Living Reference Work Entry

Encyclopedia of Algorithms

pp 1-5

Date: Latest Version

Binary Space Partitions

  • Adrian DumitrescuAffiliated withComputer Science, University of Wisconsin–Milwaukee Email author 
  • , Csaba D. TóthAffiliated withDepartment of Mathematics, California State University NorthridgeDepartment of Computer Science, Tufts University


Computational geometry Recursive partition Convex decomposition BSP tree

Years and Authors of Summarized Original Work

1990; Paterson, Yao

1992; Paterson, Yao

1992; D’Amore, Franciosa

2002; Berman, DasGupta, Muthukrishnan

2003; Tóth

2004; Dumitrescu, Mitchell, Sharir

2005; Hershberger, Suri, Tóth

2011; Tóth

Problem Definition

The binary space partition (for short, BSP) is a scheme for subdividing the ambient space \(\mathbb{R}^{d}\) into open convex sets (called cells) by hyperplanes in a recursive fashion. Each subdivision step for a cell results in two cells, in which the process may continue, independently of other cells, until a stopping criterion is met. The binary recursion tree, also called BSP-tree, is traditionally used as a data structure in computer graphics for efficient rendering of polyhedral scenes. Each node v of the BSP-tree, except for the leaves, corresponds to a cell ...

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