Topological tools

import mefikit as mf
import numpy as np
import pyvista as pv

pv.set_plot_theme("dark")
pv.set_jupyter_backend("static")

Submesh functionality

x = range(3)
y = np.linspace(0.0, 3.0, 5, endpoint=True)
z = np.logspace(-0.5, 1, 4, endpoint=True)
volumes = mf.build_cmesh(x, y, z)

Simple descending_mesh

This functionality is able to compute the descending connectivity of the porvided mesh. It can act on elements of dimension 1, 2 or 3.

faces = volumes.descend()
edges = faces.descend()
vertex = edges.descend()

plotter = pv.Plotter(shape=(1, 3))
plotter.subplot(0, 0)
plotter.add_mesh(faces.to_pyvista().shrink(0.8), show_edges=True)
plotter.subplot(0, 1)
plotter.add_mesh(edges.to_pyvista().shrink(0.8))
plotter.subplot(0, 2)
plotter.add_mesh(vertex.to_pyvista())
plotter.show()

png

Submesh in one go

You might want to directly access either the node mesh or the edges mesh. You can ! And going into one step is ever faster than chaining mutliple .descend() calls.

edges = volumes.descend(target_dim=1)
nodes = volumes.descend(target_dim=0)

plotter = pv.Plotter(shape=(1, 2))
plotter.subplot(0, 0)
plotter.add_mesh(edges.to_pyvista().shrink(0.8))
plotter.subplot(0, 1)
plotter.add_mesh(vertex.to_pyvista())
plotter.show()

png

Boundaries computation

As it is very common to compute boundaries on a mesh (for boundary counditions for ex), there is a custom boundaries computation method.

face_bounds = volumes.boundaries()
edge_bounds = volumes.boundaries(target_dim=1)
vertex_bounds = volumes.boundaries(target_dim=0)

plotter = pv.Plotter(shape=(1, 3))
plotter.subplot(0, 0)
plotter.add_mesh(face_bounds.to_pyvista().shrink(0.8), show_edges=True)
plotter.subplot(0, 1)
plotter.add_mesh(edge_bounds.to_pyvista().shrink(0.8))
plotter.subplot(0, 2)
plotter.add_mesh(vertex_bounds.to_pyvista())
plotter.show()

png

Descend / boundaries update

You can directly update the mesh inplace when computing the descending mesh or the boundaries mesh.

volumes.boundaries_update()
volumes.boundaries_update(target_dim=1)
volumes.to_pyvista().shrink(0.8).plot(show_edges=True)

png

When using the _update version, the elements of the same dimension of the generated mesh are returned as a new mesh.

old_face_mesh = volumes.descend_update()
volumes.to_pyvista().shrink(0.8).plot(show_edges=True)

png

old_face_mesh.to_pyvista().shrink(0.8).plot(show_edges=True)

png

Connected components

x, y = np.meshgrid(np.linspace(0.0, 1.0, 5), np.linspace(0.0, 1.0, 5))
coords = np.c_[x.flatten(), y.flatten()]
conn = np.array(
    [
        [0, 1, 6, 5],
        [6, 7, 12, 11],
        # [2, 3, 8, 7],
        [11, 12, 17, 16],
    ],
    dtype=np.uint,
)
mesh = mf.UMesh(coords)
mesh.add_regular_block("QUAD4", conn)
mesh.add_regular_block("VERTEX", np.arange(len(coords), dtype=np.uint)[..., np.newaxis])

compos_link_edge = mesh.connected_components(link_dim=1)
compos_link_node = mesh.connected_components(link_dim=0)

print(f"{len(compos_link_edge)=}")
print(f"{len(compos_link_node)=}")

len(compos_link_edge)=2
len(compos_link_node)=1

edges = mesh.descend()

shape = (3, 2)
row_weights = [1.0, 0.5, 0.5]
groups = [
    (0, np.s_[:]),
    (1, 0),
    (2, 0),
    (np.s_[1:], 1),
]

plotter = pv.Plotter(shape=shape, groups=groups, row_weights=row_weights)
plotter.subplot(0, 0)
plotter.add_text("Original mesh")
plotter.add_mesh(mesh.to_pyvista(), show_edges=True)
plotter.camera_position = "xy"

for i, compo in enumerate(compos_link_edge):
    plotter.subplot(i + 1, 0)
    plotter.add_text(f"Compo linked by edge: n°{i}")
    plotter.add_mesh(edges.to_pyvista())
    plotter.add_mesh(compo.to_pyvista(), show_edges=True)
    plotter.camera_position = "xy"

for i, compo in enumerate(compos_link_node):
    plotter.subplot(i + 1, 1)
    plotter.add_text(f"Compo linked by node: n°{i}")
    plotter.add_mesh(edges.to_pyvista())
    plotter.add_mesh(compo.to_pyvista(), show_edges=True)
    plotter.camera_position = "xy"
plotter.show()

png

Crack

This feature is the contrary of the merge_nodes feature. It duplicates nodes such that the resulting mesh does not connect on the descending_mesh given.

x = range(2)
y = np.linspace(0.0, 3.0, 3, endpoint=True)
z = np.logspace(0.0, 1.0, 3, endpoint=True)
volumes = mf.build_cmesh(x, y, z)
faces = volumes.descend()

cracked = volumes.crack(faces)

edges = faces.descend()
compos_original = volumes.connected_components()
compos_cracked = cracked.connected_components()

assert len(compos_original) == 1

n_compos = len(compos_cracked)

shape = (3, n_compos + 1)
groups = [
    (0, 0),
    (0, np.s_[1:]),
    (np.s_[1:], 0),
    (1, np.s_[1:]),
    *((2, i + 1) for i in range(n_compos)),
]
row_weights = [1.0, 0.1, 1.0]
col_weights = [1.5, *(0.5,) * n_compos]
pv.set_jupyter_backend("static")
plotter = pv.Plotter(
    shape=shape, groups=groups, row_weights=row_weights, col_weights=col_weights
)

plotter.subplot(0, 0)
plotter.add_text("Original mesh")
plotter.add_mesh(volumes.to_pyvista(), show_edges=True)
plotter.subplot(0, 1)
plotter.add_text("Cut mesh used for the crack")
plotter.add_mesh(faces.to_pyvista().shrink(0.8), show_edges=True)

plotter.subplot(1, 0)
plotter.add_text("Compo of original mesh")
plotter.add_mesh(edges.to_pyvista())
plotter.add_mesh(compos_original[0].to_pyvista(), show_edges=True)

plotter.subplot(1, 1)
plotter.add_text("Compos of cracked mesh")

for i, compo in enumerate(compos_cracked):
    plotter.subplot(2, i + 1)
    plotter.add_mesh(edges.to_pyvista())
    plotter.add_mesh(compo.to_pyvista(), show_edges=True)
    plotter.camera.zoom(2)
plotter.show()

png

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