Open CASCADE Technology  6.5.4
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Public Member Functions
Geom_OffsetCurve Class Reference

This class implements the basis services for an offset curve
in 3D 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 in a reference direction V. The offset curve
takes its parametrization from the basis curve.
The Offset curve is in the direction of of the normal N
defined with the cross product V^T where the vector T
is given by the first derivative on the basis curve with
non zero length.
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 ^ V)) / ||T ^ V||

At any point the Offset direction V must not be parallel to the
vector T and the vector T must not have null length else the
offset curve is not defined. So the offset curve has not the
same continuity as the basis curve.

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^V|| != 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.

#include <Geom_OffsetCurve.hxx>

Inheritance diagram for Geom_OffsetCurve:
Inheritance graph
[legend]

Public Member Functions

 Geom_OffsetCurve (const Handle< Geom_Curve > &C, const Standard_Real Offset, const gp_Dir &V)
 C is the basis curve, Offset is the distance between <me> and
the basis curve at any point. V defines the fixed reference
direction (offset direction). If P is a point on the basis
curve and T the first derivative with non zero length
at this point, the corresponding point on the offset curve is
in the direction of the vector-product N = V ^ T where
N is a unitary vector.
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
Raised if the basis curve C is not at least C1.
Warnings :
No check is done to know if ||V^T|| != 0.0 at any point.

void Reverse ()
 Changes the orientation of this offset curve.
As a result:

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.

void SetBasisCurve (const Handle< Geom_Curve > &C)
 Changes this offset curve by assigning C as the basis curve from which it is built.
Exceptions
Standard_ConstructionError if the curve C is not at least "C1" continuous.

void SetDirection (const gp_Dir &V)
 Changes this offset curve by assigning V as the
reference vector used to compute the offset direction.

void SetOffsetValue (const Standard_Real D)
 Changes this offset curve by assigning D as the offset value.

Handle_Geom_Curve BasisCurve () const
 Returns the basis curve of this offset curve.
Note: The basis curve can be an offset curve.

GeomAbs_Shape Continuity () const
 Returns the global continuity of this offset curve as a
value of the GeomAbs_Shape enumeration.
The degree of continuity of this offset curve is equal
to the degree of continuity of the basis curve minus 1.
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 offset direction defined
at any point.

const gp_DirDirection () const
 Returns the reference vector of this offset curve.
//! 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
V the offset direction the relation ||T(U) ^ V|| != 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.

void D0 (const Standard_Real U, gp_Pnt &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

void D1 (const Standard_Real U, gp_Pnt &P, gp_Vec &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

void D2 (const Standard_Real U, gp_Pnt &P, gp_Vec &V1, gp_Vec &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

void D3 (const Standard_Real U, gp_Pnt &P, gp_Vec &V1, gp_Vec &V2, gp_Vec &V3) const
 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.

gp_Vec 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.
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

Warning:
The exception UndefinedValue or UndefinedDerivative is
raised if it is not possible to compute a unique offset
direction.
//! Raised if N < 1.


void Value (const Standard_Real U, gp_Pnt &P, gp_Pnt &Pbasis, gp_Vec &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

void D0 (const Standard_Real U, gp_Pnt &P, gp_Pnt &Pbasis, gp_Vec &V1basis) 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 D1 (const Standard_Real U, gp_Pnt &P, gp_Pnt &Pbasis, gp_Vec &V1, gp_Vec &V1basis, gp_Vec &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 D2 (const Standard_Real U, gp_Pnt &P, gp_Pnt &Pbasis, gp_Vec &V1, gp_Vec &V2, gp_Vec &V1basis, gp_Vec &V2basis, gp_Vec &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

Standard_Real FirstParameter () const
 Returns the value of the first parameter.
Warnings :
It can be RealFirst from package Standard
if the curve is infinite

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.

Standard_Real Offset () const
 Returns the offset value of this offset curve.

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.

Standard_Boolean IsCN (const Standard_Integer N) const
 Returns true if the degree of continuity of the basis
curve of this offset curve is at least N + 1.
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_Boolean IsPeriodic () const
 Returns true if this offset curve is periodic, i.e. if the
basis curve of this offset curve is periodic.

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.

void Transform (const gp_Trsf &T)
 Applies the transformation T to this offset curve.
Note: the basis curve is also modified.

virtual Standard_Real TransformedParameter (const Standard_Real U, const gp_Trsf &T) const
 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.

virtual Standard_Real ParametricTransformation (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 calls the basis curve method.

Handle_Geom_Geometry Copy () const
 Creates a new object which is a copy of this offset curve.


Constructor & Destructor Documentation


Member Function Documentation

Handle_Geom_Curve Geom_OffsetCurve::BasisCurve ( ) const

Implements Geom_Curve.

Handle_Geom_Geometry Geom_OffsetCurve::Copy ( ) const [virtual]

Implements Geom_Geometry.

void Geom_OffsetCurve::D0 ( const Standard_Real  U,
gp_Pnt P 
) const [virtual]

Implements Geom_Curve.

void Geom_OffsetCurve::D0 ( const Standard_Real  U,
gp_Pnt P,
gp_Pnt Pbasis,
gp_Vec V1basis 
) const
void Geom_OffsetCurve::D1 ( const Standard_Real  U,
gp_Pnt P,
gp_Vec V1 
) const [virtual]

Implements Geom_Curve.

void Geom_OffsetCurve::D1 ( const Standard_Real  U,
gp_Pnt P,
gp_Pnt Pbasis,
gp_Vec V1,
gp_Vec V1basis,
gp_Vec V2basis 
) const
void Geom_OffsetCurve::D2 ( const Standard_Real  U,
gp_Pnt P,
gp_Vec V1,
gp_Vec V2 
) const [virtual]

Implements Geom_Curve.

void Geom_OffsetCurve::D2 ( const Standard_Real  U,
gp_Pnt P,
gp_Pnt Pbasis,
gp_Vec V1,
gp_Vec V2,
gp_Vec V1basis,
gp_Vec V2basis,
gp_Vec V3basis 
) const
void Geom_OffsetCurve::D3 ( const Standard_Real  U,
gp_Pnt P,
gp_Vec V1,
gp_Vec V2,
gp_Vec V3 
) const [virtual]

Implements Geom_Curve.

Implements Geom_Curve.

Implements Geom_Curve.

Implements Geom_Curve.

Implements Geom_Curve.

Implements Geom_Curve.

Implements Geom_Curve.

Reimplemented from Geom_Curve.

virtual Standard_Real Geom_OffsetCurve::Period ( ) const [virtual]

Reimplemented from Geom_Curve.

  • 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 Geom_Curve.

Implements Geom_Curve.

Implements Geom_Geometry.

Reimplemented from Geom_Curve.

void Geom_OffsetCurve::Value ( const Standard_Real  U,
gp_Pnt P,
gp_Pnt Pbasis,
gp_Vec V1basis 
) const

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