OCC Main Page | ModelingAlgorithms | Toolkits | Packages | Class Hierarchy | Data Structures | File List | Data Fields | Globals

ModelingAlgorithms
TKGeomAlgo
Law


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 :

- Uniform if all multiplicities are 1.

- Quasi-uniform if all multiplicities are 1
but the first and the last which are Degree+1.

- PiecewiseBezier if all multiplicites are
Degree but the first and the last which are
Degree+1.

The curve may be periodic.

On a periodic curve if there are k knots and p
poles. the period is knot(k) - knot(1)

the poles and knots are infinite vectors with :

knot(i+k) = knot(i) + period

pole(i+p) = pole(i)


References :
. A survey of curve and surface methods in CADG Wolfgang BOHM
CAGD 1 (1984)
. On de Boor-like algorithms and blossoming Wolfgang BOEHM
cagd 5 (1988)
. Blossoming and knot insertion algorithms for B-spline curves
Ronald N. GOLDMAN
. Modelisation des surfaces en CAO, Henri GIAUME Peugeot SA
. Curves and Surfaces for Computer Aided Geometric Design,
a practical guide Gerald Farin
.

#include <Law_BSpline.hxx>


Public Member Functions

Standard_EXPORT 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>.
.
Standard_EXPORT 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>.
.
Standard_EXPORT void IncreaseDegree (const Standard_Integer Degree)
 Increase the degree to <degree>. Nothing is done
if <degree> is lower or equal to the current
degree.
.
Standard_EXPORT 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]
.
Standard_EXPORT 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]
.
Standard_EXPORT 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]
.
Standard_EXPORT 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.
.
Standard_EXPORT 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_EXPORT 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.
.
Standard_EXPORT 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_EXPORT 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
.
Standard_EXPORT 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.
.
Standard_EXPORT 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
.
Standard_EXPORT 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
.
Standard_EXPORT 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
.
Standard_EXPORT void PeriodicNormalization (Standard_Real &U) const
 returns the parameter normalized within
the period if the curve is periodic : otherwise
does not do anything

Standard_EXPORT 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.
.
Standard_EXPORT 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]
.
Standard_EXPORT void SetNotPeriodic ()
 Makes a non periodic curve. If the curve was non periodic
the curve is not modified.
.
Standard_EXPORT void SetPole (const Standard_Integer Index, const Standard_Real P)
 Substitutes the Pole of range Index with P.
Raised if Index < 1 || Index > NbPoles
.
Standard_EXPORT 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
.
Standard_EXPORT 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_EXPORT 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_EXPORT 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_EXPORT Standard_Boolean IsPeriodic () const
 Returns True if the curve is periodic.
.
Standard_EXPORT Standard_Boolean IsRational () const
 Returns True if the weights are not identical.
The tolerance criterion is Epsilon of the class Real.
.
Standard_EXPORT 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_EXPORT Standard_Integer Degree () const
 Computation of value and derivatives
.
Standard_EXPORT Standard_Real Value (const Standard_Real U) const
Standard_EXPORT void D0 (const Standard_Real U, Standard_Real &P) const
Standard_EXPORT void D1 (const Standard_Real U, Standard_Real &P, Standard_Real &V1) const
Standard_EXPORT void D2 (const Standard_Real U, Standard_Real &P, Standard_Real &V1, Standard_Real &V2) const
Standard_EXPORT void D3 (const Standard_Real U, Standard_Real &P, Standard_Real &V1, Standard_Real &V2, Standard_Real &V3) const
Standard_EXPORT 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_EXPORT Standard_Real LocalValue (const Standard_Real U, const Standard_Integer FromK1, const Standard_Integer ToK2) const
Standard_EXPORT void LocalD0 (const Standard_Real U, const Standard_Integer FromK1, const Standard_Integer ToK2, Standard_Real &P) const
Standard_EXPORT void LocalD1 (const Standard_Real U, const Standard_Integer FromK1, const Standard_Integer ToK2, Standard_Real &P, Standard_Real &V1) const
Standard_EXPORT void LocalD2 (const Standard_Real U, const Standard_Integer FromK1, const Standard_Integer ToK2, Standard_Real &P, Standard_Real &V1, Standard_Real &V2) const
Standard_EXPORT 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_EXPORT Standard_Real LocalDN (const Standard_Real U, const Standard_Integer FromK1, const Standard_Integer ToK2, const Standard_Integer N) const
Standard_EXPORT 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_EXPORT 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_EXPORT Standard_Real FirstParameter () const
 Computes the parametric value of the start point of the curve.
It is a knot value.
.
Standard_EXPORT 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
.
Standard_EXPORT 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.

Standard_EXPORT 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
.
Standard_EXPORT 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 :
- 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.
.
Standard_EXPORT 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_EXPORT Standard_Real LastParameter () const
 Computes the parametric value of the end point of the curve.
It is a knot value.
.
Standard_EXPORT 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_EXPORT Standard_Integer Multiplicity (const Standard_Integer Index) const
 Returns the multiplicity of the knots of range Index.
//! Raised if Index < 1 or Index > NbKnots
.
Standard_EXPORT 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_EXPORT Standard_Integer NbKnots () const
 Returns the number of knots. This method returns the number of
knot without repetition of multiple knots.
.
Standard_EXPORT Standard_Integer NbPoles () const
 Returns the number of poles
.
Standard_EXPORT Standard_Real Pole (const Standard_Integer Index) const
 Returns the pole of range Index.
//! Raised if Index < 1 or Index > NbPoles.
.
Standard_EXPORT 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_EXPORT 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_EXPORT Standard_Real Weight (const Standard_Integer Index) const
 Returns the weight of the pole of range Index .
//! Raised if Index < 1 or Index > NbPoles.
.
Standard_EXPORT 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.
.
Standard_EXPORT 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

.
Standard_EXPORT 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

Standard_EXPORT Handle_Law_BSpline Copy () const
Standard_EXPORT const Handle (Standard_Type)&DynamicType() const

Static Public Member Functions

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

Private Member Functions

Standard_EXPORT Standard_Boolean IsCacheValid (const Standard_Real Parameter) const
 Tells whether the Cache is valid for the
given parameter
Warnings : the parameter must be normalized within
the period if the curve is periodic. Otherwise
the answer will be false

.
Standard_EXPORT void UpdateKnots ()
 Recompute the flatknots, the knotsdistribution, the
continuity.
.

Private Attributes

Standard_Boolean rational
Standard_Boolean periodic
GeomAbs_BSplKnotDistribution knotSet
GeomAbs_Shape smooth
Standard_Integer deg
Handle_TColStd_HArray1OfReal poles
Handle_TColStd_HArray1OfReal weights
Handle_TColStd_HArray1OfReal flatknots
Handle_TColStd_HArray1OfReal knots
Handle_TColStd_HArray1OfInteger mults


Constructor & Destructor Documentation

Standard_EXPORT 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
 

Standard_EXPORT 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

Standard_EXPORT GeomAbs_Shape Law_BSpline::Continuity  )  const
 

Standard_EXPORT Handle_Law_BSpline Law_BSpline::Copy  )  const
 

Standard_EXPORT void Law_BSpline::D0 const Standard_Real  U,
Standard_Real &  P
const
 

Standard_EXPORT void Law_BSpline::D1 const Standard_Real  U,
Standard_Real &  P,
Standard_Real &  V1
const
 

Standard_EXPORT void Law_BSpline::D2 const Standard_Real  U,
Standard_Real &  P,
Standard_Real &  V1,
Standard_Real &  V2
const
 

Standard_EXPORT void Law_BSpline::D3 const Standard_Real  U,
Standard_Real &  P,
Standard_Real &  V1,
Standard_Real &  V2,
Standard_Real &  V3
const
 

Standard_EXPORT Standard_Integer Law_BSpline::Degree  )  const
 

Standard_EXPORT Standard_Real Law_BSpline::DN const Standard_Real  U,
const Standard_Integer  N
const
 

Standard_EXPORT Standard_Real Law_BSpline::EndPoint  )  const
 

Standard_EXPORT Standard_Real Law_BSpline::FirstParameter  )  const
 

Standard_EXPORT Standard_Integer Law_BSpline::FirstUKnotIndex  )  const
 

Standard_EXPORT const Law_BSpline::Handle Standard_Type   )  const
 

Standard_EXPORT void Law_BSpline::IncreaseDegree const Standard_Integer  Degree  ) 
 

Standard_EXPORT void Law_BSpline::IncreaseMultiplicity const Standard_Integer  I1,
const Standard_Integer  I2,
const Standard_Integer  M
 

Standard_EXPORT void Law_BSpline::IncreaseMultiplicity const Standard_Integer  Index,
const Standard_Integer  M
 

Standard_EXPORT void Law_BSpline::IncrementMultiplicity const Standard_Integer  I1,
const Standard_Integer  I2,
const Standard_Integer  M
 

Standard_EXPORT 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
 

Standard_EXPORT 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_EXPORT Standard_Boolean Law_BSpline::IsCacheValid const Standard_Real  Parameter  )  const [private]
 

Standard_EXPORT Standard_Boolean Law_BSpline::IsClosed  )  const
 

Standard_EXPORT Standard_Boolean Law_BSpline::IsCN const Standard_Integer  N  )  const
 

Standard_EXPORT Standard_Boolean Law_BSpline::IsPeriodic  )  const
 

Standard_EXPORT Standard_Boolean Law_BSpline::IsRational  )  const
 

Standard_EXPORT Standard_Real Law_BSpline::Knot const Standard_Integer  Index  )  const
 

Standard_EXPORT GeomAbs_BSplKnotDistribution Law_BSpline::KnotDistribution  )  const
 

Standard_EXPORT void Law_BSpline::Knots TColStd_Array1OfReal &  K  )  const
 

Standard_EXPORT void Law_BSpline::KnotSequence TColStd_Array1OfReal &  K  )  const
 

Standard_EXPORT Standard_Real Law_BSpline::LastParameter  )  const
 

Standard_EXPORT Standard_Integer Law_BSpline::LastUKnotIndex  )  const
 

Standard_EXPORT void Law_BSpline::LocalD0 const Standard_Real  U,
const Standard_Integer  FromK1,
const Standard_Integer  ToK2,
Standard_Real &  P
const
 

Standard_EXPORT void Law_BSpline::LocalD1 const Standard_Real  U,
const Standard_Integer  FromK1,
const Standard_Integer  ToK2,
Standard_Real &  P,
Standard_Real &  V1
const
 

Standard_EXPORT 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
 

Standard_EXPORT 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_EXPORT Standard_Real Law_BSpline::LocalDN const Standard_Real  U,
const Standard_Integer  FromK1,
const Standard_Integer  ToK2,
const Standard_Integer  N
const
 

Standard_EXPORT Standard_Real Law_BSpline::LocalValue const Standard_Real  U,
const Standard_Integer  FromK1,
const Standard_Integer  ToK2
const
 

Standard_EXPORT 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_EXPORT Standard_Integer Law_BSpline::MaxDegree  )  [static]
 

Standard_EXPORT 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
 

Standard_EXPORT void Law_BSpline::Multiplicities TColStd_Array1OfInteger &  M  )  const
 

Standard_EXPORT Standard_Integer Law_BSpline::Multiplicity const Standard_Integer  Index  )  const
 

Standard_EXPORT Standard_Integer Law_BSpline::NbKnots  )  const
 

Standard_EXPORT Standard_Integer Law_BSpline::NbPoles  )  const
 

Standard_EXPORT void Law_BSpline::PeriodicNormalization Standard_Real &  U  )  const
 

Standard_EXPORT Standard_Real Law_BSpline::Pole const Standard_Integer  Index  )  const
 

Standard_EXPORT void Law_BSpline::Poles TColStd_Array1OfReal &  P  )  const
 

Standard_EXPORT Standard_Boolean Law_BSpline::RemoveKnot const Standard_Integer  Index,
const Standard_Integer  M,
const Standard_Real  Tolerance
 

Standard_EXPORT void Law_BSpline::Resolution const Standard_Real  Tolerance3D,
Standard_Real &  UTolerance
const
 

Standard_EXPORT void Law_BSpline::Reverse  ) 
 

Standard_EXPORT Standard_Real Law_BSpline::ReversedParameter const Standard_Real  U  )  const
 

Standard_EXPORT void Law_BSpline::Segment const Standard_Real  U1,
const Standard_Real  U2
 

Standard_EXPORT void Law_BSpline::SetKnot const Standard_Integer  Index,
const Standard_Real  K,
const Standard_Integer  M
 

Standard_EXPORT void Law_BSpline::SetKnot const Standard_Integer  Index,
const Standard_Real  K
 

Standard_EXPORT void Law_BSpline::SetKnots const TColStd_Array1OfReal &  K  ) 
 

Standard_EXPORT void Law_BSpline::SetNotPeriodic  ) 
 

Standard_EXPORT void Law_BSpline::SetOrigin const Standard_Integer  Index  ) 
 

Standard_EXPORT void Law_BSpline::SetPeriodic  ) 
 

Standard_EXPORT void Law_BSpline::SetPole const Standard_Integer  Index,
const Standard_Real  P,
const Standard_Real  Weight
 

Standard_EXPORT void Law_BSpline::SetPole const Standard_Integer  Index,
const Standard_Real  P
 

Standard_EXPORT void Law_BSpline::SetWeight const Standard_Integer  Index,
const Standard_Real  Weight
 

Standard_EXPORT Standard_Real Law_BSpline::StartPoint  )  const
 

Standard_EXPORT void Law_BSpline::UpdateKnots  )  [private]
 

Standard_EXPORT Standard_Real Law_BSpline::Value const Standard_Real  U  )  const
 

Standard_EXPORT Standard_Real Law_BSpline::Weight const Standard_Integer  Index  )  const
 

Standard_EXPORT void Law_BSpline::Weights TColStd_Array1OfReal &  W  )  const
 


Field Documentation

Standard_Integer Law_BSpline::deg [private]
 

Handle_TColStd_HArray1OfReal Law_BSpline::flatknots [private]
 

Handle_TColStd_HArray1OfReal Law_BSpline::knots [private]
 

GeomAbs_BSplKnotDistribution Law_BSpline::knotSet [private]
 

Handle_TColStd_HArray1OfInteger Law_BSpline::mults [private]
 

Standard_Boolean Law_BSpline::periodic [private]
 

Handle_TColStd_HArray1OfReal Law_BSpline::poles [private]
 

Standard_Boolean Law_BSpline::rational [private]
 

GeomAbs_Shape Law_BSpline::smooth [private]
 

Handle_TColStd_HArray1OfReal Law_BSpline::weights [private]
 


The documentation for this class was generated from the following file:
Generated on Mon Aug 25 13:42:22 2008 for OpenCASCADE by  doxygen 1.4.1