1
0
mirror of https://git.dev.opencascade.org/repos/occt.git synced 2025-04-10 18:51:21 +03:00
occt/src/Geom/Geom_BSplineCurve_1.cxx
luz paz 21c7c45701 0031939: Coding - correction of spelling errors in comments
Fix various typos

Fixed via `codespell v2.0.dev`
2020-11-21 12:19:49 +03:00

843 lines
26 KiB
C++

// Created on: 1991-07-05
// Created by: JCV
// Copyright (c) 1991-1999 Matra Datavision
// Copyright (c) 1999-2014 OPEN CASCADE SAS
//
// This file is part of Open CASCADE Technology software library.
//
// This library is free software; you can redistribute it and/or modify it under
// the terms of the GNU Lesser General Public License version 2.1 as published
// by the Free Software Foundation, with special exception defined in the file
// OCCT_LGPL_EXCEPTION.txt. Consult the file LICENSE_LGPL_21.txt included in OCCT
// distribution for complete text of the license and disclaimer of any warranty.
//
// Alternatively, this file may be used under the terms of Open CASCADE
// commercial license or contractual agreement.
#include <BSplCLib.hxx>
#include <Geom_BSplineCurve.hxx>
#include <Geom_Geometry.hxx>
#include <Geom_UndefinedDerivative.hxx>
#include <gp.hxx>
#include <gp_Pnt.hxx>
#include <gp_Trsf.hxx>
#include <gp_Vec.hxx>
#include <Precision.hxx>
#include <Standard_ConstructionError.hxx>
#include <Standard_DimensionError.hxx>
#include <Standard_DomainError.hxx>
#include <Standard_NoSuchObject.hxx>
#include <Standard_OutOfRange.hxx>
#include <Standard_RangeError.hxx>
#define POLES (poles->Array1())
#define KNOTS (knots->Array1())
#define FKNOTS (flatknots->Array1())
#define FMULTS (BSplCLib::NoMults())
//=======================================================================
//function : IsCN
//purpose :
//=======================================================================
Standard_Boolean Geom_BSplineCurve::IsCN ( const Standard_Integer N) const
{
Standard_RangeError_Raise_if
(N < 0, "Geom_BSplineCurve::IsCN");
switch (smooth) {
case GeomAbs_CN : return Standard_True;
case GeomAbs_C0 : return N <= 0;
case GeomAbs_G1 : return N <= 0;
case GeomAbs_C1 : return N <= 1;
case GeomAbs_G2 : return N <= 1;
case GeomAbs_C2 : return N <= 2;
case GeomAbs_C3 :
return N <= 3 ? Standard_True :
N <= deg - BSplCLib::MaxKnotMult (mults->Array1(), mults->Lower() + 1, mults->Upper() - 1);
default:
return Standard_False;
}
}
//=======================================================================
//function : IsG1
//purpose :
//=======================================================================
Standard_Boolean Geom_BSplineCurve::IsG1 ( const Standard_Real theTf,
const Standard_Real theTl,
const Standard_Real theAngTol) const
{
if(IsCN(1))
{
return Standard_True;
}
Standard_Integer start = FirstUKnotIndex()+1,
finish = LastUKnotIndex()-1;
Standard_Integer aDeg = Degree();
for(Standard_Integer aNKnot = start; aNKnot <= finish; aNKnot++)
{
const Standard_Real aTpar = Knot(aNKnot);
if(aTpar < theTf)
continue;
if(aTpar > theTl)
break;
Standard_Integer mult = Multiplicity(aNKnot);
if (mult < aDeg)
continue;
gp_Pnt aP1, aP2;
gp_Vec aV1, aV2;
LocalD1(aTpar, aNKnot-1, aNKnot, aP1, aV1);
LocalD1(aTpar, aNKnot, aNKnot+1, aP2, aV2);
if((aV1.SquareMagnitude() <= gp::Resolution()) ||
aV2.SquareMagnitude() <= gp::Resolution())
{
return Standard_False;
}
if(Abs(aV1.Angle(aV2)) > theAngTol)
return Standard_False;
}
if(!IsPeriodic())
return Standard_True;
const Standard_Real aFirstParam = FirstParameter(),
aLastParam = LastParameter();
if( ((aFirstParam - theTf)*(theTl - aFirstParam) < 0.0) &&
((aLastParam - theTf)*(theTl - aLastParam) < 0.0))
{
//Range [theTf, theTl] does not intersect curve boundaries
return Standard_True;
}
//Curve is closed or periodic and range [theTf, theTl]
//intersect curve boundary. Therefore, it is necessary to
//check if curve is smooth in its first and last point.
gp_Pnt aP;
gp_Vec aV1, aV2;
D1(Knot(FirstUKnotIndex()), aP, aV1);
D1(Knot(LastUKnotIndex()), aP, aV2);
if((aV1.SquareMagnitude() <= gp::Resolution()) ||
aV2.SquareMagnitude() <= gp::Resolution())
{
return Standard_False;
}
if(Abs(aV1.Angle(aV2)) > theAngTol)
return Standard_False;
return Standard_True;
}
//=======================================================================
//function : IsClosed
//purpose :
//=======================================================================
Standard_Boolean Geom_BSplineCurve::IsClosed () const
//-- { return (StartPoint().Distance (EndPoint())) <= gp::Resolution (); }
{ return (StartPoint().SquareDistance(EndPoint())) <= 1e-16; }
//=======================================================================
//function : IsPeriodic
//purpose :
//=======================================================================
Standard_Boolean Geom_BSplineCurve::IsPeriodic () const
{ return periodic; }
//=======================================================================
//function : Continuity
//purpose :
//=======================================================================
GeomAbs_Shape Geom_BSplineCurve::Continuity () const
{ return smooth; }
//=======================================================================
//function : Degree
//purpose :
//=======================================================================
Standard_Integer Geom_BSplineCurve::Degree () const
{ return deg; }
//=======================================================================
//function : D0
//purpose :
//=======================================================================
void Geom_BSplineCurve::D0(const Standard_Real U, gp_Pnt& P) const
{
Standard_Integer aSpanIndex = 0;
Standard_Real aNewU(U);
PeriodicNormalization(aNewU);
BSplCLib::LocateParameter(deg, knots->Array1(), &mults->Array1(), U, periodic, aSpanIndex, aNewU);
if (aNewU < knots->Value(aSpanIndex))
aSpanIndex--;
BSplCLib::D0 (aNewU, aSpanIndex, deg, periodic, POLES,
rational ? &weights->Array1() : BSplCLib::NoWeights(),
knots->Array1(), &mults->Array1(),
P);
}
//=======================================================================
//function : D1
//purpose :
//=======================================================================
void Geom_BSplineCurve::D1 (const Standard_Real U,
gp_Pnt& P,
gp_Vec& V1) const
{
Standard_Integer aSpanIndex = 0;
Standard_Real aNewU(U);
PeriodicNormalization(aNewU);
BSplCLib::LocateParameter(deg, knots->Array1(), &mults->Array1(), U, periodic, aSpanIndex, aNewU);
if (aNewU < knots->Value(aSpanIndex))
aSpanIndex--;
BSplCLib::D1 (aNewU, aSpanIndex, deg, periodic, POLES,
rational ? &weights->Array1() : BSplCLib::NoWeights(),
knots->Array1(), &mults->Array1(),
P, V1);
}
//=======================================================================
//function : D2
//purpose :
//=======================================================================
void Geom_BSplineCurve::D2(const Standard_Real U,
gp_Pnt& P,
gp_Vec& V1,
gp_Vec& V2) const
{
Standard_Integer aSpanIndex = 0;
Standard_Real aNewU(U);
PeriodicNormalization(aNewU);
BSplCLib::LocateParameter(deg, knots->Array1(), &mults->Array1(), U, periodic, aSpanIndex, aNewU);
if (aNewU < knots->Value(aSpanIndex))
aSpanIndex--;
BSplCLib::D2 (aNewU, aSpanIndex, deg, periodic, POLES,
rational ? &weights->Array1() : BSplCLib::NoWeights(),
knots->Array1(), &mults->Array1(),
P, V1, V2);
}
//=======================================================================
//function : D3
//purpose :
//=======================================================================
void Geom_BSplineCurve::D3(const Standard_Real U,
gp_Pnt& P,
gp_Vec& V1,
gp_Vec& V2,
gp_Vec& V3) const
{
Standard_Integer aSpanIndex = 0;
Standard_Real aNewU(U);
PeriodicNormalization(aNewU);
BSplCLib::LocateParameter(deg, knots->Array1(), &mults->Array1(), U, periodic, aSpanIndex, aNewU);
if (aNewU < knots->Value(aSpanIndex))
aSpanIndex--;
BSplCLib::D3 (aNewU, aSpanIndex, deg, periodic, POLES,
rational ? &weights->Array1() : BSplCLib::NoWeights(),
knots->Array1(), &mults->Array1(),
P, V1, V2, V3);
}
//=======================================================================
//function : DN
//purpose :
//=======================================================================
gp_Vec Geom_BSplineCurve::DN(const Standard_Real U,
const Standard_Integer N) const
{
gp_Vec V;
BSplCLib::DN (U, N, 0, deg, periodic, POLES,
rational ? &weights->Array1() : BSplCLib::NoWeights(),
FKNOTS, FMULTS, V);
return V;
}
//=======================================================================
//function : EndPoint
//purpose :
//=======================================================================
gp_Pnt Geom_BSplineCurve::EndPoint () const
{
if (mults->Value (knots->Upper ()) == deg + 1)
return poles->Value (poles->Upper());
else
return Value(LastParameter());
}
//=======================================================================
//function : FirstUKnotIndex
//purpose :
//=======================================================================
Standard_Integer Geom_BSplineCurve::FirstUKnotIndex () const
{
if (periodic) return 1;
else return BSplCLib::FirstUKnotIndex (deg, mults->Array1());
}
//=======================================================================
//function : FirstParameter
//purpose :
//=======================================================================
Standard_Real Geom_BSplineCurve::FirstParameter () const
{
return flatknots->Value (deg+1);
}
//=======================================================================
//function : Knot
//purpose :
//=======================================================================
Standard_Real Geom_BSplineCurve::Knot (const Standard_Integer Index) const
{
Standard_OutOfRange_Raise_if
(Index < 1 || Index > knots->Length(), "Geom_BSplineCurve::Knot");
return knots->Value (Index);
}
//=======================================================================
//function : KnotDistribution
//purpose :
//=======================================================================
GeomAbs_BSplKnotDistribution Geom_BSplineCurve::KnotDistribution () const
{
return knotSet;
}
//=======================================================================
//function : Knots
//purpose :
//=======================================================================
void Geom_BSplineCurve::Knots (TColStd_Array1OfReal& K) const
{
Standard_DomainError_Raise_if (K.Lower() < knots->Lower() ||
K.Upper() > knots->Upper(),
"Geom_BSplineCurve::Knots");
for(Standard_Integer anIdx = K.Lower(); anIdx <= K.Upper(); anIdx++)
K(anIdx) = knots->Value(anIdx);
}
const TColStd_Array1OfReal& Geom_BSplineCurve::Knots() const
{
return knots->Array1();
}
//=======================================================================
//function : KnotSequence
//purpose :
//=======================================================================
void Geom_BSplineCurve::KnotSequence (TColStd_Array1OfReal& K) const
{
Standard_DomainError_Raise_if (K.Lower() < flatknots->Lower() ||
K.Upper() > flatknots->Upper(),
"Geom_BSplineCurve::KnotSequence");
for(Standard_Integer anIdx = K.Lower(); anIdx <= K.Upper(); anIdx++)
K(anIdx) = flatknots->Value(anIdx);
}
const TColStd_Array1OfReal& Geom_BSplineCurve::KnotSequence() const
{
return flatknots->Array1();
}
//=======================================================================
//function : LastUKnotIndex
//purpose :
//=======================================================================
Standard_Integer Geom_BSplineCurve::LastUKnotIndex() const
{
if (periodic) return knots->Length();
else return BSplCLib::LastUKnotIndex (deg, mults->Array1());
}
//=======================================================================
//function : LastParameter
//purpose :
//=======================================================================
Standard_Real Geom_BSplineCurve::LastParameter () const
{
return flatknots->Value (flatknots->Upper()-deg);
}
//=======================================================================
//function : LocalValue
//purpose :
//=======================================================================
gp_Pnt Geom_BSplineCurve::LocalValue
(const Standard_Real U,
const Standard_Integer FromK1,
const Standard_Integer ToK2) const
{
gp_Pnt P;
LocalD0(U,FromK1,ToK2,P);
return P;
}
//=======================================================================
//function : LocalD0
//purpose :
//=======================================================================
void Geom_BSplineCurve::LocalD0
(const Standard_Real U,
const Standard_Integer FromK1,
const Standard_Integer ToK2,
gp_Pnt& P) const
{
Standard_DomainError_Raise_if (FromK1 == ToK2,
"Geom_BSplineCurve::LocalValue");
Standard_Real u = U;
Standard_Integer index = 0;
BSplCLib::LocateParameter(deg, FKNOTS, U, periodic,FromK1,ToK2, index,u);
index = BSplCLib::FlatIndex(deg,index,mults->Array1(),periodic);
BSplCLib::D0 (u, index, deg, periodic, POLES,
rational ? &weights->Array1() : BSplCLib::NoWeights(),
FKNOTS, FMULTS, P);
}
//=======================================================================
//function : LocalD1
//purpose :
//=======================================================================
void Geom_BSplineCurve::LocalD1 (const Standard_Real U,
const Standard_Integer FromK1,
const Standard_Integer ToK2,
gp_Pnt& P,
gp_Vec& V1) const
{
Standard_DomainError_Raise_if (FromK1 == ToK2,
"Geom_BSplineCurve::LocalD1");
Standard_Real u = U;
Standard_Integer index = 0;
BSplCLib::LocateParameter(deg, FKNOTS, U, periodic, FromK1,ToK2, index, u);
index = BSplCLib::FlatIndex(deg,index,mults->Array1(),periodic);
BSplCLib::D1 (u, index, deg, periodic, POLES,
rational ? &weights->Array1() : BSplCLib::NoWeights(),
FKNOTS,FMULTS,P,V1);
}
//=======================================================================
//function : LocalD2
//purpose :
//=======================================================================
void Geom_BSplineCurve::LocalD2
(const Standard_Real U,
const Standard_Integer FromK1,
const Standard_Integer ToK2,
gp_Pnt& P,
gp_Vec& V1,
gp_Vec& V2) const
{
Standard_DomainError_Raise_if (FromK1 == ToK2,
"Geom_BSplineCurve::LocalD2");
Standard_Real u = U;
Standard_Integer index = 0;
BSplCLib::LocateParameter(deg, FKNOTS, U, periodic, FromK1,ToK2, index, u);
index = BSplCLib::FlatIndex(deg,index,mults->Array1(),periodic);
BSplCLib::D2 (u, index, deg, periodic, POLES,
rational ? &weights->Array1() : BSplCLib::NoWeights(),
FKNOTS, FMULTS, P, V1, V2);
}
//=======================================================================
//function : LocalD3
//purpose :
//=======================================================================
void Geom_BSplineCurve::LocalD3
(const Standard_Real U,
const Standard_Integer FromK1,
const Standard_Integer ToK2,
gp_Pnt& P,
gp_Vec& V1,
gp_Vec& V2,
gp_Vec& V3) const
{
Standard_DomainError_Raise_if (FromK1 == ToK2,
"Geom_BSplineCurve::LocalD3");
Standard_Real u = U;
Standard_Integer index = 0;
BSplCLib::LocateParameter(deg, FKNOTS, U, periodic, FromK1,ToK2, index, u);
index = BSplCLib::FlatIndex(deg,index,mults->Array1(),periodic);
BSplCLib::D3 (u, index, deg, periodic, POLES,
rational ? &weights->Array1() : BSplCLib::NoWeights(),
FKNOTS, FMULTS, P, V1, V2, V3);
}
//=======================================================================
//function : LocalDN
//purpose :
//=======================================================================
gp_Vec Geom_BSplineCurve::LocalDN
(const Standard_Real U,
const Standard_Integer FromK1,
const Standard_Integer ToK2,
const Standard_Integer N ) const
{
Standard_DomainError_Raise_if (FromK1 == ToK2,
"Geom_BSplineCurve::LocalD3");
Standard_Real u = U;
Standard_Integer index = 0;
BSplCLib::LocateParameter(deg, FKNOTS, U, periodic, FromK1,ToK2, index, u);
index = BSplCLib::FlatIndex(deg,index,mults->Array1(),periodic);
gp_Vec V;
BSplCLib::DN (u, N, index, deg, periodic, POLES,
rational ? &weights->Array1() : BSplCLib::NoWeights(),
FKNOTS, FMULTS, V);
return V;
}
//=======================================================================
//function : Multiplicity
//purpose :
//=======================================================================
Standard_Integer Geom_BSplineCurve::Multiplicity
(const Standard_Integer Index) const
{
Standard_OutOfRange_Raise_if (Index < 1 || Index > mults->Length(),
"Geom_BSplineCurve::Multiplicity");
return mults->Value (Index);
}
//=======================================================================
//function : Multiplicities
//purpose :
//=======================================================================
void Geom_BSplineCurve::Multiplicities (TColStd_Array1OfInteger& M) const
{
Standard_DimensionError_Raise_if (M.Length() != mults->Length(),
"Geom_BSplineCurve::Multiplicities");
M = mults->Array1();
}
const TColStd_Array1OfInteger& Geom_BSplineCurve::Multiplicities() const
{
return mults->Array1();
}
//=======================================================================
//function : NbKnots
//purpose :
//=======================================================================
Standard_Integer Geom_BSplineCurve::NbKnots () const
{ return knots->Length(); }
//=======================================================================
//function : NbPoles
//purpose :
//=======================================================================
Standard_Integer Geom_BSplineCurve::NbPoles () const
{ return poles->Length(); }
//=======================================================================
//function : Pole
//purpose :
//=======================================================================
const gp_Pnt& Geom_BSplineCurve::Pole (const Standard_Integer Index) const
{
Standard_OutOfRange_Raise_if (Index < 1 || Index > poles->Length(),
"Geom_BSplineCurve::Pole");
return poles->Value (Index);
}
//=======================================================================
//function : Poles
//purpose :
//=======================================================================
void Geom_BSplineCurve::Poles (TColgp_Array1OfPnt& P) const
{
Standard_DimensionError_Raise_if (P.Length() != poles->Length(),
"Geom_BSplineCurve::Poles");
P = poles->Array1();
}
const TColgp_Array1OfPnt& Geom_BSplineCurve::Poles() const
{
return poles->Array1();
}
//=======================================================================
//function : StartPoint
//purpose :
//=======================================================================
gp_Pnt Geom_BSplineCurve::StartPoint () const
{
if (mults->Value (1) == deg + 1)
return poles->Value (1);
else
return Value(FirstParameter());
}
//=======================================================================
//function : Weight
//purpose :
//=======================================================================
Standard_Real Geom_BSplineCurve::Weight
(const Standard_Integer Index) const
{
Standard_OutOfRange_Raise_if (Index < 1 || Index > poles->Length(),
"Geom_BSplineCurve::Weight");
if (IsRational())
return weights->Value (Index);
else
return 1.;
}
//=======================================================================
//function : Weights
//purpose :
//=======================================================================
void Geom_BSplineCurve::Weights
(TColStd_Array1OfReal& W) const
{
Standard_DimensionError_Raise_if (W.Length() != poles->Length(),
"Geom_BSplineCurve::Weights");
if (IsRational())
W = weights->Array1();
else {
Standard_Integer i;
for (i = W.Lower(); i <= W.Upper(); i++)
W(i) = 1.;
}
}
const TColStd_Array1OfReal* Geom_BSplineCurve::Weights() const
{
if (IsRational())
return &weights->Array1();
return BSplCLib::NoWeights();
}
//=======================================================================
//function : IsRational
//purpose :
//=======================================================================
Standard_Boolean Geom_BSplineCurve::IsRational () const
{
return !weights.IsNull();
}
//=======================================================================
//function : Transform
//purpose :
//=======================================================================
void Geom_BSplineCurve::Transform
(const gp_Trsf& T)
{
TColgp_Array1OfPnt & CPoles = poles->ChangeArray1();
for (Standard_Integer I = 1; I <= CPoles.Length(); I++)
CPoles (I).Transform (T);
maxderivinvok = 0;
}
//=======================================================================
//function : LocateU
//purpose :
// pmn : 30/01/97 mise en conformite avec le cdl, lorsque U est un noeud
// (PRO6988)
//=======================================================================
void Geom_BSplineCurve::LocateU
(const Standard_Real U,
const Standard_Real ParametricTolerance,
Standard_Integer& I1,
Standard_Integer& I2,
const Standard_Boolean WithKnotRepetition) const
{
Standard_Real NewU = U;
Handle(TColStd_HArray1OfReal) TheKnots;
if (WithKnotRepetition) TheKnots = flatknots;
else TheKnots = knots;
const TColStd_Array1OfReal & CKnots = TheKnots->Array1();
PeriodicNormalization(NewU); //Attention a la periode
Standard_Real UFirst = CKnots (1);
Standard_Real ULast = CKnots (CKnots.Length());
Standard_Real PParametricTolerance = Abs(ParametricTolerance);
if (Abs (NewU - UFirst) <= PParametricTolerance) { I1 = I2 = 1; }
else if (Abs (NewU - ULast) <= PParametricTolerance) {
I1 = I2 = CKnots.Length();
}
else if (NewU < UFirst) {
I2 = 1;
I1 = 0;
}
else if (NewU > ULast) {
I1 = CKnots.Length();
I2 = I1 + 1;
}
else {
I1 = 1;
BSplCLib::Hunt (CKnots, NewU, I1);
I1 = Max (Min (I1, CKnots.Upper()), CKnots.Lower());
while (I1 + 1 <= CKnots.Upper()
&& Abs (CKnots (I1 + 1) - NewU) <= PParametricTolerance)
{
I1++;
}
if ( Abs( CKnots(I1) - NewU) <= PParametricTolerance) {
I2 = I1;
}
else {
I2 = I1 + 1;
}
}
}
//=======================================================================
//function : Resolution
//purpose :
//=======================================================================
void Geom_BSplineCurve::Resolution (const Standard_Real Tolerance3D,
Standard_Real& UTolerance)
{
if (!maxderivinvok)
{
if (periodic)
{
Standard_Integer NbKnots, NbPoles;
BSplCLib::PrepareUnperiodize (deg, mults->Array1(), NbKnots, NbPoles);
TColgp_Array1OfPnt new_poles (1, NbPoles);
TColStd_Array1OfReal new_weights(1, NbPoles);
for (Standard_Integer ii = 1; ii <= NbPoles; ii++)
{
new_poles(ii) = poles->Array1()((ii-1) % poles->Length() + 1);
}
if (rational)
{
for (Standard_Integer ii = 1; ii <= NbPoles; ii++)
{
new_weights(ii) = weights->Array1()((ii-1) % poles->Length() + 1);
}
}
BSplCLib::Resolution (new_poles,
rational ? &new_weights : BSplCLib::NoWeights(),
new_poles.Length(),
flatknots->Array1(),
deg,
1.,
maxderivinv);
}
else
{
BSplCLib::Resolution (poles->Array1(),
rational ? &weights->Array1() : BSplCLib::NoWeights(),
poles->Length(),
flatknots->Array1(),
deg,
1.,
maxderivinv);
}
maxderivinvok = 1;
}
UTolerance = Tolerance3D * maxderivinv;
}
//=======================================================================
//function : IsEqual
//purpose :
//=======================================================================
Standard_Boolean Geom_BSplineCurve::IsEqual(const Handle(Geom_BSplineCurve)& theOther,
const Standard_Real thePreci) const
{
if( knots.IsNull() || poles.IsNull() || mults.IsNull() )
return Standard_False;
if( deg != theOther->Degree())
return Standard_False;
if( knots->Length() != theOther->NbKnots() ||
poles->Length() != theOther->NbPoles())
return Standard_False;
Standard_Integer i = 1;
for( i = 1 ; i <= poles->Length(); i++ )
{
const gp_Pnt& aPole1 = poles->Value(i);
const gp_Pnt& aPole2 =theOther->Pole(i);
if( fabs( aPole1.X() - aPole2.X() ) > thePreci ||
fabs( aPole1.Y() - aPole2.Y() ) > thePreci ||
fabs( aPole1.Z() - aPole2.Z() ) > thePreci )
return Standard_False;
}
for( ; i <= knots->Length(); i++ )
{
if( fabs(knots->Value(i) - theOther->Knot(i)) > Precision::Parametric(thePreci) )
return Standard_False;
}
for( i = 1 ; i <= mults->Length(); i++ )
{
if( mults->Value(i) != theOther->Multiplicity(i) )
return Standard_False;
}
if( rational != theOther->IsRational())
return Standard_False;
if(!rational)
return Standard_True;
for( i = 1 ; i <= weights->Length(); i++ )
{
if( fabs( Standard_Real(weights->Value(i) - theOther->Weight(i))) > Epsilon(weights->Value(i)) )
return Standard_False;
}
return Standard_True;
}