be widely *irregular*, thus the $ring$ definition over them is not obvious. By irregular we mean that the vertices can be non uniformly distributed over the surface and the faces of the tessellation may have different area, shape and number of edges.

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   ![(a): in blue, two rings defined on the basis of triangles; (b): the ring around the vertex $v$ is defined by mesh vertices (red dots).[]{data-label="fig:bad_rings"}](pic/bad_ring1.png "fig:"){width="5.5cm"}   ![(a): in blue, two rings defined on the basis of triangles; (b): the ring around the vertex $v$ is defined by mesh vertices (red dots).[]{data-label="fig:bad_rings"}](pic/bad_ring2.png "fig:"){width="5.5cm"}
                                                                                                         (a)                                                                                                                                                                                                                (b)
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Figure \[fig:bad\_rings\] depicts two possible $ring$ definitions exclusively made of mesh elements (triangles in Figure \[fig:bad\_rings\](a) and vertices in Figure \[fig:bad\_rings\](b), resp.): in both cases, the irregularity of the mesh elements strongly influences these of rings.

We define the $ring$ of a vertex $v \in V$ as the intersection of the surface tessellation with a sphere of radius $R$ centered in $v$.

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   ![(a): in black, multiple closed curves defined by the set of points $P_i \in \mathcal{R}$; (b): the black dots correspond to the elements $p_i$ of the three central curves in (a).[]{data-label="fig:ring_construction"}](pic/ring_int.png "fig:"){width="5.5cm"}   ![(a): in black, multiple 