Does CGAL 3D mesh generation require condition except closed manifold?

Question

I'm trying to triangulate given coronary artery model(please refer image and file).

At first, I've tried to triangulate them using 3D constrained Delaunay triangulation in TetGen engine, but it appears that TetGen didn't generate them in all time. I've tried about 40 models with closed boundary, but only half of them was successful.

As an alternative, I found that CGAL 3D mesh generation will generate similar mesh based on Delaunay triangulation(of course, it's different from 3D constrained Delaunay triangulation).

I also tested it for 40 models which is same dataset used in TetGen test, but it appears that only 1/4 of them were successful. It is weird because even less models were processed than in TetGen test.

Is there are any condition for CGAL mesh generation except closed manifold condition(no boundary & manifold)? Here is the code I've used in my test case. It is almost same to example code from CGAL website.

// Create input polyhedron
Polyhedron polyhedron;
std::ifstream input(fileName.str());
input >> polyhedron;

// Create domain
Mesh_domain domain(polyhedron);

// Mesh criteria (no cell_size set)
Mesh_criteria criteria(facet_angle = 25, facet_size = 0.15, facet_distance = 0.008,
    cell_radius_edge_ratio = 3);

// Mesh generation
C3t3 c3t3 = CGAL::make_mesh_3<C3t3>(domain, criteria, no_perturb(), no_exude());

findMinAndMax();
cout << "Polygon finish: " << c3t3.number_of_cells_in_complex() << endl;

Here is one of CA model which was used in test case.

The image of CA model

Also, I want to preserve given model triangles in generated mesh like constrained Delaunay triangulation. Is there are any way that generate mesh without specific criteria?

Please let me know if you want to know more.

Answer 1

The problem is that the mesh generator does not construct a good enough initial point set. The current strategy is to shoot rays in random directions from the center of the bounding box of your object. Alternatively one might either take a random sample of points on the surface, or random rays shot from the points on the skeleton. I've put you a hacky solution on github. The first argument is your mesh, the second the grid cell size in order to sample points on the mesh.