... placed at the boundary of the environment).Finally, note that, as one moves the location of λifrom the center of the environment to the boundary along astraight line, the areas of the level ... makes the zone size smaller. Regarding average zone area, since the sum of the areas of the zones is equal to the area of the environment, we deduceAverage zone area=πR2m,(2)where m is the ... other λj,where the approximation of the Euclidean distance by the geodesicdistance is accurate.Note that the zones on ∂Q correspond to the level sets of h|∂Q: ∂Q → NN. Each of these zones...