Worst-case optimal hidden-surface removal
ACM Transactions on Graphics (TOG)
SIAM Journal on Computing
Efficient hidden surface removal for objects with small union size
Computational Geometry: Theory and Applications
Nonoverlap of the star unfolding
Discrete & Computational Geometry - Special issue on ACM symposium on computational geometry, North Conway
Fat Triangles Determine Linearly Many Holes
SIAM Journal on Computing
Range searching and point location among fat objects
Journal of Algorithms
Range searching in low-density environments
Information Processing Letters
On fat partitioning, fat covering and the union size of polygons
Computational Geometry: Theory and Applications
Efficient computation of geodesic shortest paths
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Computational Geometry: Theory and Applications
On the union of κ-round objects
SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
Vertical ray shooting for fat objects
SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
The Complexity of the Union of $(\alpha,\beta)$-Covered Objects
SIAM Journal on Computing
Local polyhedra and geometric graphs
Computational Geometry: Theory and Applications - Special issue on the 19th annual symposium on computational geometry - SoCG 2003
Shortest paths on realistic polyhedra
SCG '07 Proceedings of the twenty-third annual symposium on Computational geometry
Computational Geometry: Theory and Applications
The Complexity of Bisectors and Voronoi Diagrams on Realistic Terrains
ESA '08 Proceedings of the 16th annual European symposium on Algorithms
Smoothing Imprecise 1.5D Terrains
Approximation and Online Algorithms
Higher-order Voronoi diagrams on triangulated surfaces
Information Processing Letters
Visibility maps of realistic terrains have linear smoothed complexity
Proceedings of the twenty-fifth annual symposium on Computational geometry
Approximation algorithms for shortest descending paths in terrains
Journal of Discrete Algorithms
Farthest voronoi diagrams under travel time metrics
WALCOM'12 Proceedings of the 6th international conference on Algorithms and computation
I/O-Efficient flow modeling on fat terrains
WADS'07 Proceedings of the 10th international conference on Algorithms and Data Structures
The complexity of geodesic Voronoi diagrams on triangulated 2-manifold surfaces
Information Processing Letters
| Hi-index | 0.00 |
We study worst-case complexities of visibility and distance structures on terrains under realistic assumptions on edge length ratios and the angles of the triangles. We show that the visibility map of a point for a realistic terrain with n triangles has complexity Θ(n√n). We also prove that the shortest path between two points p and q on a realistic terrain passes through Θ(√n) triangles, and that the bisector between p and q has complexity O(n √n). We use these results to show that the shortest path map for any point on a realistic terrain has complexity Θ(n√n), and that the Voronoi diagram for any set of m points on a realistic terrain has complexity Ω(n + m√n) and O((n+m)√n). Our results immediately imply more efficient algorithms for computing the various structures on realistic terrains.