MySources/trianglepatterngeometry.cpp

#include "trianglepatterngeometry.hpp"
#include "trianglepattterntopology.hpp"
#include <algorithm>
#include <iterator>
#include <numeric>
#include <vcg/complex/algorithms/update/position.h>
#include <vcg/simplex/edge/topology.h>
#include <vcg/space/intersection2.h>
#include <wrap/io_trimesh/export.h>

size_t PatternGeometry::computeTiledValence(
    const size_t &nodeIndex,
    const std::vector<size_t> &numberOfNodesPerSlot) const {
  std::vector<PatternGeometry::EdgeType *> connectedEdges;
  vcg::edge::VEStarVE(&vert[nodeIndex], connectedEdges);
  const size_t nodeValence = connectedEdges.size();
  assert(nodeSlot.count(nodeIndex) != 0);
  const size_t nodeSlotIndex = nodeSlot.at(nodeIndex);
  if (nodeSlotIndex == 0) {
    return nodeValence * fanSize;
  } else if (nodeSlotIndex == 1 || nodeSlotIndex == 2) {
    size_t correspondingNodeIndex;
    if (nodeSlotIndex == 1) {
      correspondingNodeIndex = nodeIndex + 1;
    } else {
      correspondingNodeIndex = nodeIndex - 1;
    }
    std::vector<PatternGeometry::EdgeType *> connectedEdgesCorrespondingNode;
    vcg::edge::VEStarVE(&vert[correspondingNodeIndex],
                        connectedEdgesCorrespondingNode);
    size_t correspondingNodeValence = connectedEdgesCorrespondingNode.size();
    return fanSize / 2 * nodeValence + fanSize / 2 * correspondingNodeValence;
  } else if (nodeSlotIndex == 3 || nodeSlotIndex == 5) {
    size_t correspondingNodeIndex;
    size_t numberOfNodesBefore;
    size_t numberOfNodesAfter;
    if (nodeSlotIndex == 3) {
      numberOfNodesBefore =
          nodeIndex - std::accumulate(numberOfNodesPerSlot.begin(),
                                      numberOfNodesPerSlot.begin() + 3, 0);
      correspondingNodeIndex =

          std::accumulate(numberOfNodesPerSlot.begin(),
                          numberOfNodesPerSlot.begin() + 6, 0) -
          1 - numberOfNodesBefore;
    } else {
      numberOfNodesAfter =
          std::accumulate(numberOfNodesPerSlot.begin(),
                          numberOfNodesPerSlot.begin() + 6, 0) -
          1 - nodeIndex;
      correspondingNodeIndex =
          numberOfNodesAfter + std::accumulate(numberOfNodesPerSlot.begin(),
                                               numberOfNodesPerSlot.begin() + 3,
                                               0);
    }
    assert(correspondingNodeIndex < vn);
    std::vector<PatternGeometry::EdgeType *> connectedEdgesCorrespondingNode;
    vcg::edge::VEStarVE(&vert[correspondingNodeIndex],
                        connectedEdgesCorrespondingNode);
    size_t correspondingNodeValence = connectedEdgesCorrespondingNode.size();
    return nodeValence + correspondingNodeValence;
  } else if (nodeSlotIndex == 4) {
    return 2 * nodeValence;
  } else if (nodeSlotIndex == 6) {
    return nodeValence;
  } else {
    std::cerr << "Error in slot index computation" << std::endl;
  }
  assert(false);
  return 0;
}

size_t PatternGeometry::getFanSize() const { return fanSize; }

double PatternGeometry::getTriangleEdgeSize() const { return triangleEdgeSize; }

PatternGeometry::PatternGeometry() {}

std::vector<vcg::Point3d> PatternGeometry::getVertices() const {
  std::vector<VCGEdgeMesh::CoordType> verts(VN());
  for (size_t vi = 0; vi < VN(); vi++) {
    verts[vi] = vert[vi].cP();
  }
  return verts;
}

PatternGeometry PatternGeometry::createTile(PatternGeometry &pattern) {

  const size_t fanSize = PatternGeometry().getFanSize();
  PatternGeometry fan(createFan(pattern));
  PatternGeometry tile(fan);

  if (fanSize % 2 == 1) {
    vcg::Matrix44d R;
    auto rotationAxis = vcg::Point3d(0, 0, 1);
    R.SetRotateDeg(180, rotationAxis);
    vcg::tri::UpdatePosition<PatternGeometry>::Matrix(fan, R);
  }
  vcg::Matrix44d T;
  const double centerAngle = 2 * M_PI / fanSize;
  const double triangleHeight =
      std::sin((M_PI - centerAngle) / 2) * PatternGeometry().triangleEdgeSize;
  T.SetTranslate(0, -2 * triangleHeight, 0);
  vcg::tri::UpdatePosition<PatternGeometry>::Matrix(fan, T);

  PatternGeometry fanOfFan = createFan(fan);
  vcg::tri::Append<PatternGeometry, PatternGeometry>::Mesh(tile, fanOfFan);
  vcg::tri::Clean<PatternGeometry>::MergeCloseVertex(tile, 0.0000005);
  vcg::tri::Allocator<PatternGeometry>::CompactEveryVector(tile);
  vcg::tri::UpdateTopology<PatternGeometry>::VertexEdge(tile);
  vcg::tri::UpdateTopology<PatternGeometry>::EdgeEdge(tile);

  for (size_t vi = 0; vi < pattern.vn; vi++) {
    tile.vert[vi].C() = vcg::Color4b::Blue;
  }

  tile.updateEigenEdgeAndVertices();
  return tile;
}

PatternGeometry PatternGeometry::createFan(PatternGeometry &pattern) {
  const size_t fanSize = PatternGeometry().getFanSize();
  PatternGeometry fan(pattern);
  PatternGeometry rotatedPattern(pattern);
  for (int rotationCounter = 1; rotationCounter < fanSize; rotationCounter++) {
    vcg::Matrix44d R;
    auto rotationAxis = vcg::Point3d(0, 0, 1);
    R.SetRotateDeg(360 / fanSize, rotationAxis);
    vcg::tri::UpdatePosition<PatternGeometry>::Matrix(rotatedPattern, R);
    vcg::tri::Append<PatternGeometry, PatternGeometry>::Mesh(fan,
                                                             rotatedPattern);
  }
  return fan;
}

PatternGeometry::PatternGeometry(PatternGeometry &other) {
  vcg::tri::Append<PatternGeometry, PatternGeometry>::MeshCopy(*this, other);
  this->vertices = other.getVertices();
  vcg::tri::UpdateTopology<PatternGeometry>::VertexEdge(*this);
  vcg::tri::UpdateTopology<PatternGeometry>::EdgeEdge(*this);
}

bool PatternGeometry::save(const std::string plyFilename) {

  int returnValue = vcg::tri::io::ExporterPLY<PatternGeometry>::Save(
      *this, plyFilename.c_str(),
      vcg::tri::io::Mask::IOM_EDGEINDEX | vcg::tri::io::Mask::IOM_VERTCOLOR,
      false);
  if (returnValue != 0) {
    std::cerr << vcg::tri::io::ExporterPLY<PatternGeometry>::ErrorMsg(
                     returnValue)
              << std::endl;
  }

  return static_cast<bool>(returnValue);
}

void PatternGeometry::add(const std::vector<vcg::Point3d> &vertices) {
  this->vertices = vertices;
  std::for_each(vertices.begin(), vertices.end(), [&](const vcg::Point3d &p) {
    vcg::tri::Allocator<PatternGeometry>::AddVertex(*this, p);
  });
  vcg::tri::UpdateTopology<PatternGeometry>::VertexEdge(*this);
  vcg::tri::UpdateTopology<PatternGeometry>::EdgeEdge(*this);
  updateEigenEdgeAndVertices();
}

void PatternGeometry::add(const std::vector<vcg::Point2i> &edges) {
  std::for_each(edges.begin(), edges.end(), [&](const vcg::Point2i &e) {
    vcg::tri::Allocator<PatternGeometry>::AddEdge(*this, e[0], e[1]);
  });
  vcg::tri::UpdateTopology<PatternGeometry>::VertexEdge(*this);
  vcg::tri::UpdateTopology<PatternGeometry>::EdgeEdge(*this);
  updateEigenEdgeAndVertices();
}

void PatternGeometry::add(const std::vector<vcg::Point3d> &vertices,
                          const std::vector<vcg::Point2i> &edges) {
  add(vertices);
  add(edges);
  updateEigenEdgeAndVertices();
}

void PatternGeometry::add(const std::vector<size_t> &numberOfNodesPerSlot,
                          const std::vector<vcg::Point2i> &edges) {
  assert(numberOfNodesPerSlot.size() == 7);
  auto vertices =
      constructVertexVector(numberOfNodesPerSlot, fanSize, triangleEdgeSize);
  add(vertices, edges);
  vcg::tri::UpdateTopology<PatternGeometry>::VertexEdge(*this);
  vcg::tri::UpdateTopology<PatternGeometry>::EdgeEdge(*this);
  updateEigenEdgeAndVertices();
}

std::vector<vcg::Point3d> PatternGeometry::constructVertexVector(
    const std::vector<size_t> &numberOfNodesPerSlot, const size_t &fanSize,
    const double &triangleEdgeSize) {

  std::vector<vcg::Point3d> vertices;
  const double centerAngle = 2 * M_PI / fanSize;
  const double triangleHeight =
      std::sin((M_PI - centerAngle) / 2) * triangleEdgeSize;
  const double baseEdgeSize =
      2 * triangleEdgeSize * std::cos((M_PI - centerAngle) / 2);
  const vcg::Point3d triangleV0 = vcg::Point3d(0, 0, 0);
  const vcg::Point3d triangleV1 =
      vcg::Point3d(-baseEdgeSize / 2, -triangleHeight, 0);
  const vcg::Point3d triangleV2 =
      vcg::Point3d(baseEdgeSize / 2, -triangleHeight, 0);

  // Nodes
  if (numberOfNodesPerSlot[0] == 1) {
    //    vertices[0] = triangleV0;
    vertices.push_back(triangleV0);
  }
  if (numberOfNodesPerSlot[1] == 1) {
    //    vertices[1] = triangleV1;
    vertices.push_back(triangleV1);
  }
  if (numberOfNodesPerSlot[2] == 1) {
    //    vertices[2] = triangleV2;
    vertices.push_back(triangleV2);
  }

  // Edges
  if (numberOfNodesPerSlot[3] != 0) {
    const double offset0 = 1.0 / (numberOfNodesPerSlot[3] + 1);
    const vcg::Point3d edgeVector0(triangleV1 - triangleV0);
    for (size_t vertexIndex = 0; vertexIndex < numberOfNodesPerSlot[3];
         vertexIndex++) {

      //      vertices[std::accumulate(numberOfNodesPerSlot.begin(),
      //                               numberOfNodesPerSlot.begin() + 2, 0) +
      //               vertexIndex] =
      vertices.push_back(triangleV0 +
                         edgeVector0.operator*((vertexIndex + 1) * offset0));
    }
  }

  if (numberOfNodesPerSlot[4] == 1) {
    vertices.push_back(vcg::Point3d(0, -triangleHeight, 0));
  } else if (numberOfNodesPerSlot[4] != 0) {
    const double offset1 = 1.0 / (numberOfNodesPerSlot[4] + 1);
    const vcg::Point3d edgeVector1(triangleV2 - triangleV1);
    for (size_t vertexIndex = 0; vertexIndex < numberOfNodesPerSlot[4];
         vertexIndex++) {

      //      vertices[std::accumulate(numberOfNodesPerSlot.begin(),
      //                               numberOfNodesPerSlot.begin() + 3, 0) +
      //               vertexIndex] =
      vertices.push_back(triangleV1 +
                         edgeVector1.operator*((vertexIndex + 1) * offset1));
    }
  }

  if (numberOfNodesPerSlot[5] != 0) {
    const double offset2 = 1.0 / (numberOfNodesPerSlot[5] + 1);
    const vcg::Point3d edgeVector2(triangleV0 - triangleV2);
    for (size_t vertexIndex = 0; vertexIndex < numberOfNodesPerSlot[5];
         vertexIndex++) {
      //      vertices[std::accumulate(numberOfNodesPerSlot.begin(),
      //                               numberOfNodesPerSlot.begin() + 4, 0) +
      //               vertexIndex] =
      vertices.push_back(triangleV2 +
                         edgeVector2.operator*((vertexIndex + 1) * offset2));
    }
  }

  // Face
  if (numberOfNodesPerSlot[6] != 0) {
    const vcg::Point3d triangleCenter((triangleV0 + triangleV1 + triangleV2) /
                                      3);
    const double radius = 0.1;
    const double offsetRad = 2 * M_PI / numberOfNodesPerSlot[6];
    for (size_t vertexIndex = 0; vertexIndex < numberOfNodesPerSlot[6];
         vertexIndex++) {
      const double pX =
          triangleCenter[0] + radius * std::cos(vertexIndex * offsetRad);
      const double pY =
          triangleCenter[1] + radius * std::sin(vertexIndex * offsetRad);
      /*vertices[std::accumulate(numberOfNodesPerSlot.begin(),
                               numberOfNodesPerSlot.begin() + 5, 0) +
               vertexIndex] =*/
      vertices.push_back(vcg::Point3d(pX, pY, 0));
    }
  }
  return vertices;
}

void PatternGeometry::constructNodeToTiledValenceMap(
    const std::vector<size_t> &numberOfNodesPerSlot) {
  for (size_t nodeIndex = 0; nodeIndex < vn; nodeIndex++) {
    const size_t tiledValence =
        computeTiledValence(nodeIndex, numberOfNodesPerSlot);
    nodeTiledValence[nodeIndex] = tiledValence;
  }
}

bool PatternGeometry::hasDanglingEdges(
    const std::vector<size_t> &numberOfNodesPerSlot) {
  if (nodeSlot.empty()) {
    FlatPatternTopology::constructNodeToSlotMap(numberOfNodesPerSlot, nodeSlot);
  }
  if (correspondingNode.empty()) {
    constructCorresponginNodeMap(numberOfNodesPerSlot);
  }
  if (nodeTiledValence.empty()) {
    constructNodeToTiledValenceMap(numberOfNodesPerSlot);
  }
  bool hasDanglingEdges = false;
  for (size_t nodeIndex = 0; nodeIndex < vn; nodeIndex++) {
    const size_t tiledValence = nodeTiledValence[nodeIndex];
    if (tiledValence == 1) {
      vert[nodeIndex].C() = vcg::Color4b::Red;
      hasDanglingEdges = true;
    }
  }
  return hasDanglingEdges;
}

bool PatternGeometry::hasUntiledDanglingEdges() {
  //  vcg::tri::Clean<TrianglePatternGeometry>::MergeCloseVertex(*this,
  //  0.0000005);
  //  vcg::tri::Allocator<TrianglePatternGeometry>::CompactEveryVector(*this);
  //  vcg::tri::UpdateTopology<TrianglePatternGeometry>::VertexEdge(*this);
  //  vcg::tri::UpdateTopology<TrianglePatternGeometry>::EdgeEdge(*this);
  bool hasDanglingEdges = false;
  for (size_t vi = 0; vi < vn; vi++) {
    std::vector<PatternGeometry::EdgeType *> connectedEdges;
    vcg::edge::VEStarVE(&vert[vi], connectedEdges);
    const size_t nodeValence = connectedEdges.size();
    if (nodeValence == 1) {
      if (vert[vi].C().operator==(vcg::Color4b(vcg::Color4b::Red))) {

      } else {
        vert[vi].C() = vcg::Color4b::Blue;
      }
      hasDanglingEdges = true;
    }
  }
  return hasDanglingEdges;
}

// TODO: The function expects that the numberOfNodesPerSlot follows a specific
// format and that the vertex container was populated in a particular order.
void PatternGeometry::constructCorresponginNodeMap(
    const std::vector<size_t> &numberOfNodesPerSlot) {
  assert(vn != 0 && !nodeSlot.empty() && correspondingNode.empty() &&
         numberOfNodesPerSlot.size() == 7);

  for (size_t nodeIndex = 0; nodeIndex < vn; nodeIndex++) {
    const size_t slotIndex = nodeSlot[nodeIndex];
    if (slotIndex == 1) {
      correspondingNode[nodeIndex] = nodeIndex + 1;
    } else if (slotIndex == 2) {
      correspondingNode[nodeIndex] = nodeIndex - 1;
    } else if (slotIndex == 3) {
      const size_t numberOfNodesBefore =
          nodeIndex - std::accumulate(numberOfNodesPerSlot.begin(),
                                      numberOfNodesPerSlot.begin() + 3, 0);
      correspondingNode[nodeIndex] =
          std::accumulate(numberOfNodesPerSlot.begin(),
                          numberOfNodesPerSlot.begin() + 6, 0) -
          1 - numberOfNodesBefore;
    } else if (slotIndex == 5) {
      const size_t numberOfNodesAfter =
          std::accumulate(numberOfNodesPerSlot.begin(),
                          numberOfNodesPerSlot.begin() + 6, 0) -
          1 - nodeIndex;
      correspondingNode[nodeIndex] =
          numberOfNodesAfter + std::accumulate(numberOfNodesPerSlot.begin(),
                                               numberOfNodesPerSlot.begin() + 3,
                                               0);
    }
  }
}

bool PatternGeometry::isFullyConnectedWhenTiled() {
  assert(vn != 0 /* && !correspondingNode.empty()*/);
  //  TrianglePatternGeometry copyOfPattern(*this);

  // If bottom interface nodes have a valence of zero there definetely more than
  // a single cc
  bool bottomInterfaceIsConnected = false;
  for (size_t nodeIndex = 0; nodeIndex < vn; nodeIndex++) {
    if (nodeSlot[nodeIndex] == 1 || nodeSlot[nodeIndex] == 4 ||
        nodeSlot[nodeIndex] == 2) {
      std::vector<PatternGeometry::EdgeType *> connectedEdges;
      vcg::edge::VEStarVE(&vert[nodeIndex], connectedEdges);
      const size_t nodeValence = connectedEdges.size();
      if (nodeValence != 0) {
        bottomInterfaceIsConnected = true;
        break;
      }
    }
  }
  if (!bottomInterfaceIsConnected) {
    return false;
  }

  PatternGeometry fanedPattern = createFan(*this);
  vcg::tri::Clean<PatternGeometry>::MergeCloseVertex(fanedPattern, 0.000000005);
  vcg::tri::Allocator<PatternGeometry>::CompactEveryVector(fanedPattern);
  vcg::tri::UpdateTopology<PatternGeometry>::VertexEdge(fanedPattern);
  vcg::tri::UpdateTopology<PatternGeometry>::EdgeEdge(fanedPattern);
  std::vector<std::pair<int, PatternGeometry::EdgePointer>> eCC;
  vcg::tri::Clean<PatternGeometry>::edgeMeshConnectedComponents(fanedPattern,
                                                                eCC);

  const bool sideInterfaceIsConnected = 1 == eCC.size();
  if (!sideInterfaceIsConnected) {
    return false;
  }

  //  for (size_t nodeIndex = 0; nodeIndex < vn; nodeIndex++) {
  //    if (nodeTiledValence[nodeIndex] == 0)
  //      continue;
  //    const size_t slotIndex = nodeSlot[nodeIndex];
  //    // connect nodes belonging to first or third slot(nodes on the first
  //    // triangle edge)
  //    //      if (nodeTiledValence[nodeIndex] == 0 && slotIndex == 3) {
  //    //        continue;
  //    //      }
  //    if (slotIndex == 1 || slotIndex == 3) {
  //      assert(correspondingNode.count(nodeIndex) != 0);
  //      const size_t correspondingNodeIndex =
  //      correspondingNode[nodeIndex];
  //      std::vector<TrianglePatternGeometry::EdgeType *> starEdges;
  //      vcg::edge::VEStarVE(&vert[nodeIndex], starEdges);
  //      bool containsEdge = false;
  //      for (TrianglePatternGeometry::EdgeType *e : starEdges) {
  //        assert(vcg::tri::Index(*this, e->V(0)) == nodeIndex ||
  //                vcg::tri::Index(*this, e->V(1)) == nodeIndex);
  //        if (vcg::tri::Index(*this, e->V(0)) == nodeIndex) {
  //          if (vcg::tri::Index(*this, e->V(1)) == correspondingNodeIndex) {
  //            containsEdge = true;
  //            break;
  //          }
  //        } else if (vcg::tri::Index(*this, e->V(1)) == nodeIndex) {
  //          if (vcg::tri::Index(*this, e->V(0)) == correspondingNodeIndex) {
  //            containsEdge = true;
  //            break;
  //          }
  //        }
  //      }
  //      if (!containsEdge) {
  //        vcg::tri::Allocator<TrianglePatternGeometry>::AddEdge(
  //            copyOfPattern, nodeIndex, correspondingNodeIndex);
  //      }
  //    } else if (slotIndex == 2 || slotIndex == 5) {
  //      assert(correspondingNode.count(nodeIndex) != 0);
  //    } else {
  //      assert(correspondingNode.count(nodeIndex) == 0);
  //    }
  //  }

  //  std::vector<std::pair<int, TrianglePatternGeometry::EdgePointer>> eCC;
  //  vcg::tri::Clean<TrianglePatternGeometry>::edgeMeshConnectedComponents(
  //      copyOfPattern, eCC);
  //  size_t numberOfCC_edgeBased = eCC.size();
  //  size_t numberOfCC_vertexBased = numberOfCC_edgeBased;
  //  if (numberOfCC_edgeBased == 1) {
  //    vcg::tri::UpdateTopology<TrianglePatternGeometry>::VertexEdge(
  //        copyOfPattern);
  //    vcg::tri::UpdateTopology<TrianglePatternGeometry>::EdgeEdge(copyOfPattern);
  //    vcg::tri::UpdateFlags<TrianglePatternGeometry>::VertexSetV(copyOfPattern);
  //    vcg::tri::UpdateFlags<TrianglePatternGeometry>::VertexClear(copyOfPattern);
  //    for (size_t ei = 0; ei < copyOfPattern.EN(); ei++) {
  //      copyOfPattern.edge[ei].V(0)->SetV();
  //      copyOfPattern.edge[ei].V(1)->SetV();
  //    }

  //    for (size_t vi = 0; vi < copyOfPattern.VN(); vi++) {
  //      if (!copyOfPattern.vert[vi].IsV()) {
  //        numberOfCC_vertexBased++;
  //      }
  //    }
  //    return numberOfCC_vertexBased;
  //  }

  //  return numberOfCC_edgeBased == 1; // TODO: not good
  return true;
}

bool PatternGeometry::hasIntersectingEdges(
    const std::string &patternBinaryRepresentation,
    const std::unordered_map<size_t, std::unordered_set<size_t>>
        &intersectingEdges) {
  bool containsIntersectingEdges = false;
  for (size_t validEdgeIndex = 0;
       validEdgeIndex < patternBinaryRepresentation.size(); validEdgeIndex++) {
    if (patternBinaryRepresentation[validEdgeIndex] == '1' &&
        intersectingEdges.count(validEdgeIndex) != 0) {
      for (auto edgeIndexIt =
               intersectingEdges.find(validEdgeIndex)->second.begin();
           edgeIndexIt != intersectingEdges.find(validEdgeIndex)->second.end();
           edgeIndexIt++) {
        if (patternBinaryRepresentation[*edgeIndexIt] == '1') {
          containsIntersectingEdges = true;
          //            statistics.numberOfIntersectingEdgesOverAllPatterns++;
          break; // should be uncommented in order to improve
          //            performance
        }
      }
      if (containsIntersectingEdges) {
        break; // should be uncommented in order to improve performance
      }
    }
  }

  return containsIntersectingEdges;
}

std::unordered_map<size_t, std::unordered_set<size_t>>
PatternGeometry::getIntersectingEdges(
    size_t &numberOfIntersectingEdgePairs) const {
  std::unordered_map<size_t, std::unordered_set<size_t>> intersectingEdges;
  numberOfIntersectingEdgePairs = 0;
  size_t numberOfEdgePairs;
  if (en == 0 || en == 1) {
    numberOfEdgePairs = 0;
  } else {
    numberOfEdgePairs = binomialCoefficient(en, 2);
  }

  for (size_t edgePairIndex = 0; edgePairIndex < numberOfEdgePairs;
       edgePairIndex++) {
    size_t ei0 =
        en - 2 -
        floor(sqrt(-8 * edgePairIndex + 4 * en * (en - 1) - 7) / 2.0 - 0.5);
    size_t ei1 = edgePairIndex + ei0 + 1 - en * (en - 1) / 2 +
                 (en - ei0) * ((en - ei0) - 1) / 2;
    const vcg::Point2d p0(edge[ei0].cP(0)[0], edge[ei0].cP(0)[1]);
    const float epsilon = 0.000005;
    vcg::Box2d bb0(p0 - vcg::Point2d(epsilon, epsilon),
                   p0 + vcg::Point2d(epsilon, epsilon));
    const vcg::Point2d p1(edge[ei0].cP(1)[0], edge[ei0].cP(1)[1]);
    vcg::Box2d bb1(p1 - vcg::Point2d(epsilon, epsilon),
                   p1 + vcg::Point2d(epsilon, epsilon));
    const vcg::Point2d p2(edge[ei1].cP(0)[0], edge[ei1].cP(0)[1]);
    vcg::Box2d bb2(p2 - vcg::Point2d(epsilon, epsilon),
                   p2 + vcg::Point2d(epsilon, epsilon));
    if (bb2.Collide(bb1) || bb2.Collide(bb0))
      continue;
    const vcg::Point2d p3(edge[ei1].cP(1)[0], edge[ei1].cP(1)[1]);
    vcg::Box2d bb3(p3 - vcg::Point2d(epsilon, epsilon),
                   p3 + vcg::Point2d(epsilon, epsilon));
    if (bb3.Collide(bb1) || bb3.Collide(bb0))
      continue;
    const vcg::Segment2d s0(p0, p1);
    const vcg::Segment2d s1(p2, p3);

    vcg::Point2d intersectionPoint;
    const bool edgesIntersect =
        vcg::SegmentSegmentIntersection(s0, s1, intersectionPoint);
    if (edgesIntersect) {
      numberOfIntersectingEdgePairs++;
      intersectingEdges[ei0].insert(ei1);
      intersectingEdges[ei1].insert(ei0);
    }
  }
  return intersectingEdges;
}

PatternGeometry::PatternGeometry(const std::string &filename,
                                 bool addNormalsIfAbsent) {
  if (!std::filesystem::exists(std::filesystem::path(filename))) {
    assert(false);
    std::cerr << "No flat pattern with name " << filename << std::endl;
    return;
  }
  if (!load(filename)) {
    assert(false);
    std::cerr << "File could not be loaded  " << filename << std::endl;
    return;
  }
  if (addNormalsIfAbsent) {
    addNormals();
  }

  vcg::tri::UpdateTopology<PatternGeometry>::VertexEdge(*this);
  baseTriangleHeight = computeBaseTriangleHeight();

  updateEigenEdgeAndVertices();
}

double PatternGeometry::computeBaseTriangleHeight() const
{
    return vcg::Distance(vert[0].cP(), vert[interfaceNodeIndex].cP());
}

void PatternGeometry::addNormals() {
  bool normalsAreAbsent = vert[0].cN().Norm() < 0.000001;
  if (normalsAreAbsent) {
    for (auto &v : vert) {
      v.N() = CoordType(0, 0, 1);
    }
  }
}

vcg::Triangle3<double> PatternGeometry::getBaseTriangle() const
{
    double bottomEdgeHalfSize = computeBaseTriangleHeight() / std::tan(M_PI / 3);
    CoordType patternCoord0 = vert[0].cP();
    CoordType patternBottomRight = vert[interfaceNodeIndex].cP()
                                   + CoordType(bottomEdgeHalfSize, 0, 0);
    CoordType patternBottomLeft = vert[interfaceNodeIndex].cP()
                                  - CoordType(bottomEdgeHalfSize, 0, 0);
    return vcg::Triangle3<double>(patternCoord0, patternBottomLeft, patternBottomRight);
}

PatternGeometry::PatternGeometry(
    const std::vector<size_t> &numberOfNodesPerSlot,
    const std::vector<vcg::Point2i> &edges) {
  add(numberOfNodesPerSlot, edges);
  addNormals();
  baseTriangleHeight = computeBaseTriangleHeight();
  updateEigenEdgeAndVertices();
}

bool PatternGeometry::createHoneycombAtom() {
  VCGEdgeMesh honeycombQuarter;
  const VCGEdgeMesh::CoordType n(0, 0, 1);
  const double H = 0.2;
  const double height = 1.5 * H;
  const double width = 0.2;
  const double theta = 70;
  const double dy = tan(vcg::math::ToRad(90 - theta)) * width / 2;
  vcg::tri::Allocator<VCGEdgeMesh>::AddVertex(
      honeycombQuarter, VCGEdgeMesh::CoordType(0, height / 2, 0), n);
  vcg::tri::Allocator<VCGEdgeMesh>::AddVertex(
      honeycombQuarter, VCGEdgeMesh::CoordType(0, H / 2 - dy, 0), n);
  vcg::tri::Allocator<VCGEdgeMesh>::AddVertex(
      honeycombQuarter, VCGEdgeMesh::CoordType(width / 2, H / 2, 0), n);
  vcg::tri::Allocator<VCGEdgeMesh>::AddVertex(
      honeycombQuarter, VCGEdgeMesh::CoordType(width / 2, 0, 0), n);
  vcg::tri::Allocator<VCGEdgeMesh>::AddEdge(honeycombQuarter, 0, 1);
  vcg::tri::Allocator<VCGEdgeMesh>::AddEdge(honeycombQuarter, 1, 2);
  vcg::tri::Allocator<VCGEdgeMesh>::AddEdge(honeycombQuarter, 2, 3);

  VCGEdgeMesh honeycombAtom;
  // Top right
  vcg::tri::Append<VCGEdgeMesh, VCGEdgeMesh>::MeshCopy(honeycombAtom,
                                                       honeycombQuarter);
  // Bottom right
  vcg::Matrix44d rotM;
  rotM.SetRotateDeg(180, vcg::Point3d(1, 0, 0));
  vcg::tri::UpdatePosition<VCGEdgeMesh>::Matrix(honeycombQuarter, rotM);
  vcg::tri::Append<VCGEdgeMesh, VCGEdgeMesh>::Mesh(honeycombAtom,
                                                   honeycombQuarter);
  // Bottom left
  rotM.SetRotateDeg(180, vcg::Point3d(0, 1, 0));
  vcg::tri::UpdatePosition<VCGEdgeMesh>::Matrix(honeycombQuarter, rotM);
  vcg::tri::Append<VCGEdgeMesh, VCGEdgeMesh>::Mesh(honeycombAtom,
                                                   honeycombQuarter);
  // Top left
  rotM.SetRotateDeg(180, vcg::Point3d(1, 0, 0));
  vcg::tri::UpdatePosition<VCGEdgeMesh>::Matrix(honeycombQuarter, rotM);
  vcg::tri::Append<VCGEdgeMesh, VCGEdgeMesh>::Mesh(honeycombAtom,
                                                   honeycombQuarter);

  for (VertexType &v : honeycombAtom.vert) {
    v.P()[2] = 0;
  }

  return true;
}

void PatternGeometry::copy(PatternGeometry &copyFrom) {
  VCGEdgeMesh::copy(copyFrom);
  baseTriangleHeight = copyFrom.getBaseTriangleHeight();
}

void PatternGeometry::scale(const double &desiredBaseTriangleCentralEdgeSize,const int& interfaceNodeIndex) {
  this->baseTriangleHeight = desiredBaseTriangleCentralEdgeSize;
  const double baseTriangleCentralEdgeSize = getBaseTriangleHeight();
  const double scaleRatio =
      desiredBaseTriangleCentralEdgeSize / baseTriangleCentralEdgeSize;

  vcg::tri::UpdatePosition<VCGEdgeMesh>::Scale(*this, scaleRatio);
}

void PatternGeometry::createFan(const std::vector<int> &connectToNeighborsVi, const size_t &fanSize)
{
    PatternGeometry rotatedPattern;
    vcg::tri::Append<PatternGeometry, PatternGeometry>::MeshCopy(rotatedPattern, *this);
    for (int rotationCounter = 1; rotationCounter < fanSize; rotationCounter++) {
        vcg::Matrix44d R;
        auto rotationAxis = vcg::Point3d(0, 0, 1);
        R.SetRotateDeg(360 / fanSize, rotationAxis);
        vcg::tri::UpdatePosition<PatternGeometry>::Matrix(rotatedPattern, R);
        vcg::tri::Append<PatternGeometry, PatternGeometry>::Mesh(*this, rotatedPattern);
        //Add edges for connecting the desired vertices
        if (!connectToNeighborsVi.empty()) {
            if (rotationCounter == fanSize - 1) {
                for (int connectToNeighborIndex = 0;
                     connectToNeighborIndex < connectToNeighborsVi.size();
                     connectToNeighborIndex++) {
                    vcg::tri::Allocator<PatternGeometry>::AddEdge(
                        *this,
                        connectToNeighborsVi[connectToNeighborIndex],
                        this->VN() - rotatedPattern.VN()
                            + connectToNeighborsVi[connectToNeighborIndex]);
                }
            }
            for (int connectToNeighborIndex = 0;
                 connectToNeighborIndex < connectToNeighborsVi.size();
                 connectToNeighborIndex++) {
                vcg::tri::Allocator<PatternGeometry>::AddEdge(
                    *this,
                    this->VN() - 2 * rotatedPattern.VN()
                        + connectToNeighborsVi[connectToNeighborIndex],
                    this->VN() - rotatedPattern.VN() + connectToNeighborsVi[connectToNeighborIndex]);
            }
        }
        removeDuplicateVertices();
        updateEigenEdgeAndVertices();
    }
}

double PatternGeometry::getBaseTriangleHeight() const {
  return baseTriangleHeight;
}