Open CASCADE Technology
6.9.1

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 selfintersect. 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. More...
#include <Geom2d_OffsetCurve.hxx>
Public Member Functions  
Geom2d_OffsetCurve (const Handle< Geom2d_Curve > &C, const Standard_Real Offset, const Standard_Boolean isNotCheckC0=Standard_False)  
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 antitrigonometric 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 C0continuity 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. More...  
void  Reverse () 
Changes the direction of parametrization of <me>. As a result: More...  
Standard_Real  ReversedParameter (const Standard_Real U) const 
Computes the parameter on the reversed curve for the point of parameter U on this offset curve. More...  
void  SetBasisCurve (const Handle< Geom2d_Curve > &C, const Standard_Boolean isNotCheckC0=Standard_False) 
Changes this offset curve by assigning C as the basis curve from which it is built. If isNotCheckC0 = TRUE checking if basis curve has C0continuity is not made. Exceptions if isNotCheckC0 = false, Standard_ConstructionError if the curve C is not at least "C1" continuous. More...  
void  SetOffsetValue (const Standard_Real D) 
Changes this offset curve by assigning D as the offset value. More...  
Handle< Geom2d_Curve >  BasisCurve () const 
Returns the basis curve of this offset curve. The basis curve can be an offset curve. More...  
GeomAbs_Shape  Continuity () 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. More...  
void  D0 (const Standard_Real U, gp_Pnt2d &P) const 
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. More...  
void  D1 (const Standard_Real U, gp_Pnt2d &P, gp_Vec2d &V1) const 
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. More...  
void  D2 (const Standard_Real U, gp_Pnt2d &P, gp_Vec2d &V1, gp_Vec2d &V2) const 
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. More...  
void  D3 (const Standard_Real U, gp_Pnt2d &P, gp_Vec2d &V1, gp_Vec2d &V2, gp_Vec2d &V3) const 
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. More...  
gp_Vec2d  DN (const Standard_Real U, const Standard_Integer N) const 
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. More...  
void  Value (const Standard_Real U, gp_Pnt2d &P, gp_Pnt2d &Pbasis, gp_Vec2d &V1basis) const 
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. More...  
void  D1 (const Standard_Real U, gp_Pnt2d &P, gp_Pnt2d &Pbasis, gp_Vec2d &V1, gp_Vec2d &V1basis, gp_Vec2d &V2basis) const 
Warning! this should not be called if the continuity of the basis curve is not C1. Nevertheless, it's OK to use it on portion where the curve is C1. More...  
void  D2 (const Standard_Real U, gp_Pnt2d &P, gp_Pnt2d &Pbasis, gp_Vec2d &V1, gp_Vec2d &V2, gp_Vec2d &V1basis, gp_Vec2d &V2basis, gp_Vec2d &V3basis) const 
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. More...  
Standard_Real  FirstParameter () const 
Returns the value of the first parameter. Warnings : It can be RealFirst or RealLast from package Standard if the curve is infinite. More...  
Standard_Real  LastParameter () const 
Returns the value of the first or last parameter of this offset curve. The first parameter corresponds to the start point of the 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. More...  
Standard_Real  Offset () const 
Returns the offset value of this offset curve. More...  
Standard_Boolean  IsClosed () 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. More...  
Standard_Boolean  IsCN (const Standard_Integer N) const 
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. More...  
Standard_Boolean  IsPeriodic () const 
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. More...  
virtual Standard_Real  Period () const 
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. More...  
void  Transform (const gp_Trsf2d &T) 
Applies the transformation T to this offset curve. Note: the basis curve is also modified. More...  
virtual Standard_Real  TransformedParameter (const Standard_Real U, const gp_Trsf2d &T) const 
Returns the parameter on the transformed curve for the transform of the point of parameter U on <me>. More...  
virtual Standard_Real  ParametricTransformation (const gp_Trsf2d &T) const 
Returns a coefficient to compute the parameter on the transformed curve for the transform of the point on <me>. More...  
Handle< Geom2d_Geometry >  Copy () const 
Creates a new object, which is a copy of this offset curve. More...  
GeomAbs_Shape  GetBasisCurveContinuity () const 
Returns continuity of the basis curve. More...  
Public Member Functions inherited from Geom2d_Curve  
Handle< Geom2d_Curve >  Reversed () 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: More...  
gp_Pnt2d  Value (const Standard_Real U) const 
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. More...  
Public Member Functions inherited from Geom2d_Geometry  
void  Mirror (const gp_Pnt2d &P) 
Performs the symmetrical transformation of a Geometry with respect to the point P which is the center of the symmetry and assigns the result to this geometric object. More...  
void  Mirror (const gp_Ax2d &A) 
Performs the symmetrical transformation of a Geometry with respect to an axis placement which is the axis of the symmetry. More...  
void  Rotate (const gp_Pnt2d &P, const Standard_Real Ang) 
Rotates a Geometry. P is the center of the rotation. Ang is the angular value of the rotation in radians. More...  
void  Scale (const gp_Pnt2d &P, const Standard_Real S) 
Scales a Geometry. S is the scaling value. More...  
void  Translate (const gp_Vec2d &V) 
Translates a Geometry. V is the vector of the tanslation. More...  
void  Translate (const gp_Pnt2d &P1, const gp_Pnt2d &P2) 
Translates a Geometry from the point P1 to the point P2. More...  
Handle< Geom2d_Geometry >  Mirrored (const gp_Pnt2d &P) const 
Handle< Geom2d_Geometry >  Mirrored (const gp_Ax2d &A) const 
Handle< Geom2d_Geometry >  Rotated (const gp_Pnt2d &P, const Standard_Real Ang) const 
Handle< Geom2d_Geometry >  Scaled (const gp_Pnt2d &P, const Standard_Real S) const 
Handle< Geom2d_Geometry >  Transformed (const gp_Trsf2d &T) const 
Handle< Geom2d_Geometry >  Translated (const gp_Vec2d &V) const 
Handle< Geom2d_Geometry >  Translated (const gp_Pnt2d &P1, const gp_Pnt2d &P2) const 
Public Member Functions inherited from MMgt_TShared  
virtual void  Delete () const 
Memory deallocator for transient classes. More...  
Public Member Functions inherited from Standard_Transient  
Standard_Transient ()  
Empty constructor. More...  
Standard_Transient (const Standard_Transient &)  
Copy constructor – does nothing. More...  
Standard_Transient &  operator= (const Standard_Transient &) 
Assignment operator, needed to avoid copying reference counter. More...  
virtual  ~Standard_Transient () 
Destructor must be virtual. More...  
virtual const Handle_Standard_Type &  DynamicType () const 
Returns a type information object about this object. More...  
Standard_Boolean  IsInstance (const Handle_Standard_Type &theType) const 
Returns a true value if this is an instance of Type. More...  
Standard_Boolean  IsInstance (const Standard_CString theTypeName) const 
Returns a true value if this is an instance of TypeName. More...  
Standard_Boolean  IsKind (const Handle_Standard_Type &theType) const 
Returns true if this is an instance of Type or an instance of any class that inherits from Type. Note that multiple inheritance is not supported by OCCT RTTI mechanism. More...  
Standard_Boolean  IsKind (const Standard_CString theTypeName) const 
Returns true if this is an instance of TypeName or an instance of any class that inherits from TypeName. Note that multiple inheritance is not supported by OCCT RTTI mechanism. More...  
virtual Handle_Standard_Transient  This () const 
Returns a Handle which references this object. Must never be called to objects created in stack. More...  
Standard_Integer  GetRefCount () const 
Get the reference counter of this object. More...  
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 selfintersect. 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.
Geom2d_OffsetCurve::Geom2d_OffsetCurve  (  const Handle< Geom2d_Curve > &  C, 
const Standard_Real  Offset,  
const Standard_Boolean  isNotCheckC0 = Standard_False 

) 
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 antitrigonometric 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 C0continuity 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.
Handle< Geom2d_Curve > Geom2d_OffsetCurve::BasisCurve  (  )  const 
Returns the basis curve of this offset curve. The basis curve can be an offset curve.

virtual 
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.
Implements Geom2d_Curve.

virtual 
Creates a new object, which is a copy of this offset curve.
Implements Geom2d_Geometry.

virtual 
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.
Implements Geom2d_Curve.

virtual 
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.
Implements Geom2d_Curve.
void Geom2d_OffsetCurve::D1  (  const Standard_Real  U, 
gp_Pnt2d &  P,  
gp_Pnt2d &  Pbasis,  
gp_Vec2d &  V1,  
gp_Vec2d &  V1basis,  
gp_Vec2d &  V2basis  
)  const 
Warning! this should not be called if the continuity of the basis curve is not C1. Nevertheless, it's OK to use it on portion where the curve is C1.

virtual 
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.
Implements Geom2d_Curve.
void Geom2d_OffsetCurve::D2  (  const Standard_Real  U, 
gp_Pnt2d &  P,  
gp_Pnt2d &  Pbasis,  
gp_Vec2d &  V1,  
gp_Vec2d &  V2,  
gp_Vec2d &  V1basis,  
gp_Vec2d &  V2basis,  
gp_Vec2d &  V3basis  
)  const 
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.

virtual 
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.
Implements Geom2d_Curve.

virtual 
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.
Implements Geom2d_Curve.

virtual 
Returns the value of the first parameter. Warnings : It can be RealFirst or RealLast from package Standard if the curve is infinite.
Implements Geom2d_Curve.
GeomAbs_Shape Geom2d_OffsetCurve::GetBasisCurveContinuity  (  )  const 
Returns continuity of the basis curve.

virtual 
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.
Implements Geom2d_Curve.

virtual 
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.
Implements Geom2d_Curve.

virtual 
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.
Implements Geom2d_Curve.

virtual 
Returns the value of the first or last parameter of this offset curve. The first parameter corresponds to the start point of the 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.
Implements Geom2d_Curve.
Standard_Real Geom2d_OffsetCurve::Offset  (  )  const 
Returns the offset value of this offset curve.

virtual 
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.
Reimplemented from Geom2d_Curve.

virtual 
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.
Reimplemented from Geom2d_Curve.

virtual 
Changes the direction of parametrization of <me>. As a result:
Implements Geom2d_Curve.

virtual 
Computes the parameter on the reversed curve for the point of parameter U on this offset curve.
Implements Geom2d_Curve.
void Geom2d_OffsetCurve::SetBasisCurve  (  const Handle< Geom2d_Curve > &  C, 
const Standard_Boolean  isNotCheckC0 = Standard_False 

) 
Changes this offset curve by assigning C as the basis curve from which it is built. If isNotCheckC0 = TRUE checking if basis curve has C0continuity is not made. Exceptions if isNotCheckC0 = false, Standard_ConstructionError if the curve C is not at least "C1" continuous.
void Geom2d_OffsetCurve::SetOffsetValue  (  const Standard_Real  D  ) 
Changes this offset curve by assigning D as the offset value.

virtual 
Applies the transformation T to this offset curve. Note: the basis curve is also modified.
Implements Geom2d_Geometry.

virtual 
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.
Reimplemented from Geom2d_Curve.
void Geom2d_OffsetCurve::Value  (  const Standard_Real  U, 
gp_Pnt2d &  P,  
gp_Pnt2d &  Pbasis,  
gp_Vec2d &  V1basis  
)  const 
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.