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global_functions.cpp
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// This file is part of the implementation of
// Robust Structure Simplification for Hex Re-meshing
// Xifeng Gao, Daniele Panozzo, Wenping Wang, Zhigang Deng, Guoning Chen
// In ACM Transactions on Graphics (Proceedings of SIGGRAPH ASIA 2017)
//
// Copyright (C) 2017 Xifeng Gao<[email protected]>
//
// This Source Code Form is subject to the terms of the Mozilla Public License
// v. 2.0. If a copy of the MPL was not distributed with this file, You can
// obtain one at http://mozilla.org/MPL/2.0/.
#include "global_functions.h"
#include "global_types.h"
#include "igl/bounding_box_diagonal.h"
//===================================mesh connectivities===================================
void build_connectivity(Mesh &hmi) {
hmi.Es.clear(); if (hmi.Hs.size()) hmi.Fs.clear();
//either hex or tri
if (hmi.type == Mesh_type::Tri) {
std::vector<std::tuple<uint32_t, uint32_t, uint32_t, uint32_t>> temp;
temp.reserve(hmi.Fs.size() * 3);
for (uint32_t i = 0; i < hmi.Fs.size(); ++i) {
for (uint32_t j = 0; j < 3; ++j) {
uint32_t v0 = hmi.Fs[i].vs[j], v1 = hmi.Fs[i].vs[(j + 1) % 3];
if (v0 > v1) std::swap(v0, v1);
temp.push_back(std::make_tuple(v0, v1, i, j));
}
hmi.Fs[i].es.resize(3);
}
std::sort(temp.begin(), temp.end());
hmi.Es.reserve(temp.size() / 2);
uint32_t E_num = 0;
Hybrid_E e; e.boundary = true; e.vs.resize(2);
for (uint32_t i = 0; i < temp.size(); ++i) {
if (i == 0 || (i != 0 && (std::get<0>(temp[i]) != std::get<0>(temp[i - 1]) ||
std::get<1>(temp[i]) != std::get<1>(temp[i - 1])))) {
e.id = E_num; E_num++;
e.vs[0] = std::get<0>(temp[i]);
e.vs[1] = std::get<1>(temp[i]);
hmi.Es.push_back(e);
}
else if (i != 0 && (std::get<0>(temp[i]) == std::get<0>(temp[i - 1]) &&
std::get<1>(temp[i]) == std::get<1>(temp[i - 1])))
hmi.Es[E_num - 1].boundary = false;
hmi.Fs[std::get<2>(temp[i])].es[std::get<3>(temp[i])] = E_num - 1;
}
//boundary
for (auto &v : hmi.Vs) v.boundary = false;
for (uint32_t i = 0; i < hmi.Es.size(); ++i)
if (hmi.Es[i].boundary) {
hmi.Vs[hmi.Es[i].vs[0]].boundary = hmi.Vs[hmi.Es[i].vs[1]].boundary = true;
}
}
else if (hmi.type == Mesh_type::Tet) {
std::vector<std::vector<uint32_t>> total_fs(hmi.Hs.size() * 4);
std::vector<std::tuple<uint32_t, uint32_t, uint32_t, uint32_t, uint32_t, uint32_t>> tempF(hmi.Hs.size() * 4);
std::vector<uint32_t> vs(3);
for (uint32_t i = 0; i < hmi.Hs.size(); ++i) {
for (short j = 0; j < 4; j++) {
for (short k = 0; k < 3; k++) vs[k] = hmi.Hs[i].vs[tet_faces[j][k]];
uint32_t id = 4 * i + j;
total_fs[id] = vs;
std::sort(vs.begin(), vs.end());
tempF[id] = std::make_tuple(vs[0], vs[1], vs[2], id, i, j);
}
hmi.Hs[i].fs.resize(4);
}
std::sort(tempF.begin(), tempF.end());
hmi.Fs.reserve(tempF.size() / 3);
Hybrid_F f; f.boundary = true;
uint32_t F_num = 0;
for (uint32_t i = 0; i < tempF.size(); ++i) {
if (i == 0 || (i != 0 &&
(std::get<0>(tempF[i]) != std::get<0>(tempF[i - 1]) || std::get<1>(tempF[i]) != std::get<1>(tempF[i - 1]) ||
std::get<2>(tempF[i]) != std::get<2>(tempF[i - 1])))) {
f.id = F_num; F_num++;
f.vs = total_fs[std::get<3>(tempF[i])];
hmi.Fs.push_back(f);
}
else if (i != 0 && (std::get<0>(tempF[i]) == std::get<0>(tempF[i - 1]) && std::get<1>(tempF[i]) == std::get<1>(tempF[i - 1]) &&
std::get<2>(tempF[i]) == std::get<2>(tempF[i - 1])))
hmi.Fs[F_num - 1].boundary = false;
hmi.Hs[std::get<4>(tempF[i])].fs[std::get<5>(tempF[i])] = F_num - 1;
}
std::vector<std::tuple<uint32_t, uint32_t, uint32_t, uint32_t>> temp(hmi.Fs.size() * 3);
for (uint32_t i = 0; i < hmi.Fs.size(); ++i) {
for (uint32_t j = 0; j < 3; ++j) {
uint32_t v0 = hmi.Fs[i].vs[j], v1 = hmi.Fs[i].vs[(j + 1) % 3];
if (v0 > v1) std::swap(v0, v1);
temp[3 * i + j] = std::make_tuple(v0, v1, i, j);
}
hmi.Fs[i].es.resize(3);
}
std::sort(temp.begin(), temp.end());
hmi.Es.reserve(temp.size() / 2);
uint32_t E_num = 0;
Hybrid_E e; e.boundary = false; e.vs.resize(2);
for (uint32_t i = 0; i < temp.size(); ++i) {
if (i == 0 || (i != 0 && (std::get<0>(temp[i]) != std::get<0>(temp[i - 1]) ||
std::get<1>(temp[i]) != std::get<1>(temp[i - 1])))) {
e.id = E_num; E_num++;
e.vs[0] = std::get<0>(temp[i]);
e.vs[1] = std::get<1>(temp[i]);
hmi.Es.push_back(e);
}
hmi.Fs[std::get<2>(temp[i])].es[std::get<3>(temp[i])] = E_num - 1;
}
//boundary
for (auto &v : hmi.Vs) v.boundary = false;
for (uint32_t i = 0; i < hmi.Fs.size(); ++i)
if (hmi.Fs[i].boundary) for (uint32_t j = 0; j < 3; ++j) {
uint32_t eid = hmi.Fs[i].es[j];
hmi.Es[eid].boundary = true;
hmi.Vs[hmi.Es[eid].vs[0]].boundary = hmi.Vs[hmi.Es[eid].vs[1]].boundary = true;
}
}
else if(hmi.type == Mesh_type::Hex) {
std::vector<std::vector<uint32_t>> total_fs(hmi.Hs.size() * 6);
std::vector<std::tuple<uint32_t, uint32_t, uint32_t, uint32_t, uint32_t, uint32_t, uint32_t>> tempF(hmi.Hs.size() * 6);
std::vector<uint32_t> vs(4);
for (uint32_t i = 0; i < hmi.Hs.size(); ++i) {
for (short j = 0; j < 6; j++){
for (short k = 0; k < 4; k++) vs[k] = hmi.Hs[i].vs[hex_face_table[j][k]];
uint32_t id = 6 * i + j;
total_fs[id] = vs;
std::sort(vs.begin(), vs.end());
tempF[id] = std::make_tuple(vs[0], vs[1], vs[2], vs[3], id, i, j);
}
hmi.Hs[i].fs.resize(6);
}
std::sort(tempF.begin(), tempF.end());
hmi.Fs.reserve(tempF.size() / 3);
Hybrid_F f; f.boundary = true;
uint32_t F_num = 0;
for (uint32_t i = 0; i < tempF.size(); ++i) {
if (i == 0 || (i != 0 &&
(std::get<0>(tempF[i]) != std::get<0>(tempF[i - 1]) || std::get<1>(tempF[i]) != std::get<1>(tempF[i - 1]) ||
std::get<2>(tempF[i]) != std::get<2>(tempF[i - 1]) || std::get<3>(tempF[i]) != std::get<3>(tempF[i - 1])))) {
f.id = F_num; F_num++;
f.vs = total_fs[std::get<4>(tempF[i])];
hmi.Fs.push_back(f);
}
else if (i != 0 && (std::get<0>(tempF[i]) == std::get<0>(tempF[i - 1]) && std::get<1>(tempF[i]) == std::get<1>(tempF[i - 1]) &&
std::get<2>(tempF[i]) == std::get<2>(tempF[i - 1]) && std::get<3>(tempF[i]) == std::get<3>(tempF[i - 1])))
hmi.Fs[F_num - 1].boundary = false;
hmi.Hs[std::get<5>(tempF[i])].fs[std::get<6>(tempF[i])] = F_num - 1;
}
std::vector<std::tuple<uint32_t, uint32_t, uint32_t, uint32_t>> temp(hmi.Fs.size() * 4);
for (uint32_t i = 0; i < hmi.Fs.size(); ++i) {
for (uint32_t j = 0; j < 4; ++j) {
uint32_t v0 = hmi.Fs[i].vs[j], v1 = hmi.Fs[i].vs[(j + 1) % 4];
if (v0 > v1) std::swap(v0, v1);
temp[4 * i + j] = std::make_tuple(v0, v1, i, j);
}
hmi.Fs[i].es.resize(4);
}
std::sort(temp.begin(), temp.end());
hmi.Es.reserve(temp.size() / 2);
uint32_t E_num = 0;
Hybrid_E e; e.boundary = false; e.vs.resize(2);
for (uint32_t i = 0; i < temp.size(); ++i) {
if (i == 0 || (i != 0 && (std::get<0>(temp[i]) != std::get<0>(temp[i - 1]) ||
std::get<1>(temp[i]) != std::get<1>(temp[i - 1])))) {
e.id = E_num; E_num++;
e.vs[0] = std::get<0>(temp[i]);
e.vs[1] = std::get<1>(temp[i]);
hmi.Es.push_back(e);
}
hmi.Fs[std::get<2>(temp[i])].es[std::get<3>(temp[i])] = E_num - 1;
}
//boundary
for (auto &v : hmi.Vs) v.boundary = false;
for (uint32_t i = 0; i < hmi.Fs.size(); ++i)
if (hmi.Fs[i].boundary) for (uint32_t j = 0; j < 4; ++j) {
uint32_t eid = hmi.Fs[i].es[j];
hmi.Es[eid].boundary = true;
hmi.Vs[hmi.Es[eid].vs[0]].boundary = hmi.Vs[hmi.Es[eid].vs[1]].boundary = true;
}
}
//f_nhs;
for (uint32_t i = 0; i < hmi.Hs.size(); i++) {
for (uint32_t j = 0; j < hmi.Hs[i].fs.size(); j++) hmi.Fs[hmi.Hs[i].fs[j]].neighbor_hs.push_back(i);
}
//e_nfs, v_nfs
for (uint32_t i = 0; i < hmi.Fs.size(); i++) {
for (uint32_t j = 0; j < hmi.Fs[i].es.size(); j++) hmi.Es[hmi.Fs[i].es[j]].neighbor_fs.push_back(i);
for (uint32_t j = 0; j < hmi.Fs[i].vs.size(); j++) hmi.Vs[hmi.Fs[i].vs[j]].neighbor_fs.push_back(i);
}
//v_nes, v_nvs
for (uint32_t i = 0; i < hmi.Es.size(); i++) {
uint32_t v0 = hmi.Es[i].vs[0], v1 = hmi.Es[i].vs[1];
hmi.Vs[v0].neighbor_es.push_back(i);
hmi.Vs[v1].neighbor_es.push_back(i);
hmi.Vs[v0].neighbor_vs.push_back(v1);
hmi.Vs[v1].neighbor_vs.push_back(v0);
}
//e_nhs
for (uint32_t i = 0; i < hmi.Es.size(); i++) {
std::vector<uint32_t> nhs;
for (uint32_t j = 0; j < hmi.Es[i].neighbor_fs.size(); j++) {
uint32_t nfid = hmi.Es[i].neighbor_fs[j];
nhs.insert(nhs.end(), hmi.Fs[nfid].neighbor_hs.begin(), hmi.Fs[nfid].neighbor_hs.end());
}
std::sort(nhs.begin(), nhs.end()); nhs.erase(std::unique(nhs.begin(), nhs.end()), nhs.end());
hmi.Es[i].neighbor_hs = nhs;
}
}
void topology_info(Mesh &mesh, Frame &frame, Mesh_Topology & mt) {
//==================hex-mesh==================//
for (int i = 0; i < mesh.Vs.size(); i++) if (!mesh.Vs[i].neighbor_hs.size()) ;
//surface_euler, volume_euler;
uint32_t num_boundary_v = 0, num_boundary_e = 0, num_boundary_f = 0;
for (int i = 0; i<mesh.Vs.size(); i++) if (mesh.Vs[i].boundary) num_boundary_v++;
for (int i = 0; i<mesh.Es.size(); i++) if (mesh.Es[i].boundary) num_boundary_e++;
for (int i = 0; i<mesh.Fs.size(); i++) if (mesh.Fs[i].boundary) num_boundary_f++;
mt.surface_euler = num_boundary_v + num_boundary_f - num_boundary_e;
mt.genus = (2 - mt.surface_euler) / 2;
mt.volume_euler = mesh.Vs.size() + mesh.Fs.size() - mesh.Es.size() - mesh.Hs.size();
mt.euler_problem = false;
if (mt.surface_euler != 2 * mt.volume_euler) { mt.euler_problem = true; }
//surface_manifoldness;
mt.manifoldness_problem = false;
mt.surface_manifoldness = true;
vector<short> E_flag(mesh.Es.size(), 0); vector<short> V_flag(mesh.Vs.size(), 0);
for (uint32_t i = 0; i<mesh.Vs.size(); i++){//topology disk
if (!mesh.Vs[i].boundary) continue;
vector<vector<uint32_t>> fes;
for (auto fid : mesh.Vs[i].neighbor_fs) {
if (mesh.Fs[fid].boundary) fes.push_back(mesh.Fs[fid].es);
}
if (!disk_polygon(mesh, frame, fes, E_flag, V_flag, true)) {
mt.surface_manifoldness = false;
mt.manifoldness_problem = true;
break;
}
}
//volume_manifoldness;
mt.volume_manifoldness = true;
vector<bool> F_flag(mesh.Fs.size(), false);
vector<vector<uint32_t>> F_nvs;
//==================frame==================//
for (int i = 0; i < frame.FVs.size(); i++) if (!frame.FVs[i].neighbor_fhs.size()) ;
//surface_euler, volume_euler;
num_boundary_v = num_boundary_e = num_boundary_f = 0;
for (int i = 0; i<frame.FVs.size(); i++) if (frame.FVs[i].boundary) num_boundary_v++;
for (int i = 0; i<frame.FEs.size(); i++) if (frame.FEs[i].boundary) num_boundary_e++;
for (int i = 0; i<frame.FFs.size(); i++) if (frame.FFs[i].boundary) num_boundary_f++;
mt.frame_surface_euler = num_boundary_v + num_boundary_f - num_boundary_e;
mt.frame_genus = (2 - mt.frame_surface_euler) / 2;
mt.frame_volume_euler = frame.FVs.size() + frame.FFs.size() - frame.FEs.size() - frame.FHs.size();
mt.frame_euler_problem = false;
if (mt.frame_surface_euler != 2 * mt.frame_volume_euler) { mt.frame_euler_problem = true; }
//surface_manifoldness;
mt.frame_manifoldness_problem = false;
mt.frame_surface_manifoldness = true;
E_flag.resize(frame.FEs.size()); V_flag.resize(frame.FVs.size());
for (uint32_t i = 0; i<frame.FVs.size(); i++) {//topology disk
if (!frame.FVs[i].boundary) continue;
vector<vector<uint32_t>> fes;
for (auto fid : frame.FVs[i].neighbor_ffs) {
if (frame.FFs[fid].boundary) fes.push_back(frame.FFs[fid].es);
}
if (!disk_polygon(mesh, frame, fes, E_flag, V_flag, false)) {
mt.frame_surface_manifoldness = false;
mt.frame_manifoldness_problem = true;
break;
}
}
//volume_manifoldness;
mt.frame_volume_manifoldness = true;
F_flag.resize(frame.FFs.size()); E_flag.resize(frame.FEs.size()); V_flag.resize(frame.FVs.size());
F_nvs.resize(frame.FVs.size());
for (uint32_t i = 0; i<frame.FVs.size(); i++) {//topology sphere
vector<vector<uint32_t>> pfs;
for (auto hid : frame.FVs[i].neighbor_fhs) pfs.push_back(frame.FHs[hid].fs);
if (!sphere_polyhedral(mesh, frame, F_nvs, pfs, F_flag, E_flag, V_flag, false)) {
mt.frame_volume_manifoldness = false;
mt.frame_manifoldness_problem = true;
break;
}
}
}
bool disk_polygon(Mesh &mesh, Frame &frame, vector<vector<uint32_t>> &fes, vector<short> &E_flag, vector<short> &V_flag, const bool &Ismesh) {
vector<uint32_t> pes;
for (int i = 0; i < fes.size(); i++) {
for (int j = 0; j < fes[i].size(); j++)
if (E_flag[fes[i][j]]) E_flag[fes[i][j]] = false;
else E_flag[fes[i][j]] = true;
}
for (int i = 0; i < fes.size(); i++)
for (int j = 0; j < fes[i].size(); j++)
if (E_flag[fes[i][j]]) { pes.push_back(fes[i][j]); E_flag[fes[i][j]] = false; }
//test nvs for each v
function<void(vector<uint32_t> &, const uint32_t &)> two_vs = [&](vector<uint32_t> &vs, const uint32_t & eid) {
if (Ismesh) { vs = mesh.Es[eid].vs; }
else { vs = frame.FEs[eid].vs; }
};
vector<uint32_t> vs;
for (uint32_t i = 0; i < pes.size(); ++i) {
two_vs(vs, pes[i]);
V_flag[vs[0]]++; V_flag[vs[1]]++;
if (V_flag[vs[0]] > 2 || V_flag[vs[1]] > 2) {
for (uint32_t j = 0; j < pes.size(); ++j) {
two_vs(vs, pes[j]);
V_flag[vs[0]] = V_flag[vs[1]] = 0;
}
return false;
}
}
for (uint32_t i = 0; i < pes.size(); ++i) {
two_vs(vs, pes[i]);
V_flag[vs[0]] = V_flag[vs[1]] = 0;
}
//extract the polygon
if (!pes.size()) return false;
vector<uint32_t> pvs;
pvs.reserve(pes.size());
vector<bool> e_flag(pes.size(), false);
two_vs(vs, pes[0]);
pvs.insert(pvs.end(), vs.begin(),vs.end());
e_flag[0] = true;
uint32_t start_v = pvs[1];
for (uint32_t i = 2; i < pes.size(); i++) {
for (uint32_t j = 1; j < pes.size(); j++) {
if (!e_flag[j]) {
two_vs(vs, pes[j]);
if (vs[0] == start_v) {
e_flag[j] = true;
pvs.push_back(vs[1]);
start_v = vs[1];
break;
}
else if (vs[1] == start_v) {
e_flag[j] = true;
pvs.push_back(vs[0]);
start_v = vs[0];
break;
}
}
}
}
if (pvs.size() != pes.size()) return false;
return true;
}
bool sphere_polyhedral(Mesh &mesh, Frame &frame, vector<vector<uint32_t>> &F_nvs, vector<vector<uint32_t>> &pfs, vector<bool> &F_flag, vector<short> &E_flag, vector<short> &V_flag, const bool &Ismesh) {
vector<uint32_t> pf;
for (int i = 0; i < pfs.size(); i++)
for (int j = 0; j < pfs[i].size(); j++)
if (F_flag[pfs[i][j]]) F_flag[pfs[i][j]] = false;
else F_flag[pfs[i][j]] = true;
for (int i = 0; i < pfs.size(); i++)
for (int j = 0; j < pfs[i].size(); j++)
if (F_flag[pfs[i][j]]) { pf.push_back(pfs[i][j]); F_flag[pfs[i][j]] = false; }
//test each e whether non-manifold
function<void(vector<uint32_t> &, const uint32_t &)> four_es = [&](vector<uint32_t> &es, const uint32_t & fid) {
if (Ismesh) { es = mesh.Fs[fid].es; }
else { es = frame.FFs[fid].es; }
};
function<void(vector<uint32_t> &, const uint32_t &)> four_vs = [&](vector<uint32_t> &vs, const uint32_t & fid) {
if (Ismesh) { vs = mesh.Fs[fid].vs; }
else { vs = frame.FFs[fid].vs; }
};
bool non_simple = false;
vector<uint32_t> es;
for (uint32_t i = 0; i < pf.size(); ++i) {
four_es(es, pf[i]);
for (auto eid : es) {
E_flag[eid]++;
if (E_flag[eid] > 2) non_simple = true;
}
if (non_simple) {
for (uint32_t k = 0; k < pf.size(); ++k) {
four_es(es, pf[k]);
for (auto eid : es) E_flag[eid] = false;
}
return false;
}
}
for (uint32_t k = 0; k < pf.size(); ++k){
four_es(es, pf[k]);
for (auto eid : es) if(E_flag[eid]!=2) non_simple = true;
}
for (uint32_t k = 0; k < pf.size(); ++k) {
four_es(es, pf[k]);
for (auto eid : es) E_flag[eid] = false;
}
if (non_simple) return false;
//test each v whether non-manifold
std::vector<uint32_t> vs_set;
for (uint32_t i = 0; i < pf.size(); ++i) {
std::vector<uint32_t> vs;
four_vs(vs, pf[i]);
for (auto vid : vs) {
F_nvs[vid].push_back(i);
if (!V_flag[vid]) {vs_set.push_back(vid); V_flag[vid] = true;}
}
}
for (auto vid: vs_set) V_flag[vid] = false;
for (auto vid: vs_set) {
sort(F_nvs[vid].begin(), F_nvs[vid].end());
F_nvs[vid].erase(std::unique(F_nvs[vid].begin(), F_nvs[vid].end()), F_nvs[vid].end());
vector<vector<uint32_t>> fes;
for (auto fid : F_nvs[vid])
if(Ismesh) fes.push_back(mesh.Fs[fid].es); else fes.push_back(frame.FFs[fid].es);
if (!disk_polygon(mesh, frame, fes, E_flag, V_flag, Ismesh)){
non_simple = true; break;
}
}
for (auto vid : vs_set) F_nvs[vid].clear();
if (non_simple) return false;
return true;
}
bool comp_topology(Mesh_Topology & mt0, Mesh_Topology & mt1) {
if (mt1.manifoldness_problem) return false;
if (mt0.genus != mt1.genus) return false;
if (mt0.frame_genus != mt1.frame_genus) return false;
return true;
}
bool redundentV_check(Mesh &meshI, Mesh &meshO) {
bool redundentV = false;
build_connectivity(meshI);
vector<int> V_tag(meshI.Vs.size(), -1);
int vI = 0;
for (auto v : meshI.Vs) {
if (!v.neighbor_hs.size() || !v.neighbor_fs.size()) { redundentV = true; continue; }
V_tag[v.id] = vI++;
}
meshO.type = meshI.type;
meshO.V.resize(3, vI);
for (int i = 0; i < V_tag.size();i++) {
if (V_tag[i] == -1) continue;
Hybrid_V vo;
vo.id = meshO.Vs.size();
vo.boundary = false;
meshO.Vs.push_back(vo);
meshO.V.col(V_tag[i]) = meshI.V.col(i);
}
meshO.Hs = meshI.Hs;
Hybrid h;
if (meshO.type == Mesh_type::Hex)h.vs.resize(8);
else if (meshO.type == Mesh_type::Tet)h.vs.resize(4);
for (auto &h:meshO.Hs) {
for (uint32_t j = 0; j < h.vs.size(); j++) h.vs[j] = V_tag[h.vs[j]];
for (uint32_t i = 0; i < h.vs.size(); i++) meshO.Vs[h.vs[i]].neighbor_hs.push_back(h.id);
}
return redundentV;
}
double average_edge_length(Mesh &mesh) {
double ave_length = 0;
for (uint32_t i = 0; i < mesh.Fs.size(); i++) {
auto &vs = mesh.Fs[i].vs;
for (uint32_t j = 0; j < 3; j++) ave_length += (mesh.V.col(vs[j]) - mesh.V.col(vs[(j + 1) % 3])).norm();
}
int N = mesh.Fs.size() * 3;
ave_length /= N;
return ave_length;
}
void re_indexing_connectivity(Mesh &hmi, MatrixXi &H){
hmi.Vs.clear();
hmi.Es.clear();
hmi.Fs.clear();
hmi.Hs.clear();
//Vs
hmi.Vs.resize(hmi.V.cols());
for (uint32_t i = 0; i<hmi.V.cols(); i++)
{
Hybrid_V v;
v.id = i; v.boundary = false;
hmi.Vs[i] = v;
}
//Hs
hmi.Hs.resize(H.cols());
Hybrid h; ;
if (hmi.type == Mesh_type::Hex)h.vs.resize(8);
else if (hmi.type == Mesh_type::Tet)h.vs.resize(4);
for (uint32_t i = 0; i < H.cols(); i++) {
for (uint32_t j = 0; j < H.rows(); j++) h.vs[j] = H(j, i);
h.id = i; hmi.Hs[h.id] = h;
for (uint32_t i = 0; i < h.vs.size(); i++) hmi.Vs[h.vs[i]].neighbor_hs.push_back(h.id);
}
//Es, Fs, and their connectivities
build_connectivity(hmi);
}
void extract_surface_mesh(Mesh &meshi, Mesh &mesho) {
mesho.Vs.clear(); mesho.Es.clear(); mesho.Fs.clear(); mesho.Hs.clear();
mesho.type = Mesh_type::Tri;
vector<bool> V_tag(meshi.Vs.size(), false);
vector<int32_t> V_map(meshi.Vs.size(), -1), V_map_reverse;
for (auto f : meshi.Fs) if (f.boundary) {
for (auto vid : f.vs) V_tag[vid] = true;
if (f.vs.size() == 3) {
Hybrid_F hf; hf.vs = f.vs;
mesho.Fs.push_back(hf);
}
else if (f.vs.size() == 4) {
Hybrid_F hf;
hf.vs.push_back(f.vs[0]);
hf.vs.push_back(f.vs[1]);
hf.vs.push_back(f.vs[2]);
mesho.Fs.push_back(hf);
hf.vs.clear();
hf.vs.push_back(f.vs[2]);
hf.vs.push_back(f.vs[3]);
hf.vs.push_back(f.vs[0]);
mesho.Fs.push_back(hf);
}
}
//re-indexing
uint32_t newV_id = 0;
for (uint32_t i = 0; i < V_tag.size(); i++) if (V_tag[i]) {
V_map[i] = newV_id++; V_map_reverse.push_back(i);
}
mesho.V.resize(3, newV_id);
for (uint32_t i = 0; i < V_tag.size(); i++) if (V_tag[i]) {
Hybrid_V v;
v.id = mesho.Vs.size(); mesho.Vs.push_back(v);
mesho.V.col(v.id) = meshi.V.col(i);
}
for (uint32_t i = 0; i < mesho.Fs.size(); i++) for (uint32_t j = 0; j < 3; j++) mesho.Fs[i].vs[j] = V_map[mesho.Fs[i].vs[j]];
orient_surface_mesh(mesho);
}
void orient_surface_mesh(Mesh &hmi) {
vector<bool> flag(hmi.Fs.size(), true);
flag[0] = false;
std::queue<uint32_t> pf_temp; pf_temp.push(0);
while (!pf_temp.empty()) {
uint32_t fid = pf_temp.front(); pf_temp.pop();
for (auto eid : hmi.Fs[fid].es) for (auto nfid : hmi.Es[eid].neighbor_fs) {
if (!flag[nfid]) continue;
uint32_t v0 = hmi.Es[eid].vs[0], v1 = hmi.Es[eid].vs[1];
int32_t v0_pos = std::find(hmi.Fs[fid].vs.begin(), hmi.Fs[fid].vs.end(), v0) - hmi.Fs[fid].vs.begin();
int32_t v1_pos = std::find(hmi.Fs[fid].vs.begin(), hmi.Fs[fid].vs.end(), v1) - hmi.Fs[fid].vs.begin();
if ((v0_pos + 1) % hmi.Fs[fid].vs.size() != v1_pos) swap(v0, v1);
int32_t v0_pos_ = std::find(hmi.Fs[nfid].vs.begin(), hmi.Fs[nfid].vs.end(), v0) - hmi.Fs[nfid].vs.begin();
int32_t v1_pos_ = std::find(hmi.Fs[nfid].vs.begin(), hmi.Fs[nfid].vs.end(), v1) - hmi.Fs[nfid].vs.begin();
if ((v0_pos_ + 1) % hmi.Fs[nfid].vs.size() == v1_pos_) std::reverse(hmi.Fs[nfid].vs.begin(), hmi.Fs[nfid].vs.end());
pf_temp.push(nfid); flag[nfid] = false;
}
}
Float res = 0;
Vector3d ori; ori.setZero();
for (auto f : hmi.Fs) {
auto &fvs = f.vs;
Vector3d center; center.setZero(); for (auto vid : fvs) center += hmi.V.col(vid); center /= fvs.size();
for (uint32_t j = 0; j < fvs.size(); j++) {
Vector3d x = hmi.V.col(fvs[j]) - ori, y = hmi.V.col(fvs[(j + 1) % fvs.size()]) - ori, z = center - ori;
res += -((x[0] * y[1] * z[2] + x[1] * y[2] * z[0] + x[2] * y[0] * z[1]) - (x[2] * y[1] * z[0] + x[1] * y[0] * z[2] + x[0] * y[2] * z[1]));
}
}
if (res > 0) {
for (uint32_t i = 0; i < hmi.Fs.size(); i++) std::reverse(hmi.Fs[i].vs.begin(), hmi.Fs[i].vs.end());
}
}
void orient_triangle_mesh(Mesh &hmi) {
vector<vector<Float>> p(hmi.V.cols()); vector<vector<uint32_t>> f(hmi.Fs.size());
for (uint32_t i = 0; i<hmi.V.cols(); i++){
vector<Float> pv;
pv.push_back(hmi.V(0,i));
pv.push_back(hmi.V(1,i));
pv.push_back(hmi.V(2,i));
p[i] = pv;
}
for (uint32_t i = 0; i < hmi.Fs.size(); i++) f[i] = hmi.Fs[i].vs;
std::map<std::set<uint32_t>, vector<uint32_t>> edge_2_neb_tri;
std::set<vector<uint32_t>> direct_edges;
std::set<std::set<uint32_t>> no_direct_edges;
vector<bool> whe_tri_in;
vector<vector<uint32_t>> nf;
nf = f;
for (int i = 0; i<f.size(); i++)
{
std::set<uint32_t> xa, xb, xc;
xa.insert(f[i][0]);
xa.insert(f[i][1]);
xb.insert(f[i][1]);
xb.insert(f[i][2]);
xc.insert(f[i][2]);
xc.insert(f[i][0]);
whe_tri_in.push_back(false);
vector<uint32_t> ct;
ct.push_back(i);
if (edge_2_neb_tri.find(xa) == edge_2_neb_tri.end())
{
edge_2_neb_tri.insert(std::pair<std::set<uint32_t>, vector<uint32_t>>(xa, ct));
}
else
{
edge_2_neb_tri[xa].push_back(i);
}
if (edge_2_neb_tri.find(xb) == edge_2_neb_tri.end())
{
edge_2_neb_tri.insert(std::pair<std::set<uint32_t>, vector<uint32_t>>(xb, ct));
}
else
{
edge_2_neb_tri[xb].push_back(i);
}
if (edge_2_neb_tri.find(xc) == edge_2_neb_tri.end())
{
edge_2_neb_tri.insert(std::pair<std::set<uint32_t>, vector<uint32_t>>(xc, ct));
}
else
{
edge_2_neb_tri[xc].push_back(i);
}
}
std::set<uint32_t> xa, xb, xc;
vector<uint32_t> ya, yb, yc;
xa.insert(f[0][0]);
xa.insert(f[0][1]);
xb.insert(f[0][1]);
xb.insert(f[0][2]);
xc.insert(f[0][2]);
xc.insert(f[0][0]);
ya.push_back(f[0][0]);
ya.push_back(f[0][1]);
yb.push_back(f[0][1]);
yb.push_back(f[0][2]);
yc.push_back(f[0][2]);
yc.push_back(f[0][0]);
no_direct_edges.insert(xa);
no_direct_edges.insert(xb);
no_direct_edges.insert(xc);
direct_edges.insert(ya);
direct_edges.insert(yb);
direct_edges.insert(yc);
whe_tri_in[0] = true;
std::queue<uint32_t> queue_loop;
for (uint32_t i = 0; i<2; i++)
{
if (!whe_tri_in[edge_2_neb_tri[xa][i]])
{
queue_loop.push(edge_2_neb_tri[xa][i]);
whe_tri_in[edge_2_neb_tri[xa][i]] = true;
}
if (!whe_tri_in[edge_2_neb_tri[xb][i]])
{
queue_loop.push(edge_2_neb_tri[xb][i]);
whe_tri_in[edge_2_neb_tri[xb][i]] = true;
}
if (!whe_tri_in[edge_2_neb_tri[xc][i]])
{
queue_loop.push(edge_2_neb_tri[xc][i]);
whe_tri_in[edge_2_neb_tri[xc][i]] = true;
}
}
while (!queue_loop.empty())
{
xa.clear();
xb.clear();
xc.clear();
ya.clear();
yb.clear();
yc.clear();
uint32_t c;
c = queue_loop.front();
xa.insert(f[c][0]);
xa.insert(f[c][1]);
xb.insert(f[c][1]);
xb.insert(f[c][2]);
xc.insert(f[c][2]);
xc.insert(f[c][0]);
ya.push_back(f[c][0]);
ya.push_back(f[c][1]);
yb.push_back(f[c][1]);
yb.push_back(f[c][2]);
yc.push_back(f[c][2]);
yc.push_back(f[c][0]);
uint32_t cnt, ct;
cnt = 0;
ct = 0;
if (no_direct_edges.find(xa) != no_direct_edges.end())
{
cnt++;
}
if (no_direct_edges.find(xb) != no_direct_edges.end())
{
cnt++;
}
if (no_direct_edges.find(xc) != no_direct_edges.end())
{
cnt++;
}
if (direct_edges.find(ya) != direct_edges.end())
{
ct++;
}
if (direct_edges.find(yb) != direct_edges.end())
{
ct++;
}
if (direct_edges.find(yc) != direct_edges.end())
{
ct++;
}
if (cnt == 0)
{
std::cout << "Error in triangle direction solving!" << std::endl;
exit(0);
}
if (ct != 0)
{
ya.clear();
yb.clear();
yc.clear();
ya.push_back(f[c][1]);
ya.push_back(f[c][0]);
yb.push_back(f[c][2]);
yb.push_back(f[c][1]);
yc.push_back(f[c][0]);
yc.push_back(f[c][2]);
nf[c][0] = f[c][1];
nf[c][1] = f[c][0];
}
else
{
// do nothing
}
no_direct_edges.insert(xa);
no_direct_edges.insert(xb);
no_direct_edges.insert(xc);
direct_edges.insert(ya);
direct_edges.insert(yb);
direct_edges.insert(yc);
for (uint32_t i = 0; i<2; i++)
{
if (!whe_tri_in[edge_2_neb_tri[xa][i]])
{
queue_loop.push(edge_2_neb_tri[xa][i]);
whe_tri_in[edge_2_neb_tri[xa][i]] = true;
}
if (!whe_tri_in[edge_2_neb_tri[xb][i]])
{
queue_loop.push(edge_2_neb_tri[xb][i]);
whe_tri_in[edge_2_neb_tri[xb][i]] = true;
}
if (!whe_tri_in[edge_2_neb_tri[xc][i]])
{
queue_loop.push(edge_2_neb_tri[xc][i]);
whe_tri_in[edge_2_neb_tri[xc][i]] = true;
}
}
queue_loop.pop();
}
Float res = 0;
vector<Float> ori(3, 0);
for (uint32_t i = 0; i<nf.size(); i++)
res += uctet(ori, p[nf[i][0]], p[nf[i][1]], p[nf[i][2]]);
if (res > 0)
{
uint32_t tmi;
for (uint32_t i = 0; i<nf.size(); i++)
{
tmi = nf[i][0];
nf[i][0] = nf[i][1];
nf[i][1] = tmi;
}
}
for (uint32_t i = 0; i < hmi.Fs.size(); i++)
hmi.Fs[i].vs = nf[i];
}
void orient_triangle_mesh(MatrixXd &Tri_V, MatrixXi &Tri_F) {
vector<vector<Float>> p(Tri_V.cols()); vector<vector<uint32_t>> f(Tri_F.rows());
for (uint32_t i = 0; i<Tri_V.cols(); i++) {
vector<Float> pv;
pv.push_back(Tri_V(0,i));
pv.push_back(Tri_V(1,i));
pv.push_back(Tri_V(2,i));
p[i] = pv;
}
for (uint32_t i = 0; i < Tri_F.rows(); i++)
for (uint32_t j = 0; j < 3; j++)
f[i].push_back(Tri_F(i, j));
std::map<std::set<uint32_t>, vector<uint32_t>> edge_2_neb_tri;
std::set<vector<uint32_t>> direct_edges;
std::set<std::set<uint32_t>> no_direct_edges;
vector<bool> whe_tri_in;
vector<vector<uint32_t>> nf;
nf = f;
for (int i = 0; i<f.size(); i++)
{
std::set<uint32_t> xa, xb, xc;
xa.insert(f[i][0]);
xa.insert(f[i][1]);
xb.insert(f[i][1]);
xb.insert(f[i][2]);
xc.insert(f[i][2]);
xc.insert(f[i][0]);
whe_tri_in.push_back(false);
vector<uint32_t> ct;
ct.push_back(i);
if (edge_2_neb_tri.find(xa) == edge_2_neb_tri.end())
{
edge_2_neb_tri.insert(std::pair<std::set<uint32_t>, vector<uint32_t>>(xa, ct));
}
else
{
edge_2_neb_tri[xa].push_back(i);
}
if (edge_2_neb_tri.find(xb) == edge_2_neb_tri.end())
{
edge_2_neb_tri.insert(std::pair<std::set<uint32_t>, vector<uint32_t>>(xb, ct));
}
else
{
edge_2_neb_tri[xb].push_back(i);
}
if (edge_2_neb_tri.find(xc) == edge_2_neb_tri.end())
{
edge_2_neb_tri.insert(std::pair<std::set<uint32_t>, vector<uint32_t>>(xc, ct));
}
else
{
edge_2_neb_tri[xc].push_back(i);
}
}
std::set<uint32_t> xa, xb, xc;
vector<uint32_t> ya, yb, yc;
xa.insert(f[0][0]);
xa.insert(f[0][1]);
xb.insert(f[0][1]);
xb.insert(f[0][2]);
xc.insert(f[0][2]);
xc.insert(f[0][0]);
ya.push_back(f[0][0]);
ya.push_back(f[0][1]);
yb.push_back(f[0][1]);
yb.push_back(f[0][2]);
yc.push_back(f[0][2]);
yc.push_back(f[0][0]);
no_direct_edges.insert(xa);
no_direct_edges.insert(xb);
no_direct_edges.insert(xc);
direct_edges.insert(ya);
direct_edges.insert(yb);
direct_edges.insert(yc);
whe_tri_in[0] = true;
std::queue<uint32_t> queue_loop;
for (uint32_t i = 0; i<2; i++)
{
if (!whe_tri_in[edge_2_neb_tri[xa][i]])
{
queue_loop.push(edge_2_neb_tri[xa][i]);
whe_tri_in[edge_2_neb_tri[xa][i]] = true;
}
if (!whe_tri_in[edge_2_neb_tri[xb][i]])
{
queue_loop.push(edge_2_neb_tri[xb][i]);
whe_tri_in[edge_2_neb_tri[xb][i]] = true;
}
if (!whe_tri_in[edge_2_neb_tri[xc][i]])
{
queue_loop.push(edge_2_neb_tri[xc][i]);
whe_tri_in[edge_2_neb_tri[xc][i]] = true;
}
}
while (!queue_loop.empty())
{
xa.clear();
xb.clear();
xc.clear();
ya.clear();
yb.clear();
yc.clear();