Resolution of a mesh on the unit square constructed via the mshr-module

Question

I would like to initialize a mesh on the unit circle.

After reading http://fenicsproject.org/qa/5895/replacement-of-the-unitcircle, I looked at https://bitbucket.org/benjamik/mshr/src/424ad882958093d8bece893be7fc74951cdabbdc/demo/python/propeller.py?at=master&fileviewer=file-view-default from which I took the following snippet of code:

resolution = 5
domain_geometry = mshr.Circle(dolfin.Point(0.0, 0.0), 1.0)
mesh = mshr.generate_mesh(domain_geometry, resolution)

This does the job, but I would like to know in addition:

1. what the practical interpretation of the number stored in resolution is,
2. how it relates to the number of vertices in mesh,
3. and how it relates to the number of triangles in mesh.

Any advice on these three points would be appreciated.

Answer 1

The number of elements and vertices clearly scale with the square value of resolution, so it is probably some inverse length scale, but the actual scale is determined by the geometry, because the mesh is unaffected by the circle radius.