J.M. Keil and D.G. Kirkpatrick, Computational Geometry on Integer Grids, Proc. 19th Annual Allerton Conference (1981), 41-50 Home/Search Document Not in Database Summary Related Articles Check |
This paper is cited in the following contexts:
Scanline Algorithms on a Grid - Karlsson, Overmars (1986) (5 citations) (Correct)
....computational complexity of finite geometric problems. Recently, there has been a growin interest in solving problems in computational geometry on a grid, i.e. points (or line segments with endpoints) in U d = 0. u 1] d. See for example, Karlsson [7] Karlsson and Munro [8] Keil and Kirkpatrick [10], Mfiller [15] Overmars [16] and Willard [20,21] In some sense, computational geometry on a grid shows the complexity of a problem after sorting. But apart from being of great theoretical interest, it is our belief that structures on grids are potentially practical. Indeed, analysis of ....
....convex region that contains the set. The prefix orthogonal means that convexity is defined by axis parallel point connections, i.e. for each two points in the polygon on a horizontal or vertical line, the line segment in between them lies completely inside the polygon. Keil and Kirkpatrick [10] solve the similar problem of computing the non orthogonal convex hull in the same time bound. Theorem 3.3: Given n points from U 2 we can compute their orthogonal convex hull in time 0( 1 loglog.u) using O(u n) storage. Proof: We observe the following. By determining the four extreme z ....
J.M. Keil and D.G. Kirkpatrick, Computational Geometry on Integer Grids, Proc. 19th Annual Allerton Conference (1981), 41-50
Computational Geometry on the Grid: Traversal and.. - Schneider, Güting, de .. (1998) (Correct)
.... simpler than in Euclidean space [Ove88a] On the other hand, problems like how to handle the intersection point of two integer based line segments are more complicated [GM95, GY86] Finite precision computational geometry has so far only been studied by a few researchers (overviews can be found in [KK81, Ove88a, Ove88b]) More efficient solutions in comparison with their Euclidean counterparts have been found for the nearest neighbor searching problem [KM85] range searching on a grid [Ove88b, Ove88c] the point location problem [M l85] the computation of rectangle intersections and maximal elements by ....
J.M. Keil & D.G. Kirkpatrick. Computational Geometry on Integer Grids. 19th Annual Allerton Conf. on Communication, Control, and Computing, 41-50, 1981.
Implementation of the ROSE Algebra: Efficient Algorithms for.. - Güting, al. (Correct)
....points of line segments, vertices of polygons etc. have integer coordinates instead of arbitrary floating point coordinates, has been emphasized by Greene and Yao [GrY86] as well as Yao [Ya92] Finite precision geometry has so far only been studied by a few researchers (overviews can be found in [KeK81, Ov88b, Ov88c]) Problems considered are, for example, the nearest neighbour searching problem [KaM85] range searching on a grid [Ov88a, Ov88b] the point location problem [M 85] the computation of rectangle intersections and maximal elements by divide and conquer [KaO88b] computing the convex hull of a set ....
Keil, J.M., and D.G. Kirkpatrick, Computational Geometry on Integer Grids. Proc. of the 19th Annual Allerton Conference on Communication, Control, and Computing, 1981, 41-50.
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