Incremental Construction of Generalized Voronoi Diagrams on Pointerless Quadtrees

Table 1

The GVD data used by PQ-GVD builder.

Data name	Semantics
^∗𝑉𝑜𝑟𝑜	A pointerless quadtree storing the resulting GVD indicating if a grid is a GVD edge cell (by checking its state as “true/1” or “false/2”).
^∗𝑅𝑎𝑖𝑠𝑒	A pointerless quadtree indicating the processing type for a grid (by checking its state as “Raise/1” or “Lower/2”).
^∗𝑂𝑏𝑠𝑡	A pointerless quadtree indicating which site a grid belongs to (by checking its state as site ID, represented in positive integer).
Dist	A 2D integer matrix storing for each grid the distance corresponding to its nearest site cell.
Open	A priority queue storing grid cells that are enqueued when the wavefront (i.e., raise or lower) propagates to them. Entries in Open are sorted in ascending order; cells with lower value in matrix Dist possess higher priority.