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0423218095
"endl" manipulator for Message_Messenger is renamed to "Message_EndLine". The following entities from std namespace are now used with std:: explicitly specified (from Standard_Stream.hxx): std::istream,std::ostream,std::ofstream,std::ifstream,std::fstream, std::filebuf,std::streambuf,std::streampos,std::ios,std::cout,std::cerr, std::cin,std::endl,std::ends,std::flush,std::setw,std::setprecision, std::hex,std::dec.
630 lines
18 KiB
C++
630 lines
18 KiB
C++
// Copyright (c) 1999-2014 OPEN CASCADE SAS
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//
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// This file is part of Open CASCADE Technology software library.
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//
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// This library is free software; you can redistribute it and/or modify it under
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// the terms of the GNU Lesser General Public License version 2.1 as published
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// by the Free Software Foundation, with special exception defined in the file
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// OCCT_LGPL_EXCEPTION.txt. Consult the file LICENSE_LGPL_21.txt included in OCCT
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// distribution for complete text of the license and disclaimer of any warranty.
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//
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// Alternatively, this file may be used under the terms of Open CASCADE
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// commercial license or contractual agreement.
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#include <ApproxInt_KnotTools.hxx>
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#include <TColgp_Array1OfPnt2d.hxx>
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#include <TColStd_Array1OfReal.hxx>
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#include <TColStd_HArray1OfReal.hxx>
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#include <TColStd_HArray1OfInteger.hxx>
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#include <math_Vector.hxx>
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#include <Geom_BSplineCurve.hxx>
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#include <Geom2d_BSplineCurve.hxx>
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#include <GeomInt_TheMultiLineOfWLApprox.hxx>
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#include <NCollection_Sequence.hxx>
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#include <NCollection_List.hxx>
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#include <PLib.hxx>
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#include <Precision.hxx>
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#include <NCollection_Vector.hxx>
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#include <TColgp_Array1OfPnt.hxx>
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// (Sqrt(5.0) - 1.0) / 4.0
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//static const Standard_Real aSinCoeff = 0.30901699437494742410229341718282;
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static const Standard_Real aSinCoeff2 = 0.09549150281252627; // aSinCoeff^2 = (3. - Sqrt(5.)) / 8.
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static const Standard_Integer aMaxPntCoeff = 15;
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//=======================================================================
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//function : EvalCurv
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//purpose : Evaluate curvature in dim-dimension point.
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//=======================================================================
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static Standard_Real EvalCurv(const Standard_Real dim,
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const Standard_Real* V1,
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const Standard_Real* V2)
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{
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// Really V1 and V2 are arrays of size dim;
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// V1 is first derivative, V2 is second derivative
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// of n-dimension curve
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// Curvature is curv = |V1^V2|/|V1|^3
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// V1^V2 is outer product of two vectors:
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// P(i,j) = V1(i)*V2(j) - V1(j)*V2(i);
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Standard_Real mp = 0.;
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Standard_Integer i, j;
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Standard_Real p;
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for(i = 1; i < dim; ++i)
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{
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for(j = 0; j < i; ++j)
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{
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p = V1[i]*V2[j] - V1[j]*V2[i];
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mp += p*p;
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}
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}
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//
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Standard_Real q = 0.;
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for(i = 0; i < dim; ++i)
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{
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q += V1[i]*V1[i];
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}
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if (q < 1 / Precision::Infinite())
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{
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// Indeed, if q is small then we can
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// obtain equivocation of "0/0" type.
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// In this case, local curvature can be
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// not equal to 0 or Infinity.
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// However, it is good solution to insert
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// knot in the place with such singularity.
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// Therefore, we need imitation of curvature
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// jumping. Return of Precision::Infinite() is
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// enough for it.
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return Precision::Infinite();
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}
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q = Min(q, Precision::Infinite());
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q *= q*q;
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//
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Standard_Real curv = Sqrt(mp / q);
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return curv;
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}
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//=======================================================================
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//function : ComputeKnotInds
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//purpose :
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//=======================================================================
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void ApproxInt_KnotTools::ComputeKnotInds(const NCollection_LocalArray<Standard_Real>& theCoords,
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const Standard_Integer theDim,
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const math_Vector& thePars,
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NCollection_Sequence<Standard_Integer>& theInds)
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{
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//I: Create discrete curvature.
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NCollection_Sequence<Standard_Integer> aFeatureInds;
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TColStd_Array1OfReal aCurv(thePars.Lower(), thePars.Upper());
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// Arrays are allocated for max theDim = 7: 1 3d curve + 2 2d curves.
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Standard_Real Val[21], Par[3], Res[21];
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Standard_Integer i, j, m, ic;
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Standard_Real aMaxCurv = 0.;
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Standard_Integer dim = theDim;
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//
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i = aCurv.Lower();
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for(j = 0; j < 3; ++j)
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{
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Standard_Integer k = i+j;
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ic = (k - aCurv.Lower()) * dim;
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Standard_Integer l = dim*j;
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for(m = 0; m < dim; ++m)
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{
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Val[l + m] = theCoords[ic + m];
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}
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Par[j] = thePars(k);
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}
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PLib::EvalLagrange(Par[0], 2, 2, dim, *Val, *Par, *Res);
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//
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aCurv(i) = EvalCurv(dim, &Res[dim], &Res[2*dim]);
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//
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if(aCurv(i) > aMaxCurv)
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{
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aMaxCurv = aCurv(i);
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}
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//
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for(i = aCurv.Lower()+1; i < aCurv.Upper(); ++i)
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{
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for(j = 0; j < 3; ++j)
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{
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Standard_Integer k = i+j-1;
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ic = (k - aCurv.Lower()) * dim;
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Standard_Integer l = dim*j;
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for(m = 0; m < dim; ++m)
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{
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Val[l + m] = theCoords[ic + m];
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}
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Par[j] = thePars(k);
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}
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PLib::EvalLagrange(Par[1], 2, 2, dim, *Val, *Par, *Res);
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//
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aCurv(i) = EvalCurv(dim, &Res[dim], &Res[2*dim]);
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if(aCurv(i) > aMaxCurv)
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{
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aMaxCurv = aCurv(i);
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}
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}
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//
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i = aCurv.Upper();
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for(j = 0; j < 3; ++j)
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{
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Standard_Integer k = i+j-2;
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ic = (k - aCurv.Lower()) * dim;
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Standard_Integer l = dim*j;
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for(m = 0; m < dim; ++m)
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{
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Val[l + m] = theCoords[ic + m];
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}
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Par[j] = thePars(k);
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}
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PLib::EvalLagrange(Par[2], 2, 2, dim, *Val, *Par, *Res);
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//
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aCurv(i) = EvalCurv(dim, &Res[dim], &Res[2*dim]);
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if(aCurv(i) > aMaxCurv)
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{
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aMaxCurv = aCurv(i);
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}
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#ifdef APPROXINT_KNOTTOOLS_DEBUG
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std::cout << "Discrete curvature array is" << std::endl;
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for(i = aCurv.Lower(); i <= aCurv.Upper(); ++i)
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{
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std::cout << i << " " << aCurv(i) << std::endl;
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}
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#endif
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theInds.Append(aCurv.Lower());
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if(aMaxCurv <= Precision::Confusion())
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{
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// Linear case.
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theInds.Append(aCurv.Upper());
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return;
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}
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// II: Find extremas of curvature.
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// Not used Precision::PConfusion, by different from "param space" eps nature.
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Standard_Real eps = 1.0e-9,
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eps1 = 1.0e3 * eps;
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for(i = aCurv.Lower() + 1; i < aCurv.Upper(); ++i)
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{
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Standard_Real d1 = aCurv(i) - aCurv(i - 1),
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d2 = aCurv(i) - aCurv(i + 1),
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ad1 = Abs(d1), ad2 = Abs(d2);
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if(d1*d2 > 0. && ad1 > eps && ad2 > eps)
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{
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if(i != theInds.Last())
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{
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theInds.Append(i);
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aFeatureInds.Append(i);
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}
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}
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else if((ad1 < eps && ad2 > eps1) || (ad1 > eps1 && ad2 < eps))
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{
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if(i != theInds.Last())
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{
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theInds.Append(i);
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aFeatureInds.Append(i);
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}
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}
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}
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if(aCurv.Upper() != theInds.Last())
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{
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theInds.Append(aCurv.Upper());
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}
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#if defined(APPROXINT_KNOTTOOLS_DEBUG)
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{
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std::cout << "Feature indices new: " << std::endl;
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i;
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for(i = theInds.Lower(); i <= theInds.Upper(); ++i)
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{
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std::cout << i << " : " << theInds(i) << std::endl;
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}
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}
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#endif
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//III: Put knots in monotone intervals of curvature.
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Standard_Boolean Ok;
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i = 1;
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do
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{
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i++;
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//
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Ok = InsKnotBefI(i, aCurv, theCoords, dim, theInds, Standard_True);
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if(Ok)
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{
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i--;
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}
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}
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while(i < theInds.Length());
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//IV: Cheking feature points.
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j = 2;
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for(i = 1; i <= aFeatureInds.Length(); ++i)
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{
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Standard_Integer anInd = aFeatureInds(i);
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for(; j <= theInds.Length() - 1;)
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{
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if(theInds(j) == anInd)
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{
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Standard_Integer anIndPrev = theInds(j-1);
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Standard_Integer anIndNext = theInds(j+1);
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Standard_Integer ici = (anIndPrev - aCurv.Lower()) * theDim,
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ici1 = (anIndNext - aCurv.Lower()) * theDim,
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icm = (anInd - aCurv.Lower()) * theDim;
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NCollection_LocalArray<Standard_Real> V1(theDim), V2(theDim);
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Standard_Real mp = 0., m1 = 0., m2 = 0.;
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Standard_Real p;
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for(Standard_Integer k = 0; k < theDim; ++k)
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{
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V1[k] = theCoords[icm + k] - theCoords[ici + k];
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m1 += V1[k]*V1[k];
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V2[k] = theCoords[ici1 + k] - theCoords[icm + k];
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m2 += V2[k]*V2[k];
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}
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for(Standard_Integer k = 1; k < theDim; ++k)
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{
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for(Standard_Integer l = 0; l < k; ++l)
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{
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p = V1[k]*V2[l] - V1[l]*V2[k];
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mp += p*p;
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}
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}
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//mp *= 2.; //P(j,i) = -P(i,j);
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//
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if(mp > aSinCoeff2 * m1 * m2) // Sqrt (mp/(m1*m2)) > aSinCoeff
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{
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//Insert new knots
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Standard_Real d1 = Abs(aCurv(anInd) - aCurv(anIndPrev));
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Standard_Real d2 = Abs(aCurv(anInd) - aCurv(anIndNext));
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if(d1 > d2)
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{
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Ok = InsKnotBefI(j, aCurv, theCoords, dim, theInds, Standard_False);
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if(Ok)
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{
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j++;
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}
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else
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{
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break;
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}
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}
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else
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{
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Ok = InsKnotBefI(j+1, aCurv, theCoords, dim, theInds, Standard_False);
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if(!Ok)
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{
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break;
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}
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}
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}
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else
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{
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j++;
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break;
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}
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}
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else
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{
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j++;
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}
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}
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}
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//
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}
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//=======================================================================
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//function : FilterKnots
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//purpose :
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//=======================================================================
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void ApproxInt_KnotTools::FilterKnots(NCollection_Sequence<Standard_Integer>& theInds,
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const Standard_Integer theMinNbPnts,
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NCollection_Vector<Standard_Integer>& theLKnots)
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{
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// Maximum number of points per knot interval.
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Standard_Integer aMaxNbPnts = aMaxPntCoeff*theMinNbPnts;
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Standard_Integer i = 1;
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Standard_Integer aMinNbStep = theMinNbPnts / 2;
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// I: Filter too big number of points per knot interval.
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while(i < theInds.Length())
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{
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Standard_Integer nbint = theInds(i + 1) - theInds(i) + 1;
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if(nbint <= aMaxNbPnts)
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{
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++i;
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continue;
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}
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else
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{
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Standard_Integer ind = theInds(i) + nbint / 2;
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theInds.InsertAfter(i, ind);
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}
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}
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// II: Filter poins with too small amount of points per knot interval.
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i = 1;
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theLKnots.Append(theInds(i));
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Standard_Integer anIndsPrev = theInds(i);
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for(i = 2; i <= theInds.Length(); ++i)
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{
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if(theInds(i) - anIndsPrev <= theMinNbPnts)
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{
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if (i != theInds.Length())
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{
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Standard_Integer anIdx = i + 1;
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for( ; anIdx <= theInds.Length(); ++anIdx)
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{
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if (theInds(anIdx) - anIndsPrev >= theMinNbPnts)
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break;
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}
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anIdx--;
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Standard_Integer aMidIdx = (theInds(anIdx) + anIndsPrev) / 2;
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if (aMidIdx - anIndsPrev < theMinNbPnts &&
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aMidIdx - theInds(anIdx) < theMinNbPnts &&
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theInds(anIdx) - anIndsPrev >= aMinNbStep)
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{
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if (theInds(anIdx) - anIndsPrev > 2 * theMinNbPnts)
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{
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// Bad distribution points merge into one knot interval.
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theLKnots.Append(anIndsPrev + theMinNbPnts);
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anIndsPrev = anIndsPrev + theMinNbPnts;
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i = anIdx - 1;
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}
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else
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{
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if (theInds(anIdx - 1) - anIndsPrev >= theMinNbPnts / 2)
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{
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// Bad distribution points merge into one knot interval.
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theLKnots.Append(theInds(anIdx - 1));
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anIndsPrev = theInds(anIdx - 1);
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i = anIdx - 1;
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if (theInds(anIdx) - theInds(anIdx - 1) <= theMinNbPnts / 2)
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{
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theLKnots.SetValue(theLKnots.Upper(), theInds(anIdx));
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anIndsPrev = theInds(anIdx );
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i = anIdx;
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}
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}
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else
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{
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// Bad distribution points merge into one knot interval.
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theLKnots.Append(theInds(anIdx));
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anIndsPrev = theInds(anIdx);
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i = anIdx;
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}
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}
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}
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else if (anIdx == theInds.Upper() && // Last point obtained.
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theLKnots.Length() >= 2) // It is possible to modify last item.
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{
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// Current bad interval from i to last.
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// Trying to add knot to divide sequence on two parts:
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// Last good index -> Last index - theMinNbPnts -> Last index
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Standard_Integer aLastGoodIdx = theLKnots.Value(theLKnots.Upper() - 1);
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if ( theInds.Last() - 2 * theMinNbPnts >= aLastGoodIdx)
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{
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theLKnots(theLKnots.Upper()) = theInds.Last() - theMinNbPnts;
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theLKnots.Append(theInds.Last());
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anIndsPrev = theInds(anIdx);
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i = anIdx;
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}
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}
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} // if (i != theInds.Length())
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continue;
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}
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else
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{
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theLKnots.Append(theInds(i));
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anIndsPrev = theInds(i);
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}
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}
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// III: Fill Last Knot.
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if(theLKnots.Length() < 2)
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{
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theLKnots.Append(theInds.Last());
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}
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else
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{
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if(theLKnots.Last() < theInds.Last())
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{
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theLKnots(theLKnots.Upper()) = theInds.Last();
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}
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}
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}
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//=======================================================================
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//function : InsKnotBefI
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//purpose :
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//=======================================================================
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Standard_Boolean ApproxInt_KnotTools::InsKnotBefI(const Standard_Integer theI,
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const TColStd_Array1OfReal& theCurv,
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const NCollection_LocalArray<Standard_Real>& theCoords,
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const Standard_Integer theDim,
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NCollection_Sequence<Standard_Integer>& theInds,
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const Standard_Boolean ChkCurv)
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{
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Standard_Integer anInd1 = theInds(theI);
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Standard_Integer anInd = theInds(theI - 1);
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//
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if((anInd1-anInd) == 1)
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{
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return Standard_False;
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}
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//
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Standard_Real curv = 0.5*(theCurv(anInd) + theCurv(anInd1));
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Standard_Integer mid = 0, j, jj;
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const Standard_Real aLimitCurvatureChange = 3.0;
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for(j = anInd+1; j < anInd1; ++j)
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{
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mid = 0;
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// I: Curvature change criteria:
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// Non-null curvature.
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if (theCurv(j) > Precision::Confusion() &&
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theCurv(anInd) > Precision::Confusion() )
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{
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if (theCurv(j) / theCurv(anInd) > aLimitCurvatureChange ||
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theCurv(j) / theCurv(anInd) < 1.0 / aLimitCurvatureChange)
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{
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// Curvature on current interval changed more than 3 times.
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mid = j;
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theInds.InsertBefore(theI, mid);
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return Standard_True;
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}
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}
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// II: Angular criteria:
|
|
Standard_Real ac = theCurv(j - 1), ac1 = theCurv(j);
|
|
if((curv >= ac && curv <= ac1) || (curv >= ac1 && curv <= ac))
|
|
{
|
|
if(Abs(curv - ac) < Abs(curv - ac1))
|
|
{
|
|
mid = j - 1;
|
|
}
|
|
else
|
|
{
|
|
mid = j;
|
|
}
|
|
}
|
|
if(mid == anInd)
|
|
{
|
|
mid++;
|
|
}
|
|
if(mid == anInd1)
|
|
{
|
|
mid--;
|
|
}
|
|
if(mid > 0)
|
|
{
|
|
if(ChkCurv)
|
|
{
|
|
Standard_Integer ici = (anInd - theCurv.Lower()) * theDim,
|
|
ici1 = (anInd1 - theCurv.Lower()) * theDim,
|
|
icm = (mid - theCurv.Lower()) * theDim;
|
|
NCollection_LocalArray<Standard_Real> V1(theDim), V2(theDim);
|
|
Standard_Integer i;
|
|
Standard_Real mp = 0., m1 = 0., m2 = 0.;
|
|
Standard_Real p;
|
|
for(i = 0; i < theDim; ++i)
|
|
{
|
|
V1[i] = theCoords[icm + i] - theCoords[ici + i];
|
|
m1 += V1[i]*V1[i];
|
|
V2[i] = theCoords[ici1 + i] - theCoords[icm + i];
|
|
m2 += V2[i]*V2[i];
|
|
}
|
|
for(i = 1; i < theDim; ++i)
|
|
{
|
|
for(jj = 0; jj < i; ++jj)
|
|
{
|
|
p = V1[i]*V2[jj] - V1[jj]*V2[i];
|
|
mp += p*p;
|
|
}
|
|
}
|
|
//mp *= 2.; //P(j,i) = -P(i,j);
|
|
//
|
|
|
|
if (mp > aSinCoeff2 * m1 * m2) // Sqrt (mp / m1m2) > aSinCoeff
|
|
{
|
|
theInds.InsertBefore(theI, mid);
|
|
return Standard_True;
|
|
}
|
|
}
|
|
else
|
|
{
|
|
theInds.InsertBefore(theI, mid);
|
|
return Standard_True;
|
|
}
|
|
}
|
|
}
|
|
|
|
return Standard_False;
|
|
}
|
|
|
|
//=======================================================================
|
|
//function : BuildKnots
|
|
//purpose :
|
|
//=======================================================================
|
|
void ApproxInt_KnotTools::BuildKnots(const TColgp_Array1OfPnt& thePntsXYZ,
|
|
const TColgp_Array1OfPnt2d& thePntsU1V1,
|
|
const TColgp_Array1OfPnt2d& thePntsU2V2,
|
|
const math_Vector& thePars,
|
|
const Standard_Boolean theApproxXYZ,
|
|
const Standard_Boolean theApproxU1V1,
|
|
const Standard_Boolean theApproxU2V2,
|
|
const Standard_Integer theMinNbPnts,
|
|
NCollection_Vector<Standard_Integer>& theKnots)
|
|
{
|
|
NCollection_Sequence<Standard_Integer> aKnots;
|
|
Standard_Integer aDim = 0;
|
|
|
|
// I: Convert input data to the corresponding format.
|
|
if(theApproxXYZ)
|
|
aDim += 3;
|
|
if(theApproxU1V1)
|
|
aDim += 2;
|
|
if(theApproxU2V2)
|
|
aDim += 2;
|
|
|
|
NCollection_LocalArray<Standard_Real> aCoords(thePars.Length()*aDim);
|
|
Standard_Integer i, j;
|
|
for(i = thePars.Lower(); i <= thePars.Upper(); ++i)
|
|
{
|
|
j = (i - thePars.Lower()) * aDim;
|
|
if(theApproxXYZ)
|
|
{
|
|
aCoords[j] = thePntsXYZ.Value(i).X();
|
|
++j;
|
|
aCoords[j] = thePntsXYZ.Value(i).Y();
|
|
++j;
|
|
aCoords[j] = thePntsXYZ.Value(i).Z();
|
|
++j;
|
|
}
|
|
if(theApproxU1V1)
|
|
{
|
|
aCoords[j] = thePntsU1V1.Value(i).X();
|
|
++j;
|
|
aCoords[j] = thePntsU1V1.Value(i).Y();
|
|
++j;
|
|
}
|
|
if(theApproxU2V2)
|
|
{
|
|
aCoords[j] = thePntsU2V2.Value(i).X();
|
|
++j;
|
|
aCoords[j] = thePntsU2V2.Value(i).Y();
|
|
++j;
|
|
}
|
|
}
|
|
|
|
// II: Build draft knot sequence.
|
|
ComputeKnotInds(aCoords, aDim, thePars, aKnots);
|
|
|
|
#if defined(APPROXINT_KNOTTOOLS_DEBUG)
|
|
std::cout << "Draft knot sequence: " << std::endl;
|
|
for(i = aKnots.Lower(); i <= aKnots.Upper(); ++i)
|
|
{
|
|
std::cout << i << " : " << aKnots(i) << std::endl;
|
|
}
|
|
#endif
|
|
|
|
// III: Build output knot sequence.
|
|
FilterKnots(aKnots, theMinNbPnts, theKnots);
|
|
|
|
#if defined(APPROXINT_KNOTTOOLS_DEBUG)
|
|
std::cout << "Result knot sequence: " << std::endl;
|
|
for(i = theKnots.Lower(); i <= theKnots.Upper(); ++i)
|
|
{
|
|
std::cout << i << " : " << theKnots(i) << std::endl;
|
|
}
|
|
#endif
|
|
|
|
}
|