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d5f74e42d6
License statement text corrected; compiler warnings caused by Bison 2.41 disabled for MSVC; a few other compiler warnings on 54-bit Windows eliminated by appropriate type cast Wrong license statements corrected in several files. Copyright and license statements added in XSD and GLSL files. Copyright year updated in some files. Obsolete documentation files removed from DrawResources.
244 lines
6.1 KiB
C++
244 lines
6.1 KiB
C++
// Copyright (c) 1995-1999 Matra Datavision
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// 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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#define No_Standard_RangeError
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#define No_Standard_OutOfRange
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#include <AppParCurves.ixx>
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#include <BSplCLib.hxx>
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#include <TColStd_Array1OfReal.hxx>
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#include <gp_Pnt2d.hxx>
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#include <gp_Vec2d.hxx>
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void AppParCurves::BernsteinMatrix(const Standard_Integer NbPoles,
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const math_Vector& U,
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math_Matrix& A) {
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Standard_Integer i, j, id;
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Standard_Real u0, u1, y0, y1, xs;
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Standard_Integer first = U.Lower(), last = U.Upper();
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math_Vector B(1, NbPoles-1);
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for (i = first; i <= last; i++) {
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B(1) = 1;
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u0 = U(i);
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u1 = 1.-u0;
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for (id = 2; id <= NbPoles-1; id++) {
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y0 = B(1);
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y1 = u0*y0;
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B(1) = y0-y1;
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for (j = 2; j <= id-1; j++) {
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xs = y1;
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y0 = B(j);
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y1 = u0*y0;
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B(j) = y0-y1+xs;
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}
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B(id) = y1;
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}
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A(i, 1) = u1*B(1);
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A(i, NbPoles) = u0*B(NbPoles-1);
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for (j = 2; j <= NbPoles-1; j++) {
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A(i, j) = u1*B(j)+u0*B(j-1);
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}
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}
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}
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void AppParCurves::Bernstein(const Standard_Integer NbPoles,
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const math_Vector& U,
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math_Matrix& A,
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math_Matrix& DA) {
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Standard_Integer i, j, id, Ndeg = NbPoles-1;
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Standard_Real u0, u1, y0, y1, xs, bj, bj1;;
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Standard_Integer first = U.Lower(), last = U.Upper();
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math_Vector B(1, NbPoles-1);
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for (i = first; i <= last; i++) {
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B(1) = 1;
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u0 = U(i);
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u1 = 1.-u0;
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for (id = 2; id <= NbPoles-1; id++) {
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y0 = B(1);
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y1 = u0*y0;
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B(1) = y0-y1;
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for (j = 2; j <= id-1; j++) {
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xs = y1;
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y0 = B(j);
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y1 = u0*y0;
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B(j) = y0-y1+xs;
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}
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B(id) = y1;
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}
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DA(i, 1) = -Ndeg*B(1);
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DA(i, NbPoles) = Ndeg*B(NbPoles-1);
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A(i, 1) = u1*B(1);
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A(i, NbPoles) = u0*B(NbPoles-1);
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for (j = 2; j <= NbPoles-1; j++) {
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bj = B(j); bj1 = B(j-1);
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DA(i,j) = Ndeg*(bj1-bj);
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A(i, j) = u1*bj+u0*bj1;
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}
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}
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}
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void AppParCurves::SecondDerivativeBernstein(const Standard_Real U,
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math_Vector& DDA) {
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// Standard_Real U1 = 1-U, Y0, Y1, Xs;
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Standard_Real Y0, Y1, Xs;
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Standard_Integer NbPoles = DDA.Length();
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Standard_Integer id, j, N4, deg = NbPoles-1;
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N4 = deg*(deg-1);
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math_Vector B(1, deg-1);
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B(1) = 1.;
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// Cas particulier si degre = 1:
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if (deg == 1) {
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DDA(1) = 0.0;
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DDA(2) = 0.0;
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}
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else if (deg == 2) {
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DDA(1) = 2.0;
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DDA(2) = -4.0;
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DDA(3) = 2.0;
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}
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else {
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for (id = 2; id <= deg-1; id++) {
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Y0 = B(1);
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Y1 = U*Y0;
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B(1) = Y0-Y1;
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for (j = 2; j <= id-1; j++) {
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Xs = Y1;
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Y0 = B(j);
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Y1 = U*Y0;
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B(j) = Y0 - Y1 +Xs;
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}
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B(id) = Y1;
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}
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DDA(1) = N4*B(1);
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DDA(2) = N4*(-2*B(1) + B(2));
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DDA(deg) = N4*(B(deg-2) - 2*B(deg-1));
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DDA(deg+1) = N4*B(deg-1);
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for(j = 2; j <= deg-2; j++) {
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DDA(j+1) = N4*(B(j-1)-2*B(j)+B(j+1));
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}
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}
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}
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void AppParCurves::SplineFunction(const Standard_Integer nbpoles,
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const Standard_Integer deg,
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const math_Vector& Parameters,
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const math_Vector& flatknots,
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math_Matrix& A,
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math_Matrix& DA,
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math_IntegerVector& index)
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{
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// Standard_Real U, NewU, co, diff, t1, t2;
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Standard_Real U, NewU;
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// gp_Pnt2d Pt, P0;
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// gp_Vec2d V1;
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// Standard_Integer i, j, k, iter, in, ik, deg1 = deg+1;
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Standard_Integer i, j, deg1 = deg+1;
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// Standard_Integer oldkindex, kindex, theindex, ttindex;
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Standard_Integer oldkindex, kindex, theindex;
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math_Vector locpoles(1 , deg1);
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math_Vector locdpoles(1 , deg1);
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Standard_Integer firstp = Parameters.Lower(), lastp = Parameters.Upper();
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TColStd_Array1OfReal Aflatknots(flatknots.Lower(), flatknots.Upper());
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for (i = flatknots.Lower(); i <= flatknots.Upper(); i++) {
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Aflatknots(i) = flatknots(i);
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}
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oldkindex = 1;
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Standard_Integer pp, qq;
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Standard_Real Saved, Inverse, LocalInverse, locqq, locdqq, val;
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for (i = firstp; i <= lastp; i++) {
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U = Parameters(i);
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NewU = U;
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kindex = oldkindex;
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BSplCLib::LocateParameter(deg, Aflatknots, U, Standard_False,
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deg1, nbpoles+1, kindex, NewU);
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oldkindex = kindex;
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// On stocke les index:
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index(i) = kindex - deg-1;
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locpoles(1) = 1.0;
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for (qq = 2; qq <= deg; qq++) {
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locpoles(qq) = 0.0;
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for (pp = 1; pp <= qq-1; pp++) {
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Inverse = 1.0 / (flatknots(kindex + pp) - flatknots(kindex - qq + pp + 1)) ;
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Saved = (U - flatknots(kindex - qq + pp + 1)) * Inverse * locpoles(pp);
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locpoles(pp) *= (flatknots(kindex + pp) - U) * Inverse ;
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locpoles(pp) += locpoles(qq) ;
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locpoles(qq) = Saved ;
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}
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}
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qq = deg+1;
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for (pp = 1; pp <= deg; pp++) {
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locdpoles(pp)= locpoles(pp);
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}
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locqq = 0.0;
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locdqq = 0.0;
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for (pp = 1; pp <= deg; pp++) {
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Inverse = 1.0 / (flatknots(kindex + pp) - flatknots(kindex - qq + pp + 1));
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Saved = (U - flatknots(kindex - qq + pp + 1)) * Inverse * locpoles(pp);
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locpoles(pp) *= (flatknots(kindex + pp) - U) * Inverse;
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locpoles(pp) += locqq;
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locqq = Saved ;
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LocalInverse = (Standard_Real) (deg) * Inverse;
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Saved = LocalInverse * locdpoles(pp);
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locdpoles(pp) *= - LocalInverse ;
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locdpoles(pp) += locdqq;
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locdqq = Saved ;
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}
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locpoles(qq) = locqq;
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locdpoles(qq) = locdqq;
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for (j = 1; j <= deg1; j++) {
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val = locpoles(j);
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theindex = j+oldkindex-deg1;
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A(i, theindex) = val;
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DA(i, theindex) = locdpoles(j);
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}
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for (j = 1; j < oldkindex-deg; j++)
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A(i, j) = DA(i, j) = 0.0;
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for (j = oldkindex+1; j <= nbpoles; j++)
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A(i, j) = DA(i, j) = 0.0;
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}
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}
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