Compute the distance of a point to the boundary

1

Hi all,

Recently, I am working on a problem which need to calculate the distance of all the interior points to the boundary. I use the following code:

bmesh = BoundaryMesh(mesh, "exterior")
bbtree = BoundingBoxTree()
bbtree.build(bmesh)
vertex_distance_to_boundary = MeshFunction("double", mesh, 0)
for v_idx in xrange(mesh.num_vertices()):
    v = Vertex(mesh, v_idx)
    _, distance = bbtree.compute_closest_entity(v.point())
    print distance
    vertex_distance_to_boundary[v_idx] = distance

It works well, but I am wondering how FEniCS computes the distance? What’s the method/algorithm used behind? I can not find any explanation here and there.

Thanks,
Leon

2

Do you mean the nearest distance to the exterior boundary? In which case consider computing the FEM approximation of the Eikonal equation.

1 Like
3

An Implementation of such an approximation can be found here (compatible with dolfin 2018.1.0) https://bitbucket.org/Epoxid/femorph/src/c7317791c8f00d70fe16d593344cb164a53cad9b/femorph/Legacy/SAD_MeshDeform.py?at=dokken%2Frestructuring

4

Thank you very much! That’s what I want. I tried to solve the Eikonal equation by myself, but it is unstable. Your provided algorithm is very stable. I also trying to find some references for the algorithm, but I can not find the one used in the link. Do you know some references of the Algorithms?

Thanks Again,

5

I seem to recall it is referenced in this paper .

The approximation is Also mentioned in this Preprint, But be careful as ive found several typos in it.

6

Thanks for the information. I also found these two papers.

Paper 2 introduced the equation (3.7) and cited the paper 1. But I can not find any clue in paper 1.

It seems it is a good algorithm, but no paper has provided an analysis or a detailed explanation.