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:

[legend]

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>. More...

	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>. More...

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

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

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

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

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 <br> <U> is an existing knot the multiplicity is <br> increased by <M>. <br> 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. More...

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 <br> knots. <br> 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. More...

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

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. More...

Standard_Real	ReversedParameter (const Standard_Real U) const
	Returns the parameter on the reversed curve for <br> the point of parameter U on <me>. <br> returns UFirst + ULast - U More...

void	Segment (const Standard_Real U1, const Standard_Real U2)
	Segments the curve between U1 and U2. <br> 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. More...

void	SetKnot (const Standard_Integer Index, const Standard_Real K)
	Changes the knot of range Index. <br> 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 More...

void	SetKnots (const TColStd_Array1OfReal &K)
	Changes all the knots of the curve <br> 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 More...

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 More...

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

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. More...

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] More...

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

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

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 More...

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 More...

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

Standard_Boolean	IsClosed () const
	Returns true if the distance between the first point and the <br> 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. More...

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

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

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. More...

Standard_Integer	Degree () const
	Computation of value and derivatives <br> More...

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 <br> 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. More...

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. <br> 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. More...

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. More...

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

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 More...

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

void	KnotSequence (TColStd_Array1OfReal &K) const
	Returns the knots sequence. <br> 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 More...

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 : More...

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. More...

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

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) More...

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

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. More...

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

Standard_Integer	NbPoles () const
	Returns the number of poles More...

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

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

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

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

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

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 More...

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 More...

Handle_Law_BSpline	Copy () const

Public Member Functions inherited from MMgt_TShared
virtual void	Delete () const
	Memory deallocator for transient classes. More...

Public Member Functions inherited from Standard_Transient
	Standard_Transient ()
	Empty constructor. More...

	Standard_Transient (const Standard_Transient &)
	Copy constructor – does nothing. More...

Standard_Transient &	operator= (const Standard_Transient &)
	Assignment operator, needed to avoid copying reference counter. More...

virtual	~Standard_Transient ()
	Destructor must be virtual. More...

virtual void	ShallowDump (Standard_OStream &) const

virtual const Handle_Standard_Type &	DynamicType () const
	Returns a type information object about this object. More...

Standard_Boolean	IsInstance (const Handle_Standard_Type &theType) const
	Returns a true value if this is an instance of Type. More...

Standard_Boolean	IsInstance (const Standard_CString theTypeName) const
	Returns a true value if this is an instance of TypeName. More...

Standard_Boolean	IsKind (const Handle_Standard_Type &theType) const
	Returns true if this is an instance of Type or an instance of any class that inherits from Type. Note that multiple inheritance is not supported by OCCT RTTI mechanism. More...

Standard_Boolean	IsKind (const Standard_CString theTypeName) const
	Returns true if this is an instance of TypeName or an instance of any class that inherits from TypeName. Note that multiple inheritance is not supported by OCCT RTTI mechanism. More...

virtual Handle_Standard_Transient	This () const
	Returns a Handle which references this object. Must never be called to objects created in stack. More...

Standard_Integer	GetRefCount () const
	Get the reference counter of this object. More...

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. More...

Detailed Description

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. <br>

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

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`
	)

Creates a non-rational B_spline curve on the
basis <Knots, Multiplicities> of degree <Degree>.

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`
	)

Creates a rational B_spline curve on the basis
<Knots, Multiplicities> of degree <Degree>.

Member Function Documentation

GeomAbs_Shape Law_BSpline::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.

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

 Computation of value and derivatives <br>

Standard_Real Law_BSpline::DN	(	const Standard_Real	U,
		const Standard_Integer	N
	)		const

The following functions computes the point  of parameter U and <br>

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 Law_BSpline::EndPoint ( ) const

Returns the last point of the curve. <br>

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_Real Law_BSpline::FirstParameter ( ) const

Computes the parametric value of the start point of the curve.
It is a knot value.

Standard_Integer Law_BSpline::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.

void Law_BSpline::IncreaseDegree ( const Standard_Integer Degree )

Increase the degree to <Degree>. Nothing is done
if <Degree> is lower or equal to the current
degree.

void Law_BSpline::IncreaseMultiplicity	(	const Standard_Integer	Index,
		const Standard_Integer	M
	)

Increases the multiplicity  of the knot <Index> to <br>
    <M>. <br>

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 Law_BSpline::IncreaseMultiplicity	(	const Standard_Integer	I1,
		const Standard_Integer	I2,
		const Standard_Integer	M
	)

Increases  the  multiplicities   of  the knots  in <br>
    [I1,I2] to <M>. <br>

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 Law_BSpline::IncrementMultiplicity	(	const Standard_Integer	I1,
		const Standard_Integer	I2,
		const Standard_Integer	M
	)

Increment  the  multiplicities   of  the knots  in <br>
    [I1,I2] by <M>. <br>

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 Law_BSpline::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 <br>
     <U>  is an  existing knot     the multiplicity  is <br>
     increased by <M>. <br>

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 Law_BSpline::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 <br>
     knots. <br>

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 Law_BSpline::IsClosed ( ) const

Returns true if the distance between the first point and the <br>

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 Law_BSpline::IsCN ( const Standard_Integer N ) const

Returns the continuity of the curve, the curve is at least C0.
//! Raised if N < 0.

Standard_Boolean Law_BSpline::IsPeriodic ( ) const

Returns True if the curve is periodic.

Standard_Boolean Law_BSpline::IsRational ( ) const

Returns True if the weights are not identical.
The tolerance criterion is Epsilon of the class Real.

Standard_Real Law_BSpline::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

GeomAbs_BSplKnotDistribution Law_BSpline::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.

void Law_BSpline::Knots ( TColStd_Array1OfReal & K ) const

returns the knot values of the B-spline curve; <br>

Raised if the length of K is not equal to the number of knots.

void Law_BSpline::KnotSequence ( TColStd_Array1OfReal & K ) const

 Returns the knots sequence. <br>

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_Real Law_BSpline::LastParameter ( ) const

Computes the parametric value of the end point of the curve.
It is a knot value.

Standard_Integer Law_BSpline::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.

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

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)

static Standard_Integer Law_BSpline::MaxDegree ( )

static

Returns the value of the maximum degree of the normalized
B-spline basis functions in this package.

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
	)

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 Law_BSpline::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 Law_BSpline::Multiplicity ( const Standard_Integer Index ) const

Returns the multiplicity of the knots of range Index.
//! Raised if Index < 1 or Index > NbKnots

Standard_Integer Law_BSpline::NbKnots ( ) const

Returns the number of knots. This method returns the number of
knot without repetition of multiple knots.

Standard_Integer Law_BSpline::NbPoles ( ) const

Returns the number of poles

void Law_BSpline::PeriodicNormalization ( Standard_Real & U ) const

returns the parameter normalized within
the period if the curve is periodic : otherwise
does not do anything

Standard_Real Law_BSpline::Pole ( const Standard_Integer Index ) const

Returns the pole of range Index.
//! Raised if Index < 1 or Index > NbPoles.

void Law_BSpline::Poles ( TColStd_Array1OfReal & P ) const

Returns the poles of the B-spline curve; <br>

Raised if the length of P is not equal to the number of poles.

Standard_Boolean Law_BSpline::RemoveKnot	(	const Standard_Integer	Index,
		const Standard_Integer	M,
		const Standard_Real	Tolerance
	)

 Decrement the knots multiplicity to <M>. If  M is <br>
    0 the knot   is  removed. The  Poles  sequence   is <br>
    modified. <br>

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 Law_BSpline::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

void Law_BSpline::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 Law_BSpline::ReversedParameter ( const Standard_Real U ) const

 Returns the  parameter on the  reversed  curve for <br>
     the point of parameter U on <me>. <br>

returns UFirst + ULast - U

void Law_BSpline::Segment	(	const Standard_Real	U1,
		const Standard_Real	U2
	)

Segments the curve between U1 and U2. <br>

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 Law_BSpline::SetKnot	(	const Standard_Integer	Index,
		const Standard_Real	K
	)

 Changes the knot of range Index. <br>

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 Law_BSpline::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 Law_BSpline::SetKnots ( const TColStd_Array1OfReal & K )

 Changes all the knots of the curve <br>

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 Law_BSpline::SetNotPeriodic ( )

Makes a non periodic curve. If the curve was non periodic
the curve is not modified.

void Law_BSpline::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 Law_BSpline::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 Law_BSpline::SetPole	(	const Standard_Integer	Index,
		const Standard_Real	P
	)

Substitutes the Pole of range Index with P. <br>

Raised if Index < 1 || Index > NbPoles

void Law_BSpline::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 Law_BSpline::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_Real Law_BSpline::StartPoint ( ) const

Returns the start point of the curve. <br>

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 Law_BSpline::Value ( const Standard_Real U ) const

Standard_Real Law_BSpline::Weight ( const Standard_Integer Index ) const

Returns the weight of the pole of range Index .
//! Raised if Index < 1 or Index > NbPoles.

void Law_BSpline::Weights ( TColStd_Array1OfReal & W ) const

Returns the weights of the B-spline curve; <br>

Raised if the length of W is not equal to NbPoles.

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

Law_BSpline.hxx

Public Member Functions

Static Public Member Functions

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation