Calculating total sum of line segments overlapping on a line - r

Question

I'm trying to calculate the total sum of overlapping line segments across a single line. With line A, the segments are disjointed, so it's pretty simple to calculate. However, with lines B and C, there are overlapping line segments, so it's more complicated. I would need to somehow exclude parts of the previous lines that already part of the total sum.
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)
This should be the expected result.
result = read.table(text="
total_overlapping
A 0.6
B 0.75
C 0.85", header=TRUE)
EDIT: Added a picture to better illustrate what I'm trying to figure out. There's 3 different pictures of lines (solid red line), with line segments (the dashed lines) overlapping. The goal is to figure out how much of the dashed lines are covering/overlapping.
Line A
Line B
Line C

Answer 1

If I understand correctly, the small_line variable is irrelevant here. The rest of the columns can be used to get the sum of overlapping segments:
Step 1. Get the start & end point for each segment's overlap with the corresponding line:
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
Step 2. Within the rows corresponding to each line, sort the overlaps in order. consider it a new overlapping section if it is the first overlap, OR the previous overlap ends before it started. Label each new overlapping section:
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
Step 3. Within each overlapping section, take the earliest starting point & the latest ending point. Calculate the length of each overlap:
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
Step 4. Sum the length of overlaps for each line:
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
Now, your expected result shows the expected percentage of overlap on each line, rather than the sum. If that's what you are looking for, you can add the length for each line to data4, & calculate accordingly:
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