Creating a Voronoi mesh from a GMSH mesh¶

First we need to create a mesh. Here we use Gmsh and create a triangular mesh with a local grid refinement using the Frontal-Delauney-Algorithm.

// Geometry
SetFactory("OpenCASCADE");
Circle(1) = {0.0,0.0,0.0,1000.0,0.0,2*Pi};
Curve Loop(1) = {1};
Plane Surface(1) = {1};

// Mesh refinement
Field[1] = MathEval;
Field[1].F = "0.3*(Sqrt(x^2 + y^2))^0.8+1.0";
Background Field = 1;

// Options
Mesh.CharacteristicLengthFromPoints = 0;
Mesh.CharacteristicLengthExtendFromBoundary = 0;
Mesh.MeshSizeFromCurvature = 0;
Mesh.Algorithm = 6;

After meshing, we can save the mesh to a file. Now we can switch to Python and read the mesh with meshio

In [1]:

import meshio
mesh = meshio.read("./mesh/circle.msh")
points = mesh.points

points

import meshio mesh = meshio.read("./mesh/circle.msh") points = mesh.points points

Out[1]:

array([[1000.        ,    0.        ,    0.        ],
       [ 997.13604528,   75.62874588,    0.        ],
       [ 988.56058559,  150.82429716,    0.        ],
       ...,
       [ 109.65476416,  128.54861141,    0.        ],
       [ 370.80378341,  447.01151374,    0.        ],
       [ -62.24480108,  -51.78637557,    0.        ]])

We use the points from this mesh to create the Voronoi mesh. Because Voronoi() create a 2D Voronoi decomposition only, we need to pass an array with two dimensions.

In [2]:

from voromesh import Voronoi
voro = Voronoi(points[:, :2], buffer_size=40.0)
mesh = voro.to_pyvista()
mesh.save("./mesh/circle.vtu")

from voromesh import Voronoi voro = Voronoi(points[:, :2], buffer_size=40.0) mesh = voro.to_pyvista() mesh.save("./mesh/circle.vtu")

The mesh can be plotted with Pyvista.

In [3]:

# Plot the grid in notebook
import pyvista as pv
pv.set_jupyter_backend('static')
mesh.plot(notebook=True, show_edges=True)

# Plot the grid in notebook import pyvista as pv pv.set_jupyter_backend('static') mesh.plot(notebook=True, show_edges=True)