meshzoo 0.13.0

When generating meshes for FEM/FVM computations, sometimes your geometry is so simple that you don't need a complex mesh generator (like pygmsh, MeshPy, mshr, pygalmesh, dmsh), but something simple and fast that makes use of the structure of the domain. Enter meshzoo.

Installation

Install meshzoo from PyPI with

pip install meshzoo

on your machine and you're good to go.

Examples

All generators return the points as a (num_points, dim) float64 array and the cells as a (num_cells, nodes_per_cell) int64 array.

Triangle

import meshzoo

bary, cells = meshzoo.triangle(8)

# corners = np.array(
#     [
#         [0.0, -0.5 * numpy.sqrt(3.0), +0.5 * numpy.sqrt(3.0)],
#         [1.0, -0.5, -0.5],
#     ]
# )
# points = np.dot(corners, bary).T

# Process the mesh, e.g., write it to a file using meshio
# meshio.write_points_cells("triangle.vtk", points, {"triangle": cells})

Rectangle

import meshzoo
import numpy as np

points, cells = meshzoo.rectangle_tri(
    np.linspace(0.0, 1.0, 11),
    np.linspace(0.0, 1.0, 11),
    variant="zigzag",  # or "up", "down", "center"
)

points, cells = meshzoo.rectangle_quad(
    np.linspace(0.0, 1.0, 11),
    np.linspace(0.0, 1.0, 11),
    cell_type="quad4",  # or "quad8", "quad9"
)

Regular polygon

meshzoo.ngon(4, 8)	meshzoo.ngon(6, 8)	meshzoo.ngon(9, 8)

import meshzoo

points, cells = meshzoo.ngon(5, 11)

Disk

meshzoo.disk(4, 8)	meshzoo.disk(6, 8)	meshzoo.disk(9, 8)

The disk meshes are inflations of regular polygons.

import meshzoo

points, cells = meshzoo.disk(6, 11)

points, cells = meshzoo.disk_quad(10, cell_type="quad4")  # or "quad8", "quad9"

Annulus

import meshzoo
import numpy as np

points, cells = meshzoo.annulus_tri(
    np.linspace(0.5, 1.0, 6),  # radii of the circles of points
    40,  # points per circle
    variant="zigzag",  # or "up", "down"
)

points, cells = meshzoo.annulus_quad(
    np.linspace(0.5, 1.0, 6), 40, cell_type="quad4"  # or "quad8", "quad9"
)

L-shape

The domain [-1, 1]^2 without the quadrant (0, 1]^2, with the re-entrant corner at the origin.

import meshzoo

points, cells = meshzoo.lshape_tri(10, variant="zigzag")  # or "up", "down", "center"
points, cells = meshzoo.lshape_quad(10, cell_type="quad4")  # or "quad8", "quad9"

Möbius strip

import meshzoo

points, cells = meshzoo.moebius(num_twists=1, nl=60, nw=11)

Sphere (surface)

import meshzoo

points, cells = meshzoo.uv_sphere(num_points_per_circle=20, num_circles=10, radius=1.0)
points, tri, quad = meshzoo.geo_sphere(
    num_points_per_circle=20, num_circles=10, radius=1.0
)

Spheres can also be generated by refining the faces of platonic solids and then "inflating" them. meshzoo implements a few of them. The sphere generated from the icosahedron has the highest-quality (most equilateral) triangles.

All cells are oriented such that their normals point outwards.

meshzoo.tetra_sphere(10)	meshzoo.octa_sphere(10)	meshzoo.icosa_sphere(10)

Ball (solid)

import meshzoo

points, cells = meshzoo.ball_tetra(10)
points, cells = meshzoo.ball_hexa(10)

Tube

import meshzoo

points, cells = meshzoo.tube(length=1.0, radius=1.0, n=30)

Torus

import meshzoo

points, cells = meshzoo.torus(
    num_points_major=60, num_points_minor=20, major_radius=1.0, minor_radius=0.3
)

Cube

import meshzoo
import numpy as np

points, cells = meshzoo.cube_tetra(
    np.linspace(0.0, 1.0, 11), np.linspace(0.0, 1.0, 11), np.linspace(0.0, 1.0, 11)
)
points, cells = meshzoo.cube_hexa(
    np.linspace(0.0, 1.0, 11), np.linspace(0.0, 1.0, 11), np.linspace(0.0, 1.0, 11)
)

Extrusion

Any planar mesh can be extruded along the z-axis: triangles become wedges or tetrahedra, quadrilaterals become hexahedra. This gives, e.g., cylinders and pipes.

import meshzoo
import numpy as np

z = np.linspace(0.0, 2.0, 11)

points, tri = meshzoo.disk(6, 10)
points, wedges = meshzoo.extrude(points, tri, z)  # cylinder
points, tets = meshzoo.extrude(points, tri, z, cell_type="tetra")

points, quads = meshzoo.annulus_quad(np.linspace(0.5, 1.0, 6), 40)
points, hexa = meshzoo.extrude(points, quads, z)  # pipe