geosphere/R: Calculate intersection points between two great circles defined with 4 points

Question

I'm trying to use geosphere to calculate intersection points between two great circles that are given in a dataframe format like this:

library(dplyr)
library(geosphere)

df <- data.frame(
  # first line
  ln1_lonb = 1:4,
  ln1_lone = 2:5,
  ln1_latb = 10:13,
  ln1_late = 11:14,
  # second line
  ln2_lonb = 5:8,
  ln2_lone = 6:9,
  ln2_latb = 14:17,
  ln2_late = 15:18
)

I tried using the gcintersect function from geosphere that takes matrices as inputs. In order to use it in a dataframe I used cbind, but seems mutate doesn't work well with this:

df %>% 
  mutate(
    int_points = gcIntersect(
      cbind(ln1_lonb, ln1_latb),
      cbind(ln1_lone, ln1_late),
      cbind(ln2_lonb, ln2_latb),
      cbind(ln2_lone, ln2_late)
    )
  )
>Error: Column `int_points` must be length 4 (the number of rows) or one, not 16

Probably the error is due to getting longer output than expected (the number of rows of the dataframe). So I tried putting it in a list:

df %>% 
  mutate(
    int_points = list(gcIntersect(
      cbind(ln1_lonb, ln1_latb),
      cbind(ln1_lone, ln1_late),
      cbind(ln2_lonb, ln2_latb),
      cbind(ln2_lone, ln2_late)
    ))
  )

Again here I see the output is all combinations instead of getting the 4 coordinates of the 2 points of intersections per row.

Expected output would be a list in a cell in a new column that will contain the coordinates of both points.

Is there a solution without using loops (or purrr) since this will be significantly slower than mutate.

The value for int_points in the first row should be the same as the output of this:

gcIntersect(cbind(1,2), cbind(10,11), cbind(5,6), cbind(14,15))

akrun · Accepted Answer · 2019-08-25T17:19:25.447

2

We can do a rowwise

library(tidyverse)
library(geosphere)
df %>% 
      rowwise %>% 
      mutate( int_points = list(gcIntersect(
        cbind(ln1_lonb, ln1_latb),
        cbind(ln1_lone, ln1_late),
        cbind(ln2_lonb, ln2_latb),
        cbind(ln2_lone, ln2_late)
     ))) %>% 
     ungroup %>%
    mutate(int_points = map(int_points, as_tibble)) %>% 
    unnest(int_points)
# A tibble: 4 x 12
#  ln1_lonb ln1_lone ln1_latb ln1_late ln2_lonb ln2_lone ln2_latb ln2_late  lon1  lat1  lon2  lat2
#     <int>    <int>    <int>    <int>    <int>    <int>    <int>    <int> <dbl> <dbl> <dbl> <dbl>
#1        1        2       10       11        5        6       14       15 -176. -12.6  3.61  12.6
#2        2        3       11       12        6        7       15       16 -175. -13.6  4.60  13.6
#3        3        4       12       13        7        8       16       17 -174. -14.6  5.60  14.6
#4        4        5       13       14        8        9       17       18 -173. -15.6  6.59  15.6

edited Aug 25 '19 at 17:19

answered Aug 25 '19 at 16:58

akrun

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but the output is not correct because this calculates intersection points of all ln1 coordinates (all 4 rows) with all ln2 coordinates(all 4 rows). I updated the question with the expected output – adl Aug 25 '19 at 17:01
@adi I get the same as `with(df, gcIntersect( + cbind(ln1_lonb, ln1_latb), + cbind(ln1_lone, ln1_late), + cbind(ln2_lonb, ln2_latb), + cbind(ln2_lone, ln2_late) + ))` – akrun Aug 25 '19 at 17:10
yes, that would be the correct output. Is there a way to do it with `mutate` somehow ? – adl Aug 25 '19 at 17:13

score 2 · Answer 2 · answered Aug 25 '19 at 19:27

Given that the geosphere methods are vectorized (as one would expect in R), I would do

gcIntersect(df[,c(1,3)], df[,c(2,4)], df[,c(5,7)], df[,c(6,8)])

#          lon1      lat1     lon2     lat2
#[1,] -176.3902 -12.58846 3.609757 12.58846
#[2,] -175.3968 -13.58017 4.603188 13.58017
#[3,] -174.4023 -14.57291 5.597652 14.57291
#[4,] -173.4070 -15.56648 6.592953 15.56648

You could also first reorganize like this

d <- df[,c("ln1_lonb", "ln1_latb", "ln1_lone", "ln1_late", "ln2_lonb", "ln2_latb", "ln2_lone", "ln2_late")]

gcIntersect(d[,c(1,2)], d[,c(3,4)], d[,c(5,6)], d[,c(7:8)])

Or like this

begin1 <- df[,c("ln1_lonb", "ln1_latb")]
end1 <- df[,c("ln1_lone", "ln1_late")]
begin2 <- df[,c("ln2_lonb", "ln2_latb")]
end2 <- df[,c("ln2_lone", "ln2_late")]

gcIntersect(begin1, end1, begin2, end2)

I know you asked specifically for a solution with mutate, but I added these solutions for others that want a clear and simple solution instead.

geosphere/R: Calculate intersection points between two great circles defined with 4 points

2 Answers2