FillBetweenPointVectorsTools.C

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//* This file is part of the MOOSE framework
//* https://mooseframework.inl.gov
//*
//* All rights reserved, see COPYRIGHT for full restrictions
//* https://github.com/idaholab/moose/blob/master/COPYRIGHT
//*
//* Licensed under LGPL 2.1, please see LICENSE for details
//* https://www.gnu.org/licenses/lgpl-2.1.html
 
#include "FillBetweenPointVectorsTools.h"
#include "MooseMeshUtils.h"
#include "MooseMesh.h"
#include "MeshGenerator.h"
#include "MooseError.h"
 
// libMesh includes
#include "libmesh/int_range.h"
#include "libmesh/mesh_base.h"
#include "libmesh/mesh_generation.h"
#include "libmesh/mesh_serializer.h"
#include "libmesh/point.h"
#include "libmesh/elem.h"
#include "libmesh/node.h"
#include "libmesh/face_tri3.h"
#include "libmesh/face_quad4.h"
 
using namespace libMesh;
 
namespace FillBetweenPointVectorsTools
{
void
fillBetweenPointVectorsGenerator(MeshBase & mesh, // an empty mesh is expected
                                 const std::vector<Point> & boundary_points_vec_1,
                                 const std::vector<Point> & boundary_points_vec_2,
                                 const unsigned int num_layers,
                                 const subdomain_id_type transition_layer_id,
                                 const boundary_id_type input_boundary_1_id,
                                 const boundary_id_type input_boundary_2_id,
                                 const boundary_id_type begin_side_boundary_id,
                                 const boundary_id_type end_side_boundary_id,
                                 const std::string type,
                                 const std::string name,
                                 const bool quad_elem,
                                 const Real bias_parameter,
                                 const Real sigma)
{
  if (!MooseMeshUtils::isCoPlanar(
          boundary_points_vec_1, Point(0.0, 0.0, 1.0), Point(0.0, 0.0, 0.0)) ||
      !MooseMeshUtils::isCoPlanar(
          boundary_points_vec_2, Point(0.0, 0.0, 1.0), Point(0.0, 0.0, 0.0)))
    mooseError("In ",
               type,
               " ",
               name,
               ", the input vectors of points for "
               "FillBetweenPointVectorsTools::fillBetweenPointVectorsGenerator "
               "must be in XY plane.");
 
  const unsigned int vec_1_node_num = boundary_points_vec_1.size();
  const unsigned int vec_2_node_num = boundary_points_vec_2.size();
 
  if (vec_1_node_num < 2 || vec_2_node_num < 2)
    mooseError("In ",
               type,
               " ",
               name,
               ", the two input vectors of points for "
               "FillBetweenPointVectorsTools::fillBetweenPointVectorsGenerator "
               "must respectively contain at least two elements.");
 
  if (quad_elem && boundary_points_vec_1.size() != boundary_points_vec_2.size())
    mooseError("In ",
               type,
               " ",
               name,
               ", QUAD4 elements option can only be selected when the two input vectors of Points "
               "have the same length. In the current instance, the first vector has ",
               boundary_points_vec_1.size(),
               " points and the second ",
               boundary_points_vec_2.size(),
               " points");
 
  std::vector<Point> possibly_reoriented_boundary_points_vec_2;
  const std::vector<Point> * oriented_boundary_points_vec_2 = &boundary_points_vec_2;
 
  if (needFlip(boundary_points_vec_1, boundary_points_vec_2))
  {
    possibly_reoriented_boundary_points_vec_2.assign(boundary_points_vec_2.rbegin(),
                                                     boundary_points_vec_2.rend());
    oriented_boundary_points_vec_2 = &possibly_reoriented_boundary_points_vec_2;
 
    // This isn't worth warning about.  The way
    // MooseMeshUtils::makeOrderedNodeList works, we can end up
    // finding a flip necessary on one element numbering and
    // unnecessary on another.
    //
    // mooseWarning(
    //     "In FillBetweenPointVectorsTools, one of the vector of Points must be flipped to ensure "
    //     "correct transition layer shape.");
  }
 
  std::vector<Real> vec_1_index; // Unweighted index
  std::vector<Real> vec_2_index; // Unweighted index
 
  std::vector<Real> wt_1;
  std::vector<Real> index_1; // Weighted index
  std::vector<Real> wt_2;
  std::vector<Real> index_2; // Weighted index
 
  // create interpolations
  std::unique_ptr<LinearInterpolation> linear_vec_1_x;
  std::unique_ptr<LinearInterpolation> linear_vec_1_y;
  std::unique_ptr<SplineInterpolation> spline_vec_1_l;
  std::unique_ptr<LinearInterpolation> linear_vec_2_x;
  std::unique_ptr<LinearInterpolation> linear_vec_2_y;
  std::unique_ptr<SplineInterpolation> spline_vec_2_l;
 
  weightedInterpolator(vec_1_node_num,
                       boundary_points_vec_1,
                       vec_1_index,
                       wt_1,
                       index_1,
                       sigma,
                       linear_vec_1_x,
                       linear_vec_1_y,
                       spline_vec_1_l);
  weightedInterpolator(vec_2_node_num,
                       *oriented_boundary_points_vec_2,
                       vec_2_index,
                       wt_2,
                       index_2,
                       sigma,
                       linear_vec_2_x,
                       linear_vec_2_y,
                       spline_vec_2_l);
 
  // If the two input vectors have different sizes
  // The node numbers of the intermediate layers change linearly
  const Real increment = ((Real)vec_2_node_num - (Real)vec_1_node_num) / (Real)(num_layers);
  // Number of nodes in each sublayer
  std::vector<unsigned int> node_number_vec;
  // 2D vector of nodes
  std::vector<std::vector<Node *>> nodes(num_layers + 1);
  // Node counter
  unsigned int node_counter = 0;
 
  for (const auto i : make_range(num_layers + 1))
  {
    // calculate number of nodes in each sublayer
    node_number_vec.push_back(
        (unsigned int)(vec_1_node_num + (long)(increment * i + 0.5 - (increment < 0))));
    // Reserve memory for new nodes
    nodes[i] = std::vector<Node *>(node_number_vec[i]);
 
    // Calculate vectors of weighted surrogated index for side #1
    std::vector<Real> weighted_surrogate_index_1;
    std::vector<Real> unweighted_surrogate_index_1;
 
    surrogateGenerator(weighted_surrogate_index_1,
                       unweighted_surrogate_index_1,
                       node_number_vec,
                       wt_1,
                       vec_1_index,
                       vec_1_node_num,
                       i);
 
    // Calculate vectors of weighted surrogated index for side #2
    std::vector<Real> weighted_surrogate_index_2;
    std::vector<Real> unweighted_surrogate_index_2;
 
    surrogateGenerator(weighted_surrogate_index_2,
                       unweighted_surrogate_index_2,
                       node_number_vec,
                       wt_2,
                       vec_2_index,
                       vec_2_node_num,
                       i);
 
    for (const auto j : make_range(node_number_vec[i]))
    {
      // Create surrogate Points on side #1 for Point #j on the sublayer
      Point surrogate_pos_1 = Point(linear_vec_1_x->sample(weighted_surrogate_index_1[j]),
                                    linear_vec_1_y->sample(weighted_surrogate_index_1[j]),
                                    0.0);
      // Create surrogate Points on side #2 for Point #j on the sublayer
      Point surrogate_pos_2 = Point(linear_vec_2_x->sample(weighted_surrogate_index_2[j]),
                                    linear_vec_2_y->sample(weighted_surrogate_index_2[j]),
                                    0.0);
      const Real l_ratio = bias_parameter <= 0.0
                               ? std::pow(spline_vec_2_l->sample(weighted_surrogate_index_2[j]) /
                                              spline_vec_1_l->sample(weighted_surrogate_index_1[j]),
                                          1.0 / ((Real)num_layers - 1.0))
                               : bias_parameter;
      const Real index_factor =
          MooseUtils::absoluteFuzzyEqual(l_ratio, 1.0)
              ? (Real)i / (Real)num_layers
              : (1.0 - std::pow(l_ratio, (Real)i)) / (1.0 - std::pow(l_ratio, (Real)num_layers));
      Point tmp_point = surrogate_pos_2 * index_factor + surrogate_pos_1 * (1.0 - index_factor);
      nodes[i][j] = mesh.add_point(tmp_point, j + node_counter);
    }
    node_counter += node_number_vec[i];
  }
  // Create triangular elements based on the 2D Node vector
  if (quad_elem)
    elementsCreationFromNodesVectorsQuad(mesh,
                                         nodes,
                                         num_layers,
                                         node_number_vec,
                                         transition_layer_id,
                                         input_boundary_1_id,
                                         input_boundary_2_id,
                                         begin_side_boundary_id,
                                         end_side_boundary_id);
  else
    elementsCreationFromNodesVectors(mesh,
                                     nodes,
                                     num_layers,
                                     node_number_vec,
                                     transition_layer_id,
                                     input_boundary_1_id,
                                     input_boundary_2_id,
                                     begin_side_boundary_id,
                                     end_side_boundary_id);
}
 
void
fillBetweenPointVectorsGenerator(MeshBase & mesh,
                                 const std::vector<Point> & boundary_points_vec_1,
                                 const std::vector<Point> & boundary_points_vec_2,
                                 const unsigned int num_layers,
                                 const subdomain_id_type transition_layer_id,
                                 const boundary_id_type external_boundary_id,
                                 const std::string type,
                                 const std::string name,
                                 const bool quad_elem)
{
  fillBetweenPointVectorsGenerator(mesh,
                                   boundary_points_vec_1,
                                   boundary_points_vec_2,
                                   num_layers,
                                   transition_layer_id,
                                   external_boundary_id,
                                   external_boundary_id,
                                   external_boundary_id,
                                   external_boundary_id,
                                   type,
                                   name,
                                   quad_elem);
}
 
void
elementsCreationFromNodesVectorsQuad(MeshBase & mesh,
                                     const std::vector<std::vector<Node *>> & nodes,
                                     const unsigned int num_layers,
                                     const std::vector<unsigned int> & node_number_vec,
                                     const subdomain_id_type transition_layer_id,
                                     const boundary_id_type input_boundary_1_id,
                                     const boundary_id_type input_boundary_2_id,
                                     const boundary_id_type begin_side_boundary_id,
                                     const boundary_id_type end_side_boundary_id)
{
  const unsigned int node_number = node_number_vec.front();
  BoundaryInfo & boundary_info = mesh.get_boundary_info();
 
  for (const auto i : make_range(num_layers))
    for (unsigned int j = 1; j < node_number; j++)
    {
      Elem * elem = mesh.add_elem(new Quad4);
      bool is_elem_flip = buildQuadElement(elem,
                                           nodes[i][j - 1],
                                           nodes[i + 1][j - 1],
                                           nodes[i + 1][j],
                                           nodes[i][j],
                                           transition_layer_id);
      if (i == 0)
        boundary_info.add_side(elem, is_elem_flip ? 0 : 3, input_boundary_1_id);
      if (i == num_layers - 1)
        boundary_info.add_side(elem, is_elem_flip ? 2 : 1, input_boundary_2_id);
      if (j == 1)
        boundary_info.add_side(elem, is_elem_flip ? 3 : 0, begin_side_boundary_id);
      if (j == node_number - 1)
        boundary_info.add_side(elem, is_elem_flip ? 1 : 2, end_side_boundary_id);
    }
}
 
void
elementsCreationFromNodesVectors(MeshBase & mesh,
                                 const std::vector<std::vector<Node *>> & nodes,
                                 const unsigned int num_layers,
                                 const std::vector<unsigned int> & node_number_vec,
                                 const subdomain_id_type transition_layer_id,
                                 const boundary_id_type input_boundary_1_id,
                                 const boundary_id_type input_boundary_2_id,
                                 const boundary_id_type begin_side_boundary_id,
                                 const boundary_id_type end_side_boundary_id)
{
  BoundaryInfo & boundary_info = mesh.get_boundary_info();
 
  for (const auto i : make_range(num_layers))
  {
    unsigned int nodes_up_it = 0;
    unsigned int nodes_down_it = 0;
    const unsigned int node_number_up = node_number_vec[i + 1];
    const unsigned int node_number_down = node_number_vec[i];
 
    while (nodes_up_it < node_number_up - 1 && nodes_down_it < node_number_down - 1 &&
           nodes_up_it + nodes_down_it < node_number_up + node_number_down - 3)
    {
      // Define the two possible options and chose the one with shorter distance
      Real dis1 = (*nodes[i + 1][nodes_up_it] - *nodes[i][nodes_down_it + 1]).norm();
      Real dis2 = (*nodes[i + 1][nodes_up_it + 1] - *nodes[i][nodes_down_it]).norm();
      if (MooseUtils::absoluteFuzzyGreaterThan(dis1, dis2))
      {
        Elem * elem = mesh.add_elem(new Tri3);
        bool is_elem_flip = buildTriElement(elem,
                                            nodes[i + 1][nodes_up_it],
                                            nodes[i][nodes_down_it],
                                            nodes[i + 1][nodes_up_it + 1],
                                            transition_layer_id);
        if (i == num_layers - 1)
          boundary_info.add_side(elem, is_elem_flip ? 0 : 2, input_boundary_2_id);
        if (nodes_up_it == 0 && nodes_down_it == 0)
          boundary_info.add_side(elem, is_elem_flip ? 2 : 0, begin_side_boundary_id);
        nodes_up_it++;
      }
      else
      {
        Elem * elem = mesh.add_elem(new Tri3);
        bool is_elem_flip = buildTriElement(elem,
                                            nodes[i + 1][nodes_up_it],
                                            nodes[i][nodes_down_it],
                                            nodes[i][nodes_down_it + 1],
                                            transition_layer_id);
        if (i == 0)
          boundary_info.add_side(elem, 1, input_boundary_1_id);
        if (nodes_up_it == 0 && nodes_down_it == 0)
          boundary_info.add_side(elem, is_elem_flip ? 2 : 0, begin_side_boundary_id);
        nodes_down_it++;
      }
    }
    // Handle the end
    while (nodes_up_it < node_number_up - 1)
    {
      Elem * elem = mesh.add_elem(new Tri3);
      bool is_elem_flip = buildTriElement(elem,
                                          nodes[i + 1][nodes_up_it],
                                          nodes[i][nodes_down_it],
                                          nodes[i + 1][nodes_up_it + 1],
                                          transition_layer_id);
      nodes_up_it++;
      if (i == num_layers - 1)
        boundary_info.add_side(elem, is_elem_flip ? 0 : 2, input_boundary_2_id);
      if (nodes_up_it == node_number_up - 1 && nodes_down_it == node_number_down - 1)
        boundary_info.add_side(elem, 1, end_side_boundary_id);
    }
    while (nodes_down_it < node_number_down - 1)
    {
      Elem * elem = mesh.add_elem(new Tri3);
      bool is_elem_flip = buildTriElement(elem,
                                          nodes[i + 1][nodes_up_it],
                                          nodes[i][nodes_down_it],
                                          nodes[i][nodes_down_it + 1],
                                          transition_layer_id);
      nodes_down_it++;
      if (i == 0)
        boundary_info.add_side(elem, 1, input_boundary_1_id);
      if (nodes_up_it == node_number_up - 1 && nodes_down_it == node_number_down - 1)
        boundary_info.add_side(elem, is_elem_flip ? 0 : 2, end_side_boundary_id);
    }
  }
}
 
void
weightedInterpolator(const unsigned int vec_node_num,
                     const std::vector<Point> & boundary_points_vec,
                     std::vector<Real> & vec_index,
                     std::vector<Real> & wt,
                     std::vector<Real> & index,
                     const Real sigma,
                     std::unique_ptr<LinearInterpolation> & linear_vec_x,
                     std::unique_ptr<LinearInterpolation> & linear_vec_y,
                     std::unique_ptr<SplineInterpolation> & spline_vec_l)
{
  std::vector<Real> pos_x;
  std::vector<Real> pos_y;
  std::vector<Real> dist_vec;
  std::vector<Real> pos_l;
 
  for (const auto i : make_range(vec_node_num))
  {
    // Unweighted, the index interval is just uniform
    // Normalized range 0~1
    vec_index.push_back((Real)i / ((Real)vec_node_num - 1.0));
    // X and Y coordinates cooresponding to the index
    pos_x.push_back(boundary_points_vec[i](0));
    pos_y.push_back(boundary_points_vec[i](1));
    // Use Point-to-Point distance as unnormalized weight
    if (i > 0)
    {
      wt.push_back((boundary_points_vec[i] - boundary_points_vec[i - 1]).norm());
      dist_vec.push_back(wt.back());
    }
    // Accumulated unnormalized weights to get unnormalized weighted index
    index.push_back(std::accumulate(wt.begin(), wt.end(), 0.0));
  }
  const Real dist_vec_total = index.back(); // Total accumulated distances
  const Real wt_norm_factor = dist_vec_total / ((Real)vec_node_num - 1.0); // Normalization factor
  // Normalization for both weights and weighted indices
  std::transform(
      wt.begin(), wt.end(), wt.begin(), [wt_norm_factor](Real & c) { return c / wt_norm_factor; });
  std::transform(index.begin(),
                 index.end(),
                 index.begin(),
                 [dist_vec_total](Real & c) { return c / dist_vec_total; });
  // Use Gaussian blurring to smoothen local density
  for (const auto i : make_range(vec_node_num))
  {
    Real gaussian_factor(0.0);
    Real sum_tmp(0.0);
    // Use interval as parameter now, consider distance in the future
    for (const auto j : make_range(vec_node_num - 1))
    {
      // dis_vec and index are off by 0.5
      const Real tmp_factor =
          exp(-((Real)(i - j) - 0.5) * ((Real)(i - j) - 0.5) / 2.0 / sigma / sigma);
      gaussian_factor += tmp_factor;
      sum_tmp += tmp_factor * dist_vec[j];
    }
    pos_l.push_back(sum_tmp / gaussian_factor);
  }
  // Interpolate positions based on weighted indices
  linear_vec_x = std::make_unique<LinearInterpolation>(index, pos_x);
  linear_vec_y = std::make_unique<LinearInterpolation>(index, pos_y);
  spline_vec_l = std::make_unique<SplineInterpolation>(index, pos_l);
}
 
void
surrogateGenerator(std::vector<Real> & weighted_surrogate_index,
                   std::vector<Real> & unweighted_surrogate_index,
                   const std::vector<unsigned int> & node_number_vec,
                   const std::vector<Real> & wt,
                   const std::vector<Real> & index,
                   const unsigned int boundary_node_num,
                   const unsigned int i)
{
  // First element is trivial
  weighted_surrogate_index.push_back(0.0);
  unweighted_surrogate_index.push_back(0.0);
  for (unsigned int j = 1; j < node_number_vec[i]; j++)
  {
    // uniform interval for unweighted index
    unweighted_surrogate_index.push_back((Real)j / ((Real)node_number_vec[i] - 1.0));
    // >
    const auto it_0 =
        std::upper_bound(index.begin(), index.end(), unweighted_surrogate_index[j - 1]);
    // >=
    const auto it_1 = std::lower_bound(index.begin(), index.end(), unweighted_surrogate_index[j]);
    //
    const auto it_dist = std::distance(it_0, it_1);
    //
    const auto it_start = std::distance(index.begin(), it_0);
 
    if (it_0 == it_1)
      weighted_surrogate_index.push_back(weighted_surrogate_index[j - 1] +
                                         wt[it_start - 1] / ((Real)node_number_vec[i] - 1.0));
    else
    {
      weighted_surrogate_index.push_back(weighted_surrogate_index[j - 1]);
      weighted_surrogate_index[j] += (*it_0 - unweighted_surrogate_index[j - 1]) * wt[it_start - 1];
      weighted_surrogate_index[j] +=
          (unweighted_surrogate_index[j] - *(it_1 - 1)) * wt[it_start + it_dist - 1];
      for (unsigned int k = 1; k < it_dist; k++)
        weighted_surrogate_index[j] += wt[it_start + k - 1] / ((Real)boundary_node_num - 1.0);
    }
  }
}
 
bool
needFlip(const std::vector<Point> & vec_pts_1, const std::vector<Point> & vec_pts_2)
{
  const Real th1 =
      acos((vec_pts_1.back() - vec_pts_1.front()) * (vec_pts_2.front() - vec_pts_1.front()) /
           (vec_pts_1.back() - vec_pts_1.front()).norm() /
           (vec_pts_2.front() - vec_pts_1.front()).norm());
  const Real th2 = acos(
      (vec_pts_2.back() - vec_pts_1.back()) * (vec_pts_1.front() - vec_pts_1.back()) /
      (vec_pts_2.back() - vec_pts_1.back()).norm() / (vec_pts_1.front() - vec_pts_1.back()).norm());
  const Real th3 = acos(
      (vec_pts_2.front() - vec_pts_2.back()) * (vec_pts_1.back() - vec_pts_2.back()) /
      (vec_pts_2.front() - vec_pts_2.back()).norm() / (vec_pts_1.back() - vec_pts_2.back()).norm());
  const Real th4 =
      acos((vec_pts_1.front() - vec_pts_2.front()) * (vec_pts_2.back() - vec_pts_2.front()) /
           (vec_pts_1.front() - vec_pts_2.front()).norm() /
           (vec_pts_2.back() - vec_pts_2.front()).norm());
  if (MooseUtils::absoluteFuzzyEqual(th1 + th2 + th3 + th4, 2 * M_PI))
    return false;
  return true;
}
 
bool
isBoundarySimpleClosedLoop(MeshBase & mesh,
                           Real & max_node_radius,
                           std::vector<dof_id_type> & boundary_ordered_node_list,
                           const Point origin_pt,
                           const boundary_id_type bid)
{
  // This has no communication and expects elem_ptr to find any
  // element, so it only works on serialized meshes
  libMesh::MeshSerializer serial(mesh);
 
  max_node_radius = 0.0;
  BoundaryInfo & boundary_info = mesh.get_boundary_info();
  auto side_list_tmp = boundary_info.build_side_list();
  std::vector<std::pair<dof_id_type, dof_id_type>> boundary_node_assm;
  std::vector<dof_id_type> boundary_midpoint_node_list;
  for (const auto i : index_range(side_list_tmp))
  {
    if (std::get<2>(side_list_tmp[i]) == bid)
    {
      // store two nodes of each side
      const auto elem = mesh.elem_ptr(std::get<0>(side_list_tmp[i]));
      const auto side = elem->side_ptr(std::get<1>(side_list_tmp[i]));
      boundary_node_assm.push_back(std::make_pair(side->node_id(0), side->node_id(1)));
      // see if there is a midpoint
      const auto & side_type = elem->side_type(std::get<1>(side_list_tmp[i]));
      if (side_type == EDGE3)
        boundary_midpoint_node_list.push_back(
            elem->node_id(elem->n_vertices() + std::get<1>(side_list_tmp[i])));
      else
        boundary_midpoint_node_list.push_back(DofObject::invalid_id);
    }
  }
  bool is_closed_loop;
  isClosedLoop(mesh,
               max_node_radius,
               boundary_ordered_node_list,
               boundary_node_assm,
               boundary_midpoint_node_list,
               origin_pt,
               "external boundary",
               is_closed_loop);
  return is_closed_loop;
}
 
bool
isBoundarySimpleClosedLoop(MeshBase & mesh,
                           Real & max_node_radius,
                           const Point origin_pt,
                           const boundary_id_type bid)
{
  std::vector<dof_id_type> dummy_boundary_ordered_node_list;
  return isBoundarySimpleClosedLoop(
      mesh, max_node_radius, dummy_boundary_ordered_node_list, origin_pt, bid);
}
 
bool
isBoundarySimpleClosedLoop(MeshBase & mesh, const Point origin_pt, const boundary_id_type bid)
{
  Real dummy_max_node_radius;
  return isBoundarySimpleClosedLoop(mesh, dummy_max_node_radius, origin_pt, bid);
}
 
bool
isBoundaryOpenSingleSegment(MeshBase & mesh,
                            Real & max_node_radius,
                            std::vector<dof_id_type> & boundary_ordered_node_list,
                            const Point origin_pt,
                            const boundary_id_type bid)
{
  try
  {
    isBoundarySimpleClosedLoop(mesh, max_node_radius, boundary_ordered_node_list, origin_pt, bid);
  }
  catch (MooseException & e)
  {
    if (((std::string)e.what())
            .compare("This mesh generator does not work for the provided external boundary as it "
                     "is not a closed loop.") != 0)
      throw MooseException("The provided boundary is not an open single-segment boundary.");
    else
      return true;
  }
 
  throw MooseException("The provided boundary is closed loop, which is not supported.");
}
 
bool
isExternalBoundary(MeshBase & mesh, const boundary_id_type bid)
{
  // This has no communication and expects elem_ptr to find any
  // element, so it only works on serialized meshes
  libMesh::MeshSerializer serial(mesh);
 
  if (!mesh.is_prepared())
    mesh.find_neighbors();
  BoundaryInfo & boundary_info = mesh.get_boundary_info();
  auto side_list = boundary_info.build_side_list();
  for (const auto i : index_range(side_list))
  {
    if (std::get<2>(side_list[i]) == bid)
      if (mesh.elem_ptr(std::get<0>(side_list[i]))->neighbor_ptr(std::get<1>(side_list[i])) !=
          nullptr)
        return false;
  }
  return true;
}
 
bool
isCurveSimpleClosedLoop(MeshBase & mesh,
                        Real & max_node_radius,
                        std::vector<dof_id_type> & ordered_node_list,
                        const Point origin_pt)
{
  // This has no communication and expects to loop over all elements
  // on every processor, so it only works on serialized meshes
  libMesh::MeshSerializer serial(mesh);
 
  max_node_radius = 0.0;
  std::vector<std::pair<dof_id_type, dof_id_type>> node_assm;
  for (auto it = mesh.active_elements_begin(); it != mesh.active_elements_end(); it++)
    node_assm.push_back(std::make_pair((*it)->node_id(0), (*it)->node_id(1)));
  bool is_closed_loop;
  isClosedLoop(
      mesh, max_node_radius, ordered_node_list, node_assm, origin_pt, "curve", is_closed_loop);
  return is_closed_loop;
}
 
bool
isCurveSimpleClosedLoop(MeshBase & mesh, Real & max_node_radius, const Point origin_pt)
{
  std::vector<dof_id_type> dummy_ordered_node_list;
  return isCurveSimpleClosedLoop(mesh, max_node_radius, dummy_ordered_node_list, origin_pt);
}
 
bool
isCurveSimpleClosedLoop(MeshBase & mesh, const Point origin_pt)
{
  Real dummy_max_node_radius;
  return isCurveSimpleClosedLoop(mesh, dummy_max_node_radius, origin_pt);
}
 
bool
isCurveOpenSingleSegment(MeshBase & mesh,
                         Real & max_node_radius,
                         std::vector<dof_id_type> & ordered_node_list,
                         const Point origin_pt)
{
  try
  {
    isCurveSimpleClosedLoop(mesh, max_node_radius, ordered_node_list, origin_pt);
  }
  catch (MooseException & e)
  {
    if (((std::string)e.what())
            .compare("This mesh generator does not work for the provided curve as it is not a "
                     "closed loop.") != 0)
      throw MooseException("The provided curve is not an open single-segment boundary.");
    else
      return true;
  }
  throw MooseException("The provided curve is closed loop, which is not supported.");
  return false;
}
 
void
isClosedLoop(MeshBase & mesh,
             Real & max_node_radius,
             std::vector<dof_id_type> & ordered_node_list,
             std::vector<std::pair<dof_id_type, dof_id_type>> & node_assm,
             std::vector<dof_id_type> & midpoint_node_list,
             const Point origin_pt,
             const std::string input_type,
             bool & is_closed_loop,
             const bool suppress_exception)
{
  // This has no communication and expects node_ptr to find any
  // node, so it only works on serialized meshes
  libMesh::MeshSerializer serial(mesh);
 
  std::vector<dof_id_type> dummy_elem_list = std::vector<dof_id_type>(node_assm.size(), 0);
  std::vector<dof_id_type> ordered_dummy_elem_list;
  is_closed_loop = false;
  MooseMeshUtils::makeOrderedNodeList(
      node_assm, dummy_elem_list, midpoint_node_list, ordered_node_list, ordered_dummy_elem_list);
  // If the code ever gets here, node_assm is empty.
  // If the ordered_node_list front and back are not the same, the boundary is not a loop.
  // This is not done inside the loop just for some potential applications in the future.
  if (ordered_node_list.front() != ordered_node_list.back())
  {
    // This is invalid type #2
    if (!suppress_exception)
      throw MooseException("This mesh generator does not work for the provided ",
                           input_type,
                           " as it is not a closed loop.");
  }
  // It the curve is a loop, check if azimuthal angles change monotonically
  else
  {
    // Utilize cross product here.
    // If azimuthal angles change monotonically,
    // the z components of the cross products are always negative or positive.
    std::vector<Real> ordered_node_azi_list;
    for (const auto i : make_range(ordered_node_list.size() - 1))
    {
      ordered_node_azi_list.push_back(
          (*mesh.node_ptr(ordered_node_list[i]) - origin_pt)
              .cross(*mesh.node_ptr(ordered_node_list[i + 1]) - origin_pt)(2));
      // Use this opportunity to calculate maximum radius
      max_node_radius =
          std::max((*mesh.node_ptr(ordered_node_list[i]) - origin_pt).norm(), max_node_radius);
    }
    std::sort(ordered_node_azi_list.begin(), ordered_node_azi_list.end());
    if (ordered_node_azi_list.front() * ordered_node_azi_list.back() < 0.0)
    {
      // This is invalid type #3
      if (!suppress_exception)
        throw MooseException(
            "This mesh generator does not work for the provided ",
            input_type,
            " as azimuthal angles of consecutive nodes do not change monotonically.");
    }
    else
      is_closed_loop = true;
  }
}
 
void
isClosedLoop(MeshBase & mesh,
             Real & max_node_radius,
             std::vector<dof_id_type> & ordered_node_list,
             std::vector<std::pair<dof_id_type, dof_id_type>> & node_assm,
             const Point origin_pt,
             const std::string input_type,
             bool & is_closed_loop,
             const bool suppress_exception)
{
  std::vector<dof_id_type> dummy_midpoint_node_list(node_assm.size(), DofObject::invalid_id);
  isClosedLoop(mesh,
               max_node_radius,
               ordered_node_list,
               node_assm,
               dummy_midpoint_node_list,
               origin_pt,
               input_type,
               is_closed_loop,
               suppress_exception);
}
 
bool
buildQuadElement(Elem * elem,
                 Node * nd_0,
                 Node * nd_1,
                 Node * nd_2,
                 Node * nd_3,
                 const subdomain_id_type transition_layer_id)
{
  // Adjust the order of nodes in an element so that the mesh can be extruded in (0 0 1)
  // direction.
  elem->subdomain_id() = transition_layer_id;
  if (((*nd_1 - *nd_0).cross((*nd_2 - *nd_0)).unit())(2) > 0)
  {
    elem->set_node(0, nd_0);
    elem->set_node(1, nd_1);
    elem->set_node(2, nd_2);
    elem->set_node(3, nd_3);
    return false;
  }
  else
  {
    elem->set_node(0, nd_0);
    elem->set_node(3, nd_1);
    elem->set_node(2, nd_2);
    elem->set_node(1, nd_3);
    return true;
  }
}
 
bool
buildTriElement(
    Elem * elem, Node * nd_0, Node * nd_1, Node * nd_2, const subdomain_id_type transition_layer_id)
{
  // Adjust the order of nodes in an element so that the mesh can be extruded in (0 0 1)
  // direction.
  elem->subdomain_id() = transition_layer_id;
  if (((*nd_1 - *nd_0).cross((*nd_2 - *nd_0)).unit())(2) > 0)
  {
    elem->set_node(0, nd_0);
    elem->set_node(1, nd_1);
    elem->set_node(2, nd_2);
    return false;
  }
  else
  {
    elem->set_node(0, nd_0);
    elem->set_node(2, nd_1);
    elem->set_node(1, nd_2);
    return true;
  }
}
}