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Showing papers on "Line segment 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


Journal ArticleDOI
TL;DR: In this paper, the random process of line segments in the Euclidean plane was studied under conditions more general than Poisson, and expressions for Borel A ⊂ R 2, for the first moments of M (A ), the number of segment mid-points in A ; N ( A ), the numbers of segments which intersect with convex A ; S (A), the total length within A of segments crossing A ; and C ( A ) the numberof segment-segment crossings within A.
Abstract: This paper formulates the random process of line-segments in the Euclidean plane. Under conditions more general than Poisson, expressions are obtained, for Borel A ⊂ R 2 , for the first moments of M ( A ), the number of segment mid-points in A ; N ( A ), the number of segments which intersect with convex A ; S ( A ), the total length within A of segments crossing A ; and C ( A ) the number of segment-segment crossings within A . In the case of Poisson mid-points, the distribution of the r th nearest line-segment to a given point is found.

36 citations


Journal ArticleDOI
TL;DR: In a complete identification experiment, the three sides of an equilateral triangle were briefly presented as stimuli either singly or in pairs, and the resulting 6×6 confusion matrices obtained with three subjects were analyzed according to Rumelhart's (1970, 1971) multicomponent theory of perception (MCTP) in order to test assumptions about feature extraction and decision processes as discussed by the authors.
Abstract: In a complete identification experiment the three sides of an equilateral triangle were briefly presented as stimuli either singly or in pairs. The resulting 6×6 confusion matrices obtained with three subjects were analyzed according to Rumelhart's (1970, 1971) multicomponent theory of perception (MCTP) in order to test assumptions about feature extraction and decision processes. In agreement with MCTP the detection of a line segment occurring within a pair was stochastically independent of the detection of the other line segment. Two predictions of MCTP were however not confirmed: different line segments are not detected with equal probability, and the probability of detecting a line segment depends on the presence or absence of others. Several decision assumptions of MCTP were tested. The results are the following: If at most one line segment has been detected, then several responses (the candidate set) are compatible with this sensory state. It was argued that response selection from the candidate set is better described by the choice model (Luce, 1959) than by the matching Bayesian rule assumed by MCTP. For a given sensory state the size of the candidate set appears to vary over trials, whereas MCTP assumes it to be constant. In general, the confusion matrices could be predicted quite accurately by MCTP modified according to the above assumptions. However, more accurate predictions were achieved by assuming holistic perceptual processes as well as single feature extraction.

23 citations


Journal ArticleDOI
TL;DR: In this paper, the authors show how to build models of random collections of geometrical objects: lines, circles, line segments, etc., using the theory of point processes on abstract spaces.
Abstract: We show how to build models of random collections of geometrical objects: lines, circles, line segments, etc. This basic problem in stochastic geometry is solved using the theory of point processes on abstract spaces.

20 citations


Patent
05 Mar 1976
TL;DR: In this paper, a marking device in the form of a branding iron having a plurality of sets of marking elements, mutually positioned and oriented to comprise line elements common to a plurality in a working plane for application to an animal to be identified.
Abstract: A marking device in the form of a branding iron having a plurality of sets of marking elements in the form of line segments mutually positioned and oriented to comprise line elements common to a plurality of recognizably different characters, together with a releasable latching arrangement for positioning selected ones of said elements in a working plane for application to an animal to be identified.

2 citations


Proceedings ArticleDOI
28 Jun 1976
TL;DR: This paper describes a method of checking the spacing between elements (pads, etch, ground plane, etc.) on printed wiring boards by treating the lines representing the etch as vectors.
Abstract: This paper describes a method of checking the spacing between elements (pads, etch, ground plane, etc) on printed wiring boards The etch paths are constrained to be straight line segments but not necessarily orthogonal ones The process involves treating the lines representing the etch as vectors Closeness is determined from the dot and cross products of line segment vectors

2 citations