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Transversals to line segments in R³
, 2003
"... We completely describe the structure of the connected components of transversals to a collection of n arbitrary line segments in R 3. We show that n � 3 line segments in R 3 admit 0, 1,...,n or infinitely many line transversals. In the latter case, the transversals form up to n connected components. ..."
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Cited by 8 (4 self)
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We completely describe the structure of the connected components of transversals to a collection of n arbitrary line segments in R 3. We show that n � 3 line segments in R 3 admit 0, 1,...,n or infinitely many line transversals. In the latter case, the transversals form up to n connected components.
An optimal algorithm for intersecting line segments in the plane
 J. ACM
, 1992
"... The main contribution of this work is an O(n log r ~ +k)time algorithm focomputinall k intersections among n line segments in the plane, This time complexity IS easily shown to be optimal. Within the same asymptotic cost, our algorithm can also construct the subdiwslon of the plancdefmed by the s ..."
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Cited by 176 (2 self)
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The main contribution of this work is an O(n log r ~ +k)time algorithm focomputinall k intersections among n line segments in the plane, This time complexity IS easily shown to be optimal. Within the same asymptotic cost, our algorithm can also construct the subdiwslon of the plancdefmed
Line Segment Intersections
"... in R 2, does P describe the boundary of a simple polygon? Problem 2 (Polygon Intersection) Given two simple polygons P and Q in R 2 as a (counterclockwise) sequence of their vertices, is P \ Q =;? Problem 3 (Segment Intersection Test) Given a set of n closed line segments in R 2, do any two of them ..."
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in R 2, does P describe the boundary of a simple polygon? Problem 2 (Polygon Intersection) Given two simple polygons P and Q in R 2 as a (counterclockwise) sequence of their vertices, is P \ Q =;? Problem 3 (Segment Intersection Test) Given a set of n closed line segments in R 2, do any two of them
Recognising Line Segment Strokes
, 1999
"... We build a classifer which decides whether a sequence of pixels can be adequately modelled as a line segment. 1 Introduction The purpose of this investigation is to determine whether a given stroke may be adequately modelled by a line segment. We work with strokes extracted by [5], however we shoul ..."
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Cited by 1 (1 self)
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We build a classifer which decides whether a sequence of pixels can be adequately modelled as a line segment. 1 Introduction The purpose of this investigation is to determine whether a given stroke may be adequately modelled by a line segment. We work with strokes extracted by [5], however we
Shortest Paths for Line Segments
 ALGORITHMICA
, 1992
"... We study the problem of shortest paths for a line segment in the plane. As a measure of the distance traversed by a path, we take the average curve length of the orbits of prescribed points on the line segment. This problem is nontrivial even in free space (i.e., in the absence of obstacles). We cha ..."
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Cited by 5 (3 self)
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We study the problem of shortest paths for a line segment in the plane. As a measure of the distance traversed by a path, we take the average curve length of the orbits of prescribed points on the line segment. This problem is nontrivial even in free space (i.e., in the absence of obstacles). We
Partitioning of a Line Segment
, 1997
"... Different procedures for partitioning of a line segment is studied. An interval on the real line is partitioned according to a breakage procedure, resulting in a number of smaller segments. Conditioned on the number of resulting segments the different procedures give different length distributions o ..."
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Different procedures for partitioning of a line segment is studied. An interval on the real line is partitioned according to a breakage procedure, resulting in a number of smaller segments. Conditioned on the number of resulting segments the different procedures give different length distributions
Clustering of collinear line segments
, 1980
"... Abstract A number of methods are presented for finding clusters in collinear collections of line segments. The methods are of two kinds merging methods and splitting methods. Both make use of an evaluation function, and several alternative functions are illustrated. The methods are evaluated us ..."
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Cited by 2 (0 self)
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Abstract A number of methods are presented for finding clusters in collinear collections of line segments. The methods are of two kinds merging methods and splitting methods. Both make use of an evaluation function, and several alternative functions are illustrated. The methods are evaluated
Consistent digital line segments
, 2009
"... We introduce a novel and general approach for digitalization of line segments in the plane that satisfies a set of axioms naturally arising from Euclidean axioms. In particular, we show how to derive such a system of digital segments from any total order on the integers. As a consequence, using a we ..."
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We introduce a novel and general approach for digitalization of line segments in the plane that satisfies a set of axioms naturally arising from Euclidean axioms. In particular, we show how to derive such a system of digital segments from any total order on the integers. As a consequence, using a
On Random Line Segments in the Unit Square
"... Let Q = [0, 1] × [0, 1] denote the unit square and let Ln be a set of n line segments in Q. Two line segments are said to be crossing if they intersect at any point. A subset of line segments is called noncrossing if no two segments in the subset are crossing. Consider the scenario where the endpo ..."
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Let Q = [0, 1] × [0, 1] denote the unit square and let Ln be a set of n line segments in Q. Two line segments are said to be crossing if they intersect at any point. A subset of line segments is called noncrossing if no two segments in the subset are crossing. Consider the scenario where
Separating and Shattering Long Line Segments
 Information Processing Letters
, 1997
"... this paper we consider the problem of finding separators for a set of linesegments. Clearly this is sufficient to treat the case of general polygonal objects as well. ..."
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Cited by 1 (0 self)
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this paper we consider the problem of finding separators for a set of linesegments. Clearly this is sufficient to treat the case of general polygonal objects as well.
Results 1  10
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7,482