
  //! if the curve is infinite
  Standard_EXPORT virtual Standard_Real LastParameter() const = 0;
  
  //! Returns true if the curve is closed.
  //! 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;
  
  //! Is the parametrization of the curve 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 the period of this curve.
  //! Exceptions Standard_NoSuchObject if this 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_Pnt& 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_Pnt& P, gp_Vec& 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_Pnt& P, gp_Vec& V1, gp_Vec& 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_Pnt& P, gp_Vec& V1, gp_Vec& V2, gp_Vec& V3) const = 0;
  

  //! The returned vector gives the value of the derivative for the
  //! order of derivation N.
  //! Raised if the continuity of the curve is not CN.
  //!
  //! Raised if the   derivative  cannot  be  computed
  //! easily. e.g. rational bspline and n > 3.
  //! Raised if N < 1.
  Standard_EXPORT virtual gp_Vec 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_Pnt Value (const Standard_Real U) const;




  DEFINE_STANDARD_RTTIEXT(Geom_Curve,Geom_Geometry)

protected:




private:




};







#endif // _Geom_Curve_HeaderFile