#include #include "meshing.hpp" namespace netgen { void Refinement :: Refine (Mesh & mesh) { // reduce 2nd order mesh.ComputeNVertices(); mesh.SetNP(mesh.GetNV()); INDEX_2_HASHTABLE between(mesh.GetNP() + 5); int oldne, oldns, oldnf; // refine edges Array epgi; oldns = mesh.GetNSeg(); for (SegmentIndex si = 0; si < oldns; si++) { const Segment & el = mesh.LineSegment(si); INDEX_2 i2 = INDEX_2::Sort(el[0], el[1]); PointIndex pinew; EdgePointGeomInfo ngi; if (between.Used(i2)) { pinew = between.Get(i2); ngi = epgi[pinew]; } else { Point<3> pnew; PointBetween (mesh.Point (el[0]), mesh.Point (el[1]), 0.5, el.surfnr1, el.surfnr2, el.epgeominfo[0], el.epgeominfo[1], pnew, ngi); pinew = mesh.AddPoint (pnew); between.Set (i2, pinew); if (pinew >= epgi.Size()+PointIndex::BASE) epgi.SetSize (pinew+1-PointIndex::BASE); epgi[pinew] = ngi; } Segment ns1 = el; Segment ns2 = el; ns1[1] = pinew; ns1.epgeominfo[1] = ngi; ns2[0] = pinew; ns2.epgeominfo[0] = ngi; mesh.LineSegment(si) = ns1; mesh.AddSegment (ns2); } // refine surface elements Array surfgi (8*mesh.GetNP()); for (int i = PointIndex::BASE; i < surfgi.Size()+PointIndex::BASE; i++) surfgi[i].trignum = -1; oldnf = mesh.GetNSE(); for (SurfaceElementIndex sei = 0; sei < oldnf; sei++) { int j, k; const Element2d & el = mesh.SurfaceElement(sei); switch (el.GetType()) { case TRIG: case TRIG6: { ArrayMem pnums(6); ArrayMem pgis(6); static int betw[3][3] = { { 2, 3, 4 }, { 1, 3, 5 }, { 1, 2, 6 } }; for (j = 1; j <= 3; j++) { pnums.Elem(j) = el.PNum(j); pgis.Elem(j) = el.GeomInfoPi(j); } for (j = 0; j < 3; j++) { PointIndex pi1 = pnums.Elem(betw[j][0]); PointIndex pi2 = pnums.Elem(betw[j][1]); INDEX_2 i2 (pi1, pi2); i2.Sort(); Point<3> pb; PointGeomInfo pgi; PointBetween (mesh.Point (pi1), mesh.Point (pi2), 0.5, mesh.GetFaceDescriptor(el.GetIndex ()).SurfNr(), el.GeomInfoPi (betw[j][0]), el.GeomInfoPi (betw[j][1]), pb, pgi); pgis.Elem(4+j) = pgi; if (between.Used(i2)) pnums.Elem(4+j) = between.Get(i2); else { pnums.Elem(4+j) = mesh.AddPoint (pb); between.Set (i2, pnums.Get(4+j)); } if (surfgi.Size() < pnums.Elem(4+j)) surfgi.SetSize (pnums.Elem(4+j)); surfgi.Elem(pnums.Elem(4+j)) = pgis.Elem(4+j); } static int reftab[4][3] = { { 1, 6, 5 }, { 2, 4, 6 }, { 3, 5, 4 }, { 6, 4, 5 } }; int ind = el.GetIndex(); for (j = 0; j < 4; j++) { Element2d nel(TRIG); for (k = 1; k <= 3; k++) { nel.PNum(k) = pnums.Get(reftab[j][k-1]); nel.GeomInfoPi(k) = pgis.Get(reftab[j][k-1]); } nel.SetIndex(ind); if (j == 0) mesh.SurfaceElement(sei) = nel; else mesh.AddSurfaceElement(nel); } break; } case QUAD: case QUAD6: case QUAD8: { ArrayMem pnums(9); ArrayMem pgis(9); static int betw[5][3] = { { 1, 2, 5 }, { 2, 3, 6 }, { 3, 4, 7 }, { 1, 4, 8 }, { 5, 7, 9 } }; for (j = 1; j <= 4; j++) { pnums.Elem(j) = el.PNum(j); pgis.Elem(j) = el.GeomInfoPi(j); } for (j = 0; j < 5; j++) { int pi1 = pnums.Elem(betw[j][0]); int pi2 = pnums.Elem(betw[j][1]); INDEX_2 i2 (pi1, pi2); i2.Sort(); if (between.Used(i2)) { pnums.Elem(5+j) = between.Get(i2); pgis.Elem(5+j) = surfgi.Get(pnums.Elem(4+j)); } else { Point<3> pb; PointBetween (mesh.Point (pi1), mesh.Point (pi2), 0.5, mesh.GetFaceDescriptor(el.GetIndex ()).SurfNr(), el.GeomInfoPi (betw[j][0]), el.GeomInfoPi (betw[j][1]), pb, pgis.Elem(5+j)); pnums.Elem(5+j) = mesh.AddPoint (pb); between.Set (i2, pnums.Get(5+j)); if (surfgi.Size() < pnums.Elem(5+j)) surfgi.SetSize (pnums.Elem(5+j)); surfgi.Elem(pnums.Elem(5+j)) = pgis.Elem(5+j); } } static int reftab[4][4] = { { 1, 5, 9, 8 }, { 5, 2, 6, 9 }, { 8, 9, 7, 4 }, { 9, 6, 3, 7 } }; int ind = el.GetIndex(); for (j = 0; j < 4; j++) { Element2d nel(QUAD); for (k = 1; k <= 4; k++) { nel.PNum(k) = pnums.Get(reftab[j][k-1]); nel.GeomInfoPi(k) = pgis.Get(reftab[j][k-1]); } nel.SetIndex(ind); if (j == 0) mesh.SurfaceElement(sei) = nel; else mesh.AddSurfaceElement(nel); } break; } default: PrintSysError ("Refine: undefined surface element type ", int(el.GetType())); } } // refine volume elements oldne = mesh.GetNE(); for (ElementIndex ei = 0; ei < oldne; ei++) { int j, k; const Element & el = mesh.VolumeElement(ei); switch (el.GetType()) { case TET: case TET10: { ArrayMem pnums(10); static int betw[6][3] = { { 1, 2, 5 }, { 1, 3, 6 }, { 1, 4, 7 }, { 2, 3, 8 }, { 2, 4, 9 }, { 3, 4, 10 } }; int elrev = el.flags.reverse; for (j = 1; j <= 4; j++) pnums.Elem(j) = el.PNum(j); if (elrev) swap (pnums.Elem(3), pnums.Elem(4)); for (j = 0; j < 6; j++) { INDEX_2 i2; i2.I1() = pnums.Get(betw[j][0]); i2.I2() = pnums.Get(betw[j][1]); i2.Sort(); if (between.Used(i2)) pnums.Elem(5+j) = between.Get(i2); else { pnums.Elem(5+j) = mesh.AddPoint (Center (mesh.Point(i2.I1()), mesh.Point(i2.I2()))); between.Set (i2, pnums.Elem(5+j)); } } static int reftab[8][4] = { { 1, 5, 6, 7 }, { 5, 2, 8, 9 }, { 6, 8, 3, 10 }, { 7, 9, 10, 4 }, { 5, 6, 7, 9 }, { 5, 6, 9, 8 }, { 6, 7, 9, 10 }, { 6, 8, 10, 9 } }; /* { { 1, 5, 6, 7 }, { 5, 2, 8, 9 }, { 6, 8, 3, 10 }, { 7, 9, 10, 4 }, { 5, 6, 7, 9 }, { 5, 6, 8, 9 }, { 6, 7, 9, 10 }, { 6, 8, 9, 10 } }; */ static bool reverse[8] = { false, false, false, false, false, true, false, true }; int ind = el.GetIndex(); for (j = 0; j < 8; j++) { Element nel; for (k = 1; k <= 4; k++) nel.PNum(k) = pnums.Get(reftab[j][k-1]); nel.SetIndex(ind); nel.flags.reverse = reverse[j]; if (elrev) { nel.flags.reverse = !nel.flags.reverse; swap (nel.PNum(3), nel.PNum(4)); } if (j == 0) mesh.VolumeElement(ei) = nel; else mesh.AddVolumeElement (nel); } break; } case HEX: { ArrayMem pnums(27); static int betw[13][3] = { { 1, 2, 9 }, { 3, 4, 10 }, { 4, 1, 11 }, { 2, 3, 12 }, { 5, 6, 13 }, { 7, 8, 14 }, { 8, 5, 15 }, { 6, 7, 16 }, { 1, 5, 17 }, { 2, 6, 18 }, { 3, 7, 19 }, { 4, 8, 20 }, { 2, 8, 21 }, }; /* static int fbetw[12][3] = { { 1, 3, 22 }, { 2, 4, 22 }, { 5, 7, 23 }, { 6, 8, 23 }, { 1, 6, 24 }, { 2, 5, 24 }, { 2, 7, 25 }, { 3, 6, 25 }, { 3, 8, 26 }, { 4, 7, 26 }, { 1, 8, 27 }, { 4, 5, 27 }, }; */ // udpated by anonymous supporter, donations please to Karo W. static int fbetw[12][3] = { { 11, 12, 22 }, { 9, 10, 22 }, { 13, 14, 23 }, { 15, 16, 23 }, { 9, 13, 24 }, { 17, 18, 24 }, { 12, 16, 25 }, { 18, 19, 25 }, { 19, 20, 26 }, { 10, 14, 26 }, { 11, 15, 27 }, { 17, 20, 27 }, }; pnums = -1; for (j = 1; j <= 8; j++) pnums.Elem(j) = el.PNum(j); for (j = 0; j < 13; j++) { INDEX_2 i2; i2.I1() = pnums.Get(betw[j][0]); i2.I2() = pnums.Get(betw[j][1]); i2.Sort(); if (between.Used(i2)) pnums.Elem(9+j) = between.Get(i2); else { pnums.Elem(9+j) = mesh.AddPoint (Center (mesh.Point(i2.I1()), mesh.Point(i2.I2()))); between.Set (i2, pnums.Elem(9+j)); } } for (j = 0; j < 6; j++) { INDEX_2 i2a, i2b; i2a.I1() = pnums.Get(fbetw[2*j][0]); i2a.I2() = pnums.Get(fbetw[2*j][1]); i2a.Sort(); i2b.I1() = pnums.Get(fbetw[2*j+1][0]); i2b.I2() = pnums.Get(fbetw[2*j+1][1]); i2b.Sort(); if (between.Used(i2a)) pnums.Elem(22+j) = between.Get(i2a); else if (between.Used(i2b)) pnums.Elem(22+j) = between.Get(i2b); else { pnums.Elem(22+j) = mesh.AddPoint (Center (mesh.Point(i2a.I1()), mesh.Point(i2a.I2()))); between.Set (i2a, pnums.Elem(22+j)); } } static int reftab[8][8] = { { 1, 9, 22, 11, 17, 24, 21, 27 }, { 9, 2, 12, 22, 24, 18, 25, 21 }, { 11, 22, 10, 4, 27, 21, 26, 20}, { 22, 12, 3, 10, 21, 25, 19, 26}, { 17, 24, 21, 27, 5, 13, 23, 15}, { 24, 18, 25, 21, 13, 6, 16, 23}, { 27, 21, 26, 20, 15, 23, 14, 8}, { 21, 25, 19, 26, 23, 16, 7, 14} }; int ind = el.GetIndex(); for (j = 0; j < 8; j++) { Element nel(HEX); for (k = 1; k <= 8; k++) nel.PNum(k) = pnums.Get(reftab[j][k-1]); nel.SetIndex(ind); if (j == 0) mesh.VolumeElement(ei) = nel; else mesh.AddVolumeElement (nel); } break; } case PRISM: { ArrayMem pnums(18); static int betw[9][3] = { { 3, 1, 7 }, { 1, 2, 8 }, { 3, 2, 9 }, { 6, 4, 10 }, { 4, 5, 11 }, { 6, 5, 12 }, { 1, 4, 13 }, { 3, 6, 14 }, { 2, 5, 15 }, }; // he: 15.jul 08, old version is wrong // produces double points ad quad faces and inconsistent mesh // static int fbetw[6][3] = // { { 1, 6, 16 }, // { 3, 4, 16 }, // { 1, 5, 17 }, // { 2, 4, 17 }, // { 2, 6, 18 }, // { 3, 5, 18 }, // }; static int fbetw[6][3] = { { 7, 10, 16 }, { 14, 13, 16 }, { 11, 8, 17 }, { 13, 15, 17 }, { 12, 9, 18 }, { 14, 15, 18 }, }; //int elrev = el.flags.reverse; pnums = -1; for (j = 1; j <= 6; j++) pnums.Elem(j) = el.PNum(j); // if (elrev) // swap (pnums.Elem(3), pnums.Elem(4)); for (j = 0; j < 9; j++) { INDEX_2 i2; i2.I1() = pnums.Get(betw[j][0]); i2.I2() = pnums.Get(betw[j][1]); i2.Sort(); if (between.Used(i2)) pnums.Elem(7+j) = between.Get(i2); else { pnums.Elem(7+j) = mesh.AddPoint (Center (mesh.Point(i2.I1()), mesh.Point(i2.I2()))); between.Set (i2, pnums.Elem(7+j)); } } for (j = 0; j < 3; j++) { INDEX_2 i2a, i2b; i2a.I1() = pnums.Get(fbetw[2*j][0]); i2a.I2() = pnums.Get(fbetw[2*j][1]); i2a.Sort(); i2b.I1() = pnums.Get(fbetw[2*j+1][0]); i2b.I2() = pnums.Get(fbetw[2*j+1][1]); i2b.Sort(); if (between.Used(i2a)) pnums.Elem(16+j) = between.Get(i2a); else if (between.Used(i2b)) pnums.Elem(16+j) = between.Get(i2b); else { pnums.Elem(16+j) = mesh.AddPoint (Center (mesh.Point(i2a.I1()), mesh.Point(i2a.I2()))); between.Set (i2a, pnums.Elem(16+j)); } } static int reftab[8][6] = { { 1, 8, 7, 13, 17, 16 }, { 7, 8, 9, 16, 17, 18 }, { 7, 9, 3, 16, 18, 14 }, { 8, 2, 9, 17, 15, 18 }, { 13, 17, 16, 4, 11, 10 }, { 16, 17, 18, 10, 11, 12 }, { 16, 18, 14, 10, 12, 6 }, { 17, 15, 18, 11, 5, 12 } }; int ind = el.GetIndex(); for (j = 0; j < 8; j++) { Element nel(PRISM); for (k = 1; k <= 6; k++) nel.PNum(k) = pnums.Get(reftab[j][k-1]); nel.SetIndex(ind); //nel.flags.reverse = reverse[j]; //if (elrev) // { //nel.flags.reverse = 1 - nel.flags.reverse; //swap (nel.PNum(3), nel.PNum(4)); if (j == 0) mesh.VolumeElement(ei) = nel; else mesh.AddVolumeElement (nel); } break; } default: PrintSysError ("Refine: undefined volume element type ", int(el.GetType())); } } // update identification tables for (int i = 1; i <= mesh.GetIdentifications().GetMaxNr(); i++) { Array identmap; mesh.GetIdentifications().GetMap (i, identmap); for (int j = 1; j <= between.GetNBags(); j++) for (int k = 1; k <= between.GetBagSize(j); k++) { INDEX_2 i2; int newpi; between.GetData (j, k, i2, newpi); INDEX_2 oi2(identmap.Get(i2.I1()), identmap.Get(i2.I2())); oi2.Sort(); if (between.Used (oi2)) { int onewpi = between.Get(oi2); mesh.GetIdentifications().Add (newpi, onewpi, i); } } } mesh.ComputeNVertices(); return; int cnttrials = 10; int wrongels = 0; for (int i = 1; i <= mesh.GetNE(); i++) if (mesh.VolumeElement(i).Volume(mesh.Points()) < 0) { wrongels++; mesh.VolumeElement(i).flags.badel = 1; } else mesh.VolumeElement(i).flags.badel = 0; if (wrongels) { cout << "WARNING: " << wrongels << " with wrong orientation found" << endl; int np = mesh.GetNP(); Array > should(np); Array > can(np); for (int i = 1; i <= np; i++) { should.Elem(i) = can.Elem(i) = mesh.Point(i); } for (int i = 1; i <= between.GetNBags(); i++) for (int j = 1; j <= between.GetBagSize(i); j++) { INDEX_2 parent; int child; between.GetData (i, j, parent, child); can.Elem(child) = Center (can.Elem(parent.I1()), can.Elem(parent.I2())); } BitArray boundp(np); boundp.Clear(); for (int i = 1; i <= mesh.GetNSE(); i++) { const Element2d & sel = mesh.SurfaceElement(i); for (int j = 1; j <= sel.GetNP(); j++) boundp.Set(sel.PNum(j)); } double lam = 0.5; while (lam < 0.9 && cnttrials > 0) { lam = 2; do { lam *= 0.5; cnttrials--; cout << "lam = " << lam << endl; for (int i = 1; i <= np; i++) if (boundp.Test(i)) { for (int j = 0; j < 3; j++) mesh.Point(i)(j) = lam * should.Get(i)(j) + (1-lam) * can.Get(i)(j); } else mesh.Point(i) = can.Get(i); BitArray free (mesh.GetNP()), fhelp(mesh.GetNP()); free.Clear(); for (int i = 1; i <= mesh.GetNE(); i++) { const Element & el = mesh.VolumeElement(i); if (el.Volume(mesh.Points()) < 0) for (int j = 1; j <= el.GetNP(); j++) free.Set (el.PNum(j)); } for (int k = 1; k <= 3; k++) { fhelp.Clear(); for (int i = 1; i <= mesh.GetNE(); i++) { const Element & el = mesh.VolumeElement(i); int freeel = 0; for (int j = 1; j <= el.GetNP(); j++) if (free.Test(el.PNum(j))) freeel = 1; if (freeel) for (int j = 1; j <= el.GetNP(); j++) fhelp.Set (el.PNum(j)); } free.Or (fhelp); } (*testout) << "smooth points: " << endl; for (int i = 1; i <= free.Size(); i++) if (free.Test(i)) (*testout) << "p " << i << endl; (*testout) << "surf points: " << endl; for (int i = 1; i <= mesh.GetNSE(); i++) for (int j = 1; j <= 3; j++) (*testout) << mesh.SurfaceElement(i).PNum(j) << endl; mesh.CalcSurfacesOfNode(); free.Invert(); mesh.FixPoints (free); mesh.ImproveMesh (OPT_REST); wrongels = 0; for (int i = 1; i <= mesh.GetNE(); i++) { if (mesh.VolumeElement(i).Volume(mesh.Points()) < 0) { wrongels++; mesh.VolumeElement(i).flags.badel = 1; (*testout) << "wrong el: "; for (int j = 1; j <= 4; j++) (*testout) << mesh.VolumeElement(i).PNum(j) << " "; (*testout) << endl; } else mesh.VolumeElement(i).flags.badel = 0; } cout << "wrongels = " << wrongels << endl; } while (wrongels && cnttrials > 0); for (int i = 1; i <= np; i++) can.Elem(i) = mesh.Point(i); } } if (cnttrials <= 0) { cerr << "ERROR: Sorry, reverted elements" << endl; } mesh.ComputeNVertices(); } }