Add an example on combining 3D Alpha Wrap and Tetrahedral Remeshing

Alpha_wrap_3/examples/Alpha_wrap_3/CMakeLists.txt

@@ -12,3 +12,4 @@ create_single_source_cgal_program("triangle_soup_wrap.cpp")
 create_single_source_cgal_program("point_set_wrap.cpp")
 create_single_source_cgal_program("wrap_from_cavity.cpp")
 create_single_source_cgal_program("mixed_inputs_wrap.cpp")
+create_single_source_cgal_program("volumetric_wrap.cpp")

Alpha_wrap_3/examples/Alpha_wrap_3/mixed_inputs_wrap.cpp

@@ -16,9 +16,9 @@ using K = CGAL::Exact_predicates_inexact_constructions_kernel;
 using Point_3 = K::Point_3;
 using Segment_3 = K::Segment_3;
 
-using Face = std::array<std::size_t, 3>;
 using Segments = std::vector<Segment_3>;
 using Points = std::vector<Point_3>;
+using Face = std::array<std::size_t, 3>;
 using Faces = std::vector<Face>;
 
 using Mesh = CGAL::Surface_mesh<Point_3>;

Alpha_wrap_3/examples/Alpha_wrap_3/volumetric_wrap.cpp

@@ -0,0 +1,173 @@
+#include <CGAL/Exact_predicates_inexact_constructions_kernel.h>
+#include <CGAL/Surface_mesh.h>
+
+#include <CGAL/alpha_wrap_3.h>
+
+#include <CGAL/tetrahedral_remeshing.h>
+#include <CGAL/Tetrahedral_remeshing/Remeshing_cell_base_3.h>
+#include <CGAL/Tetrahedral_remeshing/Remeshing_vertex_base_3.h>
+#include <CGAL/Simplicial_mesh_cell_base_3.h>
+#include <CGAL/Simplicial_mesh_vertex_base_3.h>
+
+#include <CGAL/Polygon_mesh_processing/bbox.h>
+#include <CGAL/Polygon_mesh_processing/IO/polygon_mesh_io.h>
+#include <CGAL/property_map.h>
+#include <CGAL/Real_timer.h>
+
+#include <CGAL/Delaunay_triangulation_3.h>
+#include <CGAL/draw_triangulation_3.h>
+
+#include <CGAL/IO/Triangulation_off_ostream_3.h>
+#include <CGAL/IO/File_medit.h>
+
+#include <iostream>
+#include <string>
+
+namespace PMP = CGAL::Polygon_mesh_processing;
+namespace AW3i = CGAL::Alpha_wraps_3::internal;
+
+using K = CGAL::Exact_predicates_inexact_constructions_kernel;
+using Point_3 = K::Point_3;
+
+using Points = std::vector<Point_3>;
+using Face = std::array<std::size_t, 3>;
+using Faces = std::vector<Face>;
+
+using Mesh = CGAL::Surface_mesh<Point_3>;
+
+// If we provide a triangulation, AW3 uses its Gt, so we have to make the Gt stack explicit
+using Gtb = AW3i::Alpha_wrap_AABB_geom_traits<K>; // provides Ball_3
+using Gt = CGAL::Robust_circumcenter_filtered_traits_3<Gtb>; // better inexact constructions (not mandatory)
+
+// Since we are going to use tetrahedral remeshing on the underlying triangulation,
+// we need special vertex and cell base types that meets the requirements of the
+// tetrahedral remeshing concepts
+using Vbbb = AW3i::Alpha_wrap_triangulation_vertex_base_3<K>;
+using Vbb = CGAL::Simplicial_mesh_vertex_base_3<K, int, int, int, int, Vbbb>;
+using Vb = CGAL::Tetrahedral_remeshing::Remeshing_vertex_base_3<K, Vbb>;
+
+using Cbbb = AW3i::Alpha_wrap_triangulation_cell_base_3<K>;
+using Cbb = CGAL::Simplicial_mesh_cell_base_3<K, int, int, Cbbb>;
+using Cb = CGAL::Tetrahedral_remeshing::Remeshing_cell_base_3<K, Cbb>;
+
+using Tds = CGAL::Triangulation_data_structure_3<Vb, Cb>;
+
+using Delaunay_triangulation = CGAL::Delaunay_triangulation_3<Gt, Tds, CGAL::Fast_location>;
+
+// because the Fast_location does all kinds of rebinding shenanigans + T3_hierarchy is in the stack...
+using Triangulation = CGAL::Triangulation_3<typename Delaunay_triangulation::Geom_traits,
+                                            typename Delaunay_triangulation::Triangulation_data_structure>;
+
+using Facet = Triangulation::Facet;
+
+int main(int argc, char** argv)
+{
+  // Read the input
+  const std::string filename = (argc > 1) ? argv[1] : CGAL::data_file_path("meshes/bull.off");
+  std::cout << "Reading " << filename << "..." << std::endl;
+
+  Points points;
+  Faces faces;
+  if(!CGAL::IO::read_polygon_soup(filename, points, faces) || faces.empty())
+  {
+    std::cerr << "Invalid input." << std::endl;
+    return EXIT_FAILURE;
+  }
+
+  std::cout << "Input: " << points.size() << " vertices, " << faces.size() << " faces" << std::endl;
+
+  // Compute the alpha and offset values
+  const double relative_alpha = (argc > 2) ? std::stod(argv[2]) : 20.;
+  const double relative_offset = (argc > 3) ? std::stod(argv[3]) : 600.;
+
+  CGAL::Bbox_3 bbox;
+  for(const Point_3& p : points)
+    bbox += p.bbox();
+
+  const double diag_length = std::sqrt(CGAL::square(bbox.xmax() - bbox.xmin()) +
+                                       CGAL::square(bbox.ymax() - bbox.ymin()) +
+                                       CGAL::square(bbox.zmax() - bbox.zmin()));
+
+  const double alpha = diag_length / relative_alpha;
+  const double offset = diag_length / relative_offset;
+  std::cout << "alpha: " << alpha << ", offset: " << offset << std::endl;
+
+  // Construct the wrap
+  CGAL::Real_timer t;
+  t.start();
+
+  using Oracle = CGAL::Alpha_wraps_3::internal::Triangle_soup_oracle<K>;
+
+  Oracle oracle(K{});
+  oracle.add_triangle_soup(points, faces, CGAL::parameters::default_values());
+
+  CGAL::Alpha_wraps_3::internal::Alpha_wrap_3<Oracle, Delaunay_triangulation> aw3(oracle);
+  Mesh wrap;
+  aw3(alpha, offset, wrap);
+
+  t.stop();
+  std::cout << "Result: " << num_vertices(wrap) << " vertices, " << num_faces(wrap) << " faces" << std::endl;
+  std::cout << "Took " << t.time() << " s." << std::endl;
+
+  // Get the interior tetrahedrization
+  auto dt = aw3.triangulation();
+
+  // Save the result
+  std::string input_name = std::string(filename);
+  input_name = input_name.substr(input_name.find_last_of("/") + 1, input_name.length() - 1);
+  input_name = input_name.substr(0, input_name.find_last_of("."));
+  std::string output_name = input_name
+                            + "_" + std::to_string(static_cast<int>(relative_alpha))
+                            + "_" + std::to_string(static_cast<int>(relative_offset)) + ".off";
+  std::cout << "Writing to " << output_name << std::endl;
+  CGAL::IO::write_polygon_mesh(output_name, wrap, CGAL::parameters::stream_precision(17));
+
+  // Remesh the interior of the wrap
+  const Delaunay_triangulation& aw3_dt = aw3.triangulation();
+  const Triangulation& aw3_tr = static_cast<const Triangulation&>(aw3_dt);
+  Triangulation tr = aw3_tr; // intentional copy
+
+  std::cout << "BEFORE: " << tr.number_of_vertices() << " vertices, " << tr.number_of_cells() << " cells" << std::endl;
+
+  // Set up the c3t3 information
+  for(auto v : tr.finite_vertex_handles())
+    v->set_dimension(3);
+
+  for(auto c : tr.finite_cell_handles())
+  {
+    if(c->is_outside())
+      c->set_subdomain_index(0);
+    else
+      c->set_subdomain_index(1);
+
+    // if the neighboring cell has a different outside info, put the vertices
+    // of the common face on the surface boundary
+    for(int i=0; i<4; ++i)
+    {
+      if(c->neighbor(i)->is_outside() != c->is_outside())
+      {
+        c->set_surface_patch_index(i, 1);
+        for(int j=1; j<4; ++j)
+          c->vertex((i+j)%4)->set_dimension(2);
+      }
+    }
+  }
+
+  std::ofstream out_before("before_remeshing.mesh");
+  CGAL::IO::write_MEDIT(out_before, tr);
+
+  // edge length of equilateral triangle with circumradius alpha
+  // const double l = 2 * alpha * 0.8660254037844386; // sqrt(3)/2
+
+  // edge length of regular tetrahedron with circumradius alpha
+  const double l = 1.6329931618554521 * alpha; // sqrt(8/3)
+
+  CGAL::tetrahedral_isotropic_remeshing(tr, l, CGAL::parameters::remesh_boundaries(false));
+
+  std::cout << "AFTER: " << tr.number_of_vertices() << " vertices, " << tr.number_of_cells() << " cells" << std::endl;
+
+  std::ofstream out_after("after_remeshing.mesh");
+  CGAL::IO::write_MEDIT(out_after, tr);
+
+  return EXIT_SUCCESS;
+}