Fig. 3.

[Left]Narrow-band fronts of cells belonging to three different “colors”. The corresponding zero level set curves are given by φ₁ (“red”), φ₂ (“green”), and φ₃ (“blue”), with the narrow bands given by the region where δ(φ_i) > s_thresh. At region A, the narrow band of the “red-colored” cell intersects with the narrow band of the “blue-colored” cell. We enforce an explicit rule that the narrow band of a cell, φ_i that is currently being updated cannot overlap with a different colored cell (i.e., (φ_j)). Hence, in region A, the narrow-band of the “red-colored” cell (i.e., δ(φ₁) > s_thresh does not include those areas for which φ₃ ≥ 0. A similar rule is applied when updating the “blue-colored” cell, at region B. [Right] If a “collision” occurs between cells (i.e., δ(φ_i) = δ(φ_j), i ≠ j), then depending on which order the level sets are updated, we may get either C₁ protruding into C₂ or vice-versa.