meshplex — Simplex meshes for Python

meshplex computes all sorts of interesting points, areas, and volumes in triangular and tetrahedral meshes, with a focus on efficiency. Useful in many contexts, e.g., finite-element and finite-volume computations.

For a quickstart, checkout meshplex’s GitHubPage.

Overview of classes and functions

class meshplex.MeshLine(points, cells)

Class for handling line segment “meshes”.

class meshplex.MeshTetra(points, cells, sort_cells=False)

Class for handling tetrahedral meshes.

plot_edge(edge_id)

Displays edge with ce_ratio.

Parameters

edge_id (int) – Edge ID for which to show the ce_ratio.

property q_min_sin_dihedral_angles

Get the smallest of the sines of the 6 angles between the faces of each tetrahedron, times a scaling factor that makes sure the value is 1 for the equilateral tetrahedron.

property q_vol_rms_edgelength3

For each cell, return the ratio of the volume and the cube of the root-mean-square edge length. (This is cell quality measure used by Stellar <https://people.eecs.berkeley.edu/~jrs/stellar>.)

class meshplex.MeshTri(points, cells, sort_cells=False)

Class for handling triangular meshes.

property angles

All angles in the triangle.

compute_curl(vector_field)

Computes the curl of a vector field over the mesh. While the vector field is point-based, the curl will be cell-based. The approximation is based on

\[n\cdot curl(F) = \lim_{A\to 0} |A|^{-1} <\int_{dGamma}, F> dr;\]

see https://en.wikipedia.org/wiki/Curl_(mathematics). Actually, to approximate the integral, one would only need the projection of the vector field onto the edges at the midpoint of the edges.

flip_until_delaunay(tol=0.0, max_steps=100)

Flip edges until the mesh is fully Delaunay (up to tol).

get_control_volume_centroids(cell_mask=None)

The centroid of any volume V is given by

\[c = \int_V x / \int_V 1.\]

The denominator is the control volume. The numerator can be computed by making use of the fact that the control volume around any vertex is composed of right triangles, two for each adjacent cell.

Optionally disregard the contributions from particular cells. This is useful, for example, for temporarily disregarding flat cells on the boundary when performing Lloyd mesh optimization.

num_delaunay_violations()

Number of edges where the Delaunay condition is violated.

plot(show_coedges=True, control_volume_centroid_color=None, mesh_color='k', nondelaunay_edge_color=None, boundary_edge_color=None, comesh_color=(0.8, 0.8, 0.8), show_axes=True, cell_quality_coloring=None, show_point_numbers=False, show_edge_numbers=False, show_cell_numbers=False, cell_mask=None, mark_points=None, mark_edges=None, mark_cells=None)

Show the mesh using matplotlib.

plot_vertex(point_id, show_ce_ratio=True)

Plot the vicinity of a point and its covolume/edgelength ratio.

Parameters

• point_id (int) – Node ID of the point to be shown.

• show_ce_ratio (bool, optional) – If true, shows the ce_ratio of the point, too.

save(filename, *args, **kwargs)

Save the mesh to a file.

show(*args, fullscreen=False, **kwargs)

Show the mesh (see plot()).

show_vertex(*args, **kwargs)

Show the mesh around a vertex (see plot_vertex()).

meshplex.from_meshio(mesh)

Transform from meshio to meshplex format.

Parameters

mesh (meshio.Mesh) – The meshio mesh object.

Returns mesh{2,3}d

The mesh data.

meshplex.get_signed_simplex_volumes(cells, pts)

Signed volume of a simplex in nD. Note that signing only makes sense for n-simplices in R^n.

meshplex.read(filename)

Reads an unstructured mesh into meshplex format.

Parameters

filenames (str) – The files to read from.

Returns mesh{2,3}d

The mesh data.