Open CASCADE Technology 6.6.0
Public Member Functions | Static Public Member Functions
Geom_BezierCurve Class Reference

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

Inheritance diagram for Geom_BezierCurve:
Inheritance graph
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Public Member Functions

 Geom_BezierCurve (const TColgp_Array1OfPnt &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.

 Geom_BezierCurve (const TColgp_Array1OfPnt &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_Pnt &P)
 Inserts a pole P after the pole of range Index.
If the curve <me> is rational the weight value for the new
pole of range Index is 1.0.
//! raised if Index is not in the range [1, NbPoles]
raised if the resulting number of poles is greater than
MaxDegree + 1.

void InsertPoleAfter (const Standard_Integer Index, const gp_Pnt &P, const Standard_Real Weight)
 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]
Raised if the resulting number of poles is greater than
MaxDegree + 1.
Raised if Weight is lower or equal to Resolution from package gp.

void InsertPoleBefore (const Standard_Integer Index, const gp_Pnt &P)
 Inserts a pole P before the pole of range Index.
If the curve <me> is rational the weight value for the new
pole of range Index is 1.0.
//! Raised if Index is not in the range [1, NbPoles]
Raised if the resulting number of poles is greater than
MaxDegree + 1.

void InsertPoleBefore (const Standard_Integer Index, const gp_Pnt &P, const Standard_Real Weight)
 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]
Raised if the resulting number of poles is greater than
MaxDegree + 1.
Raised if Weight is lower or equal to Resolution from
package gp.

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]
//! Raised if Degree is lower than 2.

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_Pnt &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_Pnt &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 True if the parametrization of a curve is periodic.
(P(u) = P(u + T) T = constante)

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

GeomAbs_Shape Continuity () const
 a Bezier curve is CN

Standard_Integer Degree () const
 Returns the polynomial degree of the curve.
it is the number of poles - 1
//! point P and derivatives (V1, V2, V3) computation
The Bezier Curve has a Polynomial representation so the
parameter U can be out of the bounds of the curve.

void D0 (const Standard_Real U, gp_Pnt &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_Pnt &P, gp_Vec &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_Pnt &P, gp_Vec &V1, gp_Vec &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_Pnt &P, gp_Vec &V1, gp_Vec &V2, gp_Vec &V3) const
 For this Bezier curve, computes

gp_Vec DN (const Standard_Real U, const Standard_Integer N) const
 For the point of parameter U of this Bezier curve,
computes the vector corresponding to the Nth derivative.
Note: the parameter U can be outside the bounds of the curve.
Exceptions Standard_RangeError if N is less than 1.

gp_Pnt StartPoint () const
 Returns Value (U=0.), it is the first control point of the curve.

gp_Pnt EndPoint () const
 Returns Value (U=1.), it is the last control point of the 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 of this Bezier curve.

gp_Pnt 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_Array1OfPnt &P) const
 Returns all the poles of the curve.
Raised if the length of P is not equal to the number of poles.

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_Trsf &T)
 Applies the transformation T to this Bezier curve.

void Resolution (const Standard_Real Tolerance3D, Standard_Real &UTolerance)
 Computes for this Bezier curve the parametric
tolerance UTolerance for a given 3D tolerance Tolerance3D.
If f(t) is the equation of this Bezier curve,
UTolerance ensures that:
|t1-t0| < UTolerance ===> |f(t1)-f(t0)| < Tolerance3D

Handle_Geom_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 any Geom_BezierCurve curve. This value is 25.


Detailed Description


Constructor & Destructor Documentation

Geom_BezierCurve::Geom_BezierCurve ( const TColgp_Array1OfPnt CurvePoles)
Geom_BezierCurve::Geom_BezierCurve ( const TColgp_Array1OfPnt CurvePoles,
const TColStd_Array1OfReal PoleWeights 
)

Member Function Documentation

GeomAbs_Shape Geom_BezierCurve::Continuity ( ) const [virtual]

Implements Geom_Curve.

Handle_Geom_Geometry Geom_BezierCurve::Copy ( ) const [virtual]

Implements Geom_Geometry.

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

Implements Geom_Curve.

void Geom_BezierCurve::D1 ( const Standard_Real  U,
gp_Pnt P,
gp_Vec V1 
) const [virtual]

Implements Geom_Curve.

void Geom_BezierCurve::D2 ( const Standard_Real  U,
gp_Pnt P,
gp_Vec V1,
gp_Vec V2 
) const [virtual]

Implements Geom_Curve.

void Geom_BezierCurve::D3 ( const Standard_Real  U,
gp_Pnt P,
gp_Vec V1,
gp_Vec V2,
gp_Vec V3 
) const [virtual]
  • 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.

Implements Geom_Curve.

Standard_Integer Geom_BezierCurve::Degree ( ) const
gp_Vec Geom_BezierCurve::DN ( const Standard_Real  U,
const Standard_Integer  N 
) const [virtual]

Implements Geom_Curve.

gp_Pnt Geom_BezierCurve::EndPoint ( ) const [virtual]

Implements Geom_BoundedCurve.

Standard_Real Geom_BezierCurve::FirstParameter ( ) const [virtual]

Implements Geom_Curve.

void Geom_BezierCurve::Increase ( const Standard_Integer  Degree)
void Geom_BezierCurve::InsertPoleAfter ( const Standard_Integer  Index,
const gp_Pnt P 
)
void Geom_BezierCurve::InsertPoleAfter ( const Standard_Integer  Index,
const gp_Pnt P,
const Standard_Real  Weight 
)
void Geom_BezierCurve::InsertPoleBefore ( const Standard_Integer  Index,
const gp_Pnt P 
)
void Geom_BezierCurve::InsertPoleBefore ( const Standard_Integer  Index,
const gp_Pnt P,
const Standard_Real  Weight 
)
Standard_Boolean Geom_BezierCurve::IsClosed ( ) const [virtual]

Implements Geom_Curve.

Standard_Boolean Geom_BezierCurve::IsCN ( const Standard_Integer  N) const [virtual]

Implements Geom_Curve.

Standard_Boolean Geom_BezierCurve::IsPeriodic ( ) const [virtual]

Implements Geom_Curve.

Standard_Boolean Geom_BezierCurve::IsRational ( ) const
Standard_Real Geom_BezierCurve::LastParameter ( ) const [virtual]

Implements Geom_Curve.

static Standard_Integer Geom_BezierCurve::MaxDegree ( ) [static]
Standard_Integer Geom_BezierCurve::NbPoles ( ) const
gp_Pnt Geom_BezierCurve::Pole ( const Standard_Integer  Index) const
void Geom_BezierCurve::Poles ( TColgp_Array1OfPnt P) const
void Geom_BezierCurve::RemovePole ( const Standard_Integer  Index)
void Geom_BezierCurve::Resolution ( const Standard_Real  Tolerance3D,
Standard_Real UTolerance 
)
void Geom_BezierCurve::Reverse ( ) [virtual]

Implements Geom_Curve.

Standard_Real Geom_BezierCurve::ReversedParameter ( const Standard_Real  U) const [virtual]

Implements Geom_Curve.

void Geom_BezierCurve::Segment ( const Standard_Real  U1,
const Standard_Real  U2 
)
void Geom_BezierCurve::SetPole ( const Standard_Integer  Index,
const gp_Pnt P 
)
void Geom_BezierCurve::SetPole ( const Standard_Integer  Index,
const gp_Pnt P,
const Standard_Real  Weight 
)
void Geom_BezierCurve::SetWeight ( const Standard_Integer  Index,
const Standard_Real  Weight 
)
gp_Pnt Geom_BezierCurve::StartPoint ( ) const [virtual]

Implements Geom_BoundedCurve.

void Geom_BezierCurve::Transform ( const gp_Trsf T) [virtual]

Implements Geom_Geometry.

Standard_Real Geom_BezierCurve::Weight ( const Standard_Integer  Index) const
void Geom_BezierCurve::Weights ( TColStd_Array1OfReal W) const

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