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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42
｜
第
3
章
(
e
,
f
)
，表示两个有向线段
(
p
0
,
p
1
)
和
(
p
1
,
p
2
)
。我们能够使用
(
c
-
a
)*(
f
-
b
) - (
d
-
b
)*(
e
-
a
)
这个式子来计算这两条线段是否共线（也就是在同一条线上）。如果这个式子的结果：
•
等于
0
，那么这两条线段共线。
•
小于
0
，那么这两条线段向左转（或者逆时针）。
•
大于
0
，那么这两条线段向右转（或者顺时针）
。
为了展示了
Java
浮点计算中误差是如何产生的考虑使用表
3-3
中
a
~
f
的值定义
3
个点。
表
3
-
3
：浮点算术误差
32
位单精度浮点数（float）
64
位双精度浮点数（double）
a
= 1/3
0.33333334 0.3333333333333333
b
= 5/3
1.6666666 1.6666666666666667
c
= 33
33.0 33.0
d
= 165
165.0 165.0
e
= 19
19.0 19.0
f
= 95
95.0 95.0
(
c
–
a
)*(
f
–
b
)– (
d
–
b
)*(
e
–
a
)
4.8828125 E–4 -4.547473508864641 E – 13
可以很明显地看出，这
p
0
、
p
1
、
p
2
三个点其实是共线的，而且直线方程是
y
=
5*x
。当使
用浮点数计算判断线段的共线性时，浮点运算中的固有误差影响了浮点运算的结果。使
用
32
位单精度浮点数的时候，计算结果是
0.00048828125
。而使用双精度浮点数（
64
位 ），
计算出来的结果却是一个很小的负数！这个例子生动地展现了无论是 ...
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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.