M. de Berg. On rectilinear link distance. Comput. Geom. Theory Appl., 1(1):13--34, July 1991. Home/Search Document Details and Download
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Polygon Cutting: Revisited - Bose, Czyzowicz, Kranakis, Krizanc.. (Correct)
...., be the added weight of all the vertices. It is possible to nd in O(n) time a diagonal ab of P that partitions it into two polygons, each with a weight not exceeding 2W 3. Chazelle s cutting theorem deals mainly with nding a diagonal that partitions the vertices in an equitable manner. De Berg [dB91] showed that Chazelle s cutting technique can be modi ed in the rectilinear case A rectilinear polygon is a polygon whose edges are axis parallel. Rectilinear polygons have also been called orthogonal polygons, isothetic polygons and rectanguloid polygons in the literature. with the fraction ....
....as approximations to arbitrary simple polygons; and they arise naturally in domains dominated by Cartesian coordinates, such as raster graphics, VLSI design, robotic, or architecture. A rectilinear polygon is called trapezoided if both its vertical and horizontal visibility maps are given. de Berg [dB91] presented the rectilinear version of Chazelle s polygon cutting theorem, which led to several divide and conquer algorithms inside a rectilinear polygon, such as rectilinear link query, rectilinear link diameter and rectilinear link center [dB91] An outline of the paper is as follows. In section ....
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M. de Berg. On rectilinear link distance. Comp. Geom.: Theory and Appl., 1:13-34, 1991.
An Optimal Data Structure for Shortest Rectilinear Path Queries.. - Schuierer (1996) (4 citations) (Correct)
....and needs O(n p n) preprocessing time and space. If we restrict ourselves to simple rectilinear polygons, the situation gets considerably simpler since it can be shown that there is always a rectilinear path between two points that is shortest w.r.t. both the rectilinear link and the L 1 metric [10, 11]. We call such a path a smallest path [12, 13] In this setting de Berg [10] presents a data structure that allows to answer the following types of queries. If we are given two arbitrary points inside a polygon, the rectilinear link distance and the L 1 distance between the two points can be ....
....rectilinear polygons, the situation gets considerably simpler since it can be shown that there is always a rectilinear path between two points that is shortest w.r.t. both the rectilinear link and the L 1 metric [10, 11] We call such a path a smallest path [12, 13] In this setting de Berg [10] presents a data structure that allows to answer the following types of queries. If we are given two arbitrary points inside a polygon, the rectilinear link distance and the L 1 distance between the two points can be reported in time O(log n) If we are given two vertices of the polygon, both ....
M. de Berg, "On rectilinear link distance", Computational Geometry: Theory and Applications, 1 (1991) 13--34.
International Journal of Computational Geometry Applications - Fl World Scientific (Correct)
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M. de Berg. On rectilinear link distance. Comput. Geom. Theory Appl., 1(1):13--34, July 1991.
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