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
Smoothed analysis of algorithms: Why the simplex algorithm usually takes polynomial time
Journal of the ACM (JACM)
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
Proceedings of the twenty-second annual symposium on Computational geometry
The complexity of flow on fat terrains and its i/o-efficient computation
Computational Geometry: Theory and Applications
On the expected complexity of voronoi diagrams on terrains
Proceedings of the twenty-eighth annual symposium on Computational geometry
Viewsheds on terrains in external memory
SIGSPATIAL Special
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, and a more general low-density assumption. We show that the visibility map of a point for a realistic terrain with n triangles has complexity @Q(nn). We also prove that the shortest path between two points p and q on a realistic terrain passes through @Q(n) triangles, and that the bisector of p and q has complexity O(nn). We use these results to show that the shortest path map for any point on a realistic terrain has complexity @Q(nn), and that the Voronoi diagram for any set of m points on a realistic terrain has complexity @W(n+mn) and O((n+m)n). Our results immediately imply more efficient algorithms for computing the various structures on realistic terrains.