Rings of vertices (yellow/white) surrounding a functionally defined area (red/light gray) for two cases in which: (left) the functional area is convex, and (right) the functionally defined area is made out of two discontinuous regions. For visualization purposes, only the third, sixth, and ninth neighboring outer rings and the third neighboring inner rings are drawn. [Color figure can be viewed in the online issue, which is available at www.interscience.wiley.com.]