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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■
279
9
章
計算幾何学
計算幾何学（
computational geometry
）は、幾何学構造とその特性を正確かつ効
率的に計算する数学の応用である。
n
次元問題への自然な拡張があるが、本書では
デカルト平面で表現される
2
次元構造の問題に限る。数学者はこの種の問題に何世
紀も取り組んできたが、
1970
年代からは、システム研究として認知されるように
なった。本章は、計算幾何学問題を解くのに使われる計算論的な抽象化を提示する。
これらの技法は、決して幾何学問題に限られるものではなく、多くの実世界応用で
使われる。
このカテゴリのアルゴリズムは、次のように多くの実世界問題を解く。
凸包
n
個の
2
次元点集合
P
を完全に取り囲む最小の凸形を計算する。これは、
力任せ解の
O(n
4
)
ではなく
O(n log n)
で解ける。
交差線分
n
個の
2
次元線分の集合
S
で、すべての交差を計算する。これは、力任せ
解の
O(n
2
)
ではなく
k
を交差数として
O((n
＋
k)log n)
で解ける。
ボロノイ図
n
個の
2
次元点集合
P
に対する距離に基づいて平面を分割する。
n
個の領
域はそれぞれ、点
p
i
∈
P
に他のどの
p
j
∈
P
よりも近いデカルト点からな
る。これは
O(n log n)
で解ける。
ついでに、上の
3
つの問題すべてを解くのに使われる、強力な
線分走査法
（
Line
Sweep
）を記述する。
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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.