I am looking for a reference on the following variant of a Voronoi diagram:
- Instead of seed points, there are seed rectangles which are axis-parallel and pairwise-disjoint.
- Instead of Euclidean distance, we are interested in Manhattan distance.
The goal is to partition the plane into regions, such that the points in each region $i$ are closer (in Manhattan distance) to rectangle $i$ than to every other rectangle.
What would such cells look like? Are there algorithms for finding them?