Planar Point Location | ||
Introduction Edelsbrunner Kirkpatrick Subdivision Slabs Sarnak and Tarjan Trapezoidal Maps Randomized Incremental Method Applet References & Links |
ReferencesArge, L, J Vahrenhold. (2002) I/O Efficient Dynamic Planar Point Location. SIAM Journal on Computing. Arya, S, T Malamatos, DM Mount (2000) Nearly Optimal Excpected-Case Planar Point Location. In: 41st Annual Symposium on Foundations of Computer Science. Redondo Beach, CA, USA. Nov. 12-14. de Berg, M, M van Kreveld, M Overmars, O Schwarzkopf (2000) Computational Geometry: Algorithms and Applications, 2nd Edition. Springer: Berlin Heidelberg. 367p Dobkin, D, RJ Lipton (1976) Multidimensional search problems. SIAM Journal on Computing 5(2): 181-186. Edelsbrunner, H, LJ Guibas, J Stolfi (1986) Optimal Point Location in a Monotone Subdivision. SIAM Joural on Computing. 15(2):317-340. Kirkpatrick, D (1983) Optimal Search in Planar Subdivisions. SIAM Joural on Computing. 12(1):28-35. Iacono, J., S Langerman. (2003) Proximate Planar Point Location. In: SoCG’03 June 8-10, San Diego, California, USA. Mulmuley, K (1990) A Fast Planar Partition Algorithm, I. Journal of Symbolic Computation. 10:253-280. Preparata, FP, MI Shamos (1985) Computational Geometry: An Introduction. Springer-Verlag: New York. 390p. Sarnak, N, RE Tarjan (1986) Planar point location using persistent search trees. Communications of the ACM. 29:669-679. Seidel, R (1991) A simple and fast incremental randomized algorithm for computing trapezoidal decompositions and for triangulating polygons. Computational Geometry: Theory and Applications. 1:51-64. AcknowledgementsI would like to thank Derek Bradley for providing me with Java source code from his project page for Kirkpatrick's algorithm (see below). Other ResourcesDerek Bradley's Project describing Kirkpatrick's Algorithm
Jukka Kaartinen's Project describing Trapezoid Map Generation
Another good description of planar point location using trapezoid maps is this project by Sergi Elizalde & David Pritchard |