Topological tools

import numpy as np
import pyvista as pv

import mefikit as mf

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 provided 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 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 multiple .descend() calls.

edges = volumes.descend(target_dim=1)
vertex = 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 png

Boundaries computation

As it is very common to compute boundaries on a mesh (for boundary conditions 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 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(dim="all").shrink(0.8).plot(show_edges=True)

png 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(dim="all").shrink(0.8).plot(show_edges=True)

png png

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

png 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 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 png

Split

This tool is usefull to split cells into smaller cells. It does not change the topology of the domain not the element type. Using it it gives you 2^n times the number of elements where n is the dimension of of the elements.

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

mesh_splitted = mesh.split()

pt = pv.Plotter()
pt.add_mesh(
    mesh.to_pyvista().shrink(0.95), show_edges=True, edge_color="yellow", line_width=2
)
pt.add_mesh(mesh_splitted.to_pyvista(), style="wireframe", color="red", line_width=2)
pt.show()

png png

Polyze

This functionnality is useful to generate a poly mesh from a regular one. A poly mesh is a mesh of PGON 2d elements and PHED 3d elements.

x = np.linspace(0.0, 3.0, 4, endpoint=True)
y = np.logspace(0.0, 1.0, 4, endpoint=True)
mesh = mf.build_cmesh(x, y)
print(mesh.blocks())

{'QUAD4': array([[ 0,  1,  5,  4],
       [ 1,  2,  6,  5],
       [ 2,  3,  7,  6],
       [ 4,  5,  9,  8],
       [ 5,  6, 10,  9],
       [ 6,  7, 11, 10],
       [ 8,  9, 13, 12],
       [ 9, 10, 14, 13],
       [10, 11, 15, 14]], dtype=uint64)}

mesh_polyzed = mesh.polyze()

print(mesh_polyzed.blocks())

{'PGON': (array([ 0,  1,  5,  4,  1,  2,  6,  5,  2,  3,  7,  6,  4,  5,  9,  8,  5,
        6, 10,  9,  6,  7, 11, 10,  8,  9, 13, 12,  9, 10, 14, 13, 10, 11,
       15, 14], dtype=uint64), array([ 4,  8, 12, 16, 20, 24, 28, 32, 36], dtype=uint64))}

mesh_polyzed.to_pyvista().plot(show_edges=True)

png png

unpolyzed = mesh_polyzed.unpolyze()
print(unpolyzed.blocks())
unpolyzed.to_pyvista().plot(show_edges=True)

{'QUAD4': array([[ 0,  1,  5,  4],
       [ 1,  2,  6,  5],
       [ 2,  3,  7,  6],
       [ 4,  5,  9,  8],
       [ 5,  6, 10,  9],
       [ 6,  7, 11, 10],
       [ 8,  9, 13, 12],
       [ 9, 10, 14, 13],
       [10, 11, 15, 14]], dtype=uint64)}

png png