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Statements

Subject Item
n2:RIV%2F00216208%3A11320%2F06%3A00003210%21RIV07-MSM-11320___
rdf:type
skos:Concept n11:Vysledek
dcterms:description
Dané dva body p a q v rovině chceme oddělit křivkami C_1 a C_2 tak, aby každý bod na C_1 měl stejnou vzdálenost k p a k C_2 a aby každý bod na C_2 měl stejnou vzdálenost ke q a k C_1. Elementárními geometrickými metodami ukážeme, že takové křivky existují a jsou určeny jednoznačně. Pro p=(0,1) a q=(0,-1) je C_1 grafem jisté funkce f a C_2 je grafem -f. Dokážeme, že f je konvexní analytická funkce, a popíšeme algoritmus, který pro dané x v polynomiálním čase aproximuje f(x) s předepsanou přesností. Given points p and q in the plane, we are interested in separating them by two curves C_1 and C_2 such that every point of C_1 has equal distance to p and to C_2, and every point of C_2 has equal distance to C_1 and to q. We show by elementary geometric means that such C_1 and C_2 exist and are unique. Moreover, for p=(0,1) and q=(0,-1), C_1 is the graph of a function f, C_2 is the graph of -f, and $f$ is convex and analytic. We provide an algorithm that, given x, in polynomial time approximates f(x) with a given precision. Given points p and q in the plane, we are interested in separating them by two curves C_1 and C_2 such that every point of C_1 has equal distance to p and to C_2, and every point of C_2 has equal distance to C_1 and to q. We show by elementary geometric means that such C_1 and C_2 exist and are unique. Moreover, for p=(0,1) and q=(0,-1), C_1 is the graph of a function f, C_2 is the graph of -f, and $f$ is convex and analytic. We provide an algorithm that, given x, in polynomial time approximates f(x) with a given precision.
dcterms:title
The distance trisector curve The distance trisector curve Křivka trisekce vzdálenosti
skos:prefLabel
Křivka trisekce vzdálenosti The distance trisector curve The distance trisector curve
skos:notation
RIV/00216208:11320/06:00003210!RIV07-MSM-11320___
n3:strany
336;343
n3:aktivita
n5:P n5:Z
n3:aktivity
P(1M0545), Z(MSM0021620838)
n3:dodaniDat
n12:2007
n3:domaciTvurceVysledku
n16:3374041
n3:druhVysledku
n9:D
n3:duvernostUdaju
n19:S
n3:entitaPredkladatele
n21:predkladatel
n3:idSjednocenehoVysledku
471935
n3:idVysledku
RIV/00216208:11320/06:00003210
n3:jazykVysledku
n10:eng
n3:klicovaSlova
distance; trisector; curve
n3:klicoveSlovo
n15:trisector n15:distance n15:curve
n3:kontrolniKodProRIV
[2ABEC5ADEEB5]
n3:mistoKonaniAkce
New York, NY, USA
n3:mistoVydani
New York, NY, USA
n3:nazevZdroje
Proc. 38th ACM Symposium on Theory of Computing
n3:obor
n17:BA
n3:pocetDomacichTvurcuVysledku
1
n3:pocetTvurcuVysledku
3
n3:projekt
n18:1M0545
n3:rokUplatneniVysledku
n12:2006
n3:tvurceVysledku
Matoušek, Jiří
n3:typAkce
n22:WRD
n3:zahajeniAkce
2006-01-01+01:00
n3:zamer
n4:MSM0021620838
s:numberOfPages
8
n13:hasPublisher
ACM Press
n20:isbn
1-59593-134-1
n14:organizacniJednotka
11320