mesh_from_polygon.md

Create a mesh based on its boundary

Polygon

We first create a simple, but non-convex, polygon:

from pylab import *

theta = linspace(0,2*pi,51)
r = 1 + .3*cos(5*theta)
x = r*cos(theta)
y = r*sin(theta)

plot(x,y,'o', color = 'grey')

We now want to create a mesh in this polygon, which we treat as an oriented boundary. For this we call the TriMesh_from_polygon function, which is but a wrapper for the polygon_triangulate function by J. Burkardt.

Th = pyff.TriMesh_from_polygon( array( [ x, y ] ).T )
Th.plot_triangles( color = 'lightgrey' )

List of boundaries

Often, the polygon that bounds the mesh is a list of boundaries with distinct labels. For instance:

labels = 'top', 'bottom'
i_cut = int( len(theta)/2 )
points = array([x,y]).T
boundaries = [ points[:i_cut], points[i_cut:]  ]

To keep track of these labels, we now call the TriMesh_from_boundaries function:

Th = pyff.TriMesh_from_boundaries( boundaries, labels )

We may then show the boundaries on the plot:

Th.plot_boundaries()
legend()