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(node_coords, cells)

Class for handling line segment “meshes”.

create_cell_volumes()

Computes the volumes of the “cells” in the mesh.

create_control_volumes()

Compute the control volumes of all nodes in the mesh.

class meshplex.MeshTetra(node_coords, cells)

Class for handling tetrahedral meshes.

property cell_barycenters

See cell_centroids().

property cell_centroids

The centroids (barycenters, midpoints of the circumcircles) of all tetrahedra.

property cell_incenters

Get the midpoints of the inspheres.

property control_volumes

Compute the control volumes of all nodes in the mesh.

get_ce_ratios()

Covolume-edge length ratios.

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_radius_ratio

Ratio of incircle and circumcircle ratios times 3. (“Normalized shape ratio”.) Is 1 for the equilateral tetrahedron, and is often used a quality measure for the cell.

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(nodes, cells, sort_cells=False)

Class for handling triangular meshes.

property angles

All angles in the triangle.

property cell_barycenters

See cell_centroids().

property cell_centroids

The centroids (barycenters, midpoints of the circumcircles) of all triangles.

property cell_circumradius

Get the circumradii of all cells

property cell_incenters

Get the midpoints of the incircles.

property cell_inradius

Get the inradii of all cells

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.

property control_volumes

The control volumes around each vertex.

create_edges()

Set up edge-node and edge-cell relations.

flip_until_delaunay()

Flip edges until the mesh is fully Delaunay.

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.

get_control_volumes(cell_mask=None)

The control volumes around each vertex. 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_node_numbers=False, show_cell_numbers=False, cell_mask=None, show_edge_numbers=False)

Show the mesh using matplotlib.

plot_vertex(node_id, show_ce_ratio=True)

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

Parameters
  • node_id (int) – Node ID of the node to be shown.

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

property q_radius_ratio

2 * inradius / circumradius (min 0, max 1)

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()).

property signed_cell_areas

Signed area of a triangle in 2D.

update_values()

Update all computes entities around the mesh.

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.