Using convex differences in hierarchical representations of polygonal maps

Ari Rappoport*

*Corresponding author for this work

Research output: Contribution to journalConference articlepeer-review

2 Scopus citations


We discuss adaptive, hierarchical, spatial subdivisions of planar polygonal maps. These maps are extensively used in cartography, GIS, computer graphics and computer vision. Our results are applicable to many subdivision schemes, including quad trees, k-d trees, and binary space partitioning (BSP). We focus on cell splitting rules and leaf organization methods, introducing and comparing three of them. The simple rule results in short hierarchy trees but leaf operations are costly. The convex rule enjoys efficient leaf operations at the expense of taller trees. The convex differences rule combines both short hierarchies and efficient operations to create the convex differences hierarchy (CDH). It utilizes the convex differences tree (CDT) representation of simple polygons. We also present vertex enlargement, a technique for reducing the map complexity which results in shorter trees and simplified splitting rules.

Original languageAmerican English
Pages (from-to)183-189
Number of pages7
JournalProceedings - Graphics Interface
StatePublished - May 1990
EventProceedings - Graphics Interface '90 - Halifax, NS, USA
Duration: 14 May 199018 May 1990


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