R - Coordinates of lines intersections in a plot

The sructure of the
data is the following

df1 <- structure(list(V2 = 1:10, V1 = c(1.4, 1.5, 1.9, 4.5, 6.7, 7.8, 
8.1, 8.2, 8.3, 8.9)), class = "data.frame", row.names = c(NA, -10L))

df2 <- structure(list(V2 = 1:10, V1 = c(1.43390152077191, 2.30610947613604, 
2.23775280718692, 5.41628585802391, 7.05710641788319, 8.77536501311697, 
8.48437852263451, 8.68867353517562, 8.7907762312796, 8.91225462416187
)), row.names = c(NA, -10L), class = "data.frame")

df3 <- structure(list(V2 = 1:10, V1 = c(2.04147320063785, 2.01257497165352, 
2.22035211822949, 5.08143315766938, 7.31734440829605, 8.23827453767881, 
8.27036898061633, 8.91508049662225, 9.04778654868715, 9.74391470812261
)), row.names = c(NA, -10L), class = "data.frame")

I build a plot and receive the following image.

dplyr::bind_rows(df1 = df1, df2 = df2, df3 = df3, .id = "id") %>%
  ggplot() +  aes(V2, V1, color = id) + 
  geom_line() + 
  theme(legend.position = "bottom")

Some of the lines intersect, but those intersections are probably not in the dataframes. Is it possible to find out the coordinates of intersections?

You can find the coordinates if you to make the data an sf object, and treat it as spatial data.

Adding on to the code you posted:

library(sf)

df4 <- dplyr::bind_rows(df1 = df1, df2 = df2, df3 = df3, .id = "id")

df4_sf <- df4 %>%
  st_as_sf(coords = c('V2', 'V1')) %>%
  group_by(id) %>% 
  summarise(zz = 1) %>%  ## I'm not sure this line is needed.
  st_cast('LINESTRING')

# > df4_sf
# Simple feature collection with 3 features and 2 fields
# geometry type:  LINESTRING
# dimension:      XY
# bbox:           xmin: 1 ymin: 1.4 xmax: 10 ymax: 9.743915
# epsg (SRID):    NA
# proj4string:    NA
# # A tibble: 3 x 3
# id       zz                                                                                  geometry
# * <chr> <dbl>                                                                              <LINESTRING>
# 1 df1       1                   (1 1.4, 2 1.5, 3 1.9, 4 4.5, 5 6.7, 6 7.8, 7 8.1, 8 8.2, 9 8.3, 10 8.9)
# 2 df2       1 (1 1.433902, 2 2.306109, 3 2.237753, 4 5.416286, 5 7.057106, 6 8.775365, 7 8.484379, 8...
# 3 df3       1 (1 2.041473, 2 2.012575, 3 2.220352, 4 5.081433, 5 7.317344, 6 8.238275, 7 8.270369, 8...

Now there are three rows, each representing one of the original df's.

A plot using geom_sf showing that it's still the same:

 ggplot(df4_sf) + geom_sf(aes(color = id)) + theme(legend.position = 'bottom')

We see that only 2 & 3 intersect, so we'll look at just those two.

intersections <- st_intersections(df4_sf[2,], df4_sf[3,])
st_coordinates(intersections)

#            X        Y L1
#[1,] 1.674251 2.021989  1
#[2,] 4.562692 6.339562  1
#[3,] 5.326387 7.617924  1
#[4,] 7.485925 8.583651  1

And finally plot everything together:

ggplot() +
  geom_sf(data = df4_sf, aes(color = id)) + 
  geom_sf(data = intersections) +
  theme(legend.position = 'bottom')

Gives us this plot:

Assuming that V2 is discrete and all data.frames share the same values for V2, another option is using optim to find the intersections within each sub-range:

options(digits=20)
funcLs <- lapply(list(df1, df2, df3), function(DF) approxfun(DF$V2, DF$V1))    
X <- df1$V2

Filter(Negate(is.null), unlist(combn(funcLs, 2L, FUN=function(funcs) {
    mapply(function(lower, upper) {
        res <- optim((lower+upper)/2, function(x) abs(funcs[[1L]](x) - funcs[[2L]](x)), 
            method="Brent", lower=lower, upper=upper, control=list(reltol=1e-10))
        if (res$value < 1e-4 && res$convergence==0L) return(res$par)
    }, X[-length(X)], X[-1L])
}, simplify=FALSE), recursive=FALSE))

output:

[[1]]
[1] 1.67425093704201

[[2]]
[1] 4.5626919006160991

[[3]]
[1] 5.3263874397151056

[[4]]
[1] 7.4859253126769065

checks:

sapply(ans, function(x) all.equal(funcLs[[2L]](x), funcLs[[3L]](x)))
#[1] TRUE TRUE TRUE TRUE