# 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.

show_vertex_function(u)
class meshplex.MeshTri(nodes, cells, sort_cells=False)

Class for handling triangular meshes.

angles

All angles in the triangle.

ce_ratios_per_interior_edge
cell_barycenters

See cell_centroids().

cell_centroids

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

cell_circumcenters
cell_circumradius

Get the circumradii of all cells

cell_incenters

Get the midpoints of the incircles.

cell_inradius

Get the inradii of all cells

cell_partitions
cell_quality

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.

control_volumes

The control volumes around each vertex.

create_edges()

Set up edge-node and edge-cell relations.

edge_gid_to_edge_list
edges_cells
face_partitions
flip_interior_edges(is_flip_interior_edge)
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.

is_boundary_facet
is_boundary_node
is_interior_node
mark_boundary()
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.
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()).

signed_cell_areas

Signed area of a triangle in 2D.

surface_areas
update_values()

Update all computes entities around the mesh.

class meshplex.MeshTetra(node_coords, cells)

Class for handling tetrahedral meshes.

cell_barycenters

See cell_centroids().

cell_centroids

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

cell_circumcenters
cell_circumradius
cell_incenters

Get the midpoints of the inspheres.

cell_inradius
control_volumes

Compute the control volumes of all nodes in the mesh.

create_cell_face_relationships()
create_face_edge_relationships()
get_ce_ratios()

Covolume-edge length ratios.

mark_boundary()
num_delaunay_violations()
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.

q_radius_ratio

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

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>.)

show()
show_edge(edge_id)

Displays edge with ce_ratio.

Parameters: edge_id (int) – Edge ID for which to show the ce_ratio.
meshplex.read(filename)

Reads an unstructured mesh into meshplex format.

Parameters: Returns mesh{2,3}d: filenames (str) – The files to read from. 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.