Calculate widest distance between two lines - r

Question

I would like to calculate the mean distance as well as the widest distance between two lines. I know how to find the minimum distance using st_distance() function, but I'm not sure how to find the other two metrics. The red lines are what I believe I would need to measure to find the mean and widest distances between the two lines.
Attached is some example data.
pts1<- data.frame(
x= c(-103.485342, -103.482808),
y = c(31.348758, 31.376947))
) %>%
sf::st_as_sf(coords = c("x","y"))
st_crs(pts1)<- "+init=epsg:2257"
pts2<- data.frame(
x= c(-103.492822, -103.484231),
y = c(31.348181, 31.377191))
) %>%
sf::st_as_sf(coords = c("x","y"))
st_crs(pts2)<- "+init=epsg:2257"
a <- pts1 %>% st_coordinates() %>% st_linestring()
b<- pts2 %>% st_coordinates() %>% st_linestring()
min_dist<-st_distance(a,b,by_element = T)
See second example below. From the image i calculate ~300 meters from the perpendicular line which cross both lines at its maximum.
pts1 <- data.frame(x = c(-103.485342, -103.482808),
y = c(31.348758, 31.376947)) %>%
sf::st_as_sf(coords = c("x","y"))
st_crs(pts1) <- "+proj=longlat +datum=WGS84"
pts1<- st_transform(pts1,"+init=epsg:2257")
pts2 <- data.frame(x = c(-103.492812, -103.484231),
y = c(31.318181, 31.377991)) %>%
sf::st_as_sf(coords = c("x","y"))
st_crs(pts2) <- "+proj=longlat +datum=WGS84"
pts2<- st_transform(pts2,"+init=epsg:2257")
a <- pts1 %>% st_coordinates() %>% st_linestring()
b <- pts2 %>% st_coordinates() %>% st_linestring()
st_distance(pts1, pts2, by_element = T)

Answer 1

I'll give you an insight, maybe this is not a complete answer you would imagine.
As lines are made of points, if you just make two slightly changes, you can have not only min distance, but also max distance by doing the same thing you did with the lines, but with the points from which the lines are comprised.
library(sf)
#> Linking to GEOS 3.8.0, GDAL 2.4.2, PROJ 6.2.1
pts1 <- data.frame(x = c(-103.485342, -103.482808),
y = c(31.348758, 31.376947)) %>%
sf::st_as_sf(coords = c("x","y"))
st_crs(pts1) <- "+init=epsg:2257"
pts2 <- data.frame(x = c(-103.492822, -103.484231),
y = c(31.348181, 31.377191)) %>%
sf::st_as_sf(coords = c("x","y"))
st_crs(pts2)<- "+init=epsg:2257"
a <- pts1 %>% st_coordinates() %>% st_linestring()
b <- pts2 %>% st_coordinates() %>% st_linestring()
st_distance(pts1, pts2, by_element = T)
#> Units: [US_survey_foot]
#> [1] 0.007502222 0.001443768
For having the mean distance, I am not sure if this is what you want, but I think you can obtain the centroid of both lines and then process st_distance.
ca <- st_centroid(a)
cb <- st_centroid(b)
st_distance(ca, cb, by_element = T)
#> [1] 0.004454613
EDIT: my last try based on comment
I think you can maybe have what you're trying to have if you find the longest line (b in your example), than process and find the longest distance between the points of the shorter line and the longest line itself:
(I also made some changes to your original code to make it works)
library(sf)
pts1 <- data.frame(x = c(-103.485342, -103.482808),
y = c(31.348758, 31.376947)) %>%
st_as_sf(coords = c("x","y")) %>%
st_set_crs(4326) %>%
st_transform(2257)
pts2 <- data.frame(x = c(-103.492812, -103.484231),
y = c(31.318181, 31.377991)) %>%
st_as_sf(coords = c("x","y")) %>%
st_set_crs(4326) %>%
st_transform(2257)
a <- pts1 %>%
st_union(.) %>%
st_cast(to = "LINESTRING")
b <- pts2 %>%
st_union(.) %>%
st_cast(to = "LINESTRING")
longest <- ifelse(test = st_length(a) > st_length(b),
yes = quote(a),
no = quote(b))
max(st_distance(pts1, eval(longest)))
#> 955.7374 [US_survey_foot]