Geometrical tools

import numpy as np
import pyvista as pv

import mefikit as mf

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

Snap points

x = np.linspace(0.0, 3.0, 10, endpoint=True)
mesh = mf.build_cmesh(x, x)

eps = 0.1
dec = x[-1] / len(x) + eps
x2 = np.linspace(dec, x[-1] + dec, len(x), endpoint=True)
mesh2 = mf.build_cmesh(x2, x2)

Note: epsilon value used in the following operation is big enough so that there are multiple candidates for some points, but low enough so that there is no degenerated cell created.

snaped = mesh.snap(mesh2, eps=x[-1] / len(x))

pt = pv.Plotter()
pt.add_mesh(mesh.to_pyvista(), show_edges=True)
pt.add_mesh(mesh2.descend(target_dim=0).to_pyvista(), color="red")
pt.show(cpos="xy")

pt = pv.Plotter()
pt.add_mesh(snaped.to_pyvista(), show_edges=True)
pt.add_mesh(mesh2.descend(target_dim=0).to_pyvista(), color="red")
pt.show(cpos="xy")

Merge nodes

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)

merged = cracked.merge_nodes()

edges = faces.descend()
compos_merged = merged.connected_components()
compos_cracked = cracked.connected_components()

assert len(compos_merged) == 1

n_compos = len(compos_cracked)

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

plotter.subplot(0, n_compos)
plotter.add_text("Merged mesh")
plotter.add_mesh(merged.to_pyvista(), show_edges=True)
plotter.subplot(0, 0)
plotter.add_text("Cut mesh used for the crack")
plotter.add_mesh(faces.to_pyvista().shrink(0.8), show_edges=True)

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

plotter.subplot(1, 0)
plotter.add_text("Compos of cracked mesh")

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

Overlay

The intersection is valid in the following conditions :

• mesh1 and mesh2 are valid (no self recovering),
• mesh1 and mesh2 are 2d (xy),
• correctly oriented (CCW element connectivity),
• and fully merged (no unmerged nodes).

Mesh1 and mesh2 may have any number of kind of 2d elements of the first order (TRI3, QUAD4, PGON). A future version of this algorithm will work with quadratic elements (TRI7, QUAD8, QPGON).

x = np.linspace(0.0, 3.0, 4, endpoint=True)
mesh = mf.build_cmesh(x, x)

eps = 0.5
dec = x[-1] / len(x) + eps
x2 = np.linspace(dec, x[-1] + dec, len(x), endpoint=True)
mesh2 = mf.build_cmesh(x2, x2)

imprint2on1 = mesh.overlay(mesh2, mf.OverlayOperation.IMPRINT)
imprint1on2 = mesh2.overlay(mesh, mf.OverlayOperation.IMPRINT)

union = mesh.overlay(mesh2, mf.OverlayOperation.UNION)
diff = mesh.overlay(mesh2, mf.OverlayOperation.DIFFERENCE)
symdiff = mesh.overlay(mesh2, mf.OverlayOperation.SYMMETRIC_DIFFERENCE)
intersection = mesh.overlay(mesh2, mf.OverlayOperation.INTERSECTION)

meshes = [
    [mesh, mesh2],
    [union, intersection],
    [diff, symdiff],
    [imprint2on1, imprint1on2],
]
labels = [
    ["Mesh1", "Mesh2, staggered"],
    ["Union", "Intersection"],
    ["Difference", "Symmetric difference"],
    ["Imprint over 1", "Imprint over 2"],
]

pt = pv.Plotter(shape=(4, 2))
for i in range(4):
    for j in range(2):
        m = meshes[i][j]
        t = labels[i][j]
        pt.subplot(i, j)
        pt.add_text(t)
        pt.add_mesh(m.to_pyvista(), show_edges=True)
        pt.camera_position = "xy"
pt.show(cpos="xy")

The ugly cell in the center in the difference and symmetric difference comes from the plotting of non convex cells in pyvista. It is just a known plotting bug (due to optimisation quirks).