An Algorithm for Computing the Convex Hull of a Set of Imprecise Line Segment Intersection

2014 ◽  
Vol 7 (3) ◽  
pp. 55-61
Author(s):  
Keivan Borna ◽  
Morteza Asadi
Keyword(s):  
Convex Hull ◽  
Line Segment ◽  
Line Segment Intersection

An Efficient Improved Algorithm of Convex Hull

2014 ◽  
Vol 602-605 ◽  
pp. 3104-3106
Author(s):  
Shao Hua Liu ◽  
Jia Hua Zhang
Keyword(s):  
Convex Hull ◽  
Line Segment ◽  
Main Idea ◽  
Discrete Point ◽  
Directed Line ◽  
Generation Algorithm ◽  
Simple Program ◽  
Point Set ◽  
High Computational Efficiency ◽  
Improved Algorithm

This paper introduced points and directed line segment relation judgment method, the characteristics of generation and Graham method using the original convex hull generation algorithm of convex hull discrete points of the convex hull, an improved algorithm for planar discrete point set is proposed. The main idea is to use quadrilateral to divide planar discrete point set into five blocks, and then by judgment in addition to the four district quadrilateral internally within the point is in a convex edge. The result shows that the method is relatively simple program, high computational efficiency.

Line Segment Intersection

1997 ◽  
pp. 19-43
Author(s):  
Mark de Berg ◽  
Marc van Kreveld ◽  
Mark Overmars ◽  
Otfried Schwarzkopf
Keyword(s):  
Line Segment ◽  
Line Segment Intersection

scholarly journals Line Segment Intersection Testing

Computing ◽  
2005 ◽  
Vol 75 (4) ◽  
pp. 337-357 ◽  
Author(s):  
Y.-K. Zhu ◽  
J.-H. Yong ◽  
G.-Q. Zheng
Keyword(s):  
Line Segment ◽  
Line Segment Intersection

MINIMUM POLYGON TRANSVERSALS OF LINE SEGMENTS

1995 ◽  
Vol 05 (03) ◽  
pp. 243-256 ◽  
Author(s):  
DAVID RAPPAPORT
Keyword(s):  
Convex Hull ◽  
General Problem ◽  
Line Segment ◽  
Simple Polygon ◽  
Fixed Number ◽  
Line Segments ◽  
Geometric Objects ◽  
Finite Set ◽  
Minimum Perimeter ◽  
Set Of Points

Let S be used to denote a finite set of planar geometric objects. Define a polygon transversal of S as a closed simple polygon that simultaneously intersects every object in S, and a minimum polygon transversal of S as a polygon transversal of S with minimum perimeter. If S is a set of points then the minimum polygon transversal of S is the convex hull of S. However, when the objects in S have some dimension then the minimum polygon transversal and the convex hull may no longer coincide. We consider the case where S is a set of line segments. If the line segments are constrained to lie in a fixed number of orientations we show that a minimum polygon transversal can be found in O(n log n) time. More explicitely, if m denotes the number of line segment orientations, then the complexity of the algorithm is given by O(3mn+log n). The general problem for line segments is not known to be polynomial nor is it known to be NP-hard.

Line Segment Intersection

2000 ◽  
pp. 19-43 ◽  
Author(s):  
Mark de Berg ◽  
Marc van Kreveld ◽  
Mark Overmars ◽  
Otfried Cheong Schwarzkopf
Keyword(s):  
Line Segment ◽  
Line Segment Intersection

SCALABLE ALGORITHMS FOR BICHROMATIC LINE SEGMENT INTERSECTION PROBLEMS ON COARSE GRAINED MULTICOMPUTERS

1996 ◽  
Vol 06 (04) ◽  
pp. 487-506 ◽  
Author(s):  
ANDREAS FABRI ◽  
OLIVIER DEVILLERS
Keyword(s):  
Line Segment ◽  
Time Complexity ◽  
Coarse Grained ◽  
Log P ◽  
Scalable Algorithms ◽  
Interprocessor Communication ◽  
Additional Time ◽  
Sequential Computation ◽  
Communication Time ◽  
Line Segment Intersection

We present output-sensitive scalable parallel algorithms for bichromatic line segment intersection problems for the coarse grained multicomputer model. Under the assumption that n≥p2, where n is the number of line segments and p the number of processors, we obtain an intersection counting algorithm with a time complexity of [Formula: see text], where Ts(m, p) is the time used to sort m items on a p processor machine. The first term captures the time spent in sequential computation performed locally by each processor. The second term captures the interprocessor communication time. An additional [Formula: see text] time in sequential computation is spent on the reporting of the k intersections. As the sequential time complexity is O(n log n) for counting and an additional time O(k) for reporting, we obtain a speedup of [Formula: see text] in the sequential part of the algorithm. The speedup in the communication part obviously depends on the underlying architecture. For example for a hypercube it ranges between [Formula: see text] and [Formula: see text] depending on the ratio of n and p. As the reporting does not involve more interprocessor communication than the counting, the algorithm achieves a full speedup of p for k≥ O( max (n log n log p, n log 3 p)) even on a hypercube.

Sign in / Sign up

Export Citation Format

Share Document