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local refinement for 2d curves

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This commit is contained in:
Joachim Schoeberl 2012-08-27 16:07:27 +00:00
parent 33828d132f
commit 4dcae7ec4d
4 changed files with 159 additions and 33 deletions
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20
libsrc/geom2d/genmesh2d.cpp
View File

@ -9,12 +9,14 @@ namespace netgen
void CalcPartition (double l, double h, double h1, double h2,
double hcurve, double elto0, Array<double> & points);
void CalcPartition (const SplineSegExt & spline, double l,
MeshingParameters & mp, double h, double h1, double h2,
double hcurve, double elto0,
Array<double> & points);
// partitionizes spline curve
void Partition (const SplineSegExt & spline,
double h, double elto0,
MeshingParameters & mp, double h, double elto0,
Mesh & mesh, Point3dTree & searchtree, int segnr)
{
enum { D = 2 };
@ -31,7 +33,7 @@ namespace netgen
double h2 = min (spline.EndPI().hmax, h/spline.EndPI().refatpoint);
double hcurve = min (spline.hmax, h/spline.reffak);
CalcPartition (l, h, h1, h2, hcurve, elto0, curvepoints);
CalcPartition (spline, l, mp, h, h1, h2, hcurve, elto0, curvepoints);
// cout << "curvepoints = " << curvepoints << endl;
dt = 1.0 / n;
@ -130,7 +132,7 @@ namespace netgen
void SplineGeometry2d :: PartitionBoundary (double h, Mesh & mesh2d)
void SplineGeometry2d :: PartitionBoundary (MeshingParameters & mp, double h, Mesh & mesh2d)
{
enum { D = 2 };
Box<D> bbox;
@ -166,13 +168,13 @@ namespace netgen
maximum = min2 ( maximum, h);
if ( minimum > 0 )
// GetSpline(i).Partition(minimum, elto0, mesh2d, searchtree, i+1);
Partition(GetSpline(i), minimum, elto0, mesh2d, searchtree, i+1);
Partition(GetSpline(i), mp, minimum, elto0, mesh2d, searchtree, i+1);
else if ( maximum > 0 )
// GetSpline(i).Partition(maximum, elto0, mesh2d, searchtree, i+1);
Partition(GetSpline(i), maximum, elto0, mesh2d, searchtree, i+1);
Partition(GetSpline(i), mp, maximum, elto0, mesh2d, searchtree, i+1);
else
// GetSpline(i).Partition(h, elto0, mesh2d, searchtree, i+1);
Partition(GetSpline(i), h, elto0, mesh2d, searchtree, i+1);
Partition(GetSpline(i), mp, h, elto0, mesh2d, searchtree, i+1);
}
else
{
@ -296,7 +298,7 @@ namespace netgen
mesh = new Mesh;
mesh->SetDimension (2);
geometry.PartitionBoundary (h, *mesh);
geometry.PartitionBoundary (mp, h, *mesh);
// marks mesh points for hp-refinement

145
libsrc/geom2d/geometry2d.cpp
View File

@ -827,47 +827,52 @@ namespace netgen
void CalcPartition (double l, double h, double h1, double h2,
/*
void CalcPartition (const SplineSegExt & spline,
double l, double h, double h1, double h2,
double hcurve, double elto0, Array<double> & points)
{
// cout << "calcpart, h = " << h << ", h1 = " << h1 << ", h2 = " << h2 << ", hcurve = " << hcurve << endl;
int i, j, n, nel;
double sum, t, dt, fun, fperel, oldf, f;
double fperel, oldf, f;
n = 1000;
int n = 1000;
points.SetSize (0);
sum = 0;
dt = l / n;
t = 0.5 * dt;
for (i = 1; i <= n; i++)
double dt = l / n;
double sum = 0;
for (int i = 1; i <= n; i++)
{
fun = min3 (hcurve, t/elto0 + h1, (l-t)/elto0 + h2);
double t = (i-0.5)*dt;
double fun = min3 (hcurve, t/elto0 + h1, (l-t)/elto0 + h2);
double curv = spline.CalcCurvature (t/l);
cout << "curv = " << curv << endl;
if (curv < 1e-10) curv = 1e-10;
fun = min2 (fun, 0.1/curv);
sum += dt / fun;
t += dt;
}
nel = int (sum+1);
int nel = int (sum+1);
fperel = sum / nel;
points.Append (0);
i = 1;
int i = 1;
oldf = 0;
t = 0.5 * dt;
for (j = 1; j <= n && i < nel; j++)
// t = 0.5 * dt;
for (int j = 1; j <= n && i < nel; j++)
{
fun = min3 (hcurve, t/elto0 + h1, (l-t)/elto0 + h2);
double t = (j-0.5)*dt;
double fun = min3 (hcurve, t/elto0 + h1, (l-t)/elto0 + h2);
double curv = spline.CalcCurvature (t/l);
if (curv < 1e-10) curv = 1e-10;
fun = min2 (fun, 0.1/curv);
f = oldf + dt / fun;
while (f > i * fperel && i < nel)
while (i * fperel < f && i < nel)
{
points.Append ( (l/n) * (j-1 + (i * fperel - oldf) / (f - oldf)) );
points.Append ( dt * (j-1) + (i * fperel - oldf) * fun);
i++;
}
oldf = f;
@ -875,6 +880,104 @@ namespace netgen
}
points.Append (l);
}
*/
void CalcPartition (const SplineSegExt & spline, double l,
MeshingParameters & mp, 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);
hi = h;
for (int i = 0; i < n; i++)
{
xi[i] = spline.GetPoint ( (i+0.5) / n );
double hc = 1.0/mp.curvaturesafety / (1e-20+spline.CalcCurvature ( (i+0.5) / n ));
// *testout << "t = " << (i+0.5)/n << ", xi = " << xi[i] << ", hi = " << hc << endl;
hi[i] = min2(hi[i], hc);
}
hi[0] = min (hi[0], h1);
hi[n-1] = min (hi[n-1], h2);
if ( (spline.GetPoint(0)-spline.GetPoint(1)).Length() < 1e-12 )
hi[0] = hi[n-1] = min2 (hi[0], hi[n-1]);
// limit slope
double gradh = 1/elto0;
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 dt = l / n;
double sum = 0;
for (int i = 1; i <= n; i++)
{
double t = (i-0.5)*dt;
/*
double fun = min3 (hcurve, t/elto0 + h1, (l-t)/elto0 + h2);
double curv = spline.CalcCurvature (t/l);
cout << "curv = " << curv << endl;
if (curv < 1e-10) curv = 1e-10;
fun = min2 (fun, 0.1/curv);
*/
double fun = hi[i-1];
sum += dt / fun;
}
int nel = int (sum+1);
fperel = sum / nel;
points.Append (0);
int i = 1;
oldf = 0;
// t = 0.5 * dt;
for (int j = 1; j <= n && i < nel; j++)
{
double t = (j-0.5)*dt;
double fun = hi[j-1];
/*
double fun = min3 (hcurve, t/elto0 + h1, (l-t)/elto0 + h2);
double curv = spline.CalcCurvature (t/l);
if (curv < 1e-10) curv = 1e-10;
fun = min2 (fun, 0.1/curv);
*/
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 (l);
}

11
libsrc/geom2d/geometry2d.hpp
View File

@ -97,6 +97,15 @@ namespace netgen
return seg.GetType();
}
virtual double CalcCurvature (double t) const
{
Point<2> point;
Vec<2> first, second;
GetDerivatives (t, point, first, second);
double curv = fabs(first(0)*second(1)-first(1)*second(0)) / pow(first.Length(), 3);
return curv;
}
};
@ -141,7 +150,7 @@ namespace netgen
DLL_HEADER virtual int GenerateMesh (Mesh*& mesh, MeshingParameters & mparam,
int perfstepsstart, int perfstepsend);
void PartitionBoundary (double h, Mesh & mesh2d);
void PartitionBoundary (MeshingParameters & mp, double h, Mesh & mesh2d);
void CopyEdgeMesh (int from, int to, Mesh & mesh2d, Point3dTree & searchtree);

16
libsrc/gprim/spline.hpp
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@ -54,11 +54,23 @@ namespace netgen
virtual Point<D> GetPoint (double t) const = 0;
/// returns a (not necessarily unit-length) tangent vector for 0 <= t <= 1
virtual Vec<D> GetTangent (const double t) const
{ cerr << "GetTangent not implemented for spline base-class" << endl; Vec<D> dummy; return dummy;}
{
cerr << "GetTangent not implemented for spline base-class" << endl;
Vec<D> dummy; return dummy;
}
virtual void GetDerivatives (const double t,
Point<D> & point,
Vec<D> & first,
Vec<D> & second) const {;}
Vec<D> & second) const
{
double eps = 1e-6;
point = GetPoint (t);
Point<D> pl = GetPoint (t-eps);
Point<D> pr = GetPoint (t+eps);
first = 1.0/(2*eps) * (pr-pl);
second = 1.0/sqr(eps) * ( (pr-point)+(pl-point));
}
/// returns initial point on curve