MySources/trianglepatterngeometry.cpp

#include "trianglepatterngeometry.hpp"
#include <vcg/complex/algorithms/update/position.h>
#include <vcg/simplex/edge/topology.h>
#include <vcg/space/intersection2.h>
#include <wrap/io_trimesh/export.h>
#include <algorithm>
#include <iterator>
#include <numeric>
#include "trianglepattterntopology.hpp"
/* include the support for half edges */
#include <vcg/complex/algorithms/update/halfedge_indexed.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(nodeToSlotMap.count(nodeIndex) != 0);
  const size_t nodeSlotIndex = nodeToSlotMap.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::computeVertices() 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;
  vcg::tri::UpdateBounding<PatternGeometry>::Box(fan);
  const double triangleHeight = fan.bbox.DimY() / 2;
  T.SetTranslate(0, -2 * triangleHeight, 0);
  vcg::tri::UpdatePosition<PatternGeometry>::Matrix(fan, T);
  //    fan.registerForDrawing();
  //    polyscope::show();

  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.setLabel("tilled_" + pattern.getLabel());
  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;
}

void PatternGeometry::updateBaseTriangle() {
  baseTriangle = computeBaseTriangle();
}

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

bool PatternGeometry::load(const std::filesystem::__cxx11::path& meshFilePath) {
  if (!VCGEdgeMesh::load(meshFilePath)) {
    return false;
  }
  addNormals();
  vcg::tri::UpdateTopology<PatternGeometry>::VertexEdge(*this);
  baseTriangleHeight = computeBaseTriangleHeight();
  baseTriangle = computeBaseTriangle();

  updateEigenEdgeAndVertices();
  return true;
}

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, DefaultNormal);
  });
  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;
  }
}

std::vector<VectorType> PatternGeometry::getEdgeVectorsWithVertexAsOrigin(
    std::vector<EdgePointer>& edgePointers,
    const int& vi) {
  std::vector<VectorType> incidentElementsVectors(edgePointers.size());
  for (int incidentElementsIndex = 0;
       incidentElementsIndex < edgePointers.size(); incidentElementsIndex++) {
    assert(vi == getIndex(edgePointers[incidentElementsIndex]->cV(0)) ||
           vi == getIndex(edgePointers[incidentElementsIndex]->cV(1)));

    incidentElementsVectors[incidentElementsIndex] =
        vi == getIndex(edgePointers[incidentElementsIndex]->cV(0))
            ? edgePointers[incidentElementsIndex]->cP(1) -
                  edgePointers[incidentElementsIndex]->cP(0)
            : edgePointers[incidentElementsIndex]->cP(0) -
                  edgePointers[incidentElementsIndex]->cP(1);
  }

  return incidentElementsVectors;
}

bool PatternGeometry::hasAngleSmallerThanThreshold(
    const std::vector<size_t>& numberOfNodesPerSlot,
    const double& angleThreshold_degrees,
    const bool shouldBreak) {
  assert(numberOfNodesPerSlot.size() == 7);
  // Initialize helping structs
  if (nodeToSlotMap.empty()) {
    FlatPatternTopology::constructNodeToSlotMap(numberOfNodesPerSlot,
                                                nodeToSlotMap);
  }
  if (correspondingNode.empty()) {
    constructCorrespondingNodeMap(numberOfNodesPerSlot);
  }

  //    const double theta0 = vcg::math::ToDeg(vcg::Point2d(1, 0).Angle());
  //    const double theta1 = vcg::math::ToDeg(vcg::Point2d(1, 1).Angle());
  //    const double theta2 = vcg::math::ToDeg(vcg::Point2d(0, 1).Angle());
  //    const double theta3 = vcg::math::ToDeg(vcg::Point2d(-1, 1).Angle());
  //    const double theta4 = vcg::math::ToDeg(vcg::Point2d(-1, 0).Angle());
  //    const double theta5 = vcg::math::ToDeg(vcg::Point2d(-1, -1).Angle() + 2
  //    * M_PI); const double theta6 = vcg::math::ToDeg(vcg::Point2d(0,
  //    -1).Angle() + 2 * M_PI); const double theta7 =
  //    vcg::math::ToDeg(vcg::Point2d(1, -1).Angle() + 2 * M_PI);

  //    std::set<double> test{theta0, theta1, theta2, theta3, theta4, theta5,
  //    theta6, theta7};

  bool hasAngleSmallerThan = false;
  // find tiled incident edges for each node
  using EdgeIndex = int;
  using ThetaWithXAxis = double;
  for (size_t vi = 0; vi < VN(); vi++) {
    std::vector<EdgePointer> incidentElementPointers;
    vcg::edge::VEStarVE(&vert[vi], incidentElementPointers);
    const size_t numberOfIncidentEdges = incidentElementPointers.size();
    if (numberOfIncidentEdges == 0) {
      continue;
    }
    std::vector<VectorType> incidentEdgeVectors =
        getEdgeVectorsWithVertexAsOrigin(incidentElementPointers, vi);

    std::vector<VectorType> tiledIncidentVectors = incidentEdgeVectors;
    const size_t slotIndex = nodeToSlotMap[vi];
    if (slotIndex == 2) {
      // NOTE:I assume that base triangle slots 1,2(bottom triangle nodes) are
      // not used
      std::cerr << "Slot of bottom base triangle nodes detected.This case is "
                   "not handled.Exiting.."
                << std::endl;
      std::terminate();
    } else if (slotIndex == 3 || slotIndex == 5) {
      // NOTE: I don't need to check both triangle edges
      std::vector<PatternGeometry::EdgePointer>
          correspondingVertexIncidentElementPointers;
      vcg::edge::VEStarVE(&vert[correspondingNode[vi]],
                          correspondingVertexIncidentElementPointers);
      std::vector<VectorType> correspondingVertexIncidentVectors =
          getEdgeVectorsWithVertexAsOrigin(
              correspondingVertexIncidentElementPointers,
              correspondingNode[vi]);
      //            const CoordType &correspondingVertexPosition =
      //            vert[correspondingNode[vi]].cP();
      vcg::Matrix33d R;
      if (slotIndex == 3) {
        R = vcg::RotationMatrix(vcg::Point3d(0, 0, 1),
                                vcg::math::ToRad(-360.0 / fanSize));
      } else {
        R = vcg::RotationMatrix(vcg::Point3d(0, 0, 1),
                                vcg::math::ToRad(360.0 / fanSize));
      }
      //            const CoordType &correspondingVertexPosition_rotated =
      //            vert[vi].cP();
      std::transform(correspondingVertexIncidentVectors.begin(),
                     correspondingVertexIncidentVectors.end(),
                     correspondingVertexIncidentVectors.begin(),
                     [&](const VectorType& v) {
                       //                               CoordType rotatedTarget
                       //                               = v * R; v =
                       //                               rotatedTarget -
                       //                               correspondingVertexPosition_rotated;
                       return R * v;
                     });
      tiledIncidentVectors.insert(tiledIncidentVectors.end(),
                                  correspondingVertexIncidentVectors.begin(),
                                  correspondingVertexIncidentVectors.end());
    } else if (slotIndex == 4) {
      std::vector<VectorType> reversedIncidentElementVectors(
          incidentEdgeVectors.size());
      std::transform(incidentEdgeVectors.begin(), incidentEdgeVectors.end(),
                     reversedIncidentElementVectors.begin(),
                     [&](const VectorType& v) { return -v; });
      // NOTE: for checking the angles not all opposite incident element vectors
      // are needed but rather the two "extreme" ones of slot 4 here I simply
      // add them all
      tiledIncidentVectors.insert(tiledIncidentVectors.end(),
                                  reversedIncidentElementVectors.begin(),
                                  reversedIncidentElementVectors.end());
    }
    //        if (shouldBreak) {
    //          std::vector<std::array<double, 3>> edgePoints;
    //          for (int tiledVectorIndex = 0;
    //               tiledVectorIndex < tiledIncidentVectors.size();
    //               tiledVectorIndex++) {
    //            edgePoints.push_back(std::array<double, 3>{
    //                vert[vi].cP()[0], vert[vi].cP()[1], vert[vi].cP()[2]});
    //            edgePoints.push_back(std::array<double, 3>{
    //                (vert[vi].cP() +
    //                tiledIncidentVectors[tiledVectorIndex])[0], (vert[vi].cP()
    //                + tiledIncidentVectors[tiledVectorIndex])[1],
    //                (vert[vi].cP() +
    //                tiledIncidentVectors[tiledVectorIndex])[2]});
    //          }
    //          polyscope::init();
    //          polyscope::registerCurveNetworkLine("vi:" + std::to_string(vi),
    //                                              edgePoints);

    //          polyscope::show();
    //          polyscope::removeStructure("vi:" + std::to_string(vi));
    //        }

    if (tiledIncidentVectors.size() == 1) {
      continue;
    }

    std::vector<double> thetaAnglesOfIncidentVectors(
        tiledIncidentVectors.size());
    std::transform(
        tiledIncidentVectors.begin(), tiledIncidentVectors.end(),
        thetaAnglesOfIncidentVectors.begin(),
        [](const VectorType& v) { return vcg::Point2d(v[0], v[1]).Angle(); });
    // sort them using theta angles
    std::sort(thetaAnglesOfIncidentVectors.begin(),
              thetaAnglesOfIncidentVectors.end());

    //        std::vector<double> angles_theta(thetaAnglesOfIncidentVectors);
    //        for (double &theta_rad : angles_theta) {
    //            theta_rad = vcg::math::ToDeg(theta_rad);
    //        }

    // find nodes that contain incident edges with relative angles less than the
    // threshold
    const double angleThreshold_rad = vcg::math::ToRad(angleThreshold_degrees);
    for (int thetaAngleIndex = 0;
         thetaAngleIndex < thetaAnglesOfIncidentVectors.size();
         thetaAngleIndex++) {
      const auto& va_theta =
          thetaAnglesOfIncidentVectors[(thetaAngleIndex + 1) %
                                       thetaAnglesOfIncidentVectors.size()];
      const auto& vb_theta = thetaAnglesOfIncidentVectors[thetaAngleIndex];
      //            const auto &va
      //                = tiledIncidentVectors[(thetaAngleIndex + 1) %
      //                thetaAnglesOfIncidentVectors.size()];
      //            const auto &vb = tiledIncidentVectors[thetaAngleIndex];
      const double absAngleDifference = std::abs(va_theta - vb_theta);
      //            const double debug_difDegOtherway = vcg::math::ToDeg(
      //                std::acos((va * vb) / (va.Norm() * vb.Norm())));
      //            const double debug_diffDeg =
      //            vcg::math::ToDeg(absAngleDifference);
      if (absAngleDifference < angleThreshold_rad
          /*&& absAngleDifference > vcg::math::ToRad(0.01)*/) {
        //                std::cout << "Found angDiff:" << absAngleDifference <<
        //                std::endl; vert[vi].C() = vcg::Color4b::Magenta;
        //                hasAngleSmallerThan = true;
        return true;
      }
    }
    const double firstLastPairAngleDiff = std::abs(
        thetaAnglesOfIncidentVectors[0] -
        thetaAnglesOfIncidentVectors[thetaAnglesOfIncidentVectors.size() - 1]);
    if (firstLastPairAngleDiff < angleThreshold_rad &&
        firstLastPairAngleDiff > 0.01) {
      return true;
    }
  }
  return false;
}

bool PatternGeometry::hasValenceGreaterThan(
    const std::vector<size_t>& numberOfNodesPerSlot,
    const size_t& valenceThreshold) {
  // Initialize helping structs
  if (nodeToSlotMap.empty()) {
    FlatPatternTopology::constructNodeToSlotMap(numberOfNodesPerSlot,
                                                nodeToSlotMap);
  }
  if (correspondingNode.empty()) {
    constructCorrespondingNodeMap(numberOfNodesPerSlot);
  }
  if (nodeTiledValence.empty()) {
    constructNodeToTiledValenceMap(numberOfNodesPerSlot);
  }

  // Check tiled valence of the pattern's nodes
  bool hasNodeWithValenceGreaterThanDesired = false;
  for (size_t nodeIndex = 0; nodeIndex < vn; nodeIndex++) {
    const size_t tiledValence = nodeTiledValence[nodeIndex];
    if (tiledValence > valenceThreshold) {
      vert[nodeIndex].C() = vcg::Color4b::LightRed;
      hasNodeWithValenceGreaterThanDesired = true;
    }
  }
  return hasNodeWithValenceGreaterThanDesired;
}

bool PatternGeometry::hasDanglingEdges(
    const std::vector<size_t>& numberOfNodesPerSlot) {
  // Initialize helping structs
  if (nodeToSlotMap.empty()) {
    FlatPatternTopology::constructNodeToSlotMap(numberOfNodesPerSlot,
                                                nodeToSlotMap);
  }
  if (correspondingNode.empty()) {
    constructCorrespondingNodeMap(numberOfNodesPerSlot);
  }
  if (nodeTiledValence.empty()) {
    constructNodeToTiledValenceMap(numberOfNodesPerSlot);
  }

  // Check tiled valence of the pattern's nodes
  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::constructCorrespondingNodeMap(
    const std::vector<size_t>& numberOfNodesPerSlot) {
  assert(vn != 0 && !nodeToSlotMap.empty() && correspondingNode.empty() &&
         numberOfNodesPerSlot.size() == 7);

  for (size_t nodeIndex = 0; nodeIndex < vn; nodeIndex++) {
    const size_t slotIndex = nodeToSlotMap[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::isFullyConnectedWhenFanned() {
  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 (nodeToSlotMap[nodeIndex] == 1 || nodeToSlotMap[nodeIndex] == 4
  //          || nodeToSlotMap[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.contains(validEdgeIndex)) {
      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::filesystem::path& patternFilePath,
                                 bool addNormalsIfAbsent) {
  if (!std::filesystem::exists(std::filesystem::path(patternFilePath))) {
    assert(false);
    std::cerr << "No flat pattern with name " << patternFilePath << std::endl;
    return;
  }
  if (!load(patternFilePath)) {
    assert(false);
    std::cerr << "File could not be loaded  " << patternFilePath << std::endl;
    return;
  }
  if (addNormalsIfAbsent) {
    addNormals();
  }

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

  updateEigenEdgeAndVertices();
}

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

void PatternGeometry::updateBaseTriangleHeight() {
  baseTriangleHeight = computeBaseTriangleHeight();
}

void PatternGeometry::deleteDanglingVertices() {
  vcg::tri::Allocator<VCGEdgeMesh>::PointerUpdater<VertexPointer> pu;
  VCGEdgeMesh::deleteDanglingVertices(pu);
  if (!pu.remap.empty()) {
    interfaceNodeIndex = pu.remap[interfaceNodeIndex];
  }
}

void PatternGeometry::deleteDanglingVertices(
    vcg::tri::Allocator<VCGEdgeMesh>::PointerUpdater<VertexPointer>& pu) {
  VCGEdgeMesh::deleteDanglingVertices(pu);
}

vcg::Triangle3<double> PatternGeometry::getBaseTriangle() const {
  return baseTriangle;
}

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::computeBaseTriangle() const {
  const double baseTriangleHeight = computeBaseTriangleHeight();
  double bottomEdgeHalfSize = baseTriangleHeight / 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();
  baseTriangle = computeBaseTriangle();
  vcg::tri::UpdateTopology<PatternGeometry>::VertexEdge(*this);
  vcg::tri::UpdateTopology<PatternGeometry>::EdgeEdge(*this);
  updateEigenEdgeAndVertices();
}

// TODO: refactor such that it takes as an input a single pattern and tiles into
// the desired faces without requiring the each face will contain a single
// pattern
std::shared_ptr<PatternGeometry> PatternGeometry::tilePattern(
    std::vector<ConstPatternGeometry>& patterns,
    const std::vector<int>& connectToNeighborsVi,
    const VCGPolyMesh& tileInto,
    const std::vector<int>& perSurfaceFacePatternIndices,
    std::vector<size_t>& tileIntoEdgesToTiledVi,
    std::vector<std::vector<size_t>>& perPatternIndexToTiledPatternEdgeIndex) {
  perPatternIndexToTiledPatternEdgeIndex.resize(patterns.size());
  std::shared_ptr<PatternGeometry> pTiledPattern(new PatternGeometry);
  std::vector<std::vector<int>> tileIntoEdgeToInterfaceVi(
      tileInto.EN());  // ith element contains all the interface nodes that lay
                       // on the ith edge of tileInto
  // Compute the barycentric coords of the verts in the base triangle pattern
  std::vector<std::vector<CoordType>> barycentricCoordinates(patterns.size());
  for (size_t patternIndex = 0; patternIndex < patterns.size();
       patternIndex++) {
    const PatternGeometry& pattern = patterns[patternIndex];
    const vcg::Triangle3<double>& baseTriangle = pattern.getBaseTriangle();
    barycentricCoordinates[patternIndex].resize(pattern.VN());
    for (int vi = 0; vi < pattern.VN(); vi++) {
      CoordType barycentricCoords_vi;
      vcg::InterpolationParameters<vcg::Triangle3<double>, double>(
          baseTriangle, pattern.vert[vi].cP(), barycentricCoords_vi);
      barycentricCoordinates[patternIndex][vi] = barycentricCoords_vi;
    }
  }
  VCGTriMesh tileIntoEdgeMesh;

  assert(vcg::tri::HasFEAdjacency(tileInto));
  assert(vcg::tri::HasFVAdjacency(tileInto));
  for (const VCGPolyMesh::FaceType& f : tileInto.face) {
    const int patternIndex = perSurfaceFacePatternIndices[tileInto.getIndex(f)];
    if (patternIndex == -1) {
      continue;
    }
    CoordType centerOfFace(0, 0, 0);
    for (size_t vi = 0; vi < f.VN(); vi++) {
      centerOfFace = centerOfFace + f.cP(vi);
    }
    centerOfFace /= f.VN();
    vcg::tri::Allocator<VCGTriMesh>::AddVertex(tileIntoEdgeMesh, centerOfFace,
                                               vcg::Color4b::Yellow);

    std::vector<int> firstInFanConnectToNeighbor_vi(connectToNeighborsVi);
    for (int& vi : firstInFanConnectToNeighbor_vi) {
      vi += pTiledPattern->VN();
    }
    ConstPatternGeometry& pattern = patterns[patternIndex];

    for (size_t vi = 0; vi < f.VN(); vi++) {
      auto ep = f.FEp(vi);
      assert(vcg::tri::IsValidPointer(tileInto, ep));
      std::vector<vcg::Point3d> meshTrianglePoints{
          centerOfFace, f.cP(vi), vi + 1 == f.VN() ? f.cP(0) : f.cP(vi + 1)};
      //            std::vector<vcg::Point3d> meshTrianglePoints{centerOfFace,
      //            ep->cP(0), ep->cP(1)};
      auto fit = vcg::tri::Allocator<VCGTriMesh>::AddFace(
          tileIntoEdgeMesh, meshTrianglePoints[0], meshTrianglePoints[1],
          meshTrianglePoints[2]);
      //            CoordType faceNormal = ((meshTrianglePoints[1] -
      //            meshTrianglePoints[0])
      //                                    ^ (meshTrianglePoints[2] -
      //                                    meshTrianglePoints[0]))
      //                                       .Normalize();
      // TODO: in planar surfaces I should compute the face of triangle
      CoordType faceNormal = f.cN();

      fit->N() = faceNormal;
      PatternGeometry transformedPattern;
      transformedPattern.copy(pattern);
      //            pattern.registerForDrawing();
      //            polyscope::show();
      //            pattern.unregister();
      // Transform the base triangle nodes to the mesh triangle using
      // barycentric coords
      for (int vi = 0; vi < transformedPattern.VN(); vi++) {
        transformedPattern.vert[vi].P() =
            CoordType(meshTrianglePoints[0] *
                          barycentricCoordinates[patternIndex][vi][0] +
                      meshTrianglePoints[1] *
                          barycentricCoordinates[patternIndex][vi][1] +
                      meshTrianglePoints[2] *
                          barycentricCoordinates[patternIndex][vi][2]);
      }

      for (VertexType& v : transformedPattern.vert) {
        v.N() = faceNormal;
      }

      vcg::tri::Append<PatternGeometry, PatternGeometry>::Remap remap;
      vcg::tri::Append<PatternGeometry, PatternGeometry>::Mesh(
          *pTiledPattern, transformedPattern, remap);
      for (size_t ei = 0; ei < pattern.EN(); ei++) {
        perPatternIndexToTiledPatternEdgeIndex[patternIndex].push_back(
            remap.edge[ei]);
      }
      //            pTiledPattern->registerForDrawing();
      //            pTiledPattern->markVertices({remap.vert[pattern.interfaceNodeIndex]});
      //            polyscope::show();
      //            pTiledPattern->unregister();
      const size_t ei = tileInto.getIndex(ep);
      tileIntoEdgeToInterfaceVi[ei].push_back(
          remap.vert[pattern.interfaceNodeIndex]);
      // Add edges for connecting the desired vertices
      if (!connectToNeighborsVi.empty()) {
        if (vi + 1 == f.VN()) {
          for (int connectToNeighborIndex = 0;
               connectToNeighborIndex < connectToNeighborsVi.size();
               connectToNeighborIndex++) {
            auto eIt = vcg::tri::Allocator<PatternGeometry>::AddEdge(
                *pTiledPattern,
                firstInFanConnectToNeighbor_vi[connectToNeighborIndex],
                pTiledPattern->VN() - pattern.VN() +
                    connectToNeighborsVi[connectToNeighborIndex]);
            perPatternIndexToTiledPatternEdgeIndex[patternIndex].push_back(
                pTiledPattern->getIndex(*eIt));
          }
        }
        if (vi != 0) {
          for (int connectToNeighborIndex = 0;
               connectToNeighborIndex < connectToNeighborsVi.size();
               connectToNeighborIndex++) {
            auto eIt = vcg::tri::Allocator<PatternGeometry>::AddEdge(
                *pTiledPattern,
                pTiledPattern->VN() - 2 * pattern.VN() +
                    connectToNeighborsVi[connectToNeighborIndex],
                pTiledPattern->VN() - pattern.VN() +
                    connectToNeighborsVi[connectToNeighborIndex]);
            perPatternIndexToTiledPatternEdgeIndex[patternIndex].push_back(
                pTiledPattern->getIndex(*eIt));
          }
        }
      }
    }
  }
  vcg::tri::Allocator<VCGEdgeMesh>::PointerUpdater<VertexPointer> pu_vertices;
  vcg::tri::Allocator<VCGEdgeMesh>::PointerUpdater<EdgePointer> pu_edges;
  pTiledPattern->removeDuplicateVertices(pu_vertices, pu_edges);
  // Update perPattern
  //    for (std::vector<size_t> &tiledPatternEdges :
  //    perPatternIndexToTiledPatternEdgeIndex) {
  //        for (size_t &ei : tiledPatternEdges) {
  //            ei = pu_edges.remap[ei];
  //        }

  //        auto end = tiledPatternEdges.end();
  //        for (auto it = tiledPatternEdges.begin(); it != end; ++it) {
  //            end = std::remove(it + 1, end, *it);
  //        }

  //        tiledPatternEdges.erase(end, tiledPatternEdges.end());
  //    }

  const size_t sumOfEdgeIndices =
      std::accumulate(perPatternIndexToTiledPatternEdgeIndex.begin(),
                      perPatternIndexToTiledPatternEdgeIndex.end(), 0,
                      [](const size_t& sum, const std::vector<size_t>& v) {
                        return sum + v.size();
                      });

  const int en = pTiledPattern->EN();
  assert(pTiledPattern->EN() == sumOfEdgeIndices);

  tileIntoEdgesToTiledVi.clear();
  tileIntoEdgesToTiledVi.resize(tileInto.EN());
  for (int ei = 0; ei < tileInto.EN(); ei++) {
    const std::vector<int> interfaceVis = tileIntoEdgeToInterfaceVi[ei];
    if (interfaceVis.empty()) {
      continue;
    }
    assert(interfaceVis.size() == 1 || interfaceVis.size() == 2);
    assert(
        interfaceVis.size() == 1 ||
        (interfaceVis.size() == 2 && (pu_vertices.remap[interfaceVis[0]] ==
                                          std::numeric_limits<size_t>::max() ||
                                      pu_vertices.remap[interfaceVis[1]] ==
                                          std::numeric_limits<size_t>::max())));
    tileIntoEdgesToTiledVi[ei] = pu_vertices.remap[interfaceVis[0]];
  }

  pTiledPattern->deleteDanglingVertices();
  vcg::tri::Allocator<PatternGeometry>::CompactEveryVector(*pTiledPattern);
  pTiledPattern->updateEigenEdgeAndVertices();
  //    pTiledPattern->save();
  return pTiledPattern;
}

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();
  baseTriangle = copyFrom.getBaseTriangle();
  interfaceNodeIndex = copyFrom.interfaceNodeIndex;
}

void PatternGeometry::scale(const double& desiredBaseTriangleCentralEdgeSize) {
  const double baseTriangleCentralEdgeSize = getBaseTriangleHeight();
  const double scaleRatio =
      desiredBaseTriangleCentralEdgeSize / baseTriangleCentralEdgeSize;
  vcg::tri::UpdatePosition<VCGEdgeMesh>::Scale(*this, scaleRatio);
  baseTriangle = computeBaseTriangle();
  baseTriangleHeight = computeBaseTriangleHeight();
  const double debug_baseTriHeight = vcg::Distance(
      baseTriangle.cP(0), (baseTriangle.cP(1) + baseTriangle.cP(2)) / 2);
  assert(std::abs(desiredBaseTriangleCentralEdgeSize - baseTriangleHeight) <
         1e-10);
  int i = 0;
  i++;
}

void PatternGeometry::createFan(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(360.0 / fanSize, rotationAxis);
    vcg::tri::UpdatePosition<PatternGeometry>::Matrix(rotatedPattern, R);
    vcg::tri::Append<PatternGeometry, PatternGeometry>::Mesh(*this,
                                                             rotatedPattern);
    // Add edges for connecting the desired vertices
    removeDuplicateVertices();
    updateEigenEdgeAndVertices();
  }
}

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

bool PatternGeometry::isInterfaceConnected(
    const std::unordered_set<VertexIndex>& interfaceNodes) {
  std::unordered_set<VertexIndex> interfaceNodesConnected;

  for (int ei = 0; ei < EN(); ei++) {
    const int evi0 = getIndex(edge[ei].cV(0));
    const int evi1 = getIndex(edge[ei].cV(1));
    if (interfaceNodes.contains(evi0) && !interfaceNodes.contains(evi1)) {
      interfaceNodesConnected.insert(evi0);
    } else if (!interfaceNodes.contains(evi0) &&
               interfaceNodes.contains(evi1)) {
      interfaceNodesConnected.insert(evi1);
    }
  }

  if (interfaceNodesConnected.size() != interfaceNodes.size()) {
    return false;
  }
  return true;
}

std::unordered_set<VertexIndex> PatternGeometry::getInterfaceNodes(
    const std::vector<size_t>& numberOfNodesPerSlot) {
  if (nodeToSlotMap.empty()) {
    FlatPatternTopology::constructNodeToSlotMap(numberOfNodesPerSlot,
                                                nodeToSlotMap);
  }
  std::unordered_set<VertexIndex> interfaceNodes;
  for (std::pair<VertexIndex, size_t> viSlotPair : nodeToSlotMap) {
    if (viSlotPair.second == 4) {
      interfaceNodes.insert(viSlotPair.first);
    }
  }

  return interfaceNodes;
}