Point location in zones of k-flats in arrangements

✍ Scribed by Mark de Berg; Marc van Kreveld; Otfried Schwarzkopf; Jack Snoeyink

• Publisher: Elsevier Science
• Year: 1996
• Tongue: English
• Weight: 885 KB
• Volume: 6
• Category: Article
• ISSN: 0925-7721
• DOI: 10.1016/0925-7721(95)00021-6

✦ Synopsis

Let A(H) be the arrangement of a set H of n hyperplanes in d-space. A k-flat is a k-dimensional affine subspace of d-space. The zone of a k-flat f with respect to H is the set of all faces in A(H) that intersect f. In this paper we study some problems on zones of k-flats. Our most important result is a data structure for point location in the zone of a k-flat. This structure uses O(n [a/2j+E + n k+~) preprocessing time and space and has a query time of O(log 2 n). We also show how to test efficiently whether two flats are visible from each other with respect to a set of hyperplanes. Then point location in m faces in arrangements is studied. Our data structure for this problem has size O(n[d/2J+eT~ [d/zl/d) and the query time is O(log 2 n).