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Abstract: In this note we show how to traverse a subdivision and to report all cells, edges and vertices, without making use of mark bits in the structure or a stack. We do this by performing a depth-first search on the subdivision, using local criteria for deciding what is the next cell to visit. Our method is extremely simple. The algorithm has applications in the field of Geographic Information Systems (GIS), where traversing subdivisions is a common operation, but modifying the database is unwanted... (Update)
Context of citations to this paper: More
...e = entry(f; p) on the boundary of f such that e p e 0 for all e 0 on the boundary of f . Bose and Morin [4] see also de Berg et al. [6]) show that if one connects all faces f 1 and f 2 such that entry(f 1 ; p) is on the boundary of both f 1 and f 2 , the result is a spanning...
.... researchers have investigated methods of traversing subdivisions and other graph like data structures without the use of mark bits [2, 3, 4, 5, 6]. Generally speaking, these techniques use geometric properties of S to de ne a spanning tree T of the vertices, edges or faces of S...
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BibTeX entry: (Update)
M. de Berg, M. van Kreveld, R. van Oostrum, and M. Overmars. Simple traversal of a subdivision without extra storage. International Journal on Geographical Information Science, 11:359--373, 1997. http://citeseer.ist.psu.edu/article/deberg97simple.html More
@article{ deberg97simple,
author = "Mark de Berg and Marc J. van Kreveld and Rene van Oostrum and Mark H. Overmars",
title = "Simple Traversal of a Subdivision Without Extra Storage",
journal = "International Journal of Geographical Information Science",
volume = "11",
number = "4",
pages = "359-373",
year = "1997",
url = "citeseer.ist.psu.edu/article/deberg97simple.html" }
Citations (may not include all citations):114 Optimal point location in a monotone subdivision (context) - Edelsbrunner, Guibas et al. - 1986
34 Reverse search for enumeration - Avis, Fukuda - 1992
13 Automated contour mapping using triangular element data stru.. (context) - Gold, Charters et al. - 1977
12 Spatially ordered networks and topographic reconstructions (context) - Gold, Cormack - 1986
10 Combinatorial face enumeration in convex polytopes (context) - Fukuda, Rosta - 1994
8 INFO: an example of a contemporary geographic information sy.. (context) - Peuquet, Marble et al. - 1990
7 Computational Geometry by Example (context) - de Berg, van Kreveld et al. - 1995
6 Technical description of the DIME system (context) - Peuquet, Marble - 1990
5 Triangulation and spatial ordering in computer cartography (context) - Gold, Maydell - 1978
3 Personal communication (context) - Snoeyink - 1995
The graph only includes citing articles where the year of publication is known.
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On the Sectional Area of Convex Polytopes - Avis, Bose, Shermer, Snoeyink.. (1996) (Correct)
A Package for Triangulations - Ono, Kyoda, Masada, Hayase, Shibuya, .. (1996) (Correct)
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