Name
Abstract | ||
|---|---|---|
We study the problem of computing the set of all distant horizons of a terrain, represented as either: (1) the set of all edges that appear on the distant horizon from at least one viewing direction; (2) for every edge e, the set of direction intervals for which e appears on the distant horizon; or (3) a search structure to query for the edges on the distant horizon, or the precise distant horizon, from a fixed viewing direction. We describe an algorithm that solves the first and second forms of the problem in O(n(2+epsilon)) time for any constant epsilon > 0 where n is the number of edges of the terrain. This algorithm can be extended to compute a search structure for (3) in O(n(2+epsilon)) time. The search structure can return the s edges on the distant horizon in O(log n + s) time. We show solving problem (1) is 3SUM hard. Furthermore, we construct a terrain with a single local maximum in which Theta(n) edges each have Theta(n) direction intervals, showing that our solution to (2) cannot be significantly improved, in the worst case, even for such restricted terrains. This takes advantage of a novel construction in which the convex hull of a set of n linearly moving points, whose trajectories do not intersect, changes Omega(n(2)) times. |
Year | DOI | Venue |
|---|---|---|
2005 | 10.1142/S0218195905001841 | INTERNATIONAL JOURNAL OF COMPUTATIONAL GEOMETRY & APPLICATIONS |
Keywords | DocType | Volume |
horizons, orthographic views | Journal | 15 |
Issue | ISSN | Citations |
6 | 0218-1959 | 1 |
PageRank | References | Authors |
0.36 | 14 | 3 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Daniel Archambault | 1 | 705 | 39.10 |
| William S. Evans | 2 | 543 | 60.69 |
| David G. Kirkpatrick | 3 | 2394 | 541.05 |