Abstract
We present a new quick algorithm for the solution of the well-known point location problem and for the more specific problem of point-in-polygon determination. Previous approaches to this problem are presented in the first sections of this paper. In the remainder of the paper, we present a new quick location algorithm based on a quaternary partition of the space, as well as its associated cost and data structures.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Preparata, F., Shamos, M.: Computational geometry, an introduction. Springer, Heidelberg (1985)
O’Rourke, J.: Computational geometry in C. Cambridge University Press, Cambridge (2001)
Haines, E.: Point in polygon strategies. In: Heckbert, P. (ed.) Graphics Gems IV, pp. 24–46. Academic Press, Boston (1994)
Tor, S.B., Middleditch, A.E.: Convex decomposition of simple polygons. ACM Trans. on Graphics 3(4), 244–265 (1984)
Seidel, R.: A simple and fast incremental randomised algorithm for computing trapezoidal decomposition and for triangulating polygons. Comput. Geom. Theory Appl. (1991)
Edelsbrunner, H., Guibas, L.J., Stolfi, J.: Optimal point location in a monotone subdivision. SIAM J. Comput. (1986)
Kirkpatrick, D.G.: Optimal search in planar subdivisions. SIAM J. Comput (1983)
Mulmuley, K., Schwarzkopf, O.: Randomized algorithms. In: Goodman, J.E., O’Rourke, J. (eds.) Handbook of Discrete and Computational Geometry, CRC Press LLC, Boca Raton (1997)
Chiang, Y.-J., Tamassia, R.: Dynamization of the trapezoid method for planar point location. In: Seventh annual symposium on computational geometry, ACM Press, New York (1991)
de Berg, M., van Kreveld, M., Overmars, M., Schwarzkopf, O.: Computational Geometry, Algorithms and applications, 2nd edn. Springer, Heidelberg (2000)
Dobkin, D.P., Lipton, R.J.: Multidimensional searching problems. SIAM J. Comput. (1976)
Kirkpatrick, D.G., Klawe, M.M., Tarjan, R.E.: Polygon triangulation in O(n log log n) time with simple data structures. In: Proc. 6th Annu. ACM Sympos. Comput. Geom. (1990)
Poveda, J.: Contributions to the Generation, Visualisation and Storage of Digital Terrain Models: New Algorithms and Spatial Data Structures, PhD. dissertation, Universitat Jaume I, Castellon Spain (2004)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2004 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Poveda, J., Gould, M., Oliveira, A. (2004). A New Quick Point Location Algorithm. In: Wang, S., et al. Conceptual Modeling for Advanced Application Domains. ER 2004. Lecture Notes in Computer Science, vol 3289. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30466-1_17
Download citation
DOI: https://doi.org/10.1007/978-3-540-30466-1_17
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-23722-8
Online ISBN: 978-3-540-30466-1
eBook Packages: Springer Book Archive