Abstract
We consider the orthgonal clipping problem in a set of segments: Given a set of n segments in d-dimensional space, we preprocess them into a data structure such that given an orthogonal query window, the segments intersecting it can be counted/reported efficiently. We show that the efficiency of the data structure significantly depends on a geometric discrete parameter K named the projected-image complexity, which becomes Θ (n2) in the worst case but practically much smaller. If we use O(m) space, where K log4d-7 n ≥ m ≥ n log4d-7 n, the query time is O((K/m)1/2 logmax{4,4d-5} n). This is near to an Ω((K/m)1/2) lower bound.
Original language | English |
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Pages (from-to) | 229-245 |
Number of pages | 17 |
Journal | Algorithmica (New York) |
Volume | 18 |
Issue number | 2 |
DOIs | |
Publication status | Published - 1997 Jun |
Externally published | Yes |
Keywords
- Algorithms
- Clipping
- Computational geometry
- Range searching
ASJC Scopus subject areas
- Computer Science(all)
- Computer Science Applications
- Applied Mathematics