Clarification on Isotropic Explicit Remeshing Filter and Target Length

[jmespadero]

I bring here the message from Sara posted at https://stackoverflow.com/questions/79491935/clarification-on-isotropic-explicit-remeshing-filter-and-target-length

I’m working with the isotropic explicit remeshing filter and I have some doubts regarding the target length. I understand that the percentage value for the target length is relative to the diagonal of the bounding box, but I’m not sure how the filter behaves. Specifically, I would like to know if the filter removes all edges smaller than the target length, or if it only removes edges that exactly match that value. Additionally, is there a way to handle smaller edges? I am aiming for a mesh that is as uniform as possible, meaning I want to minimize the difference between the longest and shortest edges. Could anyone clarify how this part works?
Thanks in advance, Sara Amenini

[jmespadero]

The Isotropic Explicit Remeshing Filter implements the work of Botsch and Kobbelt that you can find linked in the description of the filter. In short, it repeatedly splits long edges, collapses short edges, and relocates vertices until all edges are approximately of the desired target edge length running several cycles of this loop:

Lmin = 4/5 * target_edge_length
Lmax = 4/3 * target_edge_length

for i = 0 to 10 do
    split_long_edges(Lmax)
    collapse_short_edges(Lmin,Lmax)
    equalize_valences()
    tangential_relaxation()
    project_to_surface()

• The Lmin and Lmax thresholds values ensure that after a split or collapse function, the resulting edge lengths are closer to the target lengths than before. Also, a short edge is not collapsed if the result will produce one edge longer that high.

• equalize_valences() will check if applying an edge_flip() operator will produce that the valence of the vertex will be near to 6 than previous stage. This helps the mesh to take the topology of a "pure equilateral triangle mesh".

• tangential_relaxation() will displace each vertex in the direction of the average position of their neighbor vertex, trying that every edge starting from the vertex has equal length.

Answering your questions:

I would like to know if the filter removes all edges smaller than the target length, or if it only removes edges that exactly match that value.

It will try to remove smaller edges. It is only guarantied that the result does not contain edges smaller that Lmin. But probably some edges will still be below the target_edge_length. Let's say it is normal the get some edges with 95% of the target_edge_length.

Is there a way to handle smaller edges?

There is several approach you can use here:

1. Use the Isotropic Explicit Remeshing filter and check only the Collapse Step . Adjust the target edge length to be 5/4 of your "really desired target edge length"

2. Probably the Merge close Vertices filter will be enough for you. But it can merge vertex that are not neighbors. Depends of you if this is a problem or a desired effect.

3. Also probably, you will get happy with this approach

filter "Select Faces with edges longer than"
filter "invert selection" -> Invert selected faces
filter "Quadric Edge Collapse Decimation" -> check "Simplify only selected faces"