New results on binary space partitions in the plane
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In this article, the existence of linear size binary space partitions for sets of objects in the plane under certain conditions was proved. And they showed how to turn the existence proofs into efficient algorithms.Abstract:
We prove the existence of linear size binary space partitions for sets of objects in the plane under certain conditions. In particular, we construct linear size binary space partitions for sets of fat objects, for sets of line segments where the ratio between the lengths of the longest and shortest segment is bounded by a constant, and for homothetic objects. For all cases we also show how to turn the existence proofs into efficient algorithms.read more
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Journal Article
Triangulating a simple polygon in linear time
TL;DR: A deterministic algorithm for triangulating a simple polygon in linear time is given, using the polygon-cutting theorem and the planar separator theorem, whose role is essential in the discovery of new diagonals.
Multi-functional geometric data structures
TL;DR: The final author version and the galley proof are versions of the publication after peer review and the final published version features the final layout of the paper including the volume, issue and page numbers.
Journal ArticleDOI
Linear size binary space partitions for uncluttered scenes
TL;DR: A new and simple method for constructing binary space partitions (BSPs) in arbitrary dimensions is described, which can 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.
Journal ArticleDOI
3-D vertical ray shooting and 2-D point enclosure, range searching, and arc shooting amidst convex fat objects
TL;DR: A new data structure for a set of n convex simply-shaped fat objects in the plane is presented, and it is used to obtain efficient and rather simple solutions to several problems including vertical ray shooting and bounded-size range searching.
Book ChapterDOI
Linear Size Binary Space Partitions for Fat Objects
TL;DR: A new method for constructing binary space partitions for scenes in arbitrary dimensions that produces a linear size BSP for a more general class of scenes, namely scenes that satisfy the bounding-box-fitness condition—a property that many realistic scenes exhibit.
References
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Journal ArticleDOI
Triangulating a simple polygon in linear time
TL;DR: In this paper, a deterministic algorithm for triangulating a simple polygon in linear time is presented. But the main tools used are the polygon-cutting theorem, which provides us with a balancing scheme, and the planar separator theorem, whose role is essential in the discovery of new diagonals.
Journal ArticleDOI
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Proceedings ArticleDOI
Set operations on polyhedra using binary space partitioning trees
TL;DR: A new representation for polyhedra is introduced by showing how Binary Space Partitioning Trees (BSP trees) can be used to represent regular sets and modified to represent the result of a set operation between the BSP tree and a B-rep.
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