MySources/topologyenumerator.cpp

#include "topologyenumerator.hpp"
#include <algorithm>
#include <iostream>
#include <math.h>
#include <numeric>
#include <unordered_set>

const bool debugIsOn{false};
const bool exportArticulationPointsPatterns{false};
const bool savePlyFiles{true};

// size_t binomialCoefficient(size_t n, size_t m) {
//  assert(n > m);
//  return tgamma(n + 1) / (tgamma(m + 1) * tgamma(n - m + 1));
//}

// void TopologyEnumerator::createLabelMesh(
//    const std::vector<vcg::Point3d> vertices,
//    const std::filesystem::path &savePath) const {
//  const std::string allOnes(patternTopology.getNumberOfPossibleEdges(), '1');
//  const std::vector<vcg::Point2i> allEdges =
//      TrianglePatternTopology::convertToEdges(allOnes, vertices.size());
//  TrianglePatternGeometry labelMesh;
//  std::vector<vcg::Point3d> labelVertices(allEdges.size());
//  for (size_t edgeIndex = 0; edgeIndex < allEdges.size(); edgeIndex++) {
//    const vcg::Point3d edgeMidpoint =
//        (vertices[allEdges[edgeIndex][0]] + vertices[allEdges[edgeIndex][1]])
//        / 2;
//    labelVertices[edgeIndex] = edgeMidpoint;
//  }
//  labelMesh.set(labelVertices);
//  labelMesh.savePly(std::filesystem::path(savePath)
//                        .append(std::string("labelMesh.ply"))
//                        .string());
//}

size_t TopologyEnumerator::getEdgeIndex(size_t ni0, size_t ni1) const {
  if (ni1 <= ni0) {
    std::swap(ni0, ni1);
  }
  assert(ni1 > ni0);
  const size_t &n = numberOfNodes;
  return (n * (n - 1) / 2) - (n - ni0) * ((n - ni0) - 1) / 2 + ni1 - ni0 - 1;
}

TopologyEnumerator::TopologyEnumerator() {}

void TopologyEnumerator::computeValidPatterns(
    const std::vector<size_t> &reducedNumberOfNodesPerSlot) {
  assert(reducedNumberOfNodesPerSlot.size() == 5);
  assert(reducedNumberOfNodesPerSlot[0] == 0 ||
         reducedNumberOfNodesPerSlot[0] == 1);
  assert(reducedNumberOfNodesPerSlot[1] == 0 ||
         reducedNumberOfNodesPerSlot[1] == 1);
  std::vector<size_t> numberOfNodesPerSlot{
      reducedNumberOfNodesPerSlot[0], reducedNumberOfNodesPerSlot[1],
      reducedNumberOfNodesPerSlot[1], reducedNumberOfNodesPerSlot[2],
      reducedNumberOfNodesPerSlot[3], reducedNumberOfNodesPerSlot[2],
      reducedNumberOfNodesPerSlot[4]};
  // Generate an edge mesh wih all possible edges
  numberOfNodes = std::accumulate(numberOfNodesPerSlot.begin(),
                                  numberOfNodesPerSlot.end(), 0);
  const size_t numberOfAllPossibleEdges =
      numberOfNodes * (numberOfNodes - 1) / 2;

  std::vector<vcg::Point2i> allPossibleEdges(numberOfAllPossibleEdges);
  const int &n = numberOfNodes;
  for (size_t edgeIndex = 0; edgeIndex < numberOfAllPossibleEdges;
       edgeIndex++) {
    const int ni0 =
        n - 2 -
        std::floor(std::sqrt(-8 * edgeIndex + 4 * n * (n - 1) - 7) / 2.0 - 0.5);
    const int ni1 =
        edgeIndex + ni0 + 1 - n * (n - 1) / 2 + (n - ni0) * ((n - ni0) - 1) / 2;
    allPossibleEdges[edgeIndex] = vcg::Point2i(ni0, ni1);
  }
  FlatPatternGeometry patternGeometryAllEdges;
  patternGeometryAllEdges.add(numberOfNodesPerSlot, allPossibleEdges);
  // Create Results path
  auto resultPath =
      //      std::filesystem::path("/home/iason/Documents/PhD/Research/Enumerating\\
      //      "
      //                            "2d\\ connections\\ of\\ nodes");
      std::filesystem::current_path()
          .parent_path()
          .parent_path()
          .parent_path()
          .parent_path();
  assert(std::filesystem::exists(resultPath));

  auto allResultsPath = resultPath.append("Results");
  std::filesystem::create_directory(allResultsPath);
  std::string setupString;
  //  for (size_t numberOfNodes : reducedNumberOfNodesPerSlot) {
  for (size_t numberOfNodesPerSlotIndex = 0;
       numberOfNodesPerSlotIndex < reducedNumberOfNodesPerSlot.size();
       numberOfNodesPerSlotIndex++) {
    std::string elemID;
    if (numberOfNodesPerSlotIndex == 0 || numberOfNodesPerSlotIndex == 1) {
      elemID = "v";
    } else if (numberOfNodesPerSlotIndex == 2 ||
               numberOfNodesPerSlotIndex == 3) {
      elemID = "e";
    } else {
      elemID = "c";
    }
    setupString +=
        std::to_string(reducedNumberOfNodesPerSlot[numberOfNodesPerSlotIndex]) +
        elemID + "_";
  }
  setupString += std::to_string(FlatPatternGeometry().getFanSize()) + "fan";
  if (debugIsOn) {
    setupString += "_debug";
  }
  auto resultsPath = std::filesystem::path(allResultsPath).append(setupString);
  //    std::filesystem::remove_all(resultsPath); // delete previous results
  std::filesystem::create_directory(resultsPath);
  if (debugIsOn) {
    patternGeometryAllEdges.savePly(std::filesystem::path(resultsPath)
                                        .append("allPossibleEdges.ply")
                                        .string());
  }
  //  statistics.numberOfPossibleEdges = numberOfAllPossibleEdges;

  std::vector<vcg::Point2i> validEdges =
      getValidEdges(numberOfNodesPerSlot, resultsPath, patternGeometryAllEdges,
                    allPossibleEdges);
  FlatPatternGeometry patternAllValidEdges;
  patternAllValidEdges.add(patternGeometryAllEdges.getVertices(), validEdges);
  if (debugIsOn) {
    // Export all valid edges in a ply
    patternAllValidEdges.savePly(
        std::filesystem::path(resultsPath).append("allValidEdges.ply"));
  }
  //  statistics.numberOfValidEdges = validEdges.size();

  // Find pairs of intersecting edges
  std::unordered_map<size_t, std::unordered_set<size_t>> intersectingEdges =
      patternAllValidEdges.getIntersectingEdges(
          statistics.numberOfIntersectingEdgePairs);
  if (debugIsOn) {
    auto intersectingEdgesPath = std::filesystem::path(resultsPath)
                                     .append("All_intersecting_edge_pairs");
    std::filesystem::create_directory(intersectingEdgesPath);
    // Export intersecting pairs in ply files
    for (auto mapIt = intersectingEdges.begin();
         mapIt != intersectingEdges.end(); mapIt++) {
      for (auto setIt = mapIt->second.begin(); setIt != mapIt->second.end();
           setIt++) {
        FlatPatternGeometry intersectingEdgePair;
        const size_t ei0 = mapIt->first;
        const size_t ei1 = *setIt;
        vcg::tri::Allocator<FlatPatternGeometry>::AddEdge(
            intersectingEdgePair,
            patternGeometryAllEdges.getVertices()[validEdges[ei0][0]],
            patternGeometryAllEdges.getVertices()[validEdges[ei0][1]]);
        vcg::tri::Allocator<FlatPatternGeometry>::AddEdge(
            intersectingEdgePair,
            patternGeometryAllEdges.getVertices()[validEdges[ei1][0]],
            patternGeometryAllEdges.getVertices()[validEdges[ei1][1]]);
        intersectingEdgePair.savePly(
            std::filesystem::path(intersectingEdgesPath)
                .append(std::to_string(mapIt->first) + "_" +
                        std::to_string(*setIt) + ".ply")
                .string());
      }
    }
  }

  //  assert(validEdges.size() == allPossibleEdges.size() -
  //  coincideEdges.size() -
  //                                   duplicateEdges.size());

  PatternSet patternSet;
  const std::vector<vcg::Point3d> nodes = patternGeometryAllEdges.getVertices();
  const size_t numberOfNodes = nodes.size();
  patternSet.nodes.resize(numberOfNodes);
  for (size_t nodeIndex = 0; nodeIndex < numberOfNodes; nodeIndex++) {
    patternSet.nodes[nodeIndex] =
        vcg::Point2d(nodes[nodeIndex][0], nodes[nodeIndex][1]);
  }
  if (std::filesystem::exists(std::filesystem::path(resultsPath)
                                  .append("patterns.patt")
                                  .string())) {
    std::filesystem::remove(
        std::filesystem::path(resultsPath).append("patterns.patt"));
  }
  for (size_t numberOfEdges = 2; numberOfEdges < validEdges.size();
       numberOfEdges++) {
    //  for (size_t numberOfEdges = 1; numberOfEdges < 3; numberOfEdges++) {
    std::cout << "Computing " + setupString << " with " << numberOfEdges
              << " edges." << std::endl;
    auto perEdgeResultPath = std::filesystem::path(resultsPath)
                                 .append(std::to_string(numberOfEdges));
    //        if (std::filesystem::exists(perEdgeResultPath)) {
    //          continue;
    //        }
    std::filesystem::create_directory(perEdgeResultPath);
    computeValidPatterns(numberOfNodesPerSlot, numberOfEdges, perEdgeResultPath,
                         patternGeometryAllEdges.getVertices(),
                         intersectingEdges, validEdges, patternSet);
    //    statistics.print(setupString, perEdgeResultPath);
    PatternIO::save(
        std::filesystem::path(resultsPath).append("patterns.patt").string(),
        patternSet);
  }
}

void TopologyEnumerator::computeEdgeNodes(
    const std::vector<size_t> &numberOfNodesPerSlot,
    std::vector<size_t> &nodesEdge0, std::vector<size_t> &nodesEdge1,
    std::vector<size_t> &nodesEdge2) {
  // Create vectors holding the node indices of each pattern node of each
  // triangle edge
  size_t nodeIndex = 0;
  if (numberOfNodesPerSlot[0] != 0) {
    nodesEdge0.push_back(nodeIndex++);
  }
  if (numberOfNodesPerSlot[1] != 0)
    nodesEdge1.push_back(nodeIndex++);
  if (numberOfNodesPerSlot[2] != 0)
    nodesEdge2.push_back(nodeIndex++);

  if (numberOfNodesPerSlot[3] != 0) {
    for (size_t edgeNodeIndex = 0; edgeNodeIndex < numberOfNodesPerSlot[3];
         edgeNodeIndex++) {
      nodesEdge0.push_back(nodeIndex++);
    }
  }
  if (numberOfNodesPerSlot[4] != 0) {
    for (size_t edgeNodeIndex = 0; edgeNodeIndex < numberOfNodesPerSlot[4];
         edgeNodeIndex++) {
      nodesEdge1.push_back(nodeIndex++);
    }
  }

  if (numberOfNodesPerSlot[5] != 0) {
    for (size_t edgeNodeIndex = 0; edgeNodeIndex < numberOfNodesPerSlot[5];
         edgeNodeIndex++) {
      nodesEdge2.push_back(nodeIndex++);
    }
  }
  if (numberOfNodesPerSlot[1] != 0) {
    assert(numberOfNodesPerSlot[2]);
    nodesEdge0.push_back(1);
    nodesEdge1.push_back(2);
  }

  if (numberOfNodesPerSlot[0] != 0) {
    nodesEdge2.push_back(0);
  }
}

std::unordered_set<size_t> TopologyEnumerator::computeCoincideEdges(
    const std::vector<size_t> &numberOfNodesPerSlot) {
  /*
   * A coincide edge is defined as an edge connection between two nodes that lay
   * on a triangle edge and which have another node in between
   * */
  std::vector<size_t> nodesEdge0; // left edge
  std::vector<size_t> nodesEdge1; // bottom edge
  std::vector<size_t> nodesEdge2; // right edge
  computeEdgeNodes(numberOfNodesPerSlot, nodesEdge0, nodesEdge1, nodesEdge2);

  std::vector<size_t> coincideEdges0 = getCoincideEdges(nodesEdge0);
  std::vector<size_t> coincideEdges1 = getCoincideEdges(nodesEdge1);
  std::vector<size_t> coincideEdges2 = getCoincideEdges(nodesEdge2);
  std::unordered_set<size_t> coincideEdges{coincideEdges0.begin(),
                                           coincideEdges0.end()};
  std::copy(coincideEdges1.begin(), coincideEdges1.end(),
            std::inserter(coincideEdges, coincideEdges.end()));
  std::copy(coincideEdges2.begin(), coincideEdges2.end(),
            std::inserter(coincideEdges, coincideEdges.end()));

  if (numberOfNodesPerSlot[0] && numberOfNodesPerSlot[1]) {
    coincideEdges.insert(getEdgeIndex(0, 2));
  }

  if (numberOfNodesPerSlot[0] && numberOfNodesPerSlot[2]) {
    assert(numberOfNodesPerSlot[1]);
    coincideEdges.insert(getEdgeIndex(0, 3));
  }

  return coincideEdges;
}

std::unordered_set<size_t> TopologyEnumerator::computeDuplicateEdges(
    const std::vector<size_t> &numberOfNodesPerSlot) {
  /*
   * A duplicate edges are all edges the "right" edge since due to rotational
   * symmetry "left" edge=="right" edge
   * */
  std::unordered_set<size_t> duplicateEdges;
  std::vector<size_t> nodesEdge0; // left edge
  std::vector<size_t> nodesEdge1; // bottom edge
  std::vector<size_t> nodesEdge2; // right edge
  computeEdgeNodes(numberOfNodesPerSlot, nodesEdge0, nodesEdge1, nodesEdge2);
  if (numberOfNodesPerSlot[5]) {
    for (size_t edge2NodeIndex = 0; edge2NodeIndex < nodesEdge2.size() - 1;
         edge2NodeIndex++) {
      const size_t nodeIndex = nodesEdge2[edge2NodeIndex];
      const size_t nextNodeIndex = nodesEdge2[edge2NodeIndex + 1];
      duplicateEdges.insert(getEdgeIndex(nodeIndex, nextNodeIndex));
    }
  }

  return duplicateEdges;
}

std::vector<vcg::Point2i> TopologyEnumerator::getValidEdges(
    const std::vector<size_t> &numberOfNodesPerSlot,
    const std::filesystem::path &resultsPath,
    const FlatPatternGeometry &patternGeometryAllEdges,
    const std::vector<vcg::Point2i> &allPossibleEdges) {

  std::unordered_set<size_t> coincideEdges =
      computeCoincideEdges(numberOfNodesPerSlot);
  // Export each coincide edge into a ply file
  if (!coincideEdges.empty() && debugIsOn) {
    auto coincideEdgesPath =
        std::filesystem::path(resultsPath).append("Coincide_edges");
    std::filesystem::create_directories(coincideEdgesPath);
    for (auto coincideEdgeIndex : coincideEdges) {
      FlatPatternGeometry::EdgeType e =
          patternGeometryAllEdges.edge[coincideEdgeIndex];
      FlatPatternGeometry singleEdgeMesh;
      vcg::Point3d p0 = e.cP(0);
      vcg::Point3d p1 = e.cP(1);
      std::vector<vcg::Point3d> edgeVertices;
      edgeVertices.push_back(p0);
      edgeVertices.push_back(p1);
      singleEdgeMesh.add(edgeVertices);
      singleEdgeMesh.add(std::vector<vcg::Point2i>{vcg::Point2i{0, 1}});
      singleEdgeMesh.savePly(std::filesystem::path(coincideEdgesPath)
                                 .append(std::to_string(coincideEdgeIndex))
                                 .string() +
                             ".ply");
    }
  }
  statistics.numberOfCoincideEdges = coincideEdges.size();

  // Compute duplicate edges
  std::unordered_set<size_t> duplicateEdges =
      computeDuplicateEdges(numberOfNodesPerSlot);
  if (!duplicateEdges.empty() && debugIsOn) {
    // Export duplicate edges in a single ply file
    auto duplicateEdgesPath =
        std::filesystem::path(resultsPath).append("duplicate");
    std::filesystem::create_directory(duplicateEdgesPath);
    FlatPatternGeometry patternDuplicateEdges;
    for (auto duplicateEdgeIndex : duplicateEdges) {
      FlatPatternGeometry::EdgeType e =
          patternGeometryAllEdges.edge[duplicateEdgeIndex];
      vcg::Point3d p0 = e.cP(0);
      vcg::Point3d p1 = e.cP(1);
      vcg::tri::Allocator<FlatPatternGeometry>::AddEdge(
          patternDuplicateEdges, p0, p1);
    }
    patternDuplicateEdges.savePly(
        std::filesystem::path(duplicateEdgesPath).append("duplicateEdges.ply"));
  }
  statistics.numberOfDuplicateEdges = duplicateEdges.size();

  // Create the set of all possible edges without coincide and duplicate edges
  std::vector<vcg::Point2i> validEdges;
  for (size_t edgeIndex = 0; edgeIndex < allPossibleEdges.size(); edgeIndex++) {
    if (coincideEdges.count(edgeIndex) == 0 &&
        duplicateEdges.count(edgeIndex) == 0) {
      validEdges.push_back(allPossibleEdges[edgeIndex]);
    }
  }

  return validEdges;
}

void TopologyEnumerator::computeValidPatterns(
    const std::vector<size_t> &numberOfNodesPerSlot,
    const size_t &numberOfDesiredEdges,
    const std::filesystem::path &resultsPath,
    const std::vector<vcg::Point3d> &allVertices,
    const std::unordered_map<size_t, std::unordered_set<size_t>>
        &intersectingEdges,
    const std::vector<vcg::Point2i> &validEdges, PatternSet &patternsSet) {
  assert(numberOfNodesPerSlot.size() == 7);

  // Iterate over all patterns which have numberOfDesiredEdges edges from
  // from the validEdges Identify patterns that contain dangling edges
  const bool enoughValidEdgesExist = validEdges.size() >= numberOfDesiredEdges;
  if (!enoughValidEdgesExist) {
    std::filesystem::remove_all(resultsPath); // delete previous results folder
    return;
  }
  assert(enoughValidEdgesExist);

  // Create pattern result paths
  auto validPatternsPath = std::filesystem::path(resultsPath).append("Valid");
  std::filesystem::create_directory(validPatternsPath);

  const size_t numberOfPatterns = FlatPatternGeometry::binomialCoefficient(
      validEdges.size(), numberOfDesiredEdges);
  statistics.numberOfPatterns = numberOfPatterns;

  // Initialize pattern binary representation
  std::string patternBinaryRepresentation;
  patternBinaryRepresentation = std::string(numberOfDesiredEdges, '1');
  patternBinaryRepresentation +=
      std::string(validEdges.size() - numberOfDesiredEdges, '0');
  std::sort(patternBinaryRepresentation.begin(),
            patternBinaryRepresentation.end());
  size_t patternIndex = 0;
  do {
    patternIndex++;
    const std::string patternName = std::to_string(patternIndex);
    //    std::cout << "Pattern name:" + patternBinaryRepresentation <<
    //    std::endl; isValidPattern(patternBinaryRepresentation, validEdges,
    //                   numberOfDesiredEdges);
    // Create the geometry of the pattern
    // Compute the pattern edges from the binary representation
    std::vector<vcg::Point2i> patternEdges(numberOfDesiredEdges);
    size_t patternEdgeIndex = 0;
    for (size_t validEdgeIndex = 0;
         validEdgeIndex < patternBinaryRepresentation.size();
         validEdgeIndex++) {
      if (patternBinaryRepresentation[validEdgeIndex] == '1') {
        assert(patternEdgeIndex < numberOfDesiredEdges);
        patternEdges[patternEdgeIndex++] = validEdges[validEdgeIndex];
      }
    }
    Pattern pattern;
    pattern.edges = patternEdges;

    FlatPatternGeometry patternGeometry;
    patternGeometry.add(allVertices, patternEdges);

    // Check if pattern contains intersecting edges
    const bool patternContainsIntersectingEdges =
        patternGeometry.hasIntersectingEdges(patternBinaryRepresentation,
                                             intersectingEdges);
    // Export the tiled ply file if it contains intersecting edges
    if (patternContainsIntersectingEdges) {
      // create the tiled geometry of the pattern
      statistics.numberOfPatternsWithIntersectingEdges++;
      if (debugIsOn) {
        if (savePlyFiles) {
          FlatPatternGeometry tiledPatternGeometry =
              FlatPatternGeometry::createTile(patternGeometry);
          auto intersectingPatternsPath =
              std::filesystem::path(resultsPath).append("Intersecting");
          std::filesystem::create_directory(intersectingPatternsPath);
          patternGeometry.savePly(
              std::filesystem::path(intersectingPatternsPath)
                  .append(patternName)
                  .string() +
              ".ply");
          tiledPatternGeometry.savePly(
              std::filesystem::path(intersectingPatternsPath)
                  .append(patternName + "_tiled")
                  .string() +
              ".ply");
        }
        pattern.labels.push_back(PatternLabel::IntersectingEdges);
      } else {
        continue; // should be uncommented in order to improve performance
      }
    }

    // Compute the tiled valence
    const bool tiledPatternHasDanglingEdges = patternGeometry.hasDanglingEdges(
        numberOfNodesPerSlot); // marks the nodes with valence>=1
                               // Create the tiled geometry of the pattern
    const bool hasFloatingComponents =
        !patternGeometry.isFullyConnectedWhenTiled();
    FlatPatternTopology topology(numberOfNodesPerSlot, patternEdges);
    const bool hasArticulationPoints = topology.containsArticulationPoints();
    FlatPatternGeometry tiledPatternGeometry =
        FlatPatternGeometry::createTile(
            patternGeometry); // the marked nodes of hasDanglingEdges are
    // duplicated here
    // Check dangling edges with vcg method
    //    const bool vcg_tiledPatternHasDangling =
    //        tiledPatternGeometry.hasUntiledDanglingEdges();
    if (tiledPatternHasDanglingEdges /*&& !hasFloatingComponents &&
        !hasArticulationPoints*/) {
      statistics.numberOfPatternsWithADanglingEdgeOrNode++;
      if (debugIsOn) {
        if (savePlyFiles) {
          auto danglingEdgesPath =
              std::filesystem::path(resultsPath).append("Dangling");
          std::filesystem::create_directory(danglingEdgesPath);
          patternGeometry.savePly(std::filesystem::path(danglingEdgesPath)
                                      .append(patternName)
                                      .string() +
                                  ".ply");
          tiledPatternGeometry.savePly(std::filesystem::path(danglingEdgesPath)
                                           .append(patternName + "_tiled")
                                           .string() +
                                       ".ply");
        }
        pattern.labels.push_back(PatternLabel::DanglingEdge);
      } else {
        continue;
      }
    }

    if (hasFloatingComponents /*&& !hasArticulationPoints &&
        !tiledPatternHasDanglingEdges*/) {
      statistics.numberOfPatternsWithMoreThanASingleCC++;
      if (debugIsOn) {
        if (savePlyFiles) {
          auto moreThanOneCCPath =
              std::filesystem::path(resultsPath).append("MoreThanOneCC");
          std::filesystem::create_directory(moreThanOneCCPath);
          patternGeometry.savePly(std::filesystem::path(moreThanOneCCPath)
                                      .append(patternName)
                                      .string() +
                                  ".ply");
          tiledPatternGeometry.savePly(std::filesystem::path(moreThanOneCCPath)
                                           .append(patternName + "_tiled")
                                           .string() +
                                       ".ply");
        }
        pattern.labels.push_back(PatternLabel::MultipleCC);
      } else {
        continue;
      }
    }

    if (hasArticulationPoints /*&& !hasFloatingComponents &&
        !tiledPatternHasDanglingEdges*/) {
      statistics.numberOfPatternsWithArticulationPoints++;
      if (exportArticulationPointsPatterns || debugIsOn) {
        if (savePlyFiles) {
          auto articulationPointsPath =
              std::filesystem::path(resultsPath).append("ArticulationPoints");
          std::filesystem::create_directory(articulationPointsPath);
          patternGeometry.savePly(std::filesystem::path(articulationPointsPath)
                                      .append(patternName)
                                      .string() +
                                  ".ply");
          tiledPatternGeometry.savePly(
              std::filesystem::path(articulationPointsPath)
                  .append(patternName + "_tiled")
                  .string() +
              ".ply");

          //          std::cout << "Pattern:" << patternName << std::endl;
        }
        pattern.labels.push_back(PatternLabel::ArticulationPoints);
      } else {
        continue;
      }
    }

    const bool isValidPattern =
        !patternContainsIntersectingEdges && !tiledPatternHasDanglingEdges &&
        !hasFloatingComponents && !hasArticulationPoints;
    if (isValidPattern) {
      statistics.numberOfValidPatterns++;
      if (savePlyFiles) {
        //        if (numberOfDesiredEdges == 4) {
        //          std::cout << "Saving:"
        //                    << std::filesystem::path(validPatternsPath)
        //                               .append(patternName)
        //                               .string() +
        //                           ".ply"
        //                    << std::endl;
        //        }
        patternGeometry.savePly(std::filesystem::path(validPatternsPath)
                                    .append(patternName)
                                    .string() +
                                ".ply");
        tiledPatternGeometry.savePly(std::filesystem::path(validPatternsPath)
                                         .append(patternName + "_tiled")
                                         .string() +
                                     ".ply");
      }
      pattern.labels.push_back(PatternLabel::Valid);
    }

    assert(!pattern.labels.empty());
    patternsSet.patterns.push_back(pattern);
    //    assert(vcg_tiledPatternHasDangling == tiledPatternHasDanglingEdges);
  } while (std::next_permutation(patternBinaryRepresentation.begin(),
                                 patternBinaryRepresentation.end()));
}

std::vector<size_t> TopologyEnumerator::getCoincideEdges(
    const std::vector<size_t> &edgeNodeIndices) const {
  std::vector<size_t> coincideEdges;
  if (edgeNodeIndices.size() < 3)
    return coincideEdges;
  for (size_t edgeNodeIndex = 0; edgeNodeIndex < edgeNodeIndices.size() - 2;
       edgeNodeIndex++) {
    const size_t &firstNodeIndex = edgeNodeIndices[edgeNodeIndex];
    for (size_t secondEdgeNodeIndex = edgeNodeIndex + 2;
         secondEdgeNodeIndex < edgeNodeIndices.size(); secondEdgeNodeIndex++) {
      const size_t &secondNodeIndex = edgeNodeIndices[secondEdgeNodeIndex];
      coincideEdges.push_back(getEdgeIndex(firstNodeIndex, secondNodeIndex));
    }
  }
  return coincideEdges;
}

bool TopologyEnumerator::isValidPattern(
    const std::string &patternBinaryRepresentation,
    const std::vector<vcg::Point2i> &validEdges,
    const size_t &numberOfDesiredEdges) const {
  return true;
}