计算在一条线上重叠的线段的总和

Question

我正在尝试计算单条线上重叠线段的总和。对于 A 线，线段是不相交的，因此计算起来非常简单。但是，对于 B 线和 C 线，存在重叠的线段，因此更加复杂。我需要以某种方式排除已经占总数一部分的前面几行的部分内容。

data = read.table(text="
    line    left_line   right_line  small_line  left_small_line right_small_line
    A   100 120 101 91  111
    A   100 120 129 119 139
    B   70  90  63  53  73
    B   70  90  70  60  80
    B   70  90  75  65  85
    C   20  40  11  1   21
    C   20  40  34  24  44
    C   20  40  45  35  55", header=TRUE)

这应该是预期的结果。

result = read.table(text="
    total_overlapping
A   0.6
B   0.75
C   0.85", header=TRUE)

编辑：添加了一张图片以更好地说明我想要弄清楚的内容。有 3 种不同的线条图片（红色实线），线段（虚线）重叠。目标是弄清楚有多少虚线覆盖/重叠。

A线

B 行 C线

Answer 1

如果我理解正确，small_line 变量在这里是无关紧要的。其余列可用于获取重叠段的总和：

第 1 步。获取每个线段与对应线重叠的起点和终点：

library(dplyr)

data1 <- data %>%
  rowwise() %>%
  mutate(overlap.start = max(left_line, left_small_line),
         overlap.end = min(right_line, right_small_line)) %>%
  ungroup() %>%
  select(line, overlap.start, overlap.end)

> data1
# A tibble: 8 x 3
  line  overlap.start overlap.end
  <fct>         <int>       <int>
1 A               100         111
2 A               119         120
3 B                70          73
4 B                70          80
5 B                70          85
6 C                20          21
7 C                24          40
8 C                35          40

第 2 步。在与每行对应的行中，按顺序对重叠进行排序。如果它是第一个重叠，或者之前的重叠在它开始之前结束，则认为它是一个新的重叠部分。标记每个新的重叠部分：

data2 <- data1 %>%
  arrange(line, overlap.start, overlap.end) %>%
  group_by(line) %>%
  mutate(new.section = is.na(lag(overlap.end)) | 
           lag(overlap.end) <= overlap.start) %>%
  mutate(section.number = cumsum(new.section)) %>%
  ungroup()

> data2
# A tibble: 8 x 5
  line  overlap.start overlap.end new.section section.number
  <fct>         <int>       <int> <lgl>                <int>
1 A               100         111 TRUE                     1
2 A               119         120 TRUE                     2
3 B                70          73 TRUE                     1
4 B                70          80 FALSE                    1
5 B                70          85 FALSE                    1
6 C                20          21 TRUE                     1
7 C                24          40 TRUE                     2
8 C                35          40 FALSE                    2

第 3 步。在每个重叠部分中，取最早的起点和最晚的终点。计算每个重叠的长度：

data3 <- data2 %>%
  group_by(line, section.number) %>%
  summarise(overlap.start = min(overlap.start),
            overlap.end = max(overlap.end)) %>%
  ungroup() %>%
  mutate(overlap = overlap.end - overlap.start)

> data3
# A tibble: 5 x 5
  line  section.number overlap.start overlap.end overlap
  <fct>          <int>         <dbl>       <dbl>   <dbl>
1 A                  1           100         111      11
2 A                  2           119         120       1
3 B                  1            70          85      15
4 C                  1            20          21       1
5 C                  2            24          40      16

第 4 步。将每条线的重叠长度相加：

data4 <- data3 %>%
  group_by(line) %>%
  summarise(overlap = sum(overlap)) %>%
  ungroup()

> data4
# A tibble: 3 x 2
  line  overlap
  <fct>   <dbl>
1 A          12
2 B          15
3 C          17

现在，您的预期结果显示每行重叠的预期百分比，而不是总和。如果这就是您要查找的内容，您可以将每行的长度添加到 data4，并相应地计算：

data5 <- data4 %>%
  left_join(data %>% 
              select(line, left_line, right_line) %>%
              unique() %>% 
              mutate(length = right_line - left_line) %>%
              select(line, length),
            by = "line") %>%
  mutate(overlap.percentage = overlap / length)

> data5
# A tibble: 3 x 4
  line  overlap length overlap.percentage
  <fct>   <dbl>  <int>              <dbl>
1 A          12     20               0.6 
2 B          15     20               0.75
3 C          17     20               0.85