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Geom2d_BezierCurve Class Reference

Describes a rational or non-rational Bezier curve
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#include <Geom2d_BezierCurve.hxx>

Inheritance diagram for Geom2d_BezierCurve:
Inheritance graph
[legend]

Public Member Functions

 Geom2d_BezierCurve (const TColgp_Array1OfPnt2d &CurvePoles)
 Creates a non rational Bezier curve with a set of poles :
CurvePoles. The weights are defaulted to all being 1.
Raises ConstructionError if the number of poles is greater than MaxDegree + 1
or lower than 2.

 Geom2d_BezierCurve (const TColgp_Array1OfPnt2d &CurvePoles, const TColStd_Array1OfReal &PoleWeights)
 Creates a rational Bezier curve with the set of poles
CurvePoles and the set of weights PoleWeights .
If all the weights are identical the curve is considered
as non rational. Raises ConstructionError if
the number of poles is greater than MaxDegree + 1 or lower
than 2 or CurvePoles and CurveWeights have not the same length
or one weight value is lower or equal to Resolution from
package gp.

void Increase (const Standard_Integer Degree)
 Increases the degree of a bezier curve. Degree is the new
degree of <me>.
raises ConstructionError if Degree is greater than MaxDegree or lower than 2
or lower than the initial degree of <me>.

void InsertPoleAfter (const Standard_Integer Index, const gp_Pnt2d &P, const Standard_Real Weight=1.0)
 Inserts a pole with its weight in the set of poles after the
pole of range Index. If the curve was non rational it can
become rational if all the weights are not identical.
//! Raised if Index is not in the range [0, NbPoles]
Raised if the resulting number of poles is greater than
MaxDegree + 1.

void InsertPoleBefore (const Standard_Integer Index, const gp_Pnt2d &P, const Standard_Real Weight=1.0)
 Inserts a pole with its weight in the set of poles after
the pole of range Index. If the curve was non rational it
can become rational if all the weights are not identical.
//! Raised if Index is not in the range [1, NbPoles+1]
Raised if the resulting number of poles is greater than
MaxDegree + 1.

void RemovePole (const Standard_Integer Index)
 Removes the pole of range Index.
If the curve was rational it can become non rational.
//! Raised if Index is not in the range [1, NbPoles]

void Reverse ()
 Reverses the direction of parametrization of <me>
Value (NewU) = Value (1 - OldU)

Standard_Real ReversedParameter (const Standard_Real U) const
 Returns the parameter on the reversed curve for
the point of parameter U on <me>.

returns 1-U

void Segment (const Standard_Real U1, const Standard_Real U2)
 Segments the curve between U1 and U2 which can be out
of the bounds of the curve. The curve is oriented from U1
to U2.
The control points are modified, the first and the last point
are not the same but the parametrization range is [0, 1]
else it could not be a Bezier curve.
Warnings :
Even if <me> is not closed it can become closed after the
segmentation for example if U1 or U2 are out of the bounds
of the curve <me> or if the curve makes loop.
After the segmentation the length of a curve can be null.

void SetPole (const Standard_Integer Index, const gp_Pnt2d &P)
 Substitutes the pole of range index with P.
If the curve <me> is rational the weight of range Index
is not modified.
//! raiseD if Index is not in the range [1, NbPoles]

void SetPole (const Standard_Integer Index, const gp_Pnt2d &P, const Standard_Real Weight)
 Substitutes the pole and the weights of range Index.
If the curve <me> is not rational it can become rational
if all the weights are not identical.
If the curve was rational it can become non rational if
all the weights are identical.
//! Raised if Index is not in the range [1, NbPoles]
//! Raised if Weight <= Resolution from package gp

void SetWeight (const Standard_Integer Index, const Standard_Real Weight)
 Changes the weight of the pole of range Index.
If the curve <me> is not rational it can become rational
if all the weights are not identical.
If the curve was rational it can become non rational if
all the weights are identical.
//! Raised if Index is not in the range [1, NbPoles]
//! Raised if Weight <= Resolution from package gp

Standard_Boolean IsClosed () const
 Returns True if the distance between the first point
and the last point of the curve is lower or equal to
the Resolution from package gp.

Standard_Boolean IsCN (const Standard_Integer N) const
 Continuity of the curve, returns True.

Standard_Boolean IsPeriodic () const
 Returns False. A BezierCurve cannot be periodic in this
package

Standard_Boolean IsRational () const
 Returns false if all the weights are identical. The tolerance
criterion is Resolution from package gp.

GeomAbs_Shape Continuity () const
 Returns GeomAbs_CN, which is the continuity of any Bezier curve.

Standard_Integer Degree () const
 Returns the polynomial degree of the curve. It is the number
of poles less one. In this package the Degree of a Bezier
curve cannot be greater than "MaxDegree".

void D0 (const Standard_Real U, gp_Pnt2d &P) const
 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.

void D1 (const Standard_Real U, gp_Pnt2d &P, gp_Vec2d &V1) const
 Returns the point P of parameter U and the first derivative V1.
//! Raised if the continuity of the curve is not C1.

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

void D3 (const Standard_Real U, gp_Pnt2d &P, gp_Vec2d &V1, gp_Vec2d &V2, gp_Vec2d &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_Vec2d DN (const Standard_Real U, const Standard_Integer N) const
 For this Bezier curve, computes

gp_Pnt2d EndPoint () const
 Returns the end point or start point of this Bezier curve.

Standard_Real FirstParameter () const
 Returns the value of the first parameter of this
Bezier curve. This is 0.0, which gives the start point of this Bezier curve.

Standard_Real LastParameter () const
 Returns the value of the last parameter of this
Bezier curve. This is 1.0, which gives the end point of this Bezier curve.

Standard_Integer NbPoles () const
 Returns the number of poles for this Bezier curve.

gp_Pnt2d Pole (const Standard_Integer Index) const
 Returns the pole of range Index.
//! Raised if Index is not in the range [1, NbPoles]

void Poles (TColgp_Array1OfPnt2d &P) const
 Returns all the poles of the curve.
Raised if the length of P is not equal to the number of poles.

gp_Pnt2d StartPoint () const
 Returns Value (U=1), it is the first control point
of the curve.

Standard_Real Weight (const Standard_Integer Index) const
 Returns the weight of range Index.
//! Raised if Index is not in the range [1, NbPoles]

void Weights (TColStd_Array1OfReal &W) const
 Returns all the weights of the curve.
Raised if the length of W is not equal to the number of poles.

void Transform (const gp_Trsf2d &T)
 Applies the transformation T to this Bezier curve.

void Resolution (const Standard_Real ToleranceUV, Standard_Real &UTolerance)
 Computes for this Bezier curve the parametric
tolerance UTolerance for a given tolerance
Tolerance3D (relative to dimensions in the plane).
If f(t) is the equation of this Bezier curve,
UTolerance ensures that
| t1 - t0| < Utolerance ===>
|f(t1) - f(t0)| < ToleranceUV

Handle_Geom2d_Geometry Copy () const
 Creates a new object which is a copy of this Bezier curve.

Static Public Member Functions

static Standard_Integer MaxDegree ()
 Returns the value of the maximum polynomial degree of a
BezierCurve. This value is 25.


Detailed Description


Constructor & Destructor Documentation


Member Function Documentation

Implements Geom2d_Curve.

Handle_Geom2d_Geometry Geom2d_BezierCurve::Copy ( ) const [virtual]

Implements Geom2d_Geometry.

void Geom2d_BezierCurve::D0 ( const Standard_Real  U,
gp_Pnt2d P 
) const [virtual]

Implements Geom2d_Curve.

void Geom2d_BezierCurve::D1 ( const Standard_Real  U,
gp_Pnt2d P,
gp_Vec2d V1 
) const [virtual]

Implements Geom2d_Curve.

void Geom2d_BezierCurve::D2 ( const Standard_Real  U,
gp_Pnt2d P,
gp_Vec2d V1,
gp_Vec2d V2 
) const [virtual]

Implements Geom2d_Curve.

void Geom2d_BezierCurve::D3 ( const Standard_Real  U,
gp_Pnt2d P,
gp_Vec2d V1,
gp_Vec2d V2,
gp_Vec2d V3 
) const [virtual]

Implements Geom2d_Curve.

  • the point P of parameter U, or
  • the point P and one or more of the following values:
    • V1, the first derivative vector,
    • V2, the second derivative vector,
    • V3, the third derivative vector.
      Note: the parameter U can be outside the bounds of the curve.
      Raises RangeError if N < 1.

Implements Geom2d_Curve.

Implements Geom2d_BoundedCurve.

Implements Geom2d_Curve.

Implements Geom2d_Curve.

Implements Geom2d_Curve.

Implements Geom2d_Curve.

Implements Geom2d_Curve.

Implements Geom2d_Curve.

Implements Geom2d_Curve.

Implements Geom2d_BoundedCurve.

Implements Geom2d_Geometry.


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