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Showing papers on "Computational geometry published in 1976"


Proceedings ArticleDOI
25 Oct 1976
TL;DR: An O(N log N) algorithm is given to determine whether any two intersect and use it to detect whether two simple plane polygons intersect and to show that the Simplex method is not optimal.
Abstract: We develop optimal algorithms for forming the intersection of geometric objects in the plane and apply them to such diverse problems as linear programming, hidden-line elimination, and wire layout. Given N line segments in the plane, finding all intersecting pairs requires O(N2) time. We give an O(N log N) algorithm to determine whether any two intersect and use it to detect whether two simple plane polygons intersect. We employ an O(N log N) algorithm for finding the common intersection of N half-planes to show that the Simplex method is not optimal. The emphasis throughout is on obtaining upper and lower bounds and relating these results to other problems in computational geometry.

473 citations


Proceedings ArticleDOI
03 May 1976
TL;DR: A search algorithm, called point-location algorithm, is presented, which operates on a suitably preprocessed data structure, and yields interesting and efficient solutions of other geometric problems, such as spatial convex inclusion and inclusion in an arbitrary polygon.
Abstract: Given a subdivision of the plane induced by a planar graph with n vertices, in this paper we consider the problem of identifying which region of the subdivision contains a given test point. We present a search algorithm, called point-location algorithm, which operates on a suitably preprocessed data structure. The search runs in time at most 0((log n)2), while the preprocessing task runs in time at most 0(n log n) and requires 0(n) storage. The methods are quite general, since an arbitrary subdivision can be transformed in time at most 0(n log n) into one to which the preprocessing procedure is applicable. This solution of the point-location problem yields interesting and efficient solutions of other geometric problems, such as spatial convex inclusion and inclusion in an arbitrary polygon.

125 citations


Journal ArticleDOI
TL;DR: This paper analyzes and modifies the existing method of IEEE Guide No. 80, to allow a recursive point by point integration of surface gradients through consecutive meshes, and describes a computer program for optimized grid design.
Abstract: The envelope of earth surface potential curves is distinctly convex for grounding mats with many meshes. Such a condition is difficult to analyze with the established methods, which are primarily devised for calculating the corner mesh voltage. For this reason, a large, equally spaced grid may be overdesigned toward the center and underdesigned toward the perimeter. Aiming to remedy such problems, this paper analyzes and modifies the existing method of IEEE Guide No. 80, to allow a recursive point by point integration of surface gradients through consecutive meshes. A computer program for optimized grid design is described and the effect of spacing geometry is documented by computer plotted voltage profiles.

57 citations


Journal ArticleDOI
TL;DR: The SPACEBAR pre-gram allows the direct design and analysis of mechanisms on the terminal screen, and all variables including linkage geometry, stiffness, and applied loading conditions can be input and/or changed from the terminal.
Abstract: The development of kinematic mechanisms on the design board is often an extremely complex and time-consuming task. The SPACEBAR pre-gram allows the direct design and analysis of mechanisms on the terminal screen. All variables including linkage geometry, stiffness, and applied loading conditions can be input and/or changed from the terminal. The data can be described and displayed in three dimensions. All mechanism configurations can be cycled through their range of travel and viewed in their various geometric positions, again in three dimensions. Output data includes geometric positioning in orthogonal co-ordinates of each node point in the mechanism, velocity and acceleration of the mechanism node points throughout its range of travel, and internal loads and displacements of the individual node points and linkages. All analysis calculations are performed at the v.d.u. and take, at most, a few seconds to complete. Output data can be viewed at the scope and also printed at the discretion of the user.

4 citations