face_c0polygon.C

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// The libMesh Finite Element Library.
// Copyright (C) 2002-2026 Benjamin S. Kirk, John W. Peterson, Roy H. Stogner
 
// This library is free software; you can redistribute it and/or
// modify it under the terms of the GNU Lesser General Public
// License as published by the Free Software Foundation; either
// version 2.1 of the License, or (at your option) any later version.
 
// This library is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
// Lesser General Public License for more details.
 
// You should have received a copy of the GNU Lesser General Public
// License along with this library; if not, write to the Free Software
// Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
 
// Local includes
#include "libmesh/face_c0polygon.h"
 
#include "libmesh/edge_edge2.h"
#include "libmesh/enum_order.h"
#include "libmesh/tensor_value.h"
 
// C++ headers
#include <numeric> // std::iota
 
namespace libMesh
{
 
 
C0Polygon::C0Polygon (const unsigned int num_sides, Elem * p) :
  Polygon(num_sides, num_sides, p)
{
  // A default triangulation is better than nothing
  for (int i : make_range(num_sides-2))
    this->_triangulation.push_back({0, i+1, i+2});
}
 
 
unsigned int C0Polygon::opposite_node(const unsigned int node_in,
                                      const unsigned int side_in) const
{
  const auto ns = this->n_sides();
  if (ns % 2)
    libmesh_error();
 
  libmesh_assert_less (node_in, ns);
  libmesh_assert_less (node_in, this->n_nodes());
  libmesh_assert_less (side_in, this->n_sides());
  libmesh_assert(this->is_node_on_side(node_in, side_in));
 
  if (node_in == side_in)
    return (node_in + ns/2 + 1) % ns;
 
  libmesh_assert(node_in == side_in + 1);
  return (node_in + ns/2 - 1) % ns;
}
 
 
 
// ------------------------------------------------------------
// C0Polygon class member functions
 
bool C0Polygon::is_vertex(const unsigned int libmesh_dbg_var(i)) const
{
  libmesh_assert (i < this->n_nodes());
 
  return true;
}
 
bool C0Polygon::is_edge(const unsigned int libmesh_dbg_var(i)) const
{
  libmesh_assert (i < this->n_nodes());
 
  return false;
}
 
bool C0Polygon::is_face(const unsigned int libmesh_dbg_var(i)) const
{
  libmesh_assert (i < this->n_nodes());
 
  return false;
}
 
bool C0Polygon::is_node_on_side(const unsigned int n,
                                const unsigned int s) const
{
  const auto ns = this->n_sides();
  libmesh_assert_less (s, ns);
  libmesh_assert_less (n, this->n_nodes());
 
  return ((n % ns) == s) ||
         ((n < ns) && ((s+1)%ns) == n);
}
 
std::vector<unsigned int>
C0Polygon::nodes_on_side(const unsigned int s) const
{
  const auto ns = this->n_sides();
  libmesh_assert(!(this->n_nodes() % ns));
  libmesh_assert_less(s, ns);
 
  std::vector<unsigned int> returnval(2);
  returnval[0] = s;
  returnval[1] = (s+1)%ns;
 
  return returnval;
}
 
std::vector<unsigned int>
C0Polygon::nodes_on_edge(const unsigned int e) const
{
  return this->nodes_on_side(e);
}
 
bool C0Polygon::has_affine_map() const
{
  const unsigned int ns = this->n_sides();
 
  // Get a good tolerance to use
  Real perimeter_l1 = 0;
  for (auto s : make_range(ns))
    perimeter_l1 += (this->point((s+1)%ns) - this->point(s)).l1_norm();
  const Real tol = perimeter_l1 * affine_tol;
 
  // Find the map we expect to have
  const Point veci = this->point(1) - this->point(0);
  const Point vec12 = this->point(2) - this->point(1);
 
  // Exterior angle
  const Real theta = 2 * libMesh::pi / ns;
  const Real costheta = cos(theta);
  const Real sintheta = sin(theta);
 
  RealTensor map;
  map(0, 0) = veci(0);
  map(1, 0) = veci(1);
  map(2, 0) = veci(2);
  map(0, 1) = (vec12(0) - veci(0)*costheta)/sintheta;
  map(1, 1) = (vec12(1) - veci(1)*costheta)/sintheta;
  map(2, 1) = (vec12(2) - veci(2)*costheta)/sintheta;
 
  libmesh_assert_less((map * this->master_point(1) -
                       (this->point(1) - this->point(0))).l1_norm(),
                      tol);
  libmesh_assert_less((map * this->master_point(2) -
                       (this->point(2) - this->point(0))).l1_norm(),
                      tol);
 
  for (auto i : make_range(3u, ns))
    if ((map * this->master_point(i) -
                     (this->point(i) - this->point(0))).l1_norm() >
        tol)
      return false;
 
  return true;
}
 
 
 
Order C0Polygon::default_order() const
{
  return FIRST;
}
 
 
 
std::unique_ptr<Elem> C0Polygon::build_side_ptr (const unsigned int i)
{
  const auto ns = this->n_sides();
  libmesh_assert_less (i, ns);
 
  std::unique_ptr<Elem> sidep = std::make_unique<Edge2>();
  sidep->set_node(0, this->node_ptr(i));
  sidep->set_node(1, this->node_ptr((i+1)%ns));
 
  sidep->set_interior_parent(this);
  sidep->inherit_data_from(*this);
 
  return sidep;
}
 
 
 
void C0Polygon::build_side_ptr (std::unique_ptr<Elem> & side,
                                const unsigned int i)
{
  const auto ns = this->n_sides();
  libmesh_assert_less (i, ns);
 
  if (!side.get() || side->type() != EDGE2)
    {
      side = this->build_side_ptr(i);
    }
  else
    {
      side->inherit_data_from(*this);
 
      side->set_node(0, this->node_ptr(i));
      side->set_node(1, this->node_ptr((i+1)%ns));
    }
}
 
 
 
void C0Polygon::connectivity(const unsigned int /*sf*/,
                             const IOPackage /*iop*/,
                             std::vector<dof_id_type> & /*conn*/) const
{
  libmesh_not_implemented();
}
 
 
 
Real C0Polygon::volume () const
{
  // This specialization is good for non-Lagrange mappings, but
  // remember to be more careful when we extend it to non-planar or
  // non p=1 polygon types.
  // if (this->mapping_type() != LAGRANGE_MAP)
  //   return this->Elem::volume();
 
  // We use a triangulation to calculate here; assert that it's as
  // consistent as possible.
  libmesh_assert_equal_to (this->_triangulation.size(),
                           this->n_nodes() - 2);
 
  Real double_area = 0;
  for (const auto & triangle : this->_triangulation)
    {
      Point v01 = this->point(triangle[1]) -
                  this->point(triangle[0]);
      Point v02 = this->point(triangle[2]) -
                  this->point(triangle[0]);
      double_area += std::sqrt(cross_norm_sq(v01, v02));
    }
 
  return double_area/2;
}
 
 
 
Point C0Polygon::true_centroid () const
{
  // This specialization is good for Lagrange mappings only
  if (this->mapping_type() != LAGRANGE_MAP)
    return this->Elem::true_centroid();
 
  // We use a triangulation to calculate here; assert that it's as
  // consistent as possible.
  libmesh_assert_equal_to (this->_triangulation.size(),
                           this->n_nodes() - 2);
 
  Real double_area = 0;
  Point double_area_weighted_centroid;
  for (const auto & triangle : this->_triangulation)
    {
      Point v01 = this->point(triangle[1]) -
                  this->point(triangle[0]);
      Point v02 = this->point(triangle[2]) -
                  this->point(triangle[0]);
 
      const Real  double_tri_area = std::sqrt(cross_norm_sq(v01, v02));
      const Point tri_centroid = (this->point(triangle[0]) +
                                  this->point(triangle[1]) +
                                  this->point(triangle[2]))/3;
 
      double_area += double_tri_area;
 
      double_area_weighted_centroid += double_tri_area * tri_centroid;
    }
 
  return double_area_weighted_centroid / double_area;
}
 
 
 
std::pair<unsigned short int, unsigned short int>
C0Polygon::second_order_child_vertex (const unsigned int /*n*/) const
{
  libmesh_not_implemented();
  return std::pair<unsigned short int, unsigned short int> (0, 0);
}
 
 
void C0Polygon::permute(unsigned int perm_num)
{
  const auto ns = this->n_sides();
  libmesh_assert_less (perm_num, ns);
 
  // This is mostly for unit testing so I'll just make it O(N).
  for (unsigned int p : make_range(perm_num))
    {
      libmesh_ignore(p);
 
      Node * tempnode = this->node_ptr(0);
      Elem * tempneigh = this->neighbor_ptr(0);
      for (unsigned int s : make_range(ns-1))
        {
          this->set_node(s, this->node_ptr((s+1)%ns));
          this->set_neighbor(s, this->neighbor_ptr(s+1));
        }
      this->set_node(ns-1, tempnode);
      this->set_neighbor(ns-1, tempneigh);
 
      // Keep the same triangulation, just with permuted node order,
      // so we can really expect this to act like the *same* polygon
      for (auto & triangle : this->_triangulation)
        for (auto i : make_range(3))
          triangle[i] = (triangle[i]+1)%ns;
    }
}
 
 
void C0Polygon::flip(BoundaryInfo * boundary_info)
{
  libmesh_assert(boundary_info);
 
  const auto ns = this->n_sides();
 
  // Reorder nodes in such a way as to keep side ns-1 the same
  for (auto s : make_range(0u, ns/2))
    {
      swap2nodes(s, ns-1-s);
      swap2neighbors(s, ns-2-s);
      swap2boundarysides(s, ns-2-s, boundary_info);
      swap2boundaryedges(s, ns-2-s, boundary_info);
    }
}
 
 
 
ElemType C0Polygon::side_type (const unsigned int libmesh_dbg_var(s)) const
{
  libmesh_assert_less (s, this->n_sides());
  return EDGE2;
}
 
 
Point
C0Polygon::side_vertex_average_normal(const unsigned int s) const
{
  const auto n_sides = this->n_sides();
  libmesh_assert_less (s, n_sides);
  libmesh_assert_equal_to(this->mapping_type(), LAGRANGE_MAP);
  const Point side_t = this->point((s+1) % n_sides) -
                       this->point(s);
  Point plane_normal(0, 0, 1);
  // Find out what plane we're in, if we're in 3D
  // Note we don't support non-planar C0-polygon at this time
#if LIBMESH_DIM > 2
  plane_normal(2) = 0;
  const auto vavg = this->vertex_average();
  for (auto i : make_range(n_sides))
    {
      const Point vi     = this->point(i) - vavg;
      const Point viplus = this->point((i+1)%n_sides) - vavg;
      plane_normal += vi.cross(viplus);
      // Since we know the polygon is planar
      if (plane_normal.norm_sq() > TOLERANCE)
        break;
    }
  plane_normal = plane_normal.unit();
#endif
  const Point v = side_t.cross(plane_normal);
  return v.unit();
}
 
 
void C0Polygon::retriangulate()
{
  this->_triangulation.clear();
 
  // Start with the full polygon
  std::vector<int> remaining_nodes(this->n_nodes());
  std::iota(remaining_nodes.begin(), remaining_nodes.end(), 0);
 
  const auto ns = this->n_sides();
 
  const Point vavg = this->vertex_average();
 
  // Find out what plane we're in, if we're in 3D
#if LIBMESH_DIM > 2
  Point plane_normal;
  for (auto i : make_range(ns))
    {
      const Point vi     = this->point(i) - vavg;
      const Point viplus = this->point((i+1)%ns) - vavg;
      plane_normal += vi.cross(viplus);
    }
  plane_normal = plane_normal.unit();
#endif
 
  // Greedy heuristic: find the node with the most acutely convex
  // angle and strip it out as a triangle.
  while (remaining_nodes.size() > 2)
    {
      Real min_cos_angle = 1;
      int best_vertex = -1;
      for (auto n : index_range(remaining_nodes))
        {
          const Point & pn = this->point(remaining_nodes[n]);
          const Point & pnext = this->point(remaining_nodes[(n+1)%ns]);
          const Point & pprev = this->point(remaining_nodes[(n+ns-1)%ns]);
          const Point vprev = (pn - pprev).unit();
          const Point vnext = (pnext - pn).unit();
 
          const Real sign_check = (vprev.cross(vnext)) * plane_normal;
          if (sign_check <= 0)
            continue;
 
          const Real cos_angle = vprev * vnext;
          if (cos_angle < min_cos_angle)
            {
              min_cos_angle = cos_angle;
              best_vertex = n;
            }
        }
 
      libmesh_assert(best_vertex >= 0);
 
      this->_triangulation.push_back({remaining_nodes[(best_vertex+ns-1)%ns],
                                      remaining_nodes[best_vertex],
                                      remaining_nodes[(best_vertex+1)%ns]});
      remaining_nodes.erase(remaining_nodes.begin()+best_vertex);
    }
}
 
 
 
} // namespace libMesh