Simple traversal of a subdivision without extra storage

In this paper we show how to traverse a subdivision and to report all cells, edges and vertices, without making use of mark bits in the structure or a stack. We do this by performing a depth-first search on the subdivision, using local criteria for deciding what is the next cell to visit. Our method is extremely simple and provably correct. The algorithm has applications in the held of geographic information systems (GIS), where traversing subdivisions is a common operation, but modifying the database is unwanted or impossible. We show how to adapt our algorithm to answer related queries, such as windowing queries and reporting connected subsets of cells that have a common attribute. Finally, we show how to extend our algorithm such that it can handle convex three-dimensional subdivisions.