Figure 4
A two-dimensional schematic of the LifeSoaks algorithm. The unit cell includes two internal vertices, four surface vertices, five internal edges and two artificial surface-connecting edges marked *. We note that and due to internal point symmetry. Further, r(e1) > r(e2) > r(e3). (a) The state before any edge is processed. In this iteration the bottleneck radii are determined from left to right, so vertices on these sides are marked as surface vertices (magenta coloring) and
e*1 is excluded. (b) After two iterations e1 and have been processed, since they are the largest edges. Because they connect one new vertex to a surface vertex, their incident vertex is now also accessible by one surface but not by both. (c) After three additional iterations e2, and
e*2 have been processed. Since
e*2 connects the surface vertices at the top and bottom, all vertices are now part of the same set. Since this set now contains vertices of the opposing surfaces, it represents a unit-cell-traversing path and all vertices will be annotated with the bottleneck radius r(e2). (d) Finally, e3 is processed. However, because the incident vertices are already part of the same set, no set or radius is changed. |