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

Definition of the 1D B_spline curve.

Uniform or non-uniform
Rational or non-rational
Periodic or non-periodic

a b-spline curve is defined by :

The Degree (up to 25)

The Poles (and the weights if it is rational)

The Knots and Multiplicities

The knot vector is an increasing sequence of
reals without repetition. The multiplicities are
the repetition of the knots.

If the knots are regularly spaced (the difference
of two consecutive knots is a constant), the
knots repartition is :

More...

#include <Law_BSpline.hxx>

Inheritance diagram for Law_BSpline:
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Public Member Functions

 Law_BSpline (const TColStd_Array1OfReal &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>.

 Law_BSpline (const TColStd_Array1OfReal &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>.

void IncreaseDegree (const Standard_Integer Degree)
 Increase the degree to <Degree>. Nothing is done
if <Degree> is lower or equal to the current
degree.

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.
//! If <I1,I2> are not in [FirstUKnotIndex, LastUKnotIndex]

void IncrementMultiplicity (const Standard_Integer I1, const Standard_Integer I2, const Standard_Integer M)
 Increment the multiplicities of the knots in
[I1,I2] by <M>.

If <M> is not positive nithing is done.

For each knot the resulting multiplicity is
limited to the Degree.
//! If <I1,I2> are not in [FirstUKnotIndex, LastUKnotIndex]

void InsertKnot (const Standard_Real U, const Standard_Integer M=1, const Standard_Real ParametricTolerance=0.0, const Standard_Boolean Add=Standard_True)
 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.

void InsertKnots (const TColStd_Array1OfReal &Knots, const TColStd_Array1OfInteger &Mults, const Standard_Real ParametricTolerance=0.0, const Standard_Boolean Add=Standard_False)
 Inserts a set of knots values in the sequence of
knots.

For each U = Knots(i), M = Mults(i)

If <U> is an existing knot the multiplicity is
increased by <M> if <Add> is True, increased to
<M> if <Add> is False.

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.

Standard_Boolean RemoveKnot (const Standard_Integer Index, const Standard_Integer M, const Standard_Real Tolerance)
 Decrement the knots multiplicity to <M>. If M is
0 the knot is removed. The Poles sequence is
modified.

As there are two ways to compute the new poles the
average is computed if the distance is lower than
the <Tolerance>, else False is returned.

A low tolerance is used to prevent the modification
of the curve.

A high tolerance is used to "smooth" the curve.

Raised if Index is not in the range
[FirstUKnotIndex, LastUKnotIndex]
//! pole insertion and pole removing
this operation is limited to the Uniform or QuasiUniform
BSplineCurve. The knot values are modified . If the BSpline is
NonUniform or Piecewise Bezier an exception Construction error
is raised.

void Reverse ()
 Changes the direction of parametrization of <me>. The Knot
sequence is modified, the FirstParameter and the
LastParameter are not modified. The StartPoint of the
initial curve becomes the EndPoint of the reversed curve
and the EndPoint of the initial curve becomes the StartPoint
of the reversed curve.

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

returns UFirst + ULast - U

void Segment (const Standard_Real U1, const Standard_Real U2)
 Segments the curve between U1 and U2.
The control points are modified, the first and the last point
are not the same.
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.
//! raises if U2 < U1.

void SetKnot (const Standard_Integer Index, const Standard_Real K)
 Changes the knot of range Index.
The multiplicity of the knot is not modified.
//! Raised if K >= Knots(Index+1) or K <= Knots(Index-1).
//! Raised if Index < 1 || Index > NbKnots

void SetKnots (const TColStd_Array1OfReal &K)
 Changes all the knots of the curve
The multiplicity of the knots are not modified.
Raised if there is an index such that K (Index+1) <= K (Index).
Raised if K.Lower() < 1 or K.Upper() > NbKnots

void SetKnot (const Standard_Integer Index, const Standard_Real K, const Standard_Integer M)
 Changes the knot of range Index with its multiplicity.
You can increase the multiplicity of a knot but it is
not allowed to decrease the multiplicity of an existing knot.
Raised if K >= Knots(Index+1) or K <= Knots(Index-1).
Raised if M is greater than Degree or lower than the previous
multiplicity of knot of range Index.
//! Raised if Index < 1 || Index > NbKnots

void PeriodicNormalization (Standard_Real &U) const
 returns the parameter normalized within
the period if the curve is periodic : otherwise
does not do anything

void SetPeriodic ()
 Makes a closed B-spline into a periodic curve. The curve is
periodic if the knot sequence is periodic and if the curve is
closed (The tolerance criterion is Resolution from gp).
The period T is equal to Knot(LastUKnotIndex) -
Knot(FirstUKnotIndex). A periodic B-spline can be uniform
or not.
//! Raised if the curve is not closed.

void SetOrigin (const Standard_Integer Index)
 Set the origin of a periodic curve at Knot(index)
KnotVector and poles are modified.
//! Raised if the curve is not periodic
//! Raised if index not in the range
[FirstUKnotIndex , LastUKnotIndex]

void SetNotPeriodic ()
 Makes a non periodic curve. If the curve was non periodic
the curve is not modified.

void SetPole (const Standard_Integer Index, const Standard_Real P)
 Substitutes the Pole of range Index with P.
Raised if Index < 1 || Index > NbPoles

void SetPole (const Standard_Integer Index, const Standard_Real P, const Standard_Real Weight)
 Substitutes the pole and the weight of range Index.
If the curve <me> is not rational it can become rational
If the curve was rational it can become non rational
Raised if Index < 1 || Index > NbPoles
//! Raised if Weight <= 0.0

void SetWeight (const Standard_Integer Index, const Standard_Real Weight)
 Changes the weight for the pole of range Index.
If the curve was non rational it can become rational.
If the curve was rational it can become non rational.
Raised if Index < 1 || Index > NbPoles
//! Raised if Weight <= 0.0

Standard_Boolean IsCN (const Standard_Integer N) const
 Returns the continuity of the curve, the curve is at least C0.
//! Raised if N < 0.

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
 Computation of value and derivatives


Standard_Real Value (const Standard_Real U) const
void D0 (const Standard_Real U, Standard_Real &P) const
void D1 (const Standard_Real U, Standard_Real &P, Standard_Real &V1) const
void D2 (const Standard_Real U, Standard_Real &P, Standard_Real &V1, Standard_Real &V2) const
void D3 (const Standard_Real U, Standard_Real &P, Standard_Real &V1, Standard_Real &V2, Standard_Real &V3) const
Standard_Real DN (const Standard_Real U, const Standard_Integer N) const
 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.


Standard_Real LocalValue (const Standard_Real U, const Standard_Integer FromK1, const Standard_Integer ToK2) const
void LocalD0 (const Standard_Real U, const Standard_Integer FromK1, const Standard_Integer ToK2, Standard_Real &P) const
void LocalD1 (const Standard_Real U, const Standard_Integer FromK1, const Standard_Integer ToK2, Standard_Real &P, Standard_Real &V1) const
void LocalD2 (const Standard_Real U, const Standard_Integer FromK1, const Standard_Integer ToK2, Standard_Real &P, Standard_Real &V1, Standard_Real &V2) const
void LocalD3 (const Standard_Real U, const Standard_Integer FromK1, const Standard_Integer ToK2, Standard_Real &P, Standard_Real &V1, Standard_Real &V2, Standard_Real &V3) const
Standard_Real LocalDN (const Standard_Real U, const Standard_Integer FromK1, const Standard_Integer ToK2, const Standard_Integer N) const
Standard_Real 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

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

void Poles (TColStd_Array1OfReal &P) const
 Returns the poles of the B-spline curve;
Raised if the length of P is not equal to the number of poles.

Standard_Real 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 MovePointAndTangent (const Standard_Real U, const Standard_Real NewValue, const Standard_Real Derivative, const Standard_Real Tolerance, const Standard_Integer StartingCondition, const Standard_Integer EndingCondition, Standard_Integer &ErrorStatus)
 Changes the value of the Law at parameter U to NewValue.
and makes its derivative at U be derivative.
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


void Resolution (const Standard_Real Tolerance3D, Standard_Real &UTolerance) const
 given Tolerance3D returns UTolerance
such that if f(t) is the curve we have
| t1 - t0| < Utolerance ===>
|f(t1) - f(t0)| < Tolerance3D

Handle_Law_BSpline Copy () const

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

Law_BSpline::Law_BSpline ( const TColStd_Array1OfReal Poles,
const TColStd_Array1OfReal Knots,
const TColStd_Array1OfInteger Multiplicities,
const Standard_Integer  Degree,
const Standard_Boolean  Periodic = Standard_False 
)
Law_BSpline::Law_BSpline ( const TColStd_Array1OfReal Poles,
const TColStd_Array1OfReal Weights,
const TColStd_Array1OfReal Knots,
const TColStd_Array1OfInteger Multiplicities,
const Standard_Integer  Degree,
const Standard_Boolean  Periodic = Standard_False 
)

Member Function Documentation

GeomAbs_Shape Law_BSpline::Continuity ( ) const
Handle_Law_BSpline Law_BSpline::Copy ( ) const
void Law_BSpline::D0 ( const Standard_Real  U,
Standard_Real P 
) const
void Law_BSpline::D1 ( const Standard_Real  U,
Standard_Real P,
Standard_Real V1 
) const
void Law_BSpline::D2 ( const Standard_Real  U,
Standard_Real P,
Standard_Real V1,
Standard_Real V2 
) const
void Law_BSpline::D3 ( const Standard_Real  U,
Standard_Real P,
Standard_Real V1,
Standard_Real V2,
Standard_Real V3 
) const
Standard_Integer Law_BSpline::Degree ( ) const
Standard_Real Law_BSpline::DN ( const Standard_Real  U,
const Standard_Integer  N 
) const
Standard_Real Law_BSpline::EndPoint ( ) const
Standard_Real Law_BSpline::FirstParameter ( ) const
Standard_Integer Law_BSpline::FirstUKnotIndex ( ) const
void Law_BSpline::IncreaseDegree ( const Standard_Integer  Degree)
void Law_BSpline::IncreaseMultiplicity ( const Standard_Integer  Index,
const Standard_Integer  M 
)
void Law_BSpline::IncreaseMultiplicity ( const Standard_Integer  I1,
const Standard_Integer  I2,
const Standard_Integer  M 
)
void Law_BSpline::IncrementMultiplicity ( const Standard_Integer  I1,
const Standard_Integer  I2,
const Standard_Integer  M 
)
void Law_BSpline::InsertKnot ( const Standard_Real  U,
const Standard_Integer  M = 1,
const Standard_Real  ParametricTolerance = 0.0,
const Standard_Boolean  Add = Standard_True 
)
void Law_BSpline::InsertKnots ( const TColStd_Array1OfReal Knots,
const TColStd_Array1OfInteger Mults,
const Standard_Real  ParametricTolerance = 0.0,
const Standard_Boolean  Add = Standard_False 
)
Standard_Boolean Law_BSpline::IsClosed ( ) const
Standard_Boolean Law_BSpline::IsCN ( const Standard_Integer  N) const
Standard_Boolean Law_BSpline::IsPeriodic ( ) const
Standard_Boolean Law_BSpline::IsRational ( ) const
Standard_Real Law_BSpline::Knot ( const Standard_Integer  Index) const
GeomAbs_BSplKnotDistribution Law_BSpline::KnotDistribution ( ) const
  • 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.
void Law_BSpline::Knots ( TColStd_Array1OfReal K) const
void Law_BSpline::KnotSequence ( TColStd_Array1OfReal K) const
Standard_Real Law_BSpline::LastParameter ( ) const
Standard_Integer Law_BSpline::LastUKnotIndex ( ) const
void Law_BSpline::LocalD0 ( const Standard_Real  U,
const Standard_Integer  FromK1,
const Standard_Integer  ToK2,
Standard_Real P 
) const
void Law_BSpline::LocalD1 ( const Standard_Real  U,
const Standard_Integer  FromK1,
const Standard_Integer  ToK2,
Standard_Real P,
Standard_Real V1 
) const
void Law_BSpline::LocalD2 ( const Standard_Real  U,
const Standard_Integer  FromK1,
const Standard_Integer  ToK2,
Standard_Real P,
Standard_Real V1,
Standard_Real V2 
) const
void Law_BSpline::LocalD3 ( const Standard_Real  U,
const Standard_Integer  FromK1,
const Standard_Integer  ToK2,
Standard_Real P,
Standard_Real V1,
Standard_Real V2,
Standard_Real V3 
) const
Standard_Real Law_BSpline::LocalDN ( const Standard_Real  U,
const Standard_Integer  FromK1,
const Standard_Integer  ToK2,
const Standard_Integer  N 
) const
Standard_Real Law_BSpline::LocalValue ( const Standard_Real  U,
const Standard_Integer  FromK1,
const Standard_Integer  ToK2 
) const
void Law_BSpline::LocateU ( const Standard_Real  U,
const Standard_Real  ParametricTolerance,
Standard_Integer I1,
Standard_Integer I2,
const Standard_Boolean  WithKnotRepetition = Standard_False 
) const
static Standard_Integer Law_BSpline::MaxDegree ( ) [static]
void Law_BSpline::MovePointAndTangent ( const Standard_Real  U,
const Standard_Real  NewValue,
const Standard_Real  Derivative,
const Standard_Real  Tolerance,
const Standard_Integer  StartingCondition,
const Standard_Integer  EndingCondition,
Standard_Integer ErrorStatus 
)
void Law_BSpline::Multiplicities ( TColStd_Array1OfInteger M) const
Standard_Integer Law_BSpline::Multiplicity ( const Standard_Integer  Index) const
Standard_Integer Law_BSpline::NbKnots ( ) const
Standard_Integer Law_BSpline::NbPoles ( ) const
void Law_BSpline::PeriodicNormalization ( Standard_Real U) const
Standard_Real Law_BSpline::Pole ( const Standard_Integer  Index) const
void Law_BSpline::Poles ( TColStd_Array1OfReal P) const
Standard_Boolean Law_BSpline::RemoveKnot ( const Standard_Integer  Index,
const Standard_Integer  M,
const Standard_Real  Tolerance 
)
void Law_BSpline::Resolution ( const Standard_Real  Tolerance3D,
Standard_Real UTolerance 
) const
void Law_BSpline::Reverse ( )
Standard_Real Law_BSpline::ReversedParameter ( const Standard_Real  U) const
void Law_BSpline::Segment ( const Standard_Real  U1,
const Standard_Real  U2 
)
void Law_BSpline::SetKnot ( const Standard_Integer  Index,
const Standard_Real  K,
const Standard_Integer  M 
)
void Law_BSpline::SetKnot ( const Standard_Integer  Index,
const Standard_Real  K 
)
void Law_BSpline::SetKnots ( const TColStd_Array1OfReal K)
void Law_BSpline::SetNotPeriodic ( )
void Law_BSpline::SetOrigin ( const Standard_Integer  Index)
void Law_BSpline::SetPeriodic ( )
void Law_BSpline::SetPole ( const Standard_Integer  Index,
const Standard_Real  P 
)
void Law_BSpline::SetPole ( const Standard_Integer  Index,
const Standard_Real  P,
const Standard_Real  Weight 
)
void Law_BSpline::SetWeight ( const Standard_Integer  Index,
const Standard_Real  Weight 
)
Standard_Real Law_BSpline::StartPoint ( ) const
Standard_Real Law_BSpline::Value ( const Standard_Real  U) const
Standard_Real Law_BSpline::Weight ( const Standard_Integer  Index) const
void Law_BSpline::Weights ( TColStd_Array1OfReal W) const

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