netgen/libsrc/geom2d/genmesh2d.cpp

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#include <meshing.hpp>
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#include <geometry2d.hpp>
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namespace netgen
{
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// extern DLL_HEADER MeshingParameters mparam;
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extern void Optimize2d (Mesh & mesh, MeshingParameters & mp);
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void CalcPartition (const SplineSegExt & spline,
// double l,
MeshingParameters & mp, Mesh & mesh,
// double h, double h1, double h2, double hcurve,
double elto0, Array<double> & points)
{
double fperel, oldf, f;
int n = 10000;
Array<Point<2> > xi(n);
Array<double> hi(n);
for (int i = 0; i < n; i++)
{
xi[i] = spline.GetPoint ( (i+0.5) / n );
hi[i] = mesh.GetH (Point<3> (xi[i](0), xi[i](1), 0));
}
// limit slope
double gradh = min(1/elto0,mp.grading);
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for (int i = 0; i < n-1; i++)
{
double hnext = hi[i] + gradh * (xi[i+1]-xi[i]).Length();
hi[i+1] = min(hi[i+1], hnext);
}
for (int i = n-1; i > 1; i--)
{
double hnext = hi[i] + gradh * (xi[i-1]-xi[i]).Length();
hi[i-1] = min(hi[i-1], hnext);
}
points.SetSize (0);
double len = spline.Length();
double dt = len / n;
double sum = 0;
for (int i = 1; i <= n; i++)
{
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// double t = (i-0.5)*dt;
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double fun = hi[i-1];
sum += dt / fun;
}
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int nel = int (sum+0.5);
if (nel == 0) nel = 1;
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fperel = sum / nel;
points.Append (0);
int i = 1;
oldf = 0;
for (int j = 1; j <= n && i < nel; j++)
{
double t = (j-0.5)*dt;
double fun = hi[j-1];
f = oldf + dt / fun;
while (i * fperel < f && i < nel)
{
points.Append ( dt * (j-1) + (i * fperel - oldf) * fun);
i++;
}
oldf = f;
t += dt;
}
points.Append (len);
}
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// partitionizes spline curve
void Partition (const SplineSegExt & spline,
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MeshingParameters & mp, double hxxx, double elto0,
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Mesh & mesh, Point3dTree & searchtree, int segnr)
{
int n = 100;
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Point<2> mark, oldmark;
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Array<double> curvepoints;
double edgelength, edgelengthold;
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CalcPartition (spline, mp, mesh, elto0, curvepoints);
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double dt = 1.0 / n;
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int j = 1;
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Point<2> pold = spline.GetPoint (0);
double lold = 0;
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oldmark = pold;
edgelengthold = 0;
Array<int> locsearch;
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for (int i = 1; i <= n; i++)
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{
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Point<2> p = spline.GetPoint (i*dt);
double l = lold + Dist (p, pold);
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while (j < curvepoints.Size() && (l >= curvepoints[j] || i == n))
{
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double frac = (curvepoints[j]-lold) / (l-lold);
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edgelength = i*dt + (frac-1)*dt;
mark = spline.GetPoint (edgelength);
{
PointIndex pi1 = -1, pi2 = -1;
Point3d mark3(mark(0), mark(1), 0);
Point3d oldmark3(oldmark(0), oldmark(1), 0);
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double h = mesh.GetH (Point<3> (oldmark(0), oldmark(1), 0));
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Vec<3> v (1e-4*h, 1e-4*h, 1e-4*h);
searchtree.GetIntersecting (oldmark3 - v, oldmark3 + v, locsearch);
for (int k = 0; k < locsearch.Size(); k++)
if ( mesh[PointIndex(locsearch[k])].GetLayer() == spline.layer)
pi1 = locsearch[k];
searchtree.GetIntersecting (mark3 - v, mark3 + v, locsearch);
for (int k = 0; k < locsearch.Size(); k++)
if ( mesh[PointIndex(locsearch[k])].GetLayer() == spline.layer)
pi2 = locsearch[k];
if (pi1 == -1)
{
pi1 = mesh.AddPoint(oldmark3, spline.layer);
searchtree.Insert (oldmark3, pi1);
}
if (pi2 == -1)
{
pi2 = mesh.AddPoint(mark3, spline.layer);
searchtree.Insert (mark3, pi2);
}
Segment seg;
seg.edgenr = segnr;
seg.si = spline.bc; // segnr;
seg[0] = pi1;
seg[1] = pi2;
seg.domin = spline.leftdom;
seg.domout = spline.rightdom;
seg.epgeominfo[0].edgenr = segnr;
seg.epgeominfo[0].dist = edgelengthold;
seg.epgeominfo[1].edgenr = segnr;
seg.epgeominfo[1].dist = edgelength;
seg.singedge_left = spline.hpref_left;
seg.singedge_right = spline.hpref_right;
mesh.AddSegment (seg);
}
oldmark = mark;
edgelengthold = edgelength;
j++;
}
pold = p;
lold = l;
}
}
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void SplineGeometry2d :: PartitionBoundary (MeshingParameters & mp, double h, Mesh & mesh2d)
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{
enum { D = 2 };
Box<D> bbox;
GetBoundingBox (bbox);
double dist = Dist (bbox.PMin(), bbox.PMax());
Point<3> pmin;
Point<3> pmax;
pmin(2) = -dist; pmax(2) = dist;
for(int j=0;j<D;j++)
{
pmin(j) = bbox.PMin()(j);
pmax(j) = bbox.PMax()(j);
}
Point3dTree searchtree (pmin, pmax);
for (int i = 0; i < splines.Size(); i++)
for (int side = 0; side <= 1; side++)
{
int dom = (side == 0) ? GetSpline(i).leftdom : GetSpline(i).rightdom;
if (dom != 0) GetSpline(i).layer = GetDomainLayer (dom);
}
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// mesh size restrictions ...
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for (auto & point : geompoints)
mesh2d.RestrictLocalH (Point<3> (point(0), point(1), 0), point.hmax);
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for (int i = 0; i < splines.Size(); i++)
{
const SplineSegExt & spline = GetSpline(i);
const GeomPoint<2> & p1 = spline.StartPI();
const GeomPoint<2> & p2 = spline.EndPI();
double h1 = min (p1.hmax, h/p1.refatpoint);
mesh2d.RestrictLocalH (Point<3>(p1(0),p1(1),0), h1);
double h2 = min (p2.hmax, h/p2.refatpoint);
mesh2d.RestrictLocalH (Point<3>(p2(0),p2(1),0), h2);
double len = spline.Length();
mesh2d.RestrictLocalHLine (Point<3>(p1(0),p1(1),0),
Point<3>(p2(0),p2(1),0), len/mp.segmentsperedge);
double hcurve = min (spline.hmax, h/spline.reffak);
double hl = GetDomainMaxh (spline.leftdom);
if (hl > 0) hcurve = min2 (hcurve, hl);
double hr = GetDomainMaxh (spline.rightdom);
if (hr > 0) hcurve = min2 (hcurve, hr);
int np = 1000;
for (double t = 0.5/np; t < 1; t += 1.0/np)
{
Point<2> x = spline.GetPoint(t);
double hc = 1.0/mp.curvaturesafety / (1e-99+spline.CalcCurvature (t));
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mesh2d.RestrictLocalH (Point<3> (x(0), x(1), 0), min2(hc, hcurve));
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}
}
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for (auto mspnt : mp.meshsize_points)
mesh2d.RestrictLocalH (mspnt.pnt, mspnt.h);
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// add point elements
for (auto & point : geompoints)
if (point.name.length())
{
Point<3> newp(point(0), point(1), 0);
PointIndex npi = mesh2d.AddPoint (newp, 1, FIXEDPOINT);
mesh2d.AddLockedPoint(npi);
Element0d el(npi, npi);
el.name = point.name;
mesh2d.SetCD2Name(npi, point.name);
mesh2d.pointelements.Append (el);
searchtree.Insert (newp, npi);
}
// first add all vertices (for compatible orientation on periodic bnds)
{
double diam2 = Dist2(pmin, pmax);
for (int i = 0; i < splines.Size(); i++)
for (int j : { 1, 2 })
{
Point<2> hnewp = (j == 1) ? splines[i]->StartPI() : splines[i]->EndPI();
Point<3> newp(hnewp(0), hnewp(1), 0);
int layer = GetSpline(i).layer;
int npi = -1;
for (PointIndex pi = PointIndex::BASE;
pi < mesh2d.GetNP()+PointIndex::BASE; pi++)
if (Dist2 (mesh2d.Point(pi), newp) < 1e-12 * diam2 && mesh2d.Point(pi).GetLayer() == layer)
npi = pi;
if (npi == -1)
{
npi = mesh2d.AddPoint (newp, layer);
searchtree.Insert (newp, npi);
}
}
}
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for (int i = 0; i < splines.Size(); i++)
if (GetSpline(i).copyfrom == -1)
{
// astrid - set boundary meshsize to domain meshsize h
// if no domain mesh size is given, the max h value from the bounding box is used
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double hl = GetDomainMaxh ( GetSpline(i).leftdom );
double hr = GetDomainMaxh ( GetSpline(i).rightdom );
double useh = h;
if (hl > 0) useh = min2 (h, hl);
if (hr > 0) useh = min2 (h, hr);
Partition(GetSpline(i), mp, useh, elto0, mesh2d, searchtree, i+1);
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}
else
{
CopyEdgeMesh (GetSpline(i).copyfrom, i+1, mesh2d, searchtree);
}
}
void SplineGeometry2d :: CopyEdgeMesh (int from, int to, Mesh & mesh, Point3dTree & searchtree)
{
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// const int D = 2;
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Array<int, PointIndex::BASE> mappoints (mesh.GetNP());
Array<double, PointIndex::BASE> param (mesh.GetNP());
mappoints = -1;
param = 0;
Point3d pmin, pmax;
mesh.GetBox (pmin, pmax);
double diam2 = Dist2(pmin, pmax);
if (printmessage_importance>0)
cout << "copy edge, from = " << from << " to " << to << endl;
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for (int i = 1; i <= mesh.GetNSeg(); i++)
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{
const Segment & seg = mesh.LineSegment(i);
if (seg.edgenr == from)
{
mappoints.Elem(seg[0]) = 1;
param.Elem(seg[0]) = seg.epgeominfo[0].dist;
mappoints.Elem(seg[1]) = 1;
param.Elem(seg[1]) = seg.epgeominfo[1].dist;
}
}
bool mapped = false;
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for (int i = 1; i <= mappoints.Size(); i++)
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{
if (mappoints.Get(i) != -1)
{
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Point<2> newp = splines.Get(to)->GetPoint (param.Get(i));
Point<3> newp3 (newp(0), newp(1), 0);
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int npi = -1;
for (PointIndex pi = PointIndex::BASE;
pi < mesh.GetNP()+PointIndex::BASE; pi++)
if (Dist2 (mesh.Point(pi), newp3) < 1e-12 * diam2)
npi = pi;
if (npi == -1)
{
npi = mesh.AddPoint (newp3);
searchtree.Insert (newp3, npi);
}
mappoints.Elem(i) = npi;
mesh.GetIdentifications().Add (i, npi, to);
mapped = true;
}
}
if(mapped)
mesh.GetIdentifications().SetType(to,Identifications::PERIODIC);
// copy segments
int oldnseg = mesh.GetNSeg();
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for (int i = 1; i <= oldnseg; i++)
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{
const Segment & seg = mesh.LineSegment(i);
if (seg.edgenr == from)
{
Segment nseg;
nseg.edgenr = to;
nseg.si = GetSpline(to-1).bc; // splines.Get(to)->bc;
nseg[0] = mappoints.Get(seg[0]);
nseg[1] = mappoints.Get(seg[1]);
nseg.domin = GetSpline(to-1).leftdom;
nseg.domout = GetSpline(to-1).rightdom;
nseg.epgeominfo[0].edgenr = to;
nseg.epgeominfo[0].dist = param.Get(seg[0]);
nseg.epgeominfo[1].edgenr = to;
nseg.epgeominfo[1].dist = param.Get(seg[1]);
mesh.AddSegment (nseg);
}
}
}
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void MeshFromSpline2D (SplineGeometry2d & geometry,
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shared_ptr<Mesh> & mesh,
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MeshingParameters & mp)
{
PrintMessage (1, "Generate Mesh from spline geometry");
Box<2> bbox = geometry.GetBoundingBox ();
if (bbox.Diam() < mp.maxh)
mp.maxh = bbox.Diam();
// double h = mp.maxh;
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// mesh = make_shared<Mesh>();
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mesh->SetDimension (2);
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Point3d pmin(bbox.PMin()(0), bbox.PMin()(1), -bbox.Diam());
Point3d pmax(bbox.PMax()(0), bbox.PMax()(1), bbox.Diam());
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mesh->SetLocalH (pmin, pmax, mp.grading);
mesh->SetGlobalH (mp.maxh);
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geometry.PartitionBoundary (mp, mp.maxh, *mesh);
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PrintMessage (3, "Boundary mesh done, np = ", mesh->GetNP());
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// marks mesh points for hp-refinement
for (int i = 0; i < geometry.GetNP(); i++)
if (geometry.GetPoint(i).hpref)
{
double mindist = 1e99;
PointIndex mpi(0);
Point<2> gp = geometry.GetPoint(i);
Point<3> gp3(gp(0), gp(1), 0);
for (PointIndex pi = PointIndex::BASE;
pi < mesh->GetNP()+PointIndex::BASE; pi++)
if (Dist2(gp3, (*mesh)[pi]) < mindist)
{
mpi = pi;
mindist = Dist2(gp3, (*mesh)[pi]);
}
(*mesh)[mpi].Singularity(geometry.GetPoint(i).hpref);
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}
int maxdomnr = 0;
for (SegmentIndex si = 0; si < mesh->GetNSeg(); si++)
{
if ( (*mesh)[si].domin > maxdomnr) maxdomnr = (*mesh)[si].domin;
if ( (*mesh)[si].domout > maxdomnr) maxdomnr = (*mesh)[si].domout;
}
mesh->ClearFaceDescriptors();
for (int i = 1; i <= maxdomnr; i++)
mesh->AddFaceDescriptor (FaceDescriptor (i, 0, 0, i));
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// set Array<string*> bcnames...
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// number of bcnames
int maxsegmentindex = 0;
for (SegmentIndex si = 0; si < mesh->GetNSeg(); si++)
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if ( (*mesh)[si].si > maxsegmentindex) maxsegmentindex = (*mesh)[si].si;
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mesh->SetNBCNames(maxsegmentindex);
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for ( int sindex = 0; sindex < maxsegmentindex; sindex++ )
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mesh->SetBCName ( sindex, geometry.GetBCName( sindex+1 ) );
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for (SegmentIndex si = 0; si < mesh->GetNSeg(); si++)
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(*mesh)[si].SetBCName ( (*mesh).GetBCNamePtr( (*mesh)[si].si-1 ) );
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mesh->CalcLocalH(mp.grading);
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int bnp = mesh->GetNP(); // boundary points
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auto BndPntRange = mesh->Points().Range();
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int hquad = mp.quad;
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for (int domnr = 1; domnr <= maxdomnr; domnr++)
if (geometry.GetDomainTensorMeshing (domnr))
{ // tensor product mesh
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Array<PointIndex, PointIndex::BASE> nextpi(bnp);
Array<int, PointIndex::BASE> si1(bnp), si2(bnp);
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PointIndex firstpi;
nextpi = -1;
si1 = -1;
si2 = -1;
for (SegmentIndex si = 0; si < mesh->GetNSeg(); si++)
{
int p1 = -1, p2 = -2;
if ( (*mesh)[si].domin == domnr)
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{ p1 = (*mesh)[si][0]; p2 = (*mesh)[si][1]; }
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if ( (*mesh)[si].domout == domnr)
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{ p1 = (*mesh)[si][1]; p2 = (*mesh)[si][0]; }
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if (p1 == -1) continue;
nextpi[p1] = p2; // counter-clockwise
int index = (*mesh)[si].si;
if (si1[p1] != index && si2[p1] != index)
{ si2[p1] = si1[p1]; si1[p1] = index; }
if (si1[p2] != index && si2[p2] != index)
{ si2[p2] = si1[p2]; si1[p2] = index; }
}
PointIndex c1(0), c2, c3, c4; // 4 corner points
int nex = 1, ney = 1;
for (PointIndex pi = 1; pi <= si2.Size(); pi++)
if (si2[pi] != -1)
{ c1 = pi; break; }
for (c2 = nextpi[c1]; si2[c2] == -1; c2 = nextpi[c2], nex++);
for (c3 = nextpi[c2]; si2[c3] == -1; c3 = nextpi[c3], ney++);
for (c4 = nextpi[c3]; si2[c4] == -1; c4 = nextpi[c4]);
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Array<PointIndex> pts ( (nex+1) * (ney+1) ); // x ... inner loop
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pts = -1;
for (PointIndex pi = c1, i = 0; pi != c2; pi = nextpi[pi], i++)
pts[i] = pi;
for (PointIndex pi = c2, i = 0; pi != c3; pi = nextpi[pi], i++)
pts[(nex+1)*i+nex] = pi;
for (PointIndex pi = c3, i = 0; pi != c4; pi = nextpi[pi], i++)
pts[(nex+1)*(ney+1)-i-1] = pi;
for (PointIndex pi = c4, i = 0; pi != c1; pi = nextpi[pi], i++)
pts[(nex+1)*(ney-i)] = pi;
for (PointIndex pix = nextpi[c1], ix = 0; pix != c2; pix = nextpi[pix], ix++)
for (PointIndex piy = nextpi[c2], iy = 0; piy != c3; piy = nextpi[piy], iy++)
{
Point<3> p = (*mesh)[pix] + ( (*mesh)[piy] - (*mesh)[c2] );
pts[(nex+1)*(iy+1) + ix+1] = mesh -> AddPoint (p , 1, FIXEDPOINT);
}
for (int i = 0; i < ney; i++)
for (int j = 0; j < nex; j++)
{
Element2d el(QUAD);
el[0] = pts[i*(nex+1)+j];
el[1] = pts[i*(nex+1)+j+1];
el[2] = pts[(i+1)*(nex+1)+j+1];
el[3] = pts[(i+1)*(nex+1)+j];
el.SetIndex (domnr);
mesh -> AddSurfaceElement (el);
}
}
for (int domnr = 1; domnr <= maxdomnr; domnr++)
{
if (geometry.GetDomainTensorMeshing (domnr)) continue;
double h = mp.maxh;
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if ( geometry.GetDomainMaxh ( domnr ) > 0 )
h = geometry.GetDomainMaxh(domnr);
PrintMessage (3, "Meshing domain ", domnr, " / ", maxdomnr);
int oldnf = mesh->GetNSE();
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mp.quad = hquad || geometry.GetDomainQuadMeshing (domnr);
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Meshing2 meshing (mp, Box<3> (pmin, pmax));
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Array<int, PointIndex::BASE> compress(bnp);
compress = -1;
int cnt = 0;
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for (PointIndex pi : BndPntRange)
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if ( (*mesh)[pi].GetLayer() == geometry.GetDomainLayer(domnr))
{
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meshing.AddPoint ((*mesh)[pi], pi);
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cnt++;
compress[pi] = cnt;
}
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PointGeomInfo gi;
gi.trignum = 1;
for (SegmentIndex si = 0; si < mesh->GetNSeg(); si++)
{
if ( (*mesh)[si].domin == domnr)
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{
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meshing.AddBoundaryElement (compress[(*mesh)[si][0]],
compress[(*mesh)[si][1]], gi, gi);
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}
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if ( (*mesh)[si].domout == domnr)
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{
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meshing.AddBoundaryElement (compress[(*mesh)[si][1]],
compress[(*mesh)[si][0]], gi, gi);
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}
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}
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// not complete, use at own risk ...
// meshing.Delaunay(*mesh, domnr, mp);
mp.checkoverlap = 0;
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auto res = meshing.GenerateMesh (*mesh, mp, h, domnr);
if (res != 0)
throw NgException("meshing failed");
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for (SurfaceElementIndex sei = oldnf; sei < mesh->GetNSE(); sei++)
(*mesh)[sei].SetIndex (domnr);
// astrid
char * material;
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geometry.GetMaterial (domnr, material);
if (material)
mesh->SetMaterial (domnr, material);
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}
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mp.quad = hquad;
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int hsteps = mp.optsteps2d;
mp.optimize2d = "smcm";
mp.optsteps2d = hsteps/2;
Optimize2d (*mesh, mp);
mp.optimize2d = "Smcm";
mp.optsteps2d = (hsteps+1)/2;
Optimize2d (*mesh, mp);
mp.optsteps2d = hsteps;
mesh->Compress();
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mesh->OrderElements();
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mesh -> SetNextMajorTimeStamp();
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mp.Render();
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}
}