December 2016
Intermediate to advanced
440 pages
9h 44m
Japanese
Content preview from アルゴリズムクイックリファレンス 第2版
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9.6
ボロノイ図
■
309
節点を取り除くことにある。問題の円イベントが処理されたとすると、中央の弧、
この場合は
r
1
、は
P
の他の点に対して影響しないので、汀線から取り除くことがで
きる。結果としての汀線の状態を、図9-15の右側の二分木に示す。
汀線
図9-14 3 つの点の後の汀線
円イベント
図9-15 円イベント処理後の汀線
9.6.1
入出力
入力は、平面上の
2
次元点集合である。
フォーチュン走査法
は、
n
個のボロノイ多角形からなるボロノイ図を計算する。各
ボロノイ多角形は、
P
のそれぞれの点に対する領域を定義する。数学的には半無限
領域があるが、アルゴリズムは、
P
のすべての点を囲む適当な大きさの箱の中でボ
ロノイ図を計算することによって、半無限領域を排除する。出力は線分の集合で、
310
■
9
章 計算幾何学
ボロノイ多角形は
P
の各点の周りの時計回りの辺として定義される。
実装によっては、
P
が円を形成する共円（
cocircular
）の
4
点を含まないと仮定す
る。
また別の実装によっては、
2
点が同じ
x
座標または
y
座標を持たないと仮定する。
そうすることによって、多くの特別な場合を取り除ける。これは、入力集合（
x, y
）
が整数値の座標ならたやすく実装できて、
フォーチュン走査法
を呼び出す前に、各
座標に
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I wanted to learn C and C++, but it didn't click for me until I picked up an O'Reilly book. When I went on the O’Reilly platform, I was astonished to find all the books there, plus live events and sandboxes so you could play around with the technology.Addison B.
I’ve been on the O’Reilly platform for more than eight years. I use a couple of learning platforms, but I'm on O'Reilly more than anybody else. When you're there, you start learning. I'm never disappointed.Amir M.
I'm always learning. So when I got on to O'Reilly, I was like a kid in a candy store. There are playlists. There are answers. There's on-demand training. It's worth its weight in gold, in terms of what it allows me to do.