Mesh Tutorial 6: A 2D Unstructured Mesh

Here we provide an example of a 2D unstructured mesh generated using the 2D Triangle mesh generator, with is available in Python via the MeshPy module. We export the resulting mesh using meshio in both .obj and .vtu formats. Note that only the export as VTU contains material IDs.

import numpy as np
import meshpy.triangle as triangle
import meshio
 
n_circumferential_points =20
radius = 1.0
width = 3.0
 
points = []
# Define the vertices of the square domain (centered on 0)
points = [(-width/2,-width/2), (width/2,-width/2),  (width/2,width/2),  (-width/2,width/2),]
# Create a list of points for the circle (centered on 0)
for i in range(n_circumferential_points):
    angle = i * 2 * np.pi / n_circumferential_points
    points.append((radius * np.cos(angle), radius * np.sin(angle)))
 
# Define the segments of the square domain
segments = [(0,1), (1,2), (2,3), (3,0)]
markers = [1,2,3,4]
Nbeg = len(markers)
# Define the segments for the circle
for i in range(Nbeg,n_circumferential_points+Nbeg):
    if i+1 == n_circumferential_points+Nbeg:
        ip1 = Nbeg
    else:
        ip1 = i+1
    segments.extend([(i,ip1)])
    markers.extend([0])
 
# Create a mesh info object
mesh_info = triangle.MeshInfo()
# Add points
mesh_info.set_points(points)
# Add facets
mesh_info.set_facets(segments, facet_markers=markers)
# Add regions
mesh_info.regions.resize(2)
# inside circle region
mesh_info.regions[0] = [0.0, 0.0, 1, 0.1] # 2d pt + ID + max_vol
# outside circle region
eps = 1e-2
mesh_info.regions[1] = [-width/2+eps,-width/2+eps, 2, 0.1] # 2d pt + ID + max_vol
 
# Refine the mesh
mesh = triangle.build(mesh_info, verbose=True, max_volume=0.02, min_angle=25,
                      attributes=True, generate_faces=True)
 
# Add a third dimension to the points
points_3d = [(x, y, 0) for x, y in mesh.points]
 
directory = ""
filename = "pin_01"
meshio.write_points_cells(directory + filename + ".obj",
                          points_3d,
                          {"triangle": mesh.elements})
 
# Save the mesh to an .vtk file
meshio.write_points_cells(directory + filename + ".vtu",
                          points_3d,
                          {"triangle": mesh.elements},
                          cell_data={"attribute": [mesh.element_attributes]})