Portal de Periódicos da CAPES

Simple traversal of a subdivision without extra storage

1997; Taylor & Francis; Volume: 11; Issue: 4 Linguagem: Inglês

10.1080/136588197242310

1365-8824

Mark de Berg, Marc van Kreveld, René van Oostrum, Mark Overmars,

Geographic Information Systems Studies

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 field 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 threedimensional subdivisions.