Computational geometry: an introduction
Computational geometry: an introduction
New upper bounds for neighbor searching
Information and Control
There is a planar graph almost as good as the complete graph
SCG '86 Proceedings of the second annual symposium on Computational geometry
Solving query-retrieval problems by compacting Voronoi diagrams
STOC '90 Proceedings of the twenty-second annual ACM symposium on Theory of computing
A sparse graph almost as good as the complete graph on points in K dimensions
Discrete & Computational Geometry
Classes of graphs which approximate the complete Euclidean graph
Discrete & Computational Geometry
Journal of Computer and System Sciences - Special issue: 31st IEEE conference on foundations of computer science, Oct. 22–24, 1990
Handbook of discrete and computational geometry
Faster algorithms for some geometric graph problems in higher dimensions
SODA '93 Proceedings of the fourth annual ACM-SIAM Symposium on Discrete algorithms
An optimal algorithm for approximate nearest neighbor searching
SODA '94 Proceedings of the fifth annual ACM-SIAM symposium on Discrete algorithms
Parallel Construction of Quadtrees and Quality Triangulations
WADS '93 Proceedings of the Third Workshop on Algorithms and Data Structures
Dynamic Data Structures for Realtime Management of Large Geormetric Scences (Extended Abstract)
ESA '97 Proceedings of the 5th Annual European Symposium on Algorithms
Lower Bounds for Computing Geometric Spanners and Approximate Shortest Paths
Proceedings of the 8th Canadian Conference on Computational Geometry
New Results of Fault Tolerant Geometric Spanners
WADS '99 Proceedings of the 6th International Workshop on Algorithms and Data Structures
Distributed Maintenance of Resource Efficient Wireless Network Topologies (Distinguished Paper)
Euro-Par '02 Proceedings of the 8th International Euro-Par Conference on Parallel Processing
I/O-Efficient Batched Range Counting and Its Applications to Proximity Problems
FST TCS '01 Proceedings of the 21st Conference on Foundations of Software Technology and Theoretical Computer Science
Connections between theta-graphs, delaunay triangulations, and orthogonal surfaces
WG'10 Proceedings of the 36th international conference on Graph-theoretic concepts in computer science
Spanners, weak spanners, and power spanners for wireless networks
ISAAC'04 Proceedings of the 15th international conference on Algorithms and Computation
Hi-index | 0.00 |
We study algorithmic aspects in the management of geometric scenes in interactive walkthrough animations. We consider arbitrarily large scenes consisting of unit size balls. For a smooth navigation in the scene we have to fulfill hard real time requirements. Therefore, we need algorithms whose running time is independent of the total number of objects in the scene and that use as small space as possible. In this work we focus on one of the basic operations in our walkthrough system: reporting the objects around the visitor within a certain distance. Previously a randomized data structure was presented that supports reporting the balls around the visitor in an output sensitive time and allows insertion and deletion of objects nearly as fast as searching. These results were achieved by exploiting the fact that the visitor moves "slowly" through the scene. A serious disadvantage of the aforementioned data structure is a big space overhead and the use of randomization. Our first result is a construction of weak spanners that leads to an improvement of the space requirement of the previously known data structures. Then we develop a deterministic data structure for the searching problem in which insertion of objects are allowed. Our incremental data structure supports O(1+k) reporting time, where k is a certain quantity close to the number of reported objects. The insertion time is similar to the reporting time and the space is linear to the total number of objects.