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 // Created on: 1993-03-24
 // Created by: Philippe DAUTRY
 // 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_OffsetCurve_HeaderFile
 #define _Geom2d_OffsetCurve_HeaderFile
 
 #include <Standard.hxx>
 #include <Standard_Type.hxx>
 
 #include <GeomAbs_Shape.hxx>
 #include <Geom2d_Curve.hxx>
 #include <Standard_Integer.hxx>
 #include <Geom2dEvaluator_OffsetCurve.hxx>
 
 class gp_Pnt2d;
 class gp_Vec2d;
 class gp_Trsf2d;
 class Geom2d_Geometry;
 
 
 class Geom2d_OffsetCurve;
 DEFINE_STANDARD_HANDLE(Geom2d_OffsetCurve, Geom2d_Curve)
 
 
 //! This class implements the basis services for the creation,
 //! edition, modification and evaluation of planar offset curve.
 //! The offset curve is obtained by offsetting by distance along
 //! the normal to a basis curve defined in 2D space.
 //! The offset curve in this package can be a self intersecting
 //! curve even if the basis curve does not self-intersect.
 //! The self intersecting portions are not deleted at the
 //! construction time.
 //! An offset curve is a curve at constant distance (Offset) from a
 //! basis curve and the offset curve takes its parametrization from
 //! the basis curve. The Offset curve is in the direction of the
 //! normal to the basis curve N.
 //! The distance offset may be positive or negative to indicate the
 //! preferred side of the curve :
 //! . distance offset >0 => the curve is in the direction of N
 //! . distance offset >0 => the curve is in the direction of - N
 //! On the Offset curve :
 //! Value(u) = BasisCurve.Value(U) + (Offset * (T ^ Z)) / ||T ^ Z||
 //! where T is the tangent vector to the basis curve and Z the
 //! direction of the normal vector to the plane of the curve,
 //! N = T ^ Z defines the offset direction and should not have
 //! null length.
 //!
 //! Warnings :
 //! In this package we suppose that the continuity of the offset
 //! curve is one degree less than the continuity of the
 //! basis curve and we don't check that at any point ||T^Z|| != 0.0
 //!
 //! So to evaluate the curve it is better to check that the offset
 //! curve is well defined at any point because an exception could
 //! be raised. The check is not done in this package at the creation
 //! of the offset curve because the control needs the use of an
 //! algorithm which cannot be implemented in this package.
 //! The OffsetCurve is closed if the first point and the last point
 //! are the same (The distance between these two points is lower or
 //! equal to the Resolution sea package gp) . The OffsetCurve can be
 //! closed even if the basis curve is not closed.
 class Geom2d_OffsetCurve : public Geom2d_Curve
 {
 
 public:
 
   
   //! Constructs a curve offset from the basis curve C,
   //! where Offset is the distance between the offset
   //! curve and the basis curve at any point.
   //! A point on the offset curve is built by measuring the
   //! offset value along a normal vector at a point on C.
   //! This normal vector is obtained by rotating the
   //! vector tangential to C at 90 degrees in the
   //! anti-trigonometric sense. The side of C on which
   //! the offset value is measured is indicated by this
   //! normal vector if Offset is positive, or in the inverse
   //! sense if Offset is negative.
   //! If isNotCheckC0 = TRUE checking if basis curve has C0-continuity
   //! is not made.
   //! Warnings :
   //! In this package the entities are not shared. The OffsetCurve is
   //! built with a copy of the curve C. So when C is modified the
   //! OffsetCurve is not modified
   //! Warning!  if isNotCheckC0 = false,
   //! ConstructionError  raised if the basis curve C is not at least C1.
   //! No check is done to know if ||V^Z|| != 0.0 at any point.
   Standard_EXPORT Geom2d_OffsetCurve(const Handle(Geom2d_Curve)& C, const Standard_Real Offset, const Standard_Boolean isNotCheckC0 = Standard_False);
   
   //! Changes the direction of parametrization of <me>.
   //! As a result:
   //! - the basis curve is reversed,
   //! - the start point of the initial curve becomes the end
   //! point of the reversed curve,
   //! - the end point of the initial curve becomes the start
   //! point of the reversed curve, and
   //! - the first and last parameters are recomputed.
   Standard_EXPORT void Reverse() Standard_OVERRIDE;
   
   //! Computes the parameter on the reversed curve for
   //! the point of parameter U on this offset curve.
   Standard_EXPORT Standard_Real ReversedParameter (const Standard_Real U) const Standard_OVERRIDE;
   
   //! Changes this offset curve by assigning C as the
   //! basis curve from which it is built.
   //! If isNotCheckC0 = TRUE checking if basis curve has C0-continuity
   //! is not made.
   //! Exceptions
   //! if isNotCheckC0 = false,
   //! Standard_ConstructionError if the curve C is not at least "C1" continuous.
   Standard_EXPORT void SetBasisCurve (const Handle(Geom2d_Curve)& C, const Standard_Boolean isNotCheckC0 = Standard_False);
   
   //! Changes this offset curve by assigning D as the offset value.
   Standard_EXPORT void SetOffsetValue (const Standard_Real D);
   
   //! Returns the basis curve of this offset curve. The basis curve can be an offset curve.
   Standard_EXPORT Handle(Geom2d_Curve) BasisCurve() const;
   
 
   //! Continuity of the Offset 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.
   //! Warnings :
   //! Returns the continuity of the basis curve - 1.
   //! The offset curve must have a unique normal direction defined
   //! at any point.
   //! Value and derivatives
   //!
   //! Warnings :
   //! The exception UndefinedValue or UndefinedDerivative is
   //! raised if it is not possible to compute a unique offset
   //! direction.
   //! If T is the first derivative with not null length and
   //! Z the direction normal to the plane of the curve, the
   //! relation ||T(U) ^ Z|| != 0  must be satisfied to evaluate
   //! the offset curve.
   //! No check is done at the creation time and we suppose
   //! in this package that the offset curve is well defined.
   Standard_EXPORT GeomAbs_Shape Continuity() const Standard_OVERRIDE;
   
   //! Warning! this should not be called
   //! if the basis curve is not at least C1. Nevertheless
   //! if used on portion where the curve is C1, it is OK
   Standard_EXPORT void D0 (const Standard_Real U, gp_Pnt2d& P) const Standard_OVERRIDE;
   
   //! Warning! this should not be called
   //! if the continuity of the basis curve is not C2.
   //! Nevertheless, it's OK to use it  on portion
   //! where the curve is C2
   Standard_EXPORT void D1 (const Standard_Real U, gp_Pnt2d& P, gp_Vec2d& V1) const Standard_OVERRIDE;
   
   //! Warning!  This  should  not  be called
   //! if the continuity of the basis curve is not C3.
   //! Nevertheless, it's OK to use it  on portion
   //! where the curve is C3
   Standard_EXPORT void D2 (const Standard_Real U, gp_Pnt2d& P, gp_Vec2d& V1, gp_Vec2d& V2) const Standard_OVERRIDE;
   
   //! Warning! This should not be called
   //! if the continuity of the basis curve is not C4.
   //! Nevertheless, it's OK to use it  on portion
   //! where the curve is C4
   Standard_EXPORT void D3 (const Standard_Real U, gp_Pnt2d& P, gp_Vec2d& V1, gp_Vec2d& V2, gp_Vec2d& V3) const Standard_OVERRIDE;
   
   //! The returned vector gives the value of the derivative
   //! for the order of derivation N.
   //! Warning! this should not be called
   //! raises  UndefunedDerivative   if the continuity of the basis curve is not CN+1.
   //! Nevertheless, it's OK to use it  on portion
   //! where the curve is CN+1
   //! raises  RangeError if N < 1.
   //! raises  NotImplemented if N > 3.
   //! The following functions compute the value and derivatives
   //! on the offset curve and returns the derivatives on the
   //! basis curve too.
   //! The computation of the value and derivatives on the basis
   //! curve are used to evaluate the offset curve
   //! Warnings :
   //! The exception UndefinedValue or UndefinedDerivative is
   //! raised if it is not possible to compute a unique offset direction.
   Standard_EXPORT gp_Vec2d DN (const Standard_Real U, const Standard_Integer N) const Standard_OVERRIDE;
   
   //! Returns the value of the first parameter of this
   //! offset curve. The first parameter corresponds to the
   //! start point of the curve.
   //! Note: the first and last parameters of this offset curve
   //! are also the ones of its basis curve.
   Standard_EXPORT Standard_Real FirstParameter() const Standard_OVERRIDE;
 
   //! Returns the value of the last parameter of this
   //! offset curve. The last parameter
   //! corresponds to the end point.
   //! Note: the first and last parameters of this offset curve
   //! are also the ones of its basis curve.
   Standard_EXPORT Standard_Real LastParameter() const Standard_OVERRIDE;
   
   //! Returns the offset value of this offset curve.
   Standard_EXPORT Standard_Real Offset() const;
   
 
   //! Returns True if the distance between the start point
   //! and the end point of the curve is lower or equal to
   //! Resolution from package gp.
   Standard_EXPORT Standard_Boolean IsClosed() const Standard_OVERRIDE;
   
   //! Is the order of continuity of the curve N ?
   //! Warnings :
   //! This method answer True if the continuity of the basis curve
   //! is N + 1.  We suppose in this class that a normal direction
   //! to the basis curve (used to compute the offset curve) is
   //! defined at any point on the basis curve.
   //! Raised if N < 0.
   Standard_EXPORT Standard_Boolean IsCN (const Standard_Integer N) const Standard_OVERRIDE;
   
   //! Is the parametrization of a curve is periodic ?
   //! If the basis curve is a circle or an ellipse the corresponding
   //! OffsetCurve is periodic. If the basis curve can't be periodic
   //! (for example BezierCurve) the OffsetCurve can't be periodic.
   Standard_EXPORT Standard_Boolean IsPeriodic() const Standard_OVERRIDE;
   
   //! Returns the period of this offset curve, i.e. the period
   //! of the basis curve of this offset curve.
   //! Exceptions
   //! Standard_NoSuchObject if the basis curve is not periodic.
   Standard_EXPORT virtual Standard_Real Period() const Standard_OVERRIDE;
   
   //! Applies the transformation T to this offset curve.
   //! Note: the basis curve is also modified.
   Standard_EXPORT void Transform (const gp_Trsf2d& T) Standard_OVERRIDE;
   
   //! 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 calls the basis curve method.
   Standard_EXPORT virtual Standard_Real TransformedParameter (const Standard_Real U, const gp_Trsf2d& T) const Standard_OVERRIDE;
   
   //! 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 calls the basis curve method.
   Standard_EXPORT virtual Standard_Real ParametricTransformation (const gp_Trsf2d& T) const Standard_OVERRIDE;
   
   //! Creates a new object, which is a copy of this offset curve.
   Standard_EXPORT Handle(Geom2d_Geometry) Copy() const Standard_OVERRIDE;
   
   //! Returns continuity of the basis curve.
   Standard_EXPORT GeomAbs_Shape GetBasisCurveContinuity() const;
 
   //! Dumps the content of me into the stream
   Standard_EXPORT virtual void DumpJson (Standard_OStream& theOStream, Standard_Integer theDepth = -1) const Standard_OVERRIDE;
 
 
 
 
   DEFINE_STANDARD_RTTIEXT(Geom2d_OffsetCurve,Geom2d_Curve)
 
 protected:
 
 
 
 
 private:
 
 
   Handle(Geom2d_Curve) basisCurve;
   Standard_Real offsetValue;
   GeomAbs_Shape myBasisCurveContinuity;
   Handle(Geom2dEvaluator_OffsetCurve) myEvaluator;
 
 };
 
 
 
 
 
 
 
 #endif // _Geom2d_OffsetCurve_HeaderFile

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