On the Number of Critical Free Contacts of a Convex Polygonal Object Moving in 2
On the Number of Critical Free Contacts of a Convex Polygonal Object Moving in 2
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K 5 is a line segment (a "ladder"), then it is shown in [LS] that the total number of such critical positions of B is 0{n}), which consequently leads to an 0{n^\og n) algorithm for the desired motion planning. If 5 is a convex polygonal object which is free only to translate in V but not to rotate, then the motion planning problem becomes simpler and can be accomplished in time 0{n log n) [KS], [LS2]. This follows from the property, proved in [KS] and related to the problem studied in the prese...nt paper, that the number of free positions of B (all having the same given orientation) at which it simultaneously touches two obstacles is only 0{n) (provided the obstacles are in "general position" [KS]). If 5 is also allowed to rotate then, extending the motion-planning technique of [LS], one obtains an algorithm whose complexity depends on the number of critical free positions of B at which it makes simultaneously three distinct contacts with the walls. Since each such contact is a contact of either a corner of B with a wall edge or of an edge of B with a wall comer, a crude and straightforward upper bound on the number of these critical positions of B is 0{{kny).
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To quickly assess the difficulty of the text, read a short excerpt:
K 5 is a line segment (a "ladder"), then it is shown in [LS] that the total number of such critical positions of B is 0{n}), which consequently leads to an 0{n^\og n) algorithm for the desired motion planning. If 5 is a convex polygonal object which is free only to translate in V but not to rotate, then the motion planning problem becomes simpler and can be accomplished in time 0{n log n) [KS], [LS2]. This follows from the property, proved in [KS] and related to the problem studied in the prese...nt paper, that the number of free positions of B (all having the same given orientation) at which it simultaneously touches two obstacles is only 0{n) (provided the obstacles are in "general position" [KS]). If 5 is also allowed to rotate then, extending the motion-planning technique of [LS], one obtains an algorithm whose complexity depends on the number of critical free positions of B at which it makes simultaneously three distinct contacts with the walls. Since each such contact is a contact of either a corner of B with a wall edge or of an edge of B with a wall comer, a crude and straightforward upper bound on the number of these critical positions of B is 0{{kny).
What to read after On the Number of Critical Free Contacts of a Convex Polygonal Object Moving in 2?
You can find similar books in the "Read Also" column, or choose other free books by D Leven to read onlineMoreLess
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