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Geom2d_BSplineCurve Class Reference

Describes a BSpline curve.
A BSpline curve can be:
More...

#include <Geom2d_BSplineCurve.hxx>

Inheritance diagram for Geom2d_BSplineCurve:
Inheritance graph
[legend]

Public Member Functions

 Geom2d_BSplineCurve (const TColgp_Array1OfPnt2d &Poles, const TColStd_Array1OfReal &Knots, const TColStd_Array1OfInteger &Multiplicities, const Standard_Integer Degree, const Standard_Boolean Periodic=Standard_False)
 Creates a non-rational B_spline curve on the
basis <Knots, Multiplicities> of degree <Degree>.
The following conditions must be verified.
0 < Degree <= MaxDegree.

Knots.Length() == Mults.Length() >= 2

Knots(i) < Knots(i+1) (Knots are increasing)

1 <= Mults(i) <= Degree

On a non periodic curve the first and last multiplicities
may be Degree+1 (this is even recommanded if you want the
curve to start and finish on the first and last pole).

On a periodic curve the first and the last multicities
must be the same.

on non-periodic curves

Poles.Length() == Sum(Mults(i)) - Degree - 1 >= 2

on periodic curves

Poles.Length() == Sum(Mults(i)) except the first or last

 Geom2d_BSplineCurve (const TColgp_Array1OfPnt2d &Poles, const TColStd_Array1OfReal &Weights, const TColStd_Array1OfReal &Knots, const TColStd_Array1OfInteger &Multiplicities, const Standard_Integer Degree, const Standard_Boolean Periodic=Standard_False)
 Creates a rational B_spline curve on the basis
<Knots, Multiplicities> of degree <Degree>.
The following conditions must be verified.
0 < Degree <= MaxDegree.

Knots.Length() == Mults.Length() >= 2

Knots(i) < Knots(i+1) (Knots are increasing)

1 <= Mults(i) <= Degree

On a non periodic curve the first and last multiplicities
may be Degree+1 (this is even recommanded if you want the
curve to start and finish on the first and last pole).

On a periodic curve the first and the last multicities
must be the same.

on non-periodic curves

Poles.Length() == Sum(Mults(i)) - Degree - 1 >= 2

on periodic curves

Poles.Length() == Sum(Mults(i)) except the first or last

void IncreaseDegree (const Standard_Integer Degree)
 Increases the degree of this BSpline curve to
Degree. As a result, the poles, weights and
multiplicities tables are modified; the knots table is
not changed. Nothing is done if Degree is less than
or equal to the current degree.
Exceptions
Standard_ConstructionError if Degree is greater than
Geom2d_BSplineCurve::MaxDegree().

void IncreaseMultiplicity (const Standard_Integer Index, const Standard_Integer M)
 Increases the multiplicity of the knot <Index> to
<M>.

If <M> is lower or equal to the current
multiplicity nothing is done. If <M> is higher than
the degree the degree is used.
//! If <Index> is not in [FirstUKnotIndex, LastUKnotIndex]

void IncreaseMultiplicity (const Standard_Integer I1, const Standard_Integer I2, const Standard_Integer M)
 Increases the multiplicities of the knots in
[I1,I2] to <M>.

For each knot if <M> is lower or equal to the
current multiplicity nothing is done. If <M> is
higher than the degree the degree is used.
As a result, the poles and weights tables of this curve are modified.
Warning
It is forbidden to modify the multiplicity of the first or
last knot of a non-periodic curve. Be careful as
Geom2d does not protect against this.
Exceptions
Standard_OutOfRange if either Index, I1 or I2 is
outside the bounds of the knots table.

void IncrementMultiplicity (const Standard_Integer I1, const Standard_Integer I2, const Standard_Integer M)
 Increases by M the multiplicity of the knots of indexes
I1 to I2 in the knots table of this BSpline curve. For
each knot, the resulting multiplicity is limited to the
degree of this curve. If M is negative, nothing is done.
As a result, the poles and weights tables of this
BSpline curve are modified.
Warning
It is forbidden to modify the multiplicity of the first or
last knot of a non-periodic curve. Be careful as
Geom2d does not protect against this.
Exceptions
Standard_OutOfRange if I1 or I2 is outside the
bounds of the knots table.

void InsertKnot (const Standard_Real U, const Standard_Integer M=1, const Standard_Real ParametricTolerance=0.0)
 Inserts a knot value in the sequence of knots. If
<U> is an existing knot the multiplicity is
increased by <M>.

If U is not on the parameter range nothing is
done.

If the multiplicity is negative or null nothing is
done. The new multiplicity is limited to the
degree.

The tolerance criterion for knots equality is
the max of Epsilon(U) and ParametricTolerance.
Warning

void InsertKnots (const TColStd_Array1OfReal &Knots, const TColStd_Array1OfInteger &Mults, const Standard_Real ParametricTolerance=0.0, const Standard_Boolean Add=Standard_False)
 Inserts the values of the array Knots, with the
respective multiplicities given by the array Mults, into
the knots table of this BSpline curve.
If a value of the array Knots is an existing knot, its multiplicity is:

Standard_Boolean RemoveKnot (const Standard_Integer Index, const Standard_Integer M, const Standard_Real Tolerance)
 Reduces the multiplicity of the knot of index Index
to M. If M is equal to 0, the knot is removed.
With a modification of this type, the array of poles is also modified.
Two different algorithms are systematically used to
compute the new poles of the curve. If, for each
pole, the distance between the pole calculated
using the first algorithm and the same pole
calculated using the second algorithm, is less than
Tolerance, this ensures that the curve is not
modified by more than Tolerance. Under these
conditions, true is returned; otherwise, false is returned.
A low tolerance is used to prevent modification of
the curve. A high tolerance is used to "smooth" the curve.
Exceptions
Standard_OutOfRange if Index is outside the
bounds of the knots table.

void InsertPoleAfter (const Standard_Integer Index, const gp_Pnt2d &P, const Standard_Real Weight=1.0)
 The new pole is inserted after the pole of range Index.
If the curve was non rational it can become rational.
Raised if the B-spline is NonUniform or PiecewiseBezier or if
Weight <= 0.0
//! Raised if Index is not in the range [1, Number of Poles]

void InsertPoleBefore (const Standard_Integer Index, const gp_Pnt2d &P, const Standard_Real Weight=1.0)
 The new pole is inserted before the pole of range Index.
If the curve was non rational it can become rational.
Raised if the B-spline is NonUniform or PiecewiseBezier or if
Weight <= 0.0
//! Raised if Index is not in the range [1, Number of Poles]

void RemovePole (const Standard_Integer Index)
 Removes the pole of range Index
If the curve was rational it can become non rational.
Raised if the B-spline is NonUniform or PiecewiseBezier.
Raised if the number of poles of the B-spline curve is lower or
equal to 2 before removing.
//! Raised if Index is not in the range [1, Number of Poles]

void Reverse ()
 Reverses the orientation of this BSpline 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 BSpline curve.
The returned value is: UFirst + ULast - U,
where UFirst and ULast are the values of the
first and last parameters of this BSpline curve.

void Segment (const Standard_Real U1, const Standard_Real U2)
 Modifies this BSpline curve by segmenting it
between U1 and U2. Either of these values can be
outside the bounds of the curve, but U2 must be greater than U1.
All data structure tables of this BSpline curve are
modified, but the knots located between U1 and U2
are retained. The degree of the curve is not modified.
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 SetKnot (const Standard_Integer Index, const Standard_Real K)
 Modifies this BSpline curve by assigning the value K
to the knot of index Index in the knots table. This is a
relatively local modification because K must be such that:
Knots(Index - 1) < K < Knots(Index + 1)
Exceptions
Standard_ConstructionError if:

void SetKnots (const TColStd_Array1OfReal &K)
 Modifies this BSpline curve by assigning the array
K to its knots table. The multiplicity of the knots is not modified.
Exceptions
Standard_ConstructionError if the values in the
array K are not in ascending order.
Standard_OutOfRange if the bounds of the array
K are not respectively 1 and the number of knots of this BSpline curve.

void SetKnot (const Standard_Integer Index, const Standard_Real K, const Standard_Integer M)
 Modifies this BSpline curve by assigning the value K
to the knot of index Index in the knots table. This is a
relatively local modification because K must be such that:
Knots(Index - 1) < K < Knots(Index + 1)
The second syntax allows you also to increase the
multiplicity of the knot to M (but it is not possible to
decrease the multiplicity of the knot with this function).
Exceptions
Standard_ConstructionError if:

void PeriodicNormalization (Standard_Real &U) const
 Computes the parameter normalized within the
"first" period of this BSpline curve, if it is periodic:
the returned value is in the range Param1 and
Param1 + Period, where:

void SetPeriodic ()
 Changes this BSpline curve into a periodic curve.
To become periodic, the curve must first be closed.
Next, the knot sequence must be periodic. For this,
FirstUKnotIndex and LastUKnotIndex are used to
compute I1 and I2, the indexes in the knots array
of the knots corresponding to the first and last
parameters of this BSpline curve.
The period is therefore Knot(I2) - Knot(I1).
Consequently, the knots and poles tables are modified.
Exceptions
Standard_ConstructionError if this BSpline curve is not closed.

void SetOrigin (const Standard_Integer Index)
 Assigns the knot of index Index in the knots table as
the origin of this periodic BSpline curve. As a
consequence, the knots and poles tables are modified.
Exceptions
Standard_NoSuchObject if this curve is not periodic.
Standard_DomainError if Index is outside the
bounds of the knots table.

void SetNotPeriodic ()
 Changes this BSpline curve into a non-periodic
curve. If this curve is already non-periodic, it is not modified.
Note that the poles and knots tables are modified.
Warning
If this curve is periodic, as the multiplicity of the first
and last knots is not modified, and is not equal to
Degree + 1, where Degree is the degree of
this BSpline curve, the start and end points of the
curve are not its first and last poles.

void SetPole (const Standard_Integer Index, const gp_Pnt2d &P)
 Modifies this BSpline curve by assigning P to the
pole of index Index in the poles table.
Exceptions
Standard_OutOfRange if Index is outside the
bounds of the poles table.
Standard_ConstructionError if Weight is negative or null.

void SetPole (const Standard_Integer Index, const gp_Pnt2d &P, const Standard_Real Weight)
 Modifies this BSpline curve by assigning P to the
pole of index Index in the poles table.
The second syntax also allows you to modify the
weight of the modified pole, which becomes Weight.
In this case, if this BSpline curve is non-rational, it
can become rational and vice versa.
Exceptions
Standard_OutOfRange if Index is outside the
bounds of the poles table.
Standard_ConstructionError if Weight is negative or null.

void SetWeight (const Standard_Integer Index, const Standard_Real Weight)
 Assigns the weight Weight to the pole of index Index of the poles table.
If the curve was non rational it can become rational.
If the curve was rational it can become non rational.
Exceptions
Standard_OutOfRange if Index is outside the
bounds of the poles table.
Standard_ConstructionError if Weight is negative or null.

void MovePoint (const Standard_Real U, const gp_Pnt2d &P, const Standard_Integer Index1, const Standard_Integer Index2, Standard_Integer &FirstModifiedPole, Standard_Integer &LastModifiedPole)
 Moves the point of parameter U of this BSpline
curve to P. Index1 and Index2 are the indexes in the
table of poles of this BSpline curve of the first and
last poles designated to be moved.
FirstModifiedPole and LastModifiedPole are the
indexes of the first and last poles, which are
effectively modified.
In the event of incompatibility between Index1,
Index2 and the value U:

void MovePointAndTangent (const Standard_Real U, const gp_Pnt2d &P, const gp_Vec2d &Tangent, const Standard_Real Tolerance, const Standard_Integer StartingCondition, const Standard_Integer EndingCondition, Standard_Integer &ErrorStatus)
 Move a point with parameter U to P.
and makes it tangent at U be Tangent.
StartingCondition = -1 means first can move
EndingCondition = -1 means last point can move
StartingCondition = 0 means the first point cannot move
EndingCondition = 0 means the last point cannot move
StartingCondition = 1 means the first point and tangent cannot move
EndingCondition = 1 means the last point and tangent cannot move
and so forth
ErrorStatus != 0 means that there are not enought degree of freedom
with the constrain to deform the curve accordingly

Standard_Boolean IsCN (const Standard_Integer N) const
 Returns true if the degree of continuity of this
BSpline curve is at least N. A BSpline curve is at least GeomAbs_C0.
Exceptions Standard_RangeError if N is negative.

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 Resolution
from package gp.
Warnings :
The first and the last point can be different from the first
pole and the last pole of the curve.

Standard_Boolean IsPeriodic () const
 Returns True if the curve is periodic.

Standard_Boolean IsRational () const
 Returns True if the weights are not identical.
The tolerance criterion is Epsilon of the class Real.

GeomAbs_Shape Continuity () const
 Returns the global continuity of the 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,
CN : the order of continuity is infinite.
For a B-spline curve of degree d if a knot Ui has a
multiplicity p the B-spline curve is only Cd-p continuous
at Ui. So the global continuity of the curve can't be greater
than Cd-p where p is the maximum multiplicity of the interior
Knots. In the interior of a knot span the curve is infinitely
continuously differentiable.

Standard_Integer Degree () const
 Returns the degree of this BSpline curve.
In this class the degree of the basis normalized B-spline
functions cannot be greater than "MaxDegree"
//! Computation of value and derivatives

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
 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
 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
 For this BSpline curve, computes

gp_Vec2d DN (const Standard_Real U, const Standard_Integer N) const
 For the point of parameter U of this BSpline curve,
computes the vector corresponding to the Nth derivative.
Warning
On a point where the continuity of the curve is not the
one requested, this function impacts the part defined
by the parameter with a value greater than U, i.e. the
part of the curve to the "right" of the singularity.
Raises UndefinedDerivative if the continuity of the curve is not CN.
RangeError if N < 1.
//! The following functions computes the point of parameter U
and the derivatives at this point on the B-spline curve
arc defined between the knot FromK1 and the knot ToK2.
U can be out of bounds [Knot (FromK1), Knot (ToK2)] but
for the computation we only use the definition of the curve
between these two knots. This method is useful to compute
local derivative, if the order of continuity of the whole
curve is not greater enough. Inside the parametric
domain Knot (FromK1), Knot (ToK2) the evaluations are
the same as if we consider the whole definition of the
curve. Of course the evaluations are different outside
this parametric domain.

gp_Pnt2d LocalValue (const Standard_Real U, const Standard_Integer FromK1, const Standard_Integer ToK2) const
 Raised if FromK1 = ToK2.
Raised if FromK1 and ToK2 are not in the range
[FirstUKnotIndex, LastUKnotIndex].

void LocalD0 (const Standard_Real U, const Standard_Integer FromK1, const Standard_Integer ToK2, gp_Pnt2d &P) const
void LocalD1 (const Standard_Real U, const Standard_Integer FromK1, const Standard_Integer ToK2, gp_Pnt2d &P, gp_Vec2d &V1) const
 Raised if the local continuity of the curve is not C1
between the knot K1 and the knot K2.
//! Raised if FromK1 = ToK2.
Raised if FromK1 and ToK2 are not in the range
[FirstUKnotIndex, LastUKnotIndex].

void LocalD2 (const Standard_Real U, const Standard_Integer FromK1, const Standard_Integer ToK2, gp_Pnt2d &P, gp_Vec2d &V1, gp_Vec2d &V2) const
 Raised if the local continuity of the curve is not C2
between the knot K1 and the knot K2.
//! Raised if FromK1 = ToK2.
Raised if FromK1 and ToK2 are not in the range
[FirstUKnotIndex, LastUKnotIndex].

void LocalD3 (const Standard_Real U, const Standard_Integer FromK1, const Standard_Integer ToK2, gp_Pnt2d &P, gp_Vec2d &V1, gp_Vec2d &V2, gp_Vec2d &V3) const
 Raised if the local continuity of the curve is not C3
between the knot K1 and the knot K2.
//! Raised if FromK1 = ToK2.
Raised if FromK1 and ToK2 are not in the range
[FirstUKnotIndex, LastUKnotIndex].

gp_Vec2d LocalDN (const Standard_Real U, const Standard_Integer FromK1, const Standard_Integer ToK2, const Standard_Integer N) const
 Raised if the local continuity of the curve is not CN
between the knot K1 and the knot K2.
//! Raised if FromK1 = ToK2.
//! Raised if N < 1.
Raises if FromK1 and ToK2 are not in the range
[FirstUKnotIndex, LastUKnotIndex].

gp_Pnt2d EndPoint () const
 Returns the last point of the curve.
Warnings :
The last point of the curve is different from the last
pole of the curve if the multiplicity of the last knot
is lower than Degree.

Standard_Integer FirstUKnotIndex () const
 For a B-spline curve the first parameter (which gives the start
point of the curve) is a knot value but if the multiplicity of
the first knot index is lower than Degree + 1 it is not the
first knot of the curve. This method computes the index of the
knot corresponding to the first parameter.

Standard_Real FirstParameter () const
 Computes the parametric value of the start point of the curve.
It is a knot value.

Standard_Real Knot (const Standard_Integer Index) const
 Returns the knot of range Index. When there is a knot
with a multiplicity greater than 1 the knot is not repeated.
The method Multiplicity can be used to get the multiplicity
of the Knot.
//! Raised if Index < 1 or Index > NbKnots

void Knots (TColStd_Array1OfReal &K) const
 returns the knot values of the B-spline curve;
Raised if the length of K is not equal to the number of knots.

void KnotSequence (TColStd_Array1OfReal &K) const
 Returns the knots sequence.
In this sequence the knots with a multiplicity greater than 1
are repeated.
Example :
K = {k1, k1, k1, k2, k3, k3, k4, k4, k4}
Raised if the length of K is not equal to NbPoles + Degree + 1

GeomAbs_BSplKnotDistribution KnotDistribution () const
 Returns NonUniform or Uniform or QuasiUniform or PiecewiseBezier.
If all the knots differ by a positive constant from the
preceding knot the BSpline Curve can be :

Standard_Integer LastUKnotIndex () const
 For a BSpline curve the last parameter (which gives the
end point of the curve) is a knot value but if the
multiplicity of the last knot index is lower than
Degree + 1 it is not the last knot of the curve. This
method computes the index of the knot corresponding to
the last parameter.

Standard_Real LastParameter () const
 Computes the parametric value of the end point of the curve.
It is a knot value.

void LocateU (const Standard_Real U, const Standard_Real ParametricTolerance, Standard_Integer &I1, Standard_Integer &I2, const Standard_Boolean WithKnotRepetition=Standard_False) const
 Locates the parametric value U in the sequence of knots.
If "WithKnotRepetition" is True we consider the knot's
representation with repetition of multiple knot value,
otherwise we consider the knot's representation with
no repetition of multiple knot values.
Knots (I1) <= U <= Knots (I2)
. if I1 = I2 U is a knot value (the tolerance criterion
ParametricTolerance is used).
. if I1 < 1 => U < Knots (1) - Abs(ParametricTolerance)
. if I2 > NbKnots => U > Knots (NbKnots) + Abs(ParametricTolerance)

Standard_Integer Multiplicity (const Standard_Integer Index) const
 Returns the multiplicity of the knots of range Index.
//! Raised if Index < 1 or Index > NbKnots

void Multiplicities (TColStd_Array1OfInteger &M) const
 Returns the multiplicity of the knots of the curve.
Raised if the length of M is not equal to NbKnots.

Standard_Integer NbKnots () const
 Returns the number of knots. This method returns the number of
knot without repetition of multiple knots.

Standard_Integer NbPoles () const
 Returns the number of poles

gp_Pnt2d Pole (const Standard_Integer Index) const
 Returns the pole of range Index.
//! Raised if Index < 1 or Index > NbPoles.

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

gp_Pnt2d StartPoint () const
 Returns the start point of the curve.
Warnings :
This point is different from the first pole of the curve if the
multiplicity of the first knot is lower than Degree.

Standard_Real Weight (const Standard_Integer Index) const
 Returns the weight of the pole of range Index .
//! Raised if Index < 1 or Index > NbPoles.

void Weights (TColStd_Array1OfReal &W) const
 Returns the weights of the B-spline curve;
Raised if the length of W is not equal to NbPoles.

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

void Resolution (const Standard_Real ToleranceUV, Standard_Real &UTolerance)
 Computes for this BSpline curve the parametric
tolerance UTolerance for a given tolerance
Tolerance3D (relative to dimensions in the plane).
If f(t) is the equation of this BSpline 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 BSpline curve.

Static Public Member Functions

static Standard_Integer MaxDegree ()
 Returns the value of the maximum degree of the normalized
B-spline basis functions in this package.


Detailed Description


Constructor & Destructor Documentation


Member Function Documentation

Implements Geom2d_Curve.

Handle_Geom2d_Geometry Geom2d_BSplineCurve::Copy ( ) const [virtual]

Implements Geom2d_Geometry.

void Geom2d_BSplineCurve::D0 ( const Standard_Real  U,
gp_Pnt2d P 
) const [virtual]

Implements Geom2d_Curve.

void Geom2d_BSplineCurve::D1 ( const Standard_Real  U,
gp_Pnt2d P,
gp_Vec2d V1 
) const [virtual]

Implements Geom2d_Curve.

void Geom2d_BSplineCurve::D2 ( const Standard_Real  U,
gp_Pnt2d P,
gp_Vec2d V1,
gp_Vec2d V2 
) const [virtual]

Implements Geom2d_Curve.

void Geom2d_BSplineCurve::D3 ( const Standard_Real  U,
gp_Pnt2d P,
gp_Vec2d V1,
gp_Vec2d V2,
gp_Vec2d 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.
      Warning
      On a point where the continuity of the curve is not the
      one requested, these functions impact the part
      defined by the parameter with a value greater than U,
      i.e. the part of the curve to the "right" of the singularity.
      Raises UndefinedDerivative if the continuity of the curve is not C3.

Implements Geom2d_Curve.

Implements Geom2d_Curve.

Implements Geom2d_BoundedCurve.

Implements Geom2d_Curve.

  • If U is less than the first parameter or greater than
    the last parameter of this BSpline curve, nothing is done.
  • If M is negative or null, nothing is done.
  • The multiplicity of a knot is limited to the degree of
    this BSpline curve.
  • increased by M, if Add is true, or
  • increased to M, if Add is false (default value).
    The tolerance criterion used for knot equality is the
    larger of the values ParametricTolerance (defaulted
    to 0.) and Standard_Real::Epsilon(U),
    where U is the current knot value.
    Warning
  • For a value of the array Knots which is less than
    the first parameter or greater than the last
    parameter of this BSpline curve, nothing is done.
  • For a value of the array Mults which is negative or
    null, nothing is done.
  • The multiplicity of a knot is limited to the degree of
    this BSpline curve.

Implements Geom2d_Curve.

Implements Geom2d_Curve.

Implements Geom2d_Curve.

  • Uniform if all the knots are of multiplicity 1,
  • QuasiUniform if all the knots are of multiplicity 1 except for
    the first and last knot which are of multiplicity Degree + 1,
  • PiecewiseBezier if the first and last knots have multiplicity
    Degree + 1 and if interior knots have multiplicity Degree
    A piecewise Bezier with only two knots is a BezierCurve.
    else the curve is non uniform.
    The tolerance criterion is Epsilon from class Real.

Implements Geom2d_Curve.

void Geom2d_BSplineCurve::LocateU ( const Standard_Real  U,
const Standard_Real  ParametricTolerance,
Standard_Integer I1,
Standard_Integer I2,
const Standard_Boolean  WithKnotRepetition = Standard_False 
) const
void Geom2d_BSplineCurve::MovePoint ( const Standard_Real  U,
const gp_Pnt2d P,
const Standard_Integer  Index1,
const Standard_Integer  Index2,
Standard_Integer FirstModifiedPole,
Standard_Integer LastModifiedPole 
)
  • no change is made to this BSpline curve, and
  • the FirstModifiedPole and LastModifiedPole are returned null.
    Exceptions
    Standard_OutOfRange if:
  • Index1 is greater than or equal to Index2, or
  • Index1 or Index2 is less than 1 or greater than the
    number of poles of this BSpline curve.
void Geom2d_BSplineCurve::MovePointAndTangent ( const Standard_Real  U,
const gp_Pnt2d P,
const gp_Vec2d Tangent,
const Standard_Real  Tolerance,
const Standard_Integer  StartingCondition,
const Standard_Integer  EndingCondition,
Standard_Integer ErrorStatus 
)
  • Param1 is the "first parameter", and
  • Period the period of this BSpline curve.
    Note: If this curve is not periodic, U is not modified.
  • the knots and poles tables are modified;
  • 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.

Implements Geom2d_Curve.

Implements Geom2d_Curve.

   - The segmentation of a periodic curve over an <br>

interval corresponding to its period generates a
non-periodic curve with equivalent geometry.
Exceptions
Standard_DomainError if U2 is less than U1.
//! raises if U2 < U1.

  • K is not such that:
    Knots(Index - 1) < K < Knots(Index + 1)
  • M is greater than the degree of this BSpline curve
    or lower than the previous multiplicity of knot of
    index Index in the knots table.
    Standard_OutOfRange if Index is outside the bounds of the knots table.
  • K is not such that:
    Knots(Index - 1) < K < Knots(Index + 1)
  • M is greater than the degree of this BSpline curve
    or lower than the previous multiplicity of knot of
    index Index in the knots table.
    Standard_OutOfRange if Index is outside the bounds of the knots table.

Implements Geom2d_BoundedCurve.

Implements Geom2d_Geometry.


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