195 lines
6.4 KiB
C++
195 lines
6.4 KiB
C++
// This file is part of libigl, a simple c++ geometry processing library.
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//
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// Copyright (C) 2018 Francis Williams <francis@fwilliams.info>
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//
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// This Source Code Form is subject to the terms of the Mozilla Public License
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// v. 2.0. If a copy of the MPL was not distributed with this file, You can
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// obtain one at http://mozilla.org/MPL/2.0/.
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#include "marching_tets.h"
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#include <unordered_map>
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#include <vector>
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#include <utility>
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#include <cstdint>
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#include <iostream>
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template <typename DerivedTV,
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typename DerivedTT,
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typename DerivedS,
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typename DerivedSV,
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typename DerivedSF,
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typename DerivedJ,
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typename BCType>
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void igl::marching_tets(
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const Eigen::PlainObjectBase<DerivedTV>& TV,
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const Eigen::PlainObjectBase<DerivedTT>& TT,
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const Eigen::PlainObjectBase<DerivedS>& isovals,
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double isovalue,
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Eigen::PlainObjectBase<DerivedSV>& outV,
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Eigen::PlainObjectBase<DerivedSF>& outF,
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Eigen::PlainObjectBase<DerivedJ>& J,
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Eigen::SparseMatrix<BCType>& BC)
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{
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using namespace std;
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// We're hashing edges to deduplicate using 64 bit ints. The upper and lower
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// 32 bits of a key are the indices of vertices in the mesh. The implication is
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// that you can only have 2^32 vertices which I have deemed sufficient for
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// anything reasonable.
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const auto make_edge_key = [](const pair<int32_t, int32_t>& p) -> int64_t
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{
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std::int64_t ret = 0;
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ret |= p.first;
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ret |= static_cast<std::int64_t>(p.second) << 32;
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return ret;
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};
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const int mt_cell_lookup[16][4] =
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{
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{ -1, -1, -1, -1 },
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{ 0, 2, 1, -1 },
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{ 0, 3, 4, -1 },
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{ 2, 1, 3, 4 },
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{ 5, 3, 1, -1 },
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{ 0, 2, 5, 3 },
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{ 0, 1, 5, 4 },
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{ 2, 5, 4, -1 },
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{ 4, 5, 2, -1 },
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{ 0, 4, 5, 1 },
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{ 0, 3, 5, 2 },
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{ 1, 3, 5, -1 },
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{ 4, 3, 1, 2 },
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{ 0, 4, 3, -1 },
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{ 0, 1, 2, -1 },
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{ -1, -1, -1, -1 },
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};
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const int mt_edge_lookup[6][2] =
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{
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{0, 1},
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{0, 2},
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{0, 3},
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{1, 2},
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{1, 3},
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{2, 3},
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};
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// Store the faces and the tet they are in
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vector<pair<Eigen::RowVector3i, int>> faces;
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// Store the edges in the tet mesh which we add vertices on
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// so we can deduplicate
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vector<pair<int, int>> edge_table;
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assert(TT.cols() == 4 && TT.rows() >= 1);
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assert(TV.cols() == 3 && TV.rows() >= 4);
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assert(isovals.cols() == 1);
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// For each tet
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for (int i = 0; i < TT.rows(); i++)
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{
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uint8_t key = 0;
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for (int v = 0; v < 4; v++)
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{
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const int vid = TT(i, v);
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const uint8_t flag = isovals[vid] > isovalue;
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key |= flag << v;
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}
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// This will contain the index in TV of each vertex in the tet
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int v_ids[4] = {-1, -1, -1, -1};
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// Insert any vertices if the tet intersects the level surface
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for (int e = 0; e < 4 && mt_cell_lookup[key][e] != -1; e++)
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{
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const int tv1_idx = TT(i, mt_edge_lookup[mt_cell_lookup[key][e]][0]);
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const int tv2_idx = TT(i, mt_edge_lookup[mt_cell_lookup[key][e]][1]);
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const int vertex_id = edge_table.size();
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edge_table.push_back(make_pair(min(tv1_idx, tv2_idx), max(tv1_idx, tv2_idx)));
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v_ids[e] = vertex_id;
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}
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// Insert the corresponding faces
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if (v_ids[0] != -1)
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{
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bool is_quad = mt_cell_lookup[key][3] != -1;
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if (is_quad)
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{
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const Eigen::RowVector3i f1(v_ids[0], v_ids[1], v_ids[3]);
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const Eigen::RowVector3i f2(v_ids[1], v_ids[2], v_ids[3]);
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faces.push_back(make_pair(f1, i));
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faces.push_back(make_pair(f2, i));
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}
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else
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{
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const Eigen::RowVector3i f(v_ids[0], v_ids[1], v_ids[2]);
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faces.push_back(make_pair(f, i));
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}
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}
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}
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int num_unique = 0;
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outV.resize(edge_table.size(), 3);
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outF.resize(faces.size(), 3);
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J.resize(faces.size());
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// Sparse matrix triplets for BC
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vector<Eigen::Triplet<BCType>> bc_triplets;
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bc_triplets.reserve(edge_table.size());
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// Deduplicate vertices
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unordered_map<int64_t, int> emap;
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emap.max_load_factor(0.5);
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emap.reserve(edge_table.size());
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for (int f = 0; f < faces.size(); f++)
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{
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for (int v = 0; v < 3; v++)
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{
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const int vi = faces[f].first[v];
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const int ti = faces[f].second;
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const pair<int32_t, int32_t> edge = edge_table[vi];
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const int64_t key = make_edge_key(edge);
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auto it = emap.find(key);
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if (it == emap.end()) // New unique vertex, insert it
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{
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// Typedef to make sure we handle floats properly
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typedef Eigen::Matrix<typename DerivedTV::Scalar, 1, 3, Eigen::RowMajor, 1, 3> RowVector;
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const RowVector v1 = TV.row(edge.first);
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const RowVector v2 = TV.row(edge.second);
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const double a = fabs(isovals[edge.first] - isovalue);
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const double b = fabs(isovals[edge.second] - isovalue);
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const double w = a / (a+b);
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// Create a casted copy in case BCType is a float and we need to downcast
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const BCType bc_w = static_cast<BCType>(w);
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bc_triplets.push_back(Eigen::Triplet<BCType>(num_unique, edge.first, 1-bc_w));
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bc_triplets.push_back(Eigen::Triplet<BCType>(num_unique, edge.second, bc_w));
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// Create a casted copy in case DerivedTV::Scalar is a float and we need to downcast
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const typename DerivedTV::Scalar v_w = static_cast<typename DerivedTV::Scalar>(w);
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outV.row(num_unique) = (1-v_w)*v1 + v_w*v2;
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outF(f, v) = num_unique;
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J[f] = ti;
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emap.emplace(key, num_unique);
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num_unique += 1;
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} else {
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outF(f, v) = it->second;
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}
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}
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}
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outV.conservativeResize(num_unique, 3);
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J.conservativeResize(num_unique, 1);
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BC.resize(num_unique, TV.rows());
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BC.setFromTriplets(bc_triplets.begin(), bc_triplets.end());
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}
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#ifdef IGL_STATIC_LIBRARY
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template void igl::marching_tets<Eigen::Matrix<double, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, Eigen::Matrix<double, -1, 1, 0, -1, 1>, Eigen::Matrix<double, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, 1, 0, -1, 1>, double>(Eigen::PlainObjectBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<double, -1, 1, 0, -1, 1> > const&, double, Eigen::PlainObjectBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> >&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> >&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, 1, 0, -1, 1> >&, Eigen::SparseMatrix<double, 0, int>&);
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#endif // IGL_STATIC_LIBRARY
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