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/* *************************************************************************/
/* File: surfacegeom.cpp */
/* Author: Michael Neunteufel */
/* Date: Jun. 2020 */
/* *************************************************************************/
#include <meshing.hpp>
namespace netgen
{
SurfaceGeometry :: SurfaceGeometry()
{
//identity
func = [](Point<2> p) { return Vec<3>(p[0],p[1],0.0); };
}
SurfaceGeometry :: SurfaceGeometry(function<Vec<3>(Point<2>)> _func) : func(_func)
{
;
}
SurfaceGeometry :: SurfaceGeometry(const SurfaceGeometry& geom) : func(geom.func), eps(geom.eps)
{
;
}
void SurfaceGeometry :: CalcHesse(double u, double v, Vec<3>& f_uu, Vec<3>& f_vv, Vec<3>& f_uv) const
{
Point<2> p = Point<2>(u,v);
double pr = p[0]+eps;
double pl = p[0]-eps;
double prr = p[0]+2*eps;
double pll = p[0]-2*eps;
auto dr = GetTangentVectors( pr, v );
auto dl = GetTangentVectors( pl, v );
auto drr = GetTangentVectors( prr, v );
auto dll = GetTangentVectors( pll, v );
f_uu = (1.0/(12.0*eps)) * (8.0*dr[0]-8.0*dl[0]-drr[0]+dll[0]);
f_uv = (1.0/(12.0*eps)) * (8.0*dr[1]-8.0*dl[1]-drr[1]+dll[1]);
pr = p[1]+eps;
pl = p[1]-eps;
prr = p[1]+2*eps;
pll = p[1]-2*eps;
GetTangentVectors(u, pr, dr);
GetTangentVectors(u, pl, dl);
GetTangentVectors(u, prr, drr);
GetTangentVectors(u, pll, dll);
f_vv = (1.0/(12.0*eps)) * (8.0*dr[1]-8.0*dl[1]-drr[1]+dll[1]);
}
Array<Vec<3>> SurfaceGeometry :: GetTangentVectors(double u, double v) const
{
Array<Vec<3>> tang(2);
Point<2> pru = Point<2>(u+eps,v);
Point<2> plu = Point<2>(u-eps,v);
Point<2> prru = Point<2>(u+2*eps,v);
Point<2> pllu = Point<2>(u-2*eps,v);
Point<2> prv = Point<2>(u,v+eps);
Point<2> plv = Point<2>(u,v-eps);
Point<2> prrv = Point<2>(u,v+2*eps);
Point<2> pllv = Point<2>(u,v-2*eps);
tang[0] = 1/(12.0*eps)*( 8.0*func(pru) - 8.0*func(plu) - func(prru) + func(pllu) );
tang[1] = 1/(12.0*eps)*( 8.0*func(prv) - 8.0*func(plv) - func(prrv) + func(pllv) );
return tang;
}
void SurfaceGeometry :: GetTangentVectors(double u, double v, Array<Vec<3>>& tang) const
{
Point<2> pru = Point<2>(u+eps,v);
Point<2> plu = Point<2>(u-eps,v);
Point<2> prru = Point<2>(u+2*eps,v);
Point<2> pllu = Point<2>(u-2*eps,v);
Point<2> prv = Point<2>(u,v+eps);
Point<2> plv = Point<2>(u,v-eps);
Point<2> prrv = Point<2>(u,v+2*eps);
Point<2> pllv = Point<2>(u,v-2*eps);
tang[0] = 1/(12.0*eps)*( 8.0*func(pru) - 8.0*func(plu) - func(prru) + func(pllu) );
tang[1] = 1/(12.0*eps)*( 8.0*func(prv) - 8.0*func(plv) - func(prrv) + func(pllv) );
}
Vec<3> SurfaceGeometry :: GetNormal(int surfind, const Point<3> & p, const PointGeomInfo* gi) const
{
Array<Vec<3>> tang = GetTangentVectors(gi->u, gi->v);
auto normal = Cross(tang[0], tang[1]);
normal.Normalize();
return normal;
}
PointGeomInfo SurfaceGeometry :: ProjectPoint(int surfind, Point<3> & p) const
{
throw Exception("In SurfaceGeometry::ProjectPoint");
}
void SurfaceGeometry :: ProjectPointEdge (int surfind, int surfind2, Point<3> & p,
EdgePointGeomInfo* gi) const
{
if (gi == nullptr)
throw Exception("In SurfaceGeometry::ProjectPointEdge: gi is nullptr");
throw Exception("In SurfaceGeometry::ProjectPointEdge: not implemented");
}
bool SurfaceGeometry :: ProjectPointGI (int surfind, Point<3> & p, PointGeomInfo & gi) const
{
Array<Vec<3>> tangs(2);
Vec<3> diff, f_uu, f_vv, f_uv;
Vec<2> r, dx;
double norm_r, energy=0.0, new_energy=0.0, alpha=2.0,u=0.0,v=0.0,maxerr=1e-16;
Mat<2,2> mat, inv;
int num=0, maxit=25;
double damping=0.5;
//Solve minimization problem
// argmin_(u,v) 0.5*\| f(u,v)-p\|^2
//via Neton's method:
// F(u,v) = ( (f(u,v)-p)*f_u(u,v), (f(u,v)-p)*f_v(u,v))^T = (0,0)^T
//Stiffness matrix
// F'(u,v) = ( f_u*f_u + (f-p)*f_uu, f_v*f_u + (f-p)*f_uv, f_v*f_u + (f-p)*f_uv, f_v*f_v + (f-p)*f_vv )
do
{
num++;
GetTangentVectors(gi.u, gi.v,tangs);
diff = func(Point<2>(gi.u, gi.v)) - Vec<3>(p);
energy = diff.Length2();
r = Vec<2>( diff*tangs[0], diff*tangs[1] );
norm_r = r.Length2();
CalcHesse(gi.u, gi.v, f_uu, f_vv, f_uv);
mat(0,0) = tangs[0]*tangs[0] + diff*f_uu;
mat(1,0) = mat(0,1) = tangs[0]*tangs[1]+diff*f_uv;
mat(1,1) = tangs[1]*tangs[1]+diff*f_vv;
CalcInverse(mat,inv);
dx = inv*r;
//Linesearch
alpha = 2.0;
do
{
alpha /= 2.0;
u = gi.u - min(1.0,alpha*damping*num)*dx[0];
v = gi.v - min(1.0,alpha*damping*num)*dx[1];
diff = func(Point<2>(u, v)) - Vec<3>(p);
new_energy = diff.Length2();
}
while (alpha > 1e-10 && new_energy > energy+1e-14);
if (alpha <= 1e-10)
throw Exception("In SurfaceGeometry::ProjectPointGI: Linesearch min alpha reached!");
gi.u = u;
gi.v = v;
}
while ( norm_r > maxerr && num < maxit);
//Stay in reference domain [0,1]^2
if (gi.u < 0 || gi.u > 1 || gi.v < 0 || gi.v > 1)
{
cout << "Warning: Projected point outside [0,1]^2: u=" << gi.u << ",v=" << gi.v <<". Setting back." << endl;
gi.u = min(max(gi.u,0.0),1.0);
gi.v = min(max(gi.v,0.0),1.0);
}
p = Point<3>(func(Point<2>(gi.u,gi.v)));
if (num == maxit)
{
//cout << "In SurfaceGeometry::ProjectPointGI: Newton did not converge" << endl;
throw Exception("In SurfaceGeometry::ProjectPointGI: Newton did not converge");
}
return true;
}
bool SurfaceGeometry :: CalcPointGeomInfo(int surfind, PointGeomInfo& gi, const Point<3> & p3) const
{
throw Exception("In SurfaceGeometry::CalcPointGeomInfo: not implemented");
return false;
}
void SurfaceGeometry :: PointBetweenEdge(const Point<3> & p1, const Point<3> & p2, double secpoint, int surfi1, int surfi2, const EdgePointGeomInfo & ap1, const EdgePointGeomInfo & ap2, Point<3> & newp, EdgePointGeomInfo & newgi) const
{
newgi.u = ap1.u+secpoint*(ap2.u-ap1.u);
newgi.v = ap1.v+secpoint*(ap2.v-ap1.v);
newgi.edgenr = ap1.edgenr;
newgi.body = -1;
newgi.dist = -1.0;
newp = Point<3>(func(Point<2>(newgi.u, newgi.v)));
}
void CheckForBBBPnt(const Array<Point<3>>& bbbpts, const Point<3>& pnt, Array<bool>& found, Array<PointIndex>& indbbbpts, const Array<PointIndex>& pids)
{
for (int k = 0; k < bbbpts.Size(); k++)
{
auto diff = pnt - bbbpts[k];
if(diff.Length2() < 1e-14)
{
found[k] = true;
indbbbpts[k] = pids[pids.Size()-1];
}
}
}
void CheckForSingularity(const Array<Point<3>>& hppoints, const Point<3>& pnt, const Array<float>& hpptsfac, shared_ptr<Mesh> & mesh, const Array<PointIndex>& pids)
{
for (int k = 0; k < hppoints.Size(); k++)
{
auto diff = pnt - hppoints[k];
if(diff.Length2() < 1e-14)
{
(*mesh)[pids[pids.Size()-1]].Singularity(hpptsfac[k]);
}
}
}
void SurfaceGeometry :: PointBetween(const Point<3> & p1, const Point<3> & p2, double secpoint,
int surfi,
const PointGeomInfo & gi1,
const PointGeomInfo & gi2,
Point<3> & newp, PointGeomInfo & newgi) const
{
newgi.u = gi1.u+secpoint*(gi2.u-gi1.u);
newgi.v = gi1.v+secpoint*(gi2.v-gi1.v);
newgi.trignum = -1;
newp = Point<3>(func(Point<2>(newgi.u, newgi.v)));
//newp = p1+secpoint*(p2-p1);
//ProjectPointGI(surfi, newp, newgi);
}
int SurfaceGeometry :: GenerateStructuredMesh(shared_ptr<Mesh> & mesh, bool quads, int nx, int ny, bool flip_triangles, const Array<Point<3>>& bbbpts, const Array<string>& bbbnames, const Array<Point<3>>& hppoints, const Array<float>& hpptsfac, const Array<string>& hpbnd, const Array<float>& hpbndfac, Array<double> layer_thickness[4], bool layer_quad)
{
mesh->SetDimension(3);
Array<bool> found(bbbpts.Size());
found = false;
Array<PointIndex> indbbbpts(bbbpts.Size());
int numx = nx;
int numy = ny;
size_t total_layer_el[4] = {layer_thickness[0].Size(), layer_thickness[1].Size(), layer_thickness[2].Size(), layer_thickness[3].Size()};
double interior_x = 1.0;
double interior_y = 1.0;
for(double scale : layer_thickness[0])
interior_x -= scale;
for(double scale : layer_thickness[2])
interior_x -= scale;
for(double scale : layer_thickness[1])
interior_y -= scale;
for(double scale : layer_thickness[3])
interior_y -= scale;
auto AddPoint = [&] (double offsetx, double offsety, Array<PointIndex> & pids, Array<PointGeomInfo> & pgis)
{
PointGeomInfo pgi;
pgi.trignum = -1;
pgi.u = offsetx;
pgi.v = offsety;
Point<3> pnt = Point<3>(func(Point<2>(pgi.u,pgi.v)));
pids.Append(mesh->AddPoint(pnt));
pgis.Append(pgi);
CheckForBBBPnt(bbbpts, pnt, found, indbbbpts, pids);
CheckForSingularity(hppoints, pnt, hpptsfac, mesh, pids);
};
auto InternalLoop = [&] (double offsety, Array<PointIndex> & pids, Array<PointGeomInfo> & pgis)
{
int j = 0;
double offsetx = 0.0;
for(int l=0; l < layer_thickness[0].Size(); l++,j++)
{
AddPoint(offsetx+layer_thickness[0][l]*double(j-l), offsety, pids, pgis);
offsetx += layer_thickness[0][l];
}
for(;j <= nx-total_layer_el[2]; j++)
AddPoint(offsetx + interior_x*double(j-total_layer_el[0])/(nx-total_layer_el[0]-total_layer_el[2]), offsety, pids, pgis);
offsetx += interior_x;
int startj = j;
for(int l=0; l < layer_thickness[2].Size(); l++, j++)
{
AddPoint(offsetx+layer_thickness[2][layer_thickness[2].Size()-1-l]*double(j-startj-l+1), offsety, pids, pgis);
offsetx += layer_thickness[2][layer_thickness[2].Size()-1-l];
}
};
Array<PointIndex> pids;
Array<PointGeomInfo> pgis;
int i = 0;
double offsety = 0.0;
for(int k=0; k < layer_thickness[1].Size(); k++,i++)
{
InternalLoop(offsety, pids, pgis);
offsety += layer_thickness[1][k];
}
for(; i <= ny-total_layer_el[3]; i++)
{
InternalLoop(offsety, pids, pgis);
offsety += interior_y/(ny-total_layer_el[1]-total_layer_el[3]);
}
offsety -= interior_y/(ny-total_layer_el[1]-total_layer_el[3]);
for(int k=0; k < layer_thickness[3].Size(); k++,i++)
{
offsety += layer_thickness[3][layer_thickness[3].Size()-1-k];
InternalLoop(offsety, pids, pgis);
}
for (bool f : found)
if (!f)
throw Exception("In SurfaceGeometry :: GenerateMesh: bbbpts not resolved in mesh.");
FaceDescriptor fd;
fd.SetSurfNr(1);
fd.SetDomainIn(1);
fd.SetDomainOut(0);
fd.SetBCProperty(1);
mesh->AddFaceDescriptor(fd);
for(int i=0; i < numy; i++)
{
for(int j=0; j < numx; j++)
{
int base = i * (numx+1) + j;
if (quads || (layer_quad && i < total_layer_el[1]) || (layer_quad && i > numy-1-total_layer_el[3]) || (layer_quad && j < total_layer_el[0]) || (layer_quad && j > numx-1-total_layer_el[2]) )
{
int pnum[4] = {base,base+1,base+numx+2,base+numx+1};
Element2d el = Element2d(QUAD);
for (int i = 0; i < 4; i++)
{
el[i] = pids[pnum[i]];
el.GeomInfoPi(i+1) = pgis[pnum[i]];
}
el.SetIndex(1);
mesh->AddSurfaceElement(el);
}
else
{
Array<int> pnum1(3);
Array<int> pnum2(3);
if (flip_triangles)
{
pnum1[0] = base;
pnum1[1] = base+1;
pnum1[2] = base+numx+2;
pnum2[0] = base;
pnum2[1] = base+numx+2;
pnum2[2] = base+numx+1;
}
else
{
pnum1[0] = base;
pnum1[1] = base+1;
pnum1[2] = base+numx+1;
pnum2[0] = base+1;
pnum2[1] = base+numx+2;
pnum2[2] = base+numx+1;
}
Element2d el = Element2d(TRIG);
for (int i = 0; i < 3; i++)
{
el[i] = pids[pnum1[i]];
el.GeomInfoPi(i+1) = pgis[pnum1[i]];
}
el.SetIndex(1);
mesh->AddSurfaceElement(el);
for (int i = 0; i < 3; i++)
{
el[i] = pids[pnum2[i]];
el.GeomInfoPi(i+1) = pgis[pnum2[i]];
}
mesh->AddSurfaceElement(el);
}
}
}
Segment seg;
seg.si = 1;
seg.edgenr = 1;
seg.epgeominfo[0].edgenr = 0;
seg.epgeominfo[1].edgenr = 0;
//for hp refinement
seg.singedge_left = 0;
seg.singedge_right = 0;
for (size_t i=0; i < hpbnd.Size(); i++)
{
if (hpbnd[i] == "bottom")
{
seg.singedge_left = hpbndfac[i];
seg.singedge_right = hpbndfac[i];
}
}
// needed for codim2 in 3d
seg.edgenr = 1;
for(int i=0; i < numx; i++)
{
seg[0] = pids[i];
seg[1] = pids[i+1];
seg.geominfo[0] = pgis[i];
seg.geominfo[1] = pgis[i+1];
seg.epgeominfo[0].u = pgis[i].u;
seg.epgeominfo[0].v = pgis[i].v;
seg.epgeominfo[0].edgenr = seg.edgenr;
seg.epgeominfo[1].u = pgis[i+1].u;
seg.epgeominfo[1].v = pgis[i+1].v;
seg.epgeominfo[1].edgenr = seg.edgenr;
mesh->AddSegment(seg);
}
seg.si = 2;
seg.edgenr = 2;
seg.singedge_left = 0;
seg.singedge_right = 0;
for (size_t i=0; i < hpbnd.Size(); i++)
{
if (hpbnd[i] == "right")
{
seg.singedge_left = hpbndfac[i];
seg.singedge_right = hpbndfac[i];
}
}
for(int i=0; i<numy; i++)
{
seg[0] = pids[i*(numx+1)+numx];
seg[1] = pids[(i+1)*(numx+1)+numx];
seg.geominfo[0] = pgis[i*(numx+1)+numx];
seg.geominfo[1] = pgis[(i+1)*(numx+1)+numx];
seg.epgeominfo[0].u = pgis[i*(numx+1)+numx].u;
seg.epgeominfo[0].v = pgis[i*(numx+1)+numx].v;
seg.epgeominfo[0].edgenr = seg.edgenr;
seg.epgeominfo[1].u = pgis[(i+1)*(numx+1)+numx].u;
seg.epgeominfo[1].v = pgis[(i+1)*(numx+1)+numx].v;
seg.epgeominfo[1].edgenr = seg.edgenr;
mesh->AddSegment(seg);
}
seg.si = 3;
seg.edgenr = 3;
seg.singedge_left = 0;
seg.singedge_right = 0;
for (size_t i=0; i < hpbnd.Size(); i++)
{
if (hpbnd[i] == "top")
{
seg.singedge_left = hpbndfac[i];
seg.singedge_right = hpbndfac[i];
}
}
for(int i=0; i<numx; i++)
{
seg[0] = pids[numy*(numx+1)+i+1];
seg[1] = pids[numy*(numx+1)+i];
seg.geominfo[0] = pgis[numy*(numx+1)+i+1];
seg.geominfo[1] = pgis[numy*(numx+1)+i];
seg.epgeominfo[0].u = pgis[numy*(numx+1)+i+1].u;
seg.epgeominfo[0].v = pgis[numy*(numx+1)+i+1].v;
seg.epgeominfo[0].edgenr = seg.edgenr;
seg.epgeominfo[1].u = pgis[numy*(numx+1)+i].u;
seg.epgeominfo[1].v = pgis[numy*(numx+1)+i].v;
seg.epgeominfo[1].edgenr = seg.edgenr;
mesh->AddSegment(seg);
}
seg.si = 4;
seg.edgenr = 4;
seg.singedge_left = 0;
seg.singedge_right = 0;
for (size_t i=0; i < hpbnd.Size(); i++)
{
if (hpbnd[i] == "left")
{
seg.singedge_left = hpbndfac[i];
seg.singedge_right = hpbndfac[i];
}
}
for(int i=0; i<numy; i++)
{
seg[0] = pids[(i+1)*(numx+1)];
seg[1] = pids[i*(numx+1)];
seg.geominfo[0] = pgis[(i+1)*(numx+1)];
seg.geominfo[1] = pgis[i*(numx+1)];
seg.epgeominfo[0].u = pgis[(i+1)*(numx+1)].u;
seg.epgeominfo[0].v = pgis[(i+1)*(numx+1)].v;
seg.epgeominfo[0].edgenr = seg.edgenr;
seg.epgeominfo[1].u = pgis[i*(numx+1)].u;
seg.epgeominfo[1].v = pgis[i*(numx+1)].v;
seg.epgeominfo[1].edgenr = seg.edgenr;
mesh->AddSegment(seg);
}
mesh->SetCD2Name(1, "bottom");
mesh->SetCD2Name(2, "right");
mesh->SetCD2Name(3, "top");
mesh->SetCD2Name(4, "left");
for (int i = 0; i < bbbpts.Size(); i++)
{
Element0d el;
el.pnum = indbbbpts[i];
el.index = i+1;
mesh->pointelements.Append(el);
mesh->SetCD3Name(i+1, bbbnames[i]);
}
mesh->Compress();
mesh->UpdateTopology();
return 0;
}
};
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