findpts.cpp

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// Copyright (c) 2010-2026, Lawrence Livermore National Security, LLC. Produced
// at the Lawrence Livermore National Laboratory. All Rights reserved. See files
// LICENSE and NOTICE for details. LLNL-CODE-806117.
//
// This file is part of the MFEM library. For more information and source code
// availability visit https://mfem.org.
//
// MFEM is free software; you can redistribute it and/or modify it under the
// terms of the BSD-3 license. We welcome feedback and contributions, see file
// CONTRIBUTING.md for details.
//
//      -------------------------------------------------------------
//      Find Points Miniapp: Evaluate grid function in physical space
//      -------------------------------------------------------------
//
// This miniapp demonstrates the interpolation of a high-order grid function on
// a set of points in physical-space. The miniapp is based on GSLIB-FindPoints,
// which provides two key functionalities. First, for a given set of points in
// the physical-space, it determines the computational coordinates (element
// number, reference-space coordinates inside the element, and processor number
// [in parallel]) for each point. Second, based on computational coordinates, it
// interpolates a grid function in the given points. Inside GSLIB, computation
// of the coordinates requires use of a Hash Table to identify the candidate
// processor and element for each point, followed by the Newton's method to
// determine the reference-space coordinates inside the candidate element.
//
// Compile with: make findpts
//
// Sample runs:
//    findpts -m ../../data/rt-2d-p4-tri.mesh -o 8 -mo 4
//    findpts -m ../../data/inline-tri.mesh -o 3
//    findpts -m ../../data/inline-quad.mesh -o 3
//    findpts -m ../../data/inline-quad.mesh -o 3 -po 1
//    findpts -m ../../data/inline-quad.mesh -o 3 -po 1 -fo 1 -nc 2
//    findpts -m ../../data/inline-quad.mesh -o 3 -hr -pr -mpr -mo 2
//    findpts -m ../../data/inline-quad.mesh -o 3 -hr -pr -mpr -mo 3
//    findpts -m ../../data/inline-tet.mesh -o 3
//    findpts -m ../../data/inline-hex.mesh -o 3
//    findpts -m ../../data/inline-wedge.mesh -o 3
//    findpts -m ../../data/amr-quad.mesh -o 2
//    findpts -m ../../data/rt-2d-q3.mesh -o 8 -mo 4 -ft 2
//    findpts -m ../../data/square-mixed.mesh -o 2 -mo 2
//    findpts -m ../../data/square-mixed.mesh -o 2 -mo 2 -hr -pr -mpr
//    findpts -m ../../data/square-mixed.mesh -o 2 -mo 3 -ft 2
//    findpts -m ../../data/fichera-mixed.mesh -o 3 -mo 2
//    findpts -m ../../data/inline-pyramid.mesh -o 1 -mo 1
//    findpts -m ../../data/tinyzoo-3d.mesh -o 1 -mo 1
// Surface meshes:
//    findpts -m ../../data/ref-square.mesh -o 2 -mo 1 -random 1 -surf
//    findpts -m ../../data/ref-cube.mesh -o 2 -mo 1 -random 1 -surf
//    findpts -m ../../data/square-disc-p2.mesh -o 4 -mo 2 -random 1 -surf
// Surface meshes + bounding box size increase:
//    findpts -m ../../data/square-disc-p2.mesh -o 4 -mo 2 -random 1 -surf -sabs 0.1
//    findpts -m ../../data/tinyzoo-3d.mesh -o 4 -mo 2 -random 1 -surf -sabs 0.1
 
#include "mfem.hpp"
#include "../common/mfem-common.hpp"
 
using namespace mfem;
using namespace std;
 
void VisualizeFESpacePolynomialOrder(FiniteElementSpace &fespace,
                                     const char *title, int locx)
{
   Mesh *mesh = fespace.GetMesh();
   L2_FECollection order_coll = L2_FECollection(0, mesh->Dimension());
   FiniteElementSpace order_space = FiniteElementSpace(mesh, &order_coll);
   GridFunction order_gf = GridFunction(&order_space);
 
   for (int e = 0; e < mesh->GetNE(); e++)
   {
      order_gf(e) = fespace.GetElementOrder(e);
   }
 
   socketstream vis1;
   common::VisualizeField(vis1, "localhost", 19916, order_gf, title,
                          locx, 0, 400, 400, "RjmAcp");
}
 
double func_order;
 
// Scalar function to project
double field_func(const Vector &x)
{
   const int dim = x.Size();
   double res = 0.0;
   for (int d = 0; d < dim; d++) { res += std::pow(x(d), func_order); }
   return res;
}
 
void F_exact(const Vector &p, Vector &F)
{
   F(0) = field_func(p);
   for (int i = 1; i < F.Size(); i++) { F(i) = (i+1)*F(0); }
}
 
int main (int argc, char *argv[])
{
   // Set the method's default parameters.
   const char *mesh_file = "../../data/rt-2d-q3.mesh";
   int order             = 3;
   int mesh_poly_deg     = 3;
   int rs_levels         = 0;
   bool visualization    = true;
   int fieldtype         = 0;
   int ncomp             = 1;
   bool hrefinement      = false;
   bool prefinement      = false;
   int point_ordering    = 0;
   int gf_ordering       = 0;
   bool mesh_prefinement = false;
   int randomization     = 0;
   int npt               = 100;
   bool surface          = false;
   double surf_aabb_sz_inc = 0.0;
 
   // Parse command-line options.
   OptionsParser args(argc, argv);
   args.AddOption(&mesh_file, "-m", "--mesh",
                  "Mesh file to use.");
   args.AddOption(&order, "-o", "--order",
                  "Finite element order (polynomial degree).");
   args.AddOption(&mesh_poly_deg, "-mo", "--mesh-order",
                  "Polynomial degree of mesh finite element space.");
   args.AddOption(&rs_levels, "-rs", "--refine-serial",
                  "Number of times to refine the mesh uniformly in serial.");
   args.AddOption(&fieldtype, "-ft", "--field-type",
                  "Field type: 0 - H1, 1 - L2, 2 - H(div), 3 - H(curl).");
   args.AddOption(&ncomp, "-nc", "--ncomp",
                  "Number of components for H1 or L2 GridFunctions");
   args.AddOption(&visualization, "-vis", "--visualization", "-no-vis",
                  "--no-visualization",
                  "Enable or disable GLVis visualization.");
   args.AddOption(&hrefinement, "-hr", "--h-refinement", "-no-hr",
                  "--no-h-refinement",
                  "Do random h refinements to mesh (does not work for pyramids).");
   args.AddOption(&prefinement, "-pr", "--p-refinement", "-no-pr",
                  "--no-p-refinement",
                  "Do random p refinements to solution field (does not work for pyramids).");
   args.AddOption(&point_ordering, "-po", "--point-ordering",
                  "Ordering of points to be found."
                  "0 (default): byNodes, 1: byVDIM");
   args.AddOption(&gf_ordering, "-fo", "--fespace-ordering",
                  "Ordering of fespace that will be used for grid function to be interpolated."
                  "0 (default): byNodes, 1: byVDIM");
   args.AddOption(&mesh_prefinement, "-mpr", "--mesh-p-refinement", "-no-mpr",
                  "--no-mesh-p-refinement",
                  "Do random p refinements to mesh Nodes.");
   args.AddOption(&randomization, "-random", "--random",
                  "0: generate points randomly in the bounding box of domain, "
                  "1: generate points randomly inside each element in mesh.");
   args.AddOption(&npt, "-npt", "--npt",
                  "Number of points per element when -random 1 is used.");
   args.AddOption(&surface, "-surf", "--surface", "-no-surf",
                  "--no-surface",
                  "Extract surface mesh from volume mesh.");
   args.AddOption(&surf_aabb_sz_inc, "-sabs", "--surface-aabb-size-inc",
                  "Absolute AABB expansion applied to surface-search "
                  "axis-aligned bounding boxes in FindPointsGSLIB surface meshes.");
 
   args.Parse();
   if (!args.Good())
   {
      args.PrintUsage(cout);
      return 1;
   }
   args.PrintOptions(cout);
 
   func_order = std::min(order, 2);
 
   // Initialize and optionally extract the surface mesh.
   Mesh input_mesh(mesh_file, 1, 1, false);
   Mesh *mesh = surface ? nullptr : &input_mesh;
   if (surface)
   {
      MFEM_VERIFY(input_mesh.bdr_attributes.Size() > 0,
                  "--surface requires a mesh with boundary attributes.");
      mesh = new Mesh(SubMesh::CreateFromBoundary(input_mesh,
                                                  input_mesh.bdr_attributes));
   }
 
   MFEM_VERIFY(!(surface && prefinement),
               "Surface interpolation does not support variable-order "
               "solution spaces; use -no-pr with --surface.");
 
   for (int lev = 0; lev < rs_levels; lev++) { mesh->UniformRefinement(); }
   const int dim = mesh->Dimension(),
             sdim = mesh->SpaceDimension();
   cout << "Mesh curvature of the original mesh: ";
   if (mesh->GetNodes()) { cout << mesh->GetNodes()->OwnFEC()->Name(); }
   else { cout << "(NONE)"; }
   cout << endl;
 
   // Mesh bounding box.
   Vector pos_min, pos_max;
   MFEM_VERIFY(mesh_poly_deg > 0, "The order of the mesh must be positive.");
   mesh->GetBoundingBox(pos_min, pos_max, mesh_poly_deg);
   if (hrefinement || prefinement || mesh_prefinement)
   {
      mesh->EnsureNCMesh(true);
   }
 
   cout << "--- Generating points for:\n"
        << "x in [" << pos_min(0) << ", " << pos_max(0) << "]\n";
   if (sdim >= 2)
   {
      cout << "y in [" << pos_min(1) << ", " << pos_max(1) << "]" << std::endl;
   }
   if (sdim == 3)
   {
      cout << "z in [" << pos_min(2) << ", " << pos_max(2) << "]\n";
   }
 
   // Random h-refinements to mesh
   if (hrefinement) { mesh->RandomRefinement(0.5); }
 
   // Curve the mesh based on the chosen polynomial degree.
   H1_FECollection fecm(mesh_poly_deg, dim);
   FiniteElementSpace fespace(mesh, &fecm, sdim);
   mesh->SetNodalFESpace(&fespace);
   GridFunction Nodes(&fespace);
   mesh->SetNodalGridFunction(&Nodes);
   cout << "Mesh curvature of the curved mesh: " << fecm.Name() << endl;
 
   if (mesh_prefinement)
   {
      Array<pRefinement> refs;
      for (int e = 0; e < mesh->GetNE(); e++)
      {
         if ((double) rand() / RAND_MAX < 0.2)
         {
            refs.Append(pRefinement(e,1));
         }
      }
      std::cout << refs.Size() << " elements will be p-refined for the mesh." <<
                std::endl;
      fespace.PRefineAndUpdate(refs);
      Nodes.Update();
   }
 
   MFEM_VERIFY(ncomp > 0, "Invalid number of components.");
   int vec_dim = ncomp;
   FiniteElementCollection *fec = NULL;
   if (fieldtype == 0)
   {
      fec = new H1_FECollection(order, dim);
      cout << "H1-GridFunction\n";
   }
   else if (fieldtype == 1)
   {
      fec = new L2_FECollection(order, dim);
      cout << "L2-GridFunction\n";
   }
   else if (fieldtype == 2)
   {
      fec = new RT_FECollection(order, dim);
      ncomp = 1;
      vec_dim = sdim;
      cout << "H(div)-GridFunction\n";
   }
   else if (fieldtype == 3)
   {
      fec = new ND_FECollection(order, dim);
      ncomp = 1;
      vec_dim = sdim;
      cout << "H(curl)-GridFunction\n";
   }
   else
   {
      MFEM_ABORT("Invalid field type.");
   }
   FiniteElementSpace sc_fes(mesh, fec, ncomp, gf_ordering);
   GridFunction field_vals(&sc_fes);
 
   // Random p-refinements to the solution field
   if (prefinement)
   {
      Array<pRefinement> refs;
      for (int e = 0; e < mesh->GetNE(); e++)
      {
         if ((double) rand() / RAND_MAX < 0.5)
         {
            refs.Append(pRefinement(e,1));
         }
      }
      sc_fes.PRefineAndUpdate(refs);
      field_vals.Update();
   }
 
   std::unique_ptr<GridFunction> mesh_nodes_max;
   if (mesh_prefinement) { mesh_nodes_max = Nodes.ProlongateToMaxOrder(); }
   GridFunction *mesh_nodes_pref = mesh_prefinement ?
                                   mesh_nodes_max.get() : &Nodes;
 
   if (mesh_prefinement && visualization)
   {
      mesh->SetNodalGridFunction(mesh_nodes_pref);
      VisualizeFESpacePolynomialOrder(fespace, "Mesh Polynomial Order", 400);
      mesh->SetNodalGridFunction(&Nodes);
   }
 
   if (prefinement && visualization)
   {
      mesh->SetNodalGridFunction(mesh_nodes_pref);
      VisualizeFESpacePolynomialOrder(sc_fes, "Solution Polynomial Order", 800);
      mesh->SetNodalGridFunction(&Nodes);
   }
 
   // Project the GridFunction using VectorFunctionCoefficient.
   VectorFunctionCoefficient F(vec_dim, F_exact);
   field_vals.ProjectCoefficient(F);
 
   std::unique_ptr<GridFunction> field_vals_max;
   if (prefinement) { field_vals_max = field_vals.ProlongateToMaxOrder(); }
   GridFunction *field_vals_pref = prefinement ?
                                   field_vals_max.get() : &field_vals;
 
   // Display the mesh and the field through glvis.
   if (visualization)
   {
      if (mesh_prefinement) { mesh->SetNodalGridFunction(mesh_nodes_pref); }
      socketstream vis1;
      common::VisualizeField(vis1, "localhost", 19916, *field_vals_pref,
                             "Solution",
                             0, 0, 400, 400, "RmjA*****");
      if (mesh_prefinement) { mesh->SetNodalGridFunction(&Nodes); }
   }
 
   // Generate random points in physical coordinates over the whole mesh.
   // Note that some points might be outside if the mesh is not a box.
   int pts_cnt = npt;
   Vector vxyz;
   int npt_face_per_elem = 4; // number of pts on faces when randomization != 0
   int npt_total_face = 0;
   if (randomization == 0)
   {
      vxyz.SetSize(pts_cnt * sdim);
      vxyz.Randomize(1);
 
      // Scale based on min/max dimensions
      for (int i = 0; i < pts_cnt; i++)
      {
         for (int d = 0; d < sdim; d++)
         {
            if (point_ordering == Ordering::byNODES)
            {
               vxyz(i + d*pts_cnt) =
                  pos_min(d) + vxyz(i + d*pts_cnt) * (pos_max(d) - pos_min(d));
            }
            else
            {
               vxyz(i*sdim + d) =
                  pos_min(d) + vxyz(i*sdim + d) * (pos_max(d) - pos_min(d));
            }
         }
      }
   }
   else // randomization == 1
   {
      pts_cnt = npt * mesh->GetNE();
      vxyz.SetSize(pts_cnt * sdim);
      for (int i = 0; i < mesh->GetNE(); i++)
      {
         ElementTransformation *transf = mesh->GetElementTransformation(i);
         const Geometry::Type geom = mesh->GetElementGeometry(i);
         for (int j = 0; j < npt; j++)
         {
            IntegrationPoint ip;
            Geometry::GetRandomPoint(geom, ip);
            if (j < npt_face_per_elem)
            {
               ip.x = 0.0; // force point to be on the face
               npt_total_face++;
            }
            Vector pos_i(sdim);
            transf->Transform(ip, pos_i);
            for (int d = 0; d < sdim; d++)
            {
               if (point_ordering == Ordering::byNODES)
               {
                  vxyz(j + npt*i + d*pts_cnt) = pos_i(d);
               }
               else
               {
                  vxyz((j + npt*i)*sdim + d) = pos_i(d);
               }
            }
         }
      }
   }
 
   // Find and Interpolate FE function values on the desired points.
   Vector interp_vals(pts_cnt*vec_dim);
   FindPointsGSLIB finder;
   if (surface && surf_aabb_sz_inc > 0.0)
   {
      Vector bb_size({surf_aabb_sz_inc});
      finder.SetupSurfWithAABBExpansion(*mesh, bb_size);
   }
   else
   {
      finder.Setup(*mesh);
      // finder.SetDistanceToleranceForPointsFoundOnBoundary(10);
   }
   finder.SetL2AvgType(FindPointsGSLIB::NONE);
   finder.Interpolate(vxyz, field_vals, interp_vals, point_ordering);
   Array<unsigned int> code_out    = finder.GetCode();
   Vector dist_p_out = finder.GetDist();
 
   int face_pts = 0, not_found = 0, found = 0;
   double error = 0.0, max_err = 0.0, max_dist = 0.0;
   Vector pos(sdim);
   for (int j = 0; j < vec_dim; j++)
   {
      for (int i = 0; i < pts_cnt; i++)
      {
         if (code_out[i] < 2)
         {
            if (j == 0) { found++; }
            for (int d = 0; d < sdim; d++)
            {
               pos(d) = point_ordering == Ordering::byNODES ?
                        vxyz(d*pts_cnt + i) :
                        vxyz(i*sdim + d);
            }
            Vector exact_val(vec_dim);
            F_exact(pos, exact_val);
            error = gf_ordering == Ordering::byNODES ?
                    fabs(exact_val(j) - interp_vals[i + j*pts_cnt]) :
                    fabs(exact_val(j) - interp_vals[i*vec_dim + j]);
            max_err  = std::max(max_err, error);
            max_dist = std::max(max_dist, dist_p_out(i));
            if (code_out[i] == 1 && j == 0) { face_pts++; }
         }
         else { if (j == 0) { not_found++; } }
      }
   }
 
   cout << setprecision(16)
        << "Searched points:     "   << pts_cnt
        << "\nFound points:        " << found
        << "\nMax interp error:    " << max_err
        << "\nMax dist^2 (of found): " << max_dist
        << "\nPoints not found:    " << not_found;
   if (randomization == 1)
   {
      cout << "\nPoints on faces:     " << face_pts << " out of "
           << npt_total_face << endl;
   }
   else
   {
      cout << "\nPoints on faces:     " << face_pts << endl;
   }
 
   delete fec;
   if (surface) { delete mesh; }
 
   return 0;
}