The purpose of this package is to detect topological classification of a triangular surface mesh. For instance, the orientation of the triangles can be unified across the surface mesh. The topological faces can be identified.
Given an incidence relation, t2v (triangles to vertices),
we can produce an oriented surface:
orientedt2v, orientable = orient_surface_mesh(t2v)
And, when the triangles tile a single surface, we can check that all the triangles have been classified on surface 1:
@test length(unique(attribute(orientedt2v.left, "surfid"))) == 1
Given an incidence relation, t2v (triangles to vertices),
we can classify the triangles on oriented surfaces:
t2v = make_topo_faces(t2v)
In this instance, we would expect the triangles to represent four distinct topological surfaces. We can check the "tfid" attribute of the incidence relation t2v:
@test length(unique(attribute(t2v.left, "tfid"))) == 4
The topological classification may be visualized with
t2v = make_topo_faces(t2v)
vtkwrite("mt008-classified", t2v, [(name = "tfid", )])
The topological surfaces will be labeled with the attribute "tfid".
The boundary triangles of the triangulated surface of a solid part may be classified into topological faces with:
fens, bfes = make_topo_faces(fens, bfes)
Here bfes.label records the numbers of the topological surfaces.
The classification may be visualized with
VTK.vtkexportmesh("mt013.vtk", connasarray(bfes), fens.xyz, VTK.T3; scalars=[("topological_face", bfes.label)]);
The library may be also used to create partition of the topological faces into individual patches.
surfids, partitionids = create_partitions(fens, fes, 50)
The classification into topological faces and the partitioning may then be viewed with
VTK.vtkexportmesh("mt016_part.vtk", connasarray(fes), fens.xyz, VTK.T3; scalars=[("topological_face", surfids), ("partitioning", partitionids)]);
orient_surface_mesh
orient_surface_mesh(t2v)
Orient surface mesh.
Return
- `orientedt2v`: oriented incidence relation
- `orientable`: Can the surface mesh be oriented? Bool flag.
This would be false for a Mobius strip, for instance.
This is a purely topological operation. Creases in the surface are not
recognized as edges. The operation proceeds by flooding the surface across
manifold edges, stopping at sheet or non-manifold edges.
The incidence relation `orientedt2v` includes an attribute for each triangle
that provides the surface id to which the triangle belongs
(`orientedt2v.left.attributes["surfid"]`).
make_topo_faces
make_topo_faces(t2v, crease_ang = 30/180*pi)
Make topological faces.
Topological faces are assumed to be separated by either creases or non-manifold
edges (junctions). So the boundary of topological faces consists of sheet edges,
non-manifold edges, or crease edges.
Returns
- `t2v`: the attribute `tfid` lists the numbers of the topological faces.
make_topo_faces(fens::FENodeSet, fes::E, crease_ang = 30/180*pi) where {E<:AbstractFESet}
Make topological faces.
Topological faces are assumed to be separated by either creases or non-manifold
edges (junctions). So the boundary of topological faces consists of sheet edges,
non-manifold edges, or crease edges.
Returns
- `fes`: the `fes.label` field lists the numbers of the topological faces.
create_partitions
create_partitions(fens, fes, elem_per_partition = 50;
crease_ang = 30/180*pi,
cluster_max_normal_deviation = 2 * crease_ang)
Create partitions of the triangulated boundary into clusters.
# Input
- `fens`, `fes` = finite element mesh,
- `elem_per_partition` = desired number of elements per partition,
- `crease_ang` = crease angle to determine boundaries between topological faces,
- `cluster_max_normal_deviation` = maximum deviation of the normal within the
cluster.
- `balancefraction` = fraction of the cluster size by which the cluster can
deviate from the average size so that can be considered balanced.
# Output
- `surfids` = array of surface identifiers, one for each boundary facet
- `partitionids` = array of partition identifiers (i.e. cluster identifiers),
one for each boundary facet
- `surface_elem_per_partition` = dictionary of cluster sizes, indexed by the
surface id
- 07/06/2024: Improve estimation of number of partitions.
- 07/06/2024: Update for FinEtools 8.