automata_scratch/python_isosurfaces_2018_2019/cgal_dabbling.org

CGAL dabbling

• CGAL is one of the most insanely cryptic and impenetrable libraries I have found.

• Where I am stuck now:

  • I can use 1D features in Mesh_3/mesh_two_implicit_spheres_with_balls.cpp but this is the wrong sort of data (it's a 3D mesh, yes, but not a surface mesh) and "medit" and "vtu" are all it can write. How do I extract a surface mesh to get a Polyhedron_3 so that I can write an OBJ?
  • Or: Is there any way to use 1D features with a surface mesh?
  • Even if I manage to put this Mesh_3 into the right form I have no guarantees that it is a good surface mesh. It uses a different algorithm than for the surface mesh - I'm simply trying to take the surface of the result. I should also expect this algorithm to be something more like O(N^3) with mesh resolution because it must fill the volume with tetrahedrons, and I then just throw away all of these.
• This is based around the source for mesh_implicit_sphere.cpp from CGAL: 3D Mesh Generation.
• Why am I not using facets_in_complex_3_to_triangle_mesh()?

• Mesh_3/mesh_two_implicit_spheres_with_balls.cpp shows the use of Mesh_domain_with_polyline_features_3 to explicitly give features to preserve

  • This uses the make_mesh_3 call while I'm using make_surface_mesh…
  • I can only call CGAL::print_polyhedron_wavefront if I have a Polyhedron and I cannot figure out how to get one from a C3t3. So, perhaps I am stuck with this "medit" mesh format, or else VTU.
  • I think the terminology is trying to tell me: this isn't a surface mesh, it's a 3D mesh made of tetrahedra. It sounds like the type of data from a Delaunay triangulation is inherently rather different from a surface mesh.
  • https://doc.cgal.org/latest/Mesh_3/index.html#title24 does the opposite direction of what I need
• There are Feature Detection Functions, but detect_features is in Polyhedral_complex_mesh_domain_3 and Polyhedral_mesh_domain_with_features_3

• Domains:

  • MeshDomain_3 concept
  • MeshDomainWithFeatures_3 concept
• Why make_surface_mesh, Implicit_surface_3, Complex_2_in_triangulation_3 vs. make_mesh_3, Implicit_mesh_domain_3, Mesh_complex_3_in_triangulation_3?

• parameters::features() - can do 1-dimensional features

  • now how do I use it?

• make_surface_mesh args:

  • SurfaceMeshC2T3& c2t3 - must be a model of concept SurfaceMeshComplex_2InTriangulation_3
  • SurfaceMeshTraits::Surface_3 surface - must be a model of concept Surface_3
  • SurfaceMeshTraits traits - must be a model of concept SurfaceMeshTraits_3
  • FacetsCriteria criteria - must be a model of concept SurfaceMeshFacetsCriteria_3
  • Tag
• "This algorithm of CGAL::make_surface_mesh is designed for smooth implicit surfaces. If your implicit surface is not smooth, then the sharp features of the surface will not be meshed correctly."

  (setq org-confirm-babel-evaluate nil)
  (setq org-src-fontify-natively t)
  (setq org-src-tab-acts-natively t)
  (org-version)

9.1.9

  gcc --version

Apple LLVM version 9.1.0 (clang-902.0.39.2)
Target: x86_64-apple-darwin17.7.0
Thread model: posix
InstalledDir: /Library/Developer/CommandLineTools/usr/bin

  #include <CGAL/Exact_predicates_inexact_constructions_kernel.h>

  #include <CGAL/Mesh_triangulation_3.h>
  #include <CGAL/Mesh_complex_3_in_triangulation_3.h>
  #include <CGAL/Mesh_criteria_3.h>

  #include <CGAL/Implicit_mesh_domain_3.h>
  #include <CGAL/make_mesh_3.h>

  typedef CGAL::Exact_predicates_inexact_constructions_kernel K;
  typedef K::FT FT;
  typedef K::Point_3 Point;
  typedef FT (Function)(const Point&);
  typedef CGAL::Implicit_mesh_domain_3<Function,K> Mesh_domain;

  #ifdef CGAL_CONCURRENT_MESH_3
  typedef CGAL::Parallel_tag Concurrency_tag;
  #else
  typedef CGAL::Sequential_tag Concurrency_tag;
  #endif

  typedef CGAL::Mesh_triangulation_3<Mesh_domain,CGAL::Default,Concurrency_tag>::type Tr;
  typedef CGAL::Mesh_complex_3_in_triangulation_3<Tr> C3t3;

  typedef CGAL::Mesh_criteria_3<Tr> Mesh_criteria;

  FT sphere_function (const Point& p) {
      return CGAL::squared_distance(p, Point(CGAL::ORIGIN))-1;
  }

  <<includes>>

  using namespace CGAL::parameters;

  <<typesDomain>>
  <<typesTriangulation>>
  <<typesCriteria>>
  <<sphereFunction>>

  int main()
  {
      // Domain (Warning: Sphere_3 constructor uses squared radius !)
      Mesh_domain domain(sphere_function,
                         K::Sphere_3(CGAL::ORIGIN, 2.));
      // Mesh criteria
      Mesh_criteria criteria(facet_angle=30, facet_size=0.1, facet_distance=0.025,
                             cell_radius_edge_ratio=2, cell_size=0.1);

      std::cout << "Generating..." << std::endl;
      // Mesh generation
      C3t3 c3t3 = CGAL::make_mesh_3<C3t3>(domain, criteria);

      // Output
      std::ofstream medit_file("out.mesh");
      c3t3.output_to_medit(medit_file);

      std::cout << "Done" << std::endl;

      return 0;
  }

Generating…

Done