Multi-VMap: A Multi-Scale Model for Vector Maps

representative of such regions have been created before u is applied. According to the arrangement of entities in form of forests described in Section 5, the most abstract representatives of the regions must have been created in an update of type either point-to-region or line-to-region. This situation corresponds to the example shown in Fig. 8, where in (b) we show a subsequence of sequence in (a) which is not feasible, because when update u2 [u3], of type point-to-line [point-to-region] is applied, line l3 [loop l4] becomes incident at region r2. In subsequence shown in (b), we observe that when feature-line l3 [loop l4] was created, region r2 did not exist. Thus, although r2 is created in a posterior update, l3 [l4] will be outside it, and the combinatorics of map M cannot be retrieved, as there is no atomic refinement update which can make a line that is outside a region jump inside it. • Let u be an update of type either feature-line-addition or region-split. In this case, also exactly one of the entities in {γ a , γ b , γ c } is a line, which was incident in S at two existing points (possibly coincident). We will require that the most abstract representative of such points have been created before u is applied. Such representatives must necessarily have been created in an update of type either line-split or feature-point-addition.