This class implements the basis services for the creation, <br>

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.
More...

#include <Geom2d_OffsetCurve.hxx>

Inheritance diagram for Geom2d_OffsetCurve:

[legend]

Public Member Functions
	Geom2d_OffsetCurve (const Handle< Geom2d_Curve > &C, const Standard_Real Offset)
	Constructs a curve offset from the basis curve C, <br> 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. 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! 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 <br> the point of parameter U on this offset curve. More...

void	SetBasisCurve (const Handle< Geom2d_Curve > &C)
	Changes this offset curve by assigning C as the <br> basis curve from which it is built. Exceptions 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 : <br> 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. 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 <br> 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. <br> 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 <br> 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 ? <br> 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 ? <br> 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 <br> 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. <br> 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 <br> the transform of the point of parameter U on <me>. <br> 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. More...

virtual Standard_Real	ParametricTransformation (const gp_Trsf2d &T) const
	Returns a coefficient to compute the parameter on <br> the transformed curve for the transform of the <br> point on <me>. <br> Transformed(T)->Value(U * ParametricTransformation(T)) is the same point as Value(U).Transformed(T) This methods calls the basis curve method. More...

Handle_Geom2d_Geometry	Copy () const
	Creates a new object, which is a copy of this offset 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 <br> 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>. <br> 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. More...

Public Member Functions inherited from Geom2d_Geometry
void	Mirror (const gp_Pnt2d &P)
	Performs the symmetrical transformation of a Geometry <br> 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 <br> 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. <br> 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 void	ShallowDump (Standard_OStream &) const

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...

Detailed Description

This class implements the basis services for the creation, <br>

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.

Constructor & Destructor Documentation

Geom2d_OffsetCurve::Geom2d_OffsetCurve	(	const Handle< Geom2d_Curve > &	C,
		const Standard_Real	Offset
	)

 Constructs a curve offset from the basis curve C, <br>

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.
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! 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.

Member Function Documentation

Handle_Geom2d_Curve Geom2d_OffsetCurve::BasisCurve ( ) const

Returns the basis curve of this offset curve. The basis curve can be an offset curve.

GeomAbs_Shape Geom2d_OffsetCurve::Continuity ( ) const

virtual

Continuity of the Offset curve : <br>

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.

Handle_Geom2d_Geometry Geom2d_OffsetCurve::Copy ( ) const

virtual

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

Implements Geom2d_Geometry.

void Geom2d_OffsetCurve::D0	(	const Standard_Real	U,
		gp_Pnt2d &	P
	)		const

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.

void Geom2d_OffsetCurve::D1	(	const Standard_Real	U,
		gp_Pnt2d &	P,
		gp_Vec2d &	V1
	)		const

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

void Geom2d_OffsetCurve::D2	(	const Standard_Real	U,
		gp_Pnt2d &	P,
		gp_Vec2d &	V1,
		gp_Vec2d &	V2
	)		const

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

void Geom2d_OffsetCurve::D3	(	const Standard_Real	U,
		gp_Pnt2d &	P,
		gp_Vec2d &	V1,
		gp_Vec2d &	V2,
		gp_Vec2d &	V3
	)		const

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.

gp_Vec2d Geom2d_OffsetCurve::DN	(	const Standard_Real	U,
		const Standard_Integer	N
	)		const

virtual

 The returned vector gives the value of the derivative <br>

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.

Standard_Real Geom2d_OffsetCurve::FirstParameter ( ) const

virtual

Returns the value of the first parameter. <br>

Warnings :
It can be RealFirst or RealLast from package Standard
if the curve is infinite

Implements Geom2d_Curve.

Standard_Boolean Geom2d_OffsetCurve::IsClosed ( ) const

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.

Standard_Boolean Geom2d_OffsetCurve::IsCN ( const Standard_Integer N ) const

virtual

Is the order of continuity of the curve N ? <br>

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.

Standard_Boolean Geom2d_OffsetCurve::IsPeriodic ( ) const

virtual

Is the parametrization of a curve is periodic ? <br>

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.

Standard_Real Geom2d_OffsetCurve::LastParameter ( ) const

virtual

 Returns the value of the first or last parameter of this <br>

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 Standard_Real Geom2d_OffsetCurve::ParametricTransformation ( const gp_Trsf2d & T ) const

virtual

 Returns a  coefficient to compute the parameter on <br>
     the transformed  curve  for  the transform  of the <br>
     point on <me>. <br>

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 Standard_Real Geom2d_OffsetCurve::Period ( ) const

virtual

 Returns the period of this offset curve, i.e. the period <br>

of the basis curve of this offset curve.
Exceptions
Standard_NoSuchObject if the basis curve is not periodic.

Reimplemented from Geom2d_Curve.

void Geom2d_OffsetCurve::Reverse ( )

virtual

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.

Implements Geom2d_Curve.

Standard_Real Geom2d_OffsetCurve::ReversedParameter ( const Standard_Real U ) const

virtual

 Computes the parameter on the reversed curve for <br>

the point of parameter U on this offset curve.

Implements Geom2d_Curve.

void Geom2d_OffsetCurve::SetBasisCurve ( const Handle< Geom2d_Curve > & C )

 Changes this offset curve by assigning C as the <br>

basis curve from which it is built.
Exceptions
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.

void Geom2d_OffsetCurve::Transform ( const gp_Trsf2d & T )

virtual

 Applies the transformation T to this offset curve. <br>

Note: the basis curve is also modified.

Implements Geom2d_Geometry.

virtual Standard_Real Geom2d_OffsetCurve::TransformedParameter	(	const Standard_Real	U,
		const gp_Trsf2d &	T
	)		const

virtual

 Returns the  parameter on the  transformed  curve for <br>
     the transform of the point of parameter U on <me>. <br>

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

The documentation for this class was generated from the following file:

Geom2d_OffsetCurve.hxx

Public Member Functions

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation