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Visibility of disjoint polygons (1986)

Asano, Takao ; Asano, Tetsuo ; Guibas, Leonidas ; [et al.]

Springer

Algorithmica 1 (1986), S. 49-63

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ISSN: 1432-0541

Keywords: Computational geometry ; Computer graphics ; Robotics ; Visibility ; Hidden-line Elimination ; Visibility graph ; Shortest path

Source: Springer Online Journal Archives 1860-2000

Topics: Computer Science , Mathematics

Notes: Abstract Consider a collection of disjoint polygons in the plane containing a total ofn edges. We show how to build, inO(n 2) time and space, a data structure from which inO(n) time we can compute the visibility polygon of a given point with respect to the polygon collection. As an application of this structure, the visibility graph of the given polygons can be constructed inO(n 2) time and space. This implies that the shortest path that connects two points in the plane and avoids the polygons in our collection can be computed inO(n 2) time, improving earlierO(n 2 logn) results.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/BF01840436

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Synthesis and ion-coupling reactions of telechelic polystyrene having cyclic onium salt groupsThis paper is dedicated to Professor Teiji Tsuruta in honor of his 75th birthday (1997)

Tezuka, Yasuyuki ; Imai, Hiroshi ; Shiomi, Tomoo

Weinheim : Wiley-Blackwell

Macromolecular Chemistry and Physics 198 (1997), S. 627-641

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ISSN: 1022-1352

Keywords: Chemistry ; Polymer and Materials Science

Source: Wiley InterScience Backfile Collection 1832-2000

Topics: Chemistry and Pharmacology , Physics

Notes: A series of mono- and bifunctional polystyrenes (1 c and 1′c) having 1-methylpyrrolidinium salt end groups were prepared through sequential derivatization, i.e., tosylation and quaternization reactions, of prepolymers having 3-hydroxypropyl groups (1 a and 1′a) produced by end-capping reactions of the relevant living polymers. The 1-methylpyrrolidinium salt end group was found to undergo a selective ring-opening reaction at 100°C by nucleophilic attack of a benzoate counter anion introduced by ion-exchange reaction. The ion-coupling reaction of 1 c and 1′c with poly(styrene-co-acrylate salt) was found to take place upon coprecipitation of an equimolar mixture into methanol to afford ionically linked pseudo-graft and network products, respectively. The subsequent heat treatment, converting the ionic bond into a covalent one, results in branched and crosslinked polystyrene with predetermined structural parameters.

Additional Material: 5 Ill.