Linear Size Binary Space Partitions for Uncluttered Scenes

We describe a new and simple method for constructing binary space partitions in arbitrary dimensions. We also introduce the concept of uncluttered scenes, which are scenes with a certain property that we suspect many realistic scenes exhibit, and we show that our method constructs a BSP of size On for an uncluttered scene consisting of n objects. The construction time is Onlogn. Because any set of disjoint fat objects is uncluttered, our result implies an e cient method to construct a linear size BSP for fat objects. We use our BSP to develop a data structure for point location in uncluttered scenes. The query time of our structure is Ologn, and the amount of storage is On. This result can in turn be used to perform range queries with not-too-small ranges in scenes consisting of disjoint fat objects or, more generally, in so-called low-density scenes.

• Type: Journal
• Year: 2000
• Where: ALGORITHMICA
• Authors: Mark de Berg
• Keywords: ALGORITHMICA 2000, Disjoint Fat Objects, Fat Objects, Uncluttered Scenes