August 2017
Intermediate to advanced
360 pages
8h 35m
Chinese
Content preview from 算法技术手册（原书第2 版）
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计算几何
｜
237
计算几何
9.3 凸包扫描
Andrew
发明的
凸包扫描
算法（
1979
）将整个问题分成两个部分：构建一个上凸包和一
个下凸包；将它们组合起来。首先，将点集
P
中的所有点按照
x
坐标排序（
x
坐标相同时，
按照
y
坐标排序）。我们从
P
中的最左边两个点开始构建上凸包，然后就此扩展
凸包扫
描
算法，首先要在
P
中找到这样一个点
p
（
p
∈
P
）
，满足排序后，其前一个位置即上凸
包的最后一个点
L
i
。用类似的方法构建下凸包，然后将其与上凸包加以合并，得到最终
结果。
找到点
p
之后，如果由
L
i
-1
、
L
i
和
p
这三个点组成的两条线段形成了一个右拐的线条，那
么
凸包扫描
算法会把点
p
加入上凸包（或者下凸包）中。这等价于计算图
9-2
中
3
×
3
矩
阵的行列式，也就是计算叉积。如果
cp
< 0
，那么这三个点组成的线段形成了一个右拐
的线条，
凸包扫描
算法继续进行。但是如果
cp
= 0
（即三点共线）或者
cp
> 0
（三点组
成的线段形成了一个左拐的线条），那么中间的点
L
i
将被从凸包中删除，因为这和凸多
边形的性质相冲突。计算出下凸包的思想与此类似，算法最后会将这两个凸包合并在一起。
图 9-2：检查这三个点是否组成右拐的线条
凸包扫描算法小结
最好情况、平均情况和最坏情况：
O(
n
log
n
)
convexHull (P)
sort P ascending by x coordinate (break ties by sorting y)
❶
if n < 3 then return P
upper = {p0, p1}
❷
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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.