#include #include #include #include "global.hpp" #include "debugging.hpp" #include "boundarylayer.hpp" #include "meshfunc.hpp" namespace netgen { // checks if a segment is intersecting a plane, spanned by three points, lam will be set s.t. p_intersect = seg[0] + lam * (seg[1]-seg[0]) bool isIntersectingPlane ( const array, 2> & seg, const array, 3> & trig, double & lam) { auto n = Cross(trig[1]-trig[0], trig[2]-trig[0]); auto v0n = (seg[0]-trig[0])*n; auto v1n = (seg[1]-trig[0])*n; if(v0n * v1n >= 0) return false; lam = -v0n/(v1n-v0n); lam *= 0.9; if(lam < -1e-8 || lam>1+1e-8) return false; return true; } bool isIntersectingPlane ( const array, 2> & seg, const ArrayMem, 4> & face, double & lam) { lam = 1.0; bool intersect0 = isIntersectingPlane( seg, array, 3>{face[0], face[1], face[2]}, lam ); if(face.Size()==3) return intersect0; double lam1 = 1.0; bool intersect1 = isIntersectingPlane( seg, array, 3>{face[2], face[3], face[0]}, lam1 ); lam = min(lam, lam1); return intersect0 || intersect1; } bool isIntersectingTrig ( const array, 2> & seg, const array, 3> & trig, double & lam) { if(!isIntersectingPlane(seg, trig, lam)) return false; //buffer enlargement of triangle auto pt0 = trig[0]; auto pt1 = trig[1]; auto pt2 = trig[2]; Point<3> center = { (pt0[0] + pt1[0] + pt2[0]) / 3.0, (pt0[1] + pt1[1] + pt2[1]) / 3.0, (pt0[2] + pt1[2] + pt2[2]) / 3.0 }; array, 3> larger_trig = { center + (pt0 - center) * 1.1, center + (pt1 - center) * 1.1, center + (pt2 - center) * 1.1, }; auto p = seg[0] + lam/0.9*(seg[1]-seg[0]); auto n_trig = Cross(trig[1]-trig[0], trig[2]-trig[0]).Normalize(); for(auto i : Range(3)) { // check if p0 and p are on same side of segment p1-p2 auto p0 = larger_trig[i]; auto p1 = larger_trig[(i+1)%3]; auto p2 = larger_trig[(i+2)%3]; // auto n = Cross(p2-p1, n_trig); auto v0 = (p2-p1).Normalize(); auto v1 = (p0-p1).Normalize(); auto inside_dir = (v1 - (v1*v0) * v0).Normalize(); auto v2 = (p-p1).Normalize(); if(inside_dir * v1 < 0) inside_dir = -inside_dir; if( (inside_dir*v2) < 0 ) return false; } return true; }; bool isIntersectingFace( const array, 2> & seg, const ArrayMem, 4> & face, double & lam ) { lam = 1.0; double lam0 = 1.0; bool intersect0 = isIntersectingTrig( seg, {face[0], face[1], face[2]}, lam0 ); if(intersect0) lam = min(lam, lam0); if(face.Size()==3) return intersect0; double lam1 = 1.0; bool intersect1 = isIntersectingTrig( seg, {face[2], face[3], face[0]}, lam1 ); if(intersect1) lam = min(lam, lam1); return intersect0 || intersect1; } array, 2> BoundaryLayerTool :: GetMappedSeg( PointIndex pi ) { return { mesh[pi], mesh[pi] + height*limits[pi]*growthvectors[pi] * 1.5 }; } ArrayMem, 4> BoundaryLayerTool :: GetFace( SurfaceElementIndex sei ) { const auto & sel = mesh[sei]; ArrayMem, 4> points(sel.GetNP()); for(auto i : Range(sel.GetNP())) points[i] = mesh[sel[i]]; return points; } ArrayMem, 4> BoundaryLayerTool :: GetMappedFace( SurfaceElementIndex sei ) { const auto & sel = mesh[sei]; ArrayMem, 4> points(sel.GetNP()); for(auto i : Range(sel.GetNP())) points[i] = mesh[sel[i]] + height * limits[sel[i]]*growthvectors[sel[i]]; return points; } ArrayMem, 4> BoundaryLayerTool :: GetMappedFace( SurfaceElementIndex sei, int face ) { if(face == -1) return GetFace(sei); if(face == -2) return GetMappedFace(sei); const auto & sel = mesh[sei]; auto np = sel.GetNP(); auto pi0 = sel[face % np]; auto pi1 = sel[(face+1) % np]; ArrayMem, 4> points(4); points[0] = points[3] = mesh[pi0]; points[1] = points[2] = mesh[pi1]; points[3] += height * limits[pi0]*growthvectors[pi0]; points[2] += height * limits[pi1]*growthvectors[pi1]; return points; } Vec<3> BoundaryLayerTool :: getEdgeTangent(PointIndex pi, int edgenr) { Vec<3> tangent = 0.0; ArrayMem pts; for(auto segi : topo.GetVertexSegments(pi)) { auto & seg = mesh[segi]; if(seg.edgenr != edgenr+1) continue; PointIndex other = seg[0]+seg[1]-pi; if(!pts.Contains(other)) pts.Append(other); } if(pts.Size() != 2) throw Exception("Something went wrong in getEdgeTangent!"); tangent = mesh[pts[1]] - mesh[pts[0]]; return tangent.Normalize(); } void BoundaryLayerTool :: LimitGrowthVectorLengths() { static Timer tall("BoundaryLayerTool::LimitGrowthVectorLengths"); RegionTimer rtall(tall); limits.SetSize(np); limits = 1.0; // Function to calculate the dot product of two 3D vectors // Is there netgen native function for this? const auto Dot = [](Vec<3> a, Vec<3> b) { return a[0] * b[0] + a[1] * b[1] + a[2] * b[2]; }; auto parallel_limiter = [&](PointIndex pi1, PointIndex pi2, SurfaceElementIndex si) { MeshPoint& a_base = mesh[pi1]; MeshPoint& b_base = mesh[pi2]; MeshPoint a_end = mesh[pi1] + height * limits[pi1] * growthvectors[pi1]; MeshPoint b_end = mesh[pi2] + height * limits[pi2] * growthvectors[pi2]; double ab_base = (b_base - a_base).Length(); Vec<3> a_vec = (a_end - a_base); Vec<3> b_vec = (b_end - b_base); // Calculate parallel projections Vec<3> ab_base_norm = (b_base - a_base).Normalize(); double a_vec_x = Dot(a_vec, ab_base_norm); double b_vec_x = Dot(b_vec, -ab_base_norm); double ratio_parallel = (a_vec_x + b_vec_x) / ab_base; double PARALLEL_RATIO_LIMIT = 0.85; if (ratio_parallel > PARALLEL_RATIO_LIMIT) { // Adjust limits, vectors, and projections if parallel ratio exceeds the limit double corrector = PARALLEL_RATIO_LIMIT / ratio_parallel; limits[pi1] *= corrector; limits[pi2] *= corrector; } }; auto perpendicular_limiter = [&](PointIndex pi1, PointIndex pi2, SurfaceElementIndex si) { // this part is same as in parallel limiter, but note that limits contents are already changed MeshPoint& a_base = mesh[pi1]; MeshPoint& b_base = mesh[pi2]; MeshPoint a_end = mesh[pi1] + height * limits[pi1] * growthvectors[pi1]; MeshPoint b_end = mesh[pi2] + height * limits[pi2] * growthvectors[pi2]; double ab_base = (b_base - a_base).Length(); Vec<3> a_vec = (a_end - a_base); Vec<3> b_vec = (b_end - b_base); // Calculate parallel projections Vec<3> ab_base_norm = (b_base - a_base).Normalize(); double a_vec_x = Dot(a_vec, ab_base_norm); double b_vec_x = Dot(b_vec, -ab_base_norm); // double ratio_parallel = (a_vec_x + b_vec_x) / ab_base; // Calculate surface normal at point si Vec<3> surface_normal = getNormal(mesh[si]); double a_vec_y = abs(Dot(a_vec, surface_normal)); double b_vec_y = abs(Dot(b_vec, surface_normal)); double diff_perpendicular = abs(a_vec_y - b_vec_y); double tan_alpha = diff_perpendicular / (ab_base - a_vec_x - b_vec_x); double TAN_ALPHA_LIMIT = 0.36397; // Approximately 20 degrees in radians if (tan_alpha > TAN_ALPHA_LIMIT) { if (a_vec_y > b_vec_y) { double correction = (TAN_ALPHA_LIMIT / tan_alpha * diff_perpendicular + b_vec_y) / a_vec_y; limits[pi1] *= correction; } else { double correction = (TAN_ALPHA_LIMIT / tan_alpha * diff_perpendicular + a_vec_y) / b_vec_y; limits[pi2] *= correction; } } }; auto neighbour_limiter = [&](PointIndex pi1, PointIndex pi2, SurfaceElementIndex si) { parallel_limiter(pi1, pi2, si); perpendicular_limiter(pi1, pi2, si); }; auto modifiedsmooth = [&](size_t nsteps) { for ([[maybe_unused]] auto i : Range(nsteps)) for (SurfaceElementIndex sei : mesh.SurfaceElements().Range()) { // assuming triangle neighbour_limiter(mesh[sei].PNum(1), mesh[sei].PNum(2), sei); neighbour_limiter(mesh[sei].PNum(2), mesh[sei].PNum(3), sei); neighbour_limiter(mesh[sei].PNum(3), mesh[sei].PNum(1), sei); } }; /* auto smooth = [&] (size_t nsteps) { for([[maybe_unused]] auto i : Range(nsteps)) for(const auto & sel : mesh.SurfaceElements()) { double min_limit = 999; for(auto pi : sel.PNums()) min_limit = min(min_limit, limits[pi]); for(auto pi : sel.PNums()) limits[pi] = min(limits[pi], 1.4*min_limit); } }; */ // check for self-intersection within new elements (prisms/hexes) auto self_intersection = [&] () { for(SurfaceElementIndex sei : mesh.SurfaceElements().Range()) { auto facei = mesh[sei].GetIndex(); if(facei < nfd_old && !params.surfid.Contains(facei)) continue; auto sel = mesh[sei]; auto np = sel.GetNP(); // check if a new edge intesects the plane of any opposing face double lam; for(auto i : Range(np)) for(auto fi : Range(np-2)) if(isIntersectingPlane(GetMappedSeg(sel[i]), GetMappedFace(sei, i+fi+1), lam)) if(lam < 1.0) limits[sel[i]] *= lam; } }; // first step: intersect with other surface elements that are boundary of domain the layer is grown into // second (and subsequent) steps: intersect with other boundary layers, allow restriction by 20% in each step auto changed_domains = domains; if(!params.outside) changed_domains.Invert(); bool limit_reached = true; double lam_lower_limit = 1.0; int step = 0; while(limit_reached || step<3) { Array new_limits; new_limits.SetSize(np); new_limits = 1.0; if(step>1) lam_lower_limit *= 0.8; limit_reached = false; // build search tree with all surface elements (bounding box of a surface element also covers the generated boundary layer) Box<3> bbox(Box<3>::EMPTY_BOX); for(auto pi : mesh.Points().Range()) { bbox.Add(mesh[pi]); bbox.Add(mesh[pi]+limits[pi]*height*growthvectors[pi]); } BoxTree<3> tree(bbox); for(auto sei : mesh.SurfaceElements().Range()) { const auto & sel = mesh[sei]; Box<3> box(Box<3>::EMPTY_BOX); const auto& fd = mesh.GetFaceDescriptor(sel.GetIndex()); if(!changed_domains.Test(fd.DomainIn()) && !changed_domains.Test(fd.DomainOut())) continue; for(auto pi : sel.PNums()) box.Add(mesh[pi]); // also add moved points to bounding box if(params.surfid.Contains(sel.GetIndex())) for(auto pi : sel.PNums()) box.Add(mesh[pi]+limits[pi]*height*growthvectors[pi]); tree.Insert(box, sei); } for(auto pi : mesh.Points().Range()) { if(mesh[pi].Type() == INNERPOINT) continue; if(growthvectors[pi].Length2() == 0.0) continue; Box<3> box(Box<3>::EMPTY_BOX); auto seg = GetMappedSeg(pi); box.Add(seg[0]); box.Add(seg[1]); double lam = 1.0; tree.GetFirstIntersecting(box.PMin(), box.PMax(), [&](SurfaceElementIndex sei) { const auto & sel = mesh[sei]; if(sel.PNums().Contains(pi)) return false; auto face = GetMappedFace(sei, -2); double lam_ = 999; bool is_bl_sel = params.surfid.Contains(sel.GetIndex()); if (step == 0) { face = GetMappedFace(sei, -1); if (isIntersectingFace(seg, face, lam_)) { if (is_bl_sel) lam_ *= params.limit_safety; lam = min(lam, lam_); } } if(step==1) { if(isIntersectingFace(seg, face, lam_)) { if(is_bl_sel) // allow only half the distance if the opposing surface element has a boundary layer too lam_ *= params.limit_safety; lam = min(lam, lam_); } } // if the opposing surface element has a boundary layer, we need to additionally intersect with the new faces if(step>1 && is_bl_sel) { for(auto facei : Range(-1, sel.GetNP())) { auto face = GetMappedFace(sei, facei); if(isIntersectingFace(seg, face, lam_)) // && lam_ > other_limit) { lam = min(lam, lam_); } } } return false; }); if(lam<1) { if(lam1) { limit_reached = true; lam = lam_lower_limit; } } new_limits[pi] = min(limits[pi], lam* limits[pi]); } step++; limits = new_limits; if (step > 0) modifiedsmooth(1); } self_intersection(); modifiedsmooth(1); for(auto pi : Range(growthvectors)) growthvectors[pi] *= limits[pi]; } // depending on the geometry type, the mesh contains segments multiple times (once for each face) bool HaveSingleSegments( const Mesh & mesh ) { auto& topo = mesh.GetTopology(); NgArray surf_els; for(auto segi : Range(mesh.LineSegments())) { mesh.GetTopology().GetSegmentSurfaceElements(segi+1, surf_els); if(surf_els.Size()<2) continue; auto seg = mesh[segi]; auto pi0 = min(seg[0], seg[1]); auto pi1 = max(seg[0], seg[1]); auto p0_segs = topo.GetVertexSegments(seg[0]); for(auto segi_other : p0_segs) { if(segi_other == segi) continue; auto seg_other = mesh[segi_other]; auto pi0_other = min(seg_other[0], seg_other[1]); auto pi1_other = max(seg_other[0], seg_other[1]); if( pi0_other == pi0 && pi1_other == pi1 ) return false; } // found segment with multiple adjacent surface elements but no other segments with same points -> have single segments return true; } return true; } // duplicates segments (and sets seg.si accordingly) to have a unified data structure for all geometry types Array BuildSegments( Mesh & mesh ) { Array segments; // auto& topo = mesh.GetTopology(); NgArray surf_els; for(auto segi : Range(mesh.LineSegments())) { auto seg = mesh[segi]; mesh.GetTopology().GetSegmentSurfaceElements(segi+1, surf_els); for(auto seli : surf_els) { const auto & sel = mesh[seli]; seg.si = sel.GetIndex(); auto np = sel.GetNP(); for(auto i : Range(np)) { if(sel[i] == seg[0]) { if(sel[(i+1)%np] != seg[1]) swap(seg[0], seg[1]); break; } } segments.Append(seg); } } return segments; } void MergeAndAddSegments( Mesh & mesh, FlatArray new_segments) { INDEX_2_HASHTABLE already_added( mesh.LineSegments().Size() + 2*new_segments.Size() ); for(auto & seg : mesh.LineSegments()) { INDEX_2 i2 (seg[0], seg[1]); i2.Sort(); if(!already_added.Used(i2)) already_added.Set(i2, true); } for(auto & seg : new_segments) { INDEX_2 i2 (seg[0], seg[1]); i2.Sort(); if(!already_added.Used(i2)) { mesh.AddSegment(seg); already_added.Set(i2, true); } } } void BoundaryLayerTool :: InterpolateSurfaceGrowthVectors() { static Timer tall("InterpolateSurfaceGrowthVectors"); RegionTimer rtall(tall); static Timer tsmooth("InterpolateSurfaceGrowthVectors-Smoothing"); auto np = mesh.GetNP(); BitArray is_point_on_bl_surface(np+1); is_point_on_bl_surface.Clear(); BitArray is_point_on_other_surface(np+1); is_point_on_other_surface.Clear(); Array, PointIndex> normals(np); for(auto pi : Range(growthvectors)) normals[pi] = growthvectors[pi]; ParallelForRange( mesh.SurfaceElements().Range(), [&] ( auto myrange ) { for(SurfaceElementIndex sei : myrange) { auto facei = mesh[sei].GetIndex(); if(facei < nfd_old && !params.surfid.Contains(facei)) { for(auto pi : mesh[sei].PNums()) if(mesh[pi].Type() == SURFACEPOINT) is_point_on_other_surface.SetBitAtomic(pi); } else { for(auto pi : mesh[sei].PNums()) if(mesh[pi].Type() == SURFACEPOINT) is_point_on_bl_surface.SetBitAtomic(pi); } } }); Array points; for(PointIndex pi : mesh.Points().Range()) { if(is_point_on_bl_surface[pi]) { points.Append(pi); growthvectors[pi] = 0.0; } if(is_point_on_other_surface[pi]) { points.Append(pi); } } // smooth tangential part of growth vectors from edges to surface elements RegionTimer rtsmooth(tsmooth); for([[maybe_unused]] auto i : Range(10)) { for(auto pi : points) { auto sels = p2sel[pi]; Vec<3> new_gw = growthvectors[pi]; // int cnt = 1; std::set suround; suround.insert(pi); auto normal = normals[pi]; for(auto sei: sels) { const auto & sel = mesh[sei]; for(auto pi1 : sel.PNums()) if(suround.count(pi1)==0) { suround.insert(pi1); auto gw_other = growthvectors[pi1]; auto normal_other = getNormal(mesh[sei]); auto tangent_part = gw_other - (gw_other*normal_other)*normal_other; if(is_point_on_bl_surface[pi]) new_gw += tangent_part; else new_gw += gw_other; } } growthvectors[pi] = 1.0/suround.size() * new_gw; } } for(auto pi : points) growthvectors[pi] += normals[pi]; } BoundaryLayerTool::BoundaryLayerTool(Mesh & mesh_, const BoundaryLayerParameters & params_) : mesh(mesh_), topo(mesh_.GetTopology()), params(params_) { static Timer timer("BoundaryLayerTool::ctor"); RegionTimer regt(timer); //for(auto & seg : mesh.LineSegments()) //seg.edgenr = seg.epgeominfo[1].edgenr; height = 0.0; for (auto h : params.heights) height += h; max_edge_nr = -1; for(const auto& seg : mesh.LineSegments()) if(seg.edgenr > max_edge_nr) max_edge_nr = seg.edgenr; int ndom = mesh.GetNDomains(); ndom_old = ndom; new_mat_nrs.SetSize(mesh.FaceDescriptors().Size() + 1); new_mat_nrs = -1; for(auto [bcname, matname] : params.new_mat) { mesh.SetMaterial(++ndom, matname); regex pattern(bcname); for(auto i : Range(1, mesh.GetNFD()+1)) { auto& fd = mesh.GetFaceDescriptor(i); if(regex_match(fd.GetBCName(), pattern)) new_mat_nrs[i] = ndom; } } domains = params.domains; if(!params.outside) domains.Invert(); topo.SetBuildVertex2Element(true); mesh.UpdateTopology(); have_single_segments = HaveSingleSegments(mesh); if(have_single_segments) segments = BuildSegments(mesh); else segments = mesh.LineSegments(); np = mesh.GetNP(); ne = mesh.GetNE(); nse = mesh.GetNSE(); nseg = segments.Size(); p2sel = mesh.CreatePoint2SurfaceElementTable(); nfd_old = mesh.GetNFD(); moved_surfaces.SetSize(nfd_old+1); moved_surfaces.Clear(); si_map.SetSize(nfd_old+1); for(auto i : Range(nfd_old+1)) si_map[i] = i; } void BoundaryLayerTool :: CreateNewFaceDescriptors() { surfacefacs.SetSize(nfd_old+1); surfacefacs = 0.0; // create new FaceDescriptors for(auto i : Range(1, nfd_old+1)) { const auto& fd = mesh.GetFaceDescriptor(i); string name = fd.GetBCName(); if(params.surfid.Contains(i)) { if(auto isIn = domains.Test(fd.DomainIn()); isIn != domains.Test(fd.DomainOut())) { int new_si = mesh.GetNFD()+1; surfacefacs[i] = isIn ? 1. : -1.; // -1 surf nr is so that curving does not do anything FaceDescriptor new_fd(-1, isIn ? new_mat_nrs[i] : fd.DomainIn(), isIn ? fd.DomainOut() : new_mat_nrs[i], -1); new_fd.SetBCProperty(new_si); new_fd.SetSurfColour(fd.SurfColour()); mesh.AddFaceDescriptor(new_fd); si_map[i] = new_si; moved_surfaces.SetBit(i); mesh.SetBCName(new_si-1, "mapped_" + name); } // curving of surfaces with boundary layers will often // result in pushed through elements, since we do not (yet) // curvature through layers. // Therefore we disable curving for these surfaces. if(!params.keep_surfaceindex) mesh.GetFaceDescriptor(i).SetSurfNr(-1); } } for(auto si : params.surfid) if(surfacefacs[si] == 0.0) throw Exception("Surface " + to_string(si) + " is not a boundary of the domain to be grown into!"); } void BoundaryLayerTool ::CreateFaceDescriptorsSides() { BitArray face_done(mesh.GetNFD()+1); face_done.Clear(); for(const auto& sel : mesh.SurfaceElements()) { auto facei = sel.GetIndex(); if(face_done.Test(facei)) continue; bool point_moved = false; // bool point_fixed = false; for(auto pi : sel.PNums()) { if(growthvectors[pi].Length() > 0) point_moved = true; /* else point_fixed = true; */ } if(point_moved && !moved_surfaces.Test(facei)) { int new_si = mesh.GetNFD()+1; const auto& fd = mesh.GetFaceDescriptor(facei); // auto isIn = domains.Test(fd.DomainIn()); // auto isOut = domains.Test(fd.DomainOut()); int si = params.sides_keep_surfaceindex ? facei : -1; // domin and domout can only be set later FaceDescriptor new_fd(si, -1, -1, si); new_fd.SetBCProperty(new_si); mesh.AddFaceDescriptor(new_fd); si_map[facei] = new_si; mesh.SetBCName(new_si-1, fd.GetBCName()); face_done.SetBit(facei); } } } void BoundaryLayerTool :: CalculateGrowthVectors() { growthvectors.SetSize(np); growthvectors = 0.; for(auto pi : mesh.Points().Range()) { const auto & p = mesh[pi]; if(p.Type() == INNERPOINT) continue; std::map> normals; // calculate one normal vector per face (average with angles as weights for multiple surface elements within a face) for(auto sei : p2sel[pi]) { const auto & sel = mesh[sei]; auto facei = sel.GetIndex(); if(!params.surfid.Contains(facei)) continue; auto n = surfacefacs[sel.GetIndex()] * getNormal(sel); int itrig = sel.PNums().Pos(pi); itrig += sel.GetNP(); auto v0 = (mesh[sel.PNumMod(itrig+1)] - mesh[pi]).Normalize(); auto v1 = (mesh[sel.PNumMod(itrig-1)] - mesh[pi]).Normalize(); if(normals.count(facei)==0) normals[facei] = {0.,0.,0.}; normals[facei] += acos(v0*v1)*n; } for(auto & [facei, n] : normals) n *= 1.0/n.Length(); // combine normal vectors for each face to keep uniform distances auto & np = growthvectors[pi]; ArrayMem, 3> ns; for (auto &[facei, n] : normals) { ns.Append(n); } ArrayMem, 3> removed; // reduce to full rank of max 3 while(true) { if(ns.Size() <= 1) break; if(ns.Size() == 2 && ns[0] * ns[1] < 1 - 1e-6) break; if (ns.Size() == 3) { DenseMatrix mat(3,3); for(auto i : Range(3)) for(auto j : Range(3)) mat(i,j) = ns[i][j]; if(fabs(mat.Det()) > 1e-6) break; } int maxpos1; int maxpos2; double val = 0; for (auto i : Range(ns)) { for (auto j : Range(i + 1, ns.Size())) { double ip = ns[i] * ns[j]; if(ip > val) { val = ip; maxpos1 = i; maxpos2 = j; } } } removed.Append(ns[maxpos1]); removed.Append(ns[maxpos2]); ns[maxpos1] = 0.5 * (ns[maxpos1] + ns[maxpos2]); ns.DeleteElement(maxpos2); } if(ns.Size() == 0) continue; if(ns.Size() == 1) np = ns[0]; else if(ns.Size() == 2) { np = ns[0]; auto n = ns[1]; auto npn = np * n; auto npnp = np * np; auto nn = n * n; if(nn-npn*npn/npnp == 0) { np = n; continue; } np += (nn - npn)/(nn - npn*npn/npnp) * (n - npn/npnp * np); } else // ns.Size() == 3 { DenseMatrix mat(3,3); for(auto i : Range(3)) for(auto j : Range(3)) mat(i, j) = ns[i] * ns[j]; Vector rhs(3); rhs = 1.; Vector res(3); DenseMatrix inv(3, ns.Size()); CalcInverse(mat, inv); inv.Mult(rhs, res); for(auto i : Range(ns)) np += res[i] * ns[i]; } for(auto& n : removed) if(n * np < 0) cout << "WARNING: Growth vector at point " << pi << " in opposite direction to face normal!" << endl << "Growthvector = " << np << ", face normal = " << n << endl; } } Array>, SegmentIndex> BoundaryLayerTool :: BuildSegMap() { // Bit array to keep track of segments already processed BitArray segs_done(nseg+1); segs_done.Clear(); // map for all segments with same points // points to pair of SegmentIndex, int // int is type of other segment, either: // 0 == adjacent surface grows layer // 1 == adjacent surface doesn't grow layer, but layer ends on it // 2 == adjacent surface is interior surface that ends on layer // 3 == adjacent surface is exterior surface that ends on layer (not allowed yet) Array>, SegmentIndex> segmap(segments.Size()); // moved segments is_edge_moved.SetSize(max_edge_nr+1); is_edge_moved = false; // boundaries to project endings to is_boundary_projected.SetSize(nfd_old+1); is_boundary_projected.Clear(); is_boundary_moved.SetSize(nfd_old+1); is_boundary_moved.Clear(); for(auto si : Range(segments)) { if(segs_done[si]) continue; const auto& segi = segments[si]; if(!moved_surfaces.Test(segi.si)) continue; segs_done.SetBit(si); segmap[si].Append(make_pair(si, 0)); moved_segs.Append(si); is_edge_moved.SetBit(segi.edgenr); for(auto sj : Range(segments)) { if(segs_done.Test(sj)) continue; const auto& segj = segments[sj]; if((segi[0] == segj[0] && segi[1] == segj[1]) || (segi[0] == segj[1] && segi[1] == segj[0])) { segs_done.SetBit(sj); int type; if(moved_surfaces.Test(segj.si)) type = 0; else if(const auto& fd = mesh.GetFaceDescriptor(segj.si); domains.Test(fd.DomainIn()) && domains.Test(fd.DomainOut())) { type = 2; if(fd.DomainIn() == 0 || fd.DomainOut() == 0) is_boundary_projected.SetBit(segj.si); } else if(const auto& fd = mesh.GetFaceDescriptor(segj.si); !domains.Test(fd.DomainIn()) && !domains.Test(fd.DomainOut())) { type = 3; is_boundary_moved.SetBit(segj.si); } else { type = 1; // in case 1 we project the growthvector onto the surface is_boundary_projected.SetBit(segj.si); } segmap[si].Append(make_pair(sj, type)); } } } return segmap; } BitArray BoundaryLayerTool :: ProjectGrowthVectorsOnSurface() { BitArray in_surface_direction(nfd_old+1); in_surface_direction.Clear(); // project growthvector on surface for inner angles if(params.grow_edges) { for(const auto& sel : mesh.SurfaceElements()) if(is_boundary_projected.Test(sel.GetIndex())) { auto n = getNormal(sel); for(auto i : Range(sel.PNums())) { auto pi = sel.PNums()[i]; if(growthvectors[pi].Length2() == 0.) continue; auto next = sel.PNums()[(i+1)%sel.GetNV()]; auto prev = sel.PNums()[i == 0 ? sel.GetNV()-1 : i-1]; auto v1 = (mesh[next] - mesh[pi]).Normalize(); auto v2 = (mesh[prev] - mesh[pi]).Normalize(); auto v3 = growthvectors[pi]; v3.Normalize(); auto tol = v1.Length() * 1e-12; if((v1 * v3 > -tol) && (v2 * v3 > -tol)) in_surface_direction.SetBit(sel.GetIndex()); else continue; if(!params.project_boundaries.Contains(sel.GetIndex())) continue; auto& g = growthvectors[pi]; auto ng = n * g; auto gg = g * g; auto nn = n * n; // if(fabs(ng*ng-nn*gg) < 1e-12 || fabs(ng) < 1e-12) continue; auto a = -ng*ng/(ng*ng-nn * gg); auto b = ng*gg/(ng*ng-nn*gg); g += a*g + b*n; } } } else { for(const auto& seg : segments) { int count = 0; for(const auto& seg2 : segments) if(((seg[0] == seg2[0] && seg[1] == seg2[1]) || (seg[0] == seg2[1] && seg[1] == seg2[0])) && params.surfid.Contains(seg2.si)) count++; if(count == 1) { growthvectors[seg[0]] = {0., 0., 0.}; growthvectors[seg[1]] = {0., 0., 0.}; } } } return in_surface_direction; } void BoundaryLayerTool :: InterpolateGrowthVectors() { // interpolate tangential component of growth vector along edge for(auto edgenr : Range(max_edge_nr)) { // if(!is_edge_moved[edgenr+1]) continue; // build sorted list of edge Array points; // find first vertex on edge double edge_len = 0.; auto is_end_point = [&] (PointIndex pi) { // if(mesh[pi].Type() == FIXEDPOINT) // return true; // return false; auto segs = topo.GetVertexSegments(pi); if(segs.Size() == 1) return true; auto first_edgenr = mesh[segs[0]].edgenr; for(auto segi : segs) if(mesh[segi].edgenr != first_edgenr) return true; return false; }; bool any_grows = false; for(const auto& seg : segments) { if(seg.edgenr-1 == edgenr) { if(growthvectors[seg[0]].Length2() != 0 || growthvectors[seg[1]].Length2() != 0) any_grows = true; if(points.Size() == 0 && is_end_point(seg[0])) { points.Append(seg[0]); points.Append(seg[1]); edge_len += (mesh[seg[1]] - mesh[seg[0]]).Length(); } } } if(!any_grows) continue; if(!points.Size()) throw Exception("Could not find startpoint for edge " + ToString(edgenr)); while(true) { bool point_found = false; for(auto si : topo.GetVertexSegments(points.Last())) { const auto& seg = mesh[si]; if(seg.edgenr-1 != edgenr) continue; if(seg[0] == points.Last() && points[points.Size()-2] !=seg[1]) { edge_len += (mesh[points.Last()] - mesh[seg[1]]).Length(); points.Append(seg[1]); point_found = true; break; } else if(seg[1] == points.Last() && points[points.Size()-2] != seg[0]) { edge_len += (mesh[points.Last()] - mesh[seg[0]]).Length(); points.Append(seg[0]); point_found = true; break; } } if(is_end_point(points.Last())) break; if(!point_found) { throw Exception(string("Could not find connected list of line segments for edge ") + edgenr); } } if(growthvectors[points[0]].Length2() == 0 && growthvectors[points.Last()].Length2() == 0) continue; // tangential part of growth vectors auto t1 = (mesh[points[1]]-mesh[points[0]]).Normalize(); auto gt1 = growthvectors[points[0]] * t1 * t1; auto t2 = (mesh[points.Last()]-mesh[points[points.Size()-2]]).Normalize(); auto gt2 = growthvectors[points.Last()] * t2 * t2; if(!is_edge_moved[edgenr+1]) { if(growthvectors[points[0]] * (mesh[points[1]] - mesh[points[0]]) < 0) gt1 = 0.; if(growthvectors[points.Last()] * (mesh[points[points.Size()-2]] - mesh[points.Last()]) < 0) gt2 = 0.; } double len = 0.; for(size_t i = 1; i < points.Size()-1; i++) { auto pi = points[i]; len += (mesh[pi] - mesh[points[i-1]]).Length(); auto t = getEdgeTangent(pi, edgenr); auto lam = len/edge_len; auto interpol = (1-lam) * (gt1 * t) * t + lam * (gt2 * t) * t; growthvectors[pi] += interpol; } } InterpolateSurfaceGrowthVectors(); } void BoundaryLayerTool :: InsertNewElements( FlatArray>, SegmentIndex> segmap, const BitArray & in_surface_direction ) { static Timer timer("BoundaryLayerTool::InsertNewElements"); RegionTimer rt(timer); Array, PointIndex> mapto(np); // insert new points for (PointIndex pi = 1; pi <= np; pi++) if (growthvectors[pi].Length2() != 0) { Point<3> p = mesh[pi]; for(auto i : Range(params.heights)) { p += params.heights[i] * growthvectors[pi]; mapto[pi].Append(mesh.AddPoint(p)); } } // add 2d quads on required surfaces map, int> seg2edge; if(params.grow_edges) { for(auto sei : moved_segs) { // copy here since we will add segments and this would // invalidate a reference! // auto segi = segments[sei]; for(auto [sej, type] : segmap[sei]) { auto segj = segments[sej]; if(type == 0) { Segment s; s[0] = mapto[segj[0]].Last(); s[1] = mapto[segj[1]].Last(); s[2] = PointIndex::INVALID; auto pair = s[0] < s[1] ? make_pair(s[0], s[1]) : make_pair(s[1], s[0]); if(seg2edge.find(pair) == seg2edge.end()) seg2edge[pair] = ++max_edge_nr; s.edgenr = seg2edge[pair]; s.si = si_map[segj.si]; new_segments.Append(s); } // here we need to grow the quad elements else if(type == 1) { PointIndex pp1 = segj[1]; PointIndex pp2 = segj[0]; if(in_surface_direction.Test(segj.si)) { Swap(pp1, pp2); is_boundary_moved.SetBit(segj.si); } PointIndex p1 = pp1; PointIndex p2 = pp2; PointIndex p3, p4; Segment s0; s0[0] = p1; s0[1] = p2; s0[2] = PointIndex::INVALID; s0.edgenr = segj.edgenr; s0.si = segj.si; new_segments.Append(s0); for(auto i : Range(params.heights)) { Element2d sel(QUAD); p3 = mapto[pp2][i]; p4 = mapto[pp1][i]; sel[0] = p1; sel[1] = p2; sel[2] = p3; sel[3] = p4; for(auto i : Range(4)) { sel.GeomInfo()[i].u = 0.0; sel.GeomInfo()[i].v = 0.0; } sel.SetIndex(si_map[segj.si]); mesh.AddSurfaceElement(sel); // TODO: Too many, would be enough to only add outermost ones Segment s1; s1[0] = p2; s1[1] = p3; s1[2] = PointIndex::INVALID; auto pair = make_pair(p2, p3); if(seg2edge.find(pair) == seg2edge.end()) seg2edge[pair] = ++max_edge_nr; s1.edgenr = seg2edge[pair]; s1.si = segj.si; new_segments.Append(s1); Segment s2; s2[0] = p4; s2[1] = p1; s2[2] = PointIndex::INVALID; pair = make_pair(p1, p4); if(seg2edge.find(pair) == seg2edge.end()) seg2edge[pair] = ++max_edge_nr; s2.edgenr = seg2edge[pair]; s2.si = segj.si; new_segments.Append(s2); p1 = p4; p2 = p3; } Segment s3; s3[0] = p3; s3[1] = p4; s3[2] = PointIndex::INVALID; auto pair = p3 < p4 ? make_pair(p3, p4) : make_pair(p4, p3); if(seg2edge.find(pair) == seg2edge.end()) seg2edge[pair] = ++max_edge_nr; s3.edgenr = seg2edge[pair]; s3.si = segj.si; new_segments.Append(s3); } } } } BitArray fixed_points(np+1); fixed_points.Clear(); BitArray moveboundarypoint(np+1); moveboundarypoint.Clear(); for(SurfaceElementIndex si = 0; si < nse; si++) { // copy because surfaceels array will be resized! auto sel = mesh[si]; if(moved_surfaces.Test(sel.GetIndex())) { Array points(sel.PNums()); if(surfacefacs[sel.GetIndex()] > 0) Swap(points[0], points[2]); for(auto j : Range(params.heights)) { auto eltype = points.Size() == 3 ? PRISM : HEX; Element el(eltype); for(auto i : Range(points)) el[i] = points[i]; for(auto i : Range(points)) points[i] = mapto[sel.PNums()[i]][j]; if(surfacefacs[sel.GetIndex()] > 0) Swap(points[0], points[2]); for(auto i : Range(points)) el[sel.PNums().Size() + i] = points[i]; auto new_index = new_mat_nrs[sel.GetIndex()]; if(new_index == -1) throw Exception("Boundary " + ToString(sel.GetIndex()) + " with name " + mesh.GetBCName(sel.GetIndex()-1) + " extruded, but no new material specified for it!"); el.SetIndex(new_mat_nrs[sel.GetIndex()]); mesh.AddVolumeElement(el); } Element2d newel = sel; for(auto& p : newel.PNums()) p = mapto[p].Last(); newel.SetIndex(si_map[sel.GetIndex()]); mesh.AddSurfaceElement(newel); } else { bool has_moved = false; for(auto p : sel.PNums()) if(mapto[p].Size()) has_moved = true; if(has_moved) for(auto p : sel.PNums()) { if(!mapto[p].Size()) { fixed_points.SetBit(p); if(is_boundary_moved.Test(sel.GetIndex())) moveboundarypoint.SetBit(p); } } } if(is_boundary_moved.Test(sel.GetIndex())) { for(auto& p : mesh[si].PNums()) if(mapto[p].Size()) p = mapto[p].Last(); } } for(SegmentIndex sei = 0; sei < nseg; sei++) { auto& seg = segments[sei]; if(is_boundary_moved.Test(seg.si)) for(auto& p : seg.PNums()) if(mapto[p].Size()) p = mapto[p].Last(); } for(ElementIndex ei = 0; ei < ne; ei++) { auto el = mesh[ei]; ArrayMem fixed; ArrayMem moved; bool moved_bnd = false; for(const auto& p : el.PNums()) { if(fixed_points.Test(p)) fixed.Append(p); if(mapto[p].Size()) moved.Append(p); if(moveboundarypoint.Test(p)) moved_bnd = true; } bool do_move, do_insert; if(domains.Test(el.GetIndex())) { do_move = fixed.Size() && moved_bnd; do_insert = do_move; } else { do_move = !fixed.Size() || moved_bnd; do_insert = !do_move; } if(do_move) { for(auto& p : mesh[ei].PNums()) if(mapto[p].Size()) p = mapto[p].Last(); } if(do_insert) { if(el.GetType() == TET) { if(moved.Size() == 3) // inner corner { PointIndex p1 = moved[0]; PointIndex p2 = moved[1]; PointIndex p3 = moved[2]; auto v1 = mesh[p1]; auto n = Cross(mesh[p2]-v1, mesh[p3]-v1); auto d = mesh[mapto[p1][0]] - v1; if(n*d > 0) Swap(p2,p3); PointIndex p4 = p1; PointIndex p5 = p2; PointIndex p6 = p3; for(auto i : Range(params.heights)) { Element nel(PRISM); nel[0] = p4; nel[1] = p5; nel[2] = p6; p4 = mapto[p1][i]; p5 = mapto[p2][i]; p6 = mapto[p3][i]; nel[3] = p4; nel[4] = p5; nel[5] = p6; nel.SetIndex(el.GetIndex()); mesh.AddVolumeElement(nel); } } if(moved.Size() == 2) { if(fixed.Size() == 1) { PointIndex p1 = moved[0]; PointIndex p2 = moved[1]; for(auto i : Range(params.heights)) { PointIndex p3 = mapto[moved[1]][i]; PointIndex p4 = mapto[moved[0]][i]; Element nel(PYRAMID); nel[0] = p1; nel[1] = p2; nel[2] = p3; nel[3] = p4; nel[4] = el[0] + el[1] + el[2] + el[3] - fixed[0] - moved[0] - moved[1]; if(Cross(mesh[p2]-mesh[p1], mesh[p4]-mesh[p1]) * (mesh[nel[4]]-mesh[nel[1]]) > 0) Swap(nel[1], nel[3]); nel.SetIndex(el.GetIndex()); mesh.AddVolumeElement(nel); p1 = p4; p2 = p3; } } } if(moved.Size() == 1 && fixed.Size() == 1) { PointIndex p1 = moved[0]; for(auto i : Range(params.heights)) { Element nel = el; PointIndex p2 = mapto[moved[0]][i]; for(auto& p : nel.PNums()) { if(p == moved[0]) p = p1; else if(p == fixed[0]) p = p2; } p1 = p2; mesh.AddVolumeElement(nel); } } } else if(el.GetType() == PYRAMID) { if(moved.Size() == 2) { if(fixed.Size() != 2) throw Exception("This case is not implemented yet! Fixed size = " + ToString(fixed.Size())); PointIndex p1 = moved[0]; PointIndex p2 = moved[1]; for(auto i : Range(params.heights)) { PointIndex p3 = mapto[moved[1]][i]; PointIndex p4 = mapto[moved[0]][i]; Element nel(PYRAMID); nel[0] = p1; nel[1] = p2; nel[2] = p3; nel[3] = p4; nel[4] = el[0] + el[1] + el[2] + el[3] + el[4] - fixed[0] - fixed[1] - moved[0] - moved[1]; if(Cross(mesh[p2] - mesh[p1], mesh[p4]-mesh[p1]) * (mesh[nel[4]]-mesh[nel[1]]) > 0) Swap(nel[1], nel[3]); nel.SetIndex(el.GetIndex()); mesh.AddVolumeElement(nel); p1 = p4; p2 = p3; } } else if(moved.Size() == 1) throw Exception("This case is not implemented yet!"); } else throw Exception("Boundarylayer only implemented for tets and pyramids outside yet!"); } } } void BoundaryLayerTool :: SetDomInOut() { for(auto i : Range(1, nfd_old+1)) if(moved_surfaces.Test(i)) { if(auto dom = mesh.GetFaceDescriptor(si_map[i]).DomainIn(); dom > ndom_old) mesh.GetFaceDescriptor(i).SetDomainOut(dom); else mesh.GetFaceDescriptor(i).SetDomainIn(mesh.GetFaceDescriptor(si_map[i]).DomainOut()); } } void BoundaryLayerTool :: SetDomInOutSides() { BitArray done(mesh.GetNFD()+1); done.Clear(); for(auto sei : Range(mesh.SurfaceElements())) { auto& sel = mesh[sei]; auto index = sel.GetIndex(); if(done.Test(index)) continue; done.SetBit(index); auto& fd = mesh.GetFaceDescriptor(index); if(fd.DomainIn() != -1) continue; int e1, e2; mesh.GetTopology().GetSurface2VolumeElement(sei+1, e1, e2); if(e1 == 0) fd.SetDomainIn(0); else fd.SetDomainIn(mesh.VolumeElement(e1).GetIndex()); if(e2 == 0) fd.SetDomainOut(0); else fd.SetDomainOut(mesh.VolumeElement(e2).GetIndex()); } } void BoundaryLayerTool :: AddSegments() { if(have_single_segments) MergeAndAddSegments(mesh, new_segments); else { for(auto & seg : new_segments) mesh.AddSegment(seg); } } void BoundaryLayerTool :: FixVolumeElements() { static Timer timer("BoundaryLayerTool::FixVolumeElements"); RegionTimer rt(timer); BitArray is_inner_point(mesh.GetNP()+1); is_inner_point.Clear(); auto changed_domains = domains; if(!params.outside) changed_domains.Invert(); for(ElementIndex ei : Range(ne)) if(changed_domains.Test(mesh[ei].GetIndex())) for(auto pi : mesh[ei].PNums()) if(mesh[pi].Type() == INNERPOINT) is_inner_point.SetBit(pi); Array points; for(auto pi : mesh.Points().Range()) if(is_inner_point.Test(pi)) points.Append(pi); auto p2el = mesh.CreatePoint2ElementTable(is_inner_point); // smooth growth vectors to shift additional element layers to the inside and fix flipped tets for([[maybe_unused]] auto step : Range(10)) { for(auto pi : points) { Vec<3> average_gw = 0.0; auto & els = p2el[pi]; size_t cnt = 0; for(auto ei : els) if(ei