How to convert projected coordinates back to lat and long

I am working with lat long coordinates in R. First I need to transform my coordinates to zone 17 and then add some buffer to them. For that I used next code (the data used is in orig_coords ):

library(sp)
library(rgdal)
library(rgeos)

orig_coords <- data.frame(lat=-0.1848787,lon=-78.48179)

LongLatToUTM<-function(x,y,zone){
  
  xy <- data.frame(ID = 1:length(x), X = x, Y = y)
  
  coordinates(xy) <- c("X", "Y")
  
  proj4string(xy) <- CRS("+proj=longlat +datum=WGS84")  ## for example
  
  res <- spTransform(xy, CRS(paste("+proj=utm +south=T +zone=",zone," ellps=WGS84",sep='')))
  
  #return(as.data.frame(res))
  return(res)
  
}
#Res
res <- LongLatToUTM(orig_coords$lon,orig_coords$lat,17)
#Add buffer
pc2km <- gBuffer( res, width=2000, byid=TRUE )
#Bounding box
bb <- pc2km@bbox

With that I got the bounding box which contains the projected coordinates with the buffer added to them:

bb
        min       max
x  778303.1  782303.1
y 9977545.5 9981545.5

My question is how can I transform the min and max coordinates from bb back to latitude and longitude? Many thanks.

Solution

Here is the answer using sf:

orig_coords <- data.frame(lat=-0.1848787,lon=-78.48179)

library(sf)

# Create the sf object for the points
orig_sf <- st_sfc(st_point(c(orig_coords$lon, orig_coords$lat)), crs = "epsg:4326")
> orig_sf
Geometry set for 1 feature 
Geometry type: POINT
Dimension:     XY
Bounding box:  xmin: -78.48179 ymin: -0.1848787 xmax: -78.48179 ymax: -0.1848787
Geodetic CRS:  WGS 84
POINT (-78.48179 -0.1848787)

# Transform to 32617 based on "+proj=utm +south=T +zone=17 +ellps=WGS84" and https://epsg.io/32717
utm_sf <- st_transform(orig_sf, crs = "epsg:32717")
> utm_sf
Geometry set for 1 feature 
Geometry type: POINT
Dimension:     XY
Bounding box:  xmin: 780303.1 ymin: 9979545 xmax: 780303.1 ymax: 9979545
Projected CRS: WGS 84 / UTM zone 17S
POINT (780303.1 9979545)

# Create buffer
utm_buff_sf <- st_buffer(utm_sf, 2000)

# Print buffer coordinates. You can also see them in the object itself
st_bbox(utm_buff_sf)
     xmin      ymin      xmax      ymax 
 778303.1 9977545.5  782303.1 9981545.5 

# Transform back to lat & long
latlon_sf <- st_transform(utm_buff_sf, crs = "epsg:4326")
st_bbox(latlon_sf)
       xmin        ymin        xmax        ymax 
-78.4997462  -0.2029557 -78.4638340  -0.1668017

And this is the answer with terra:

library(terra)

# Could also use vect(<sf object>), if the sf object already exists.
orig_te <- vect(orig_coords, crs = "epsg:4326")
> orig_te
 class       : SpatVector 
 geometry    : points 
 dimensions  : 1, 0  (geometries, attributes)
 extent      : -78.48179, -78.48179, -0.1848787, -0.1848787  (xmin, xmax, ymin, ymax)
 coord. ref. : lon/lat WGS 84 (EPSG:4326) 

# "Transform" 
utm_te <- project(orig_te, y = "epsg:32717")

# Buffer
buff_te <- buffer(utm_te, 2000)

# Get bounding box
bbox_te <- ext(buff_te)
bbox_te
SpatExtent : 778303.140207565, 782303.140207565, 9977545.46221348, 9981545.46221348 (xmin, xmax, ymin, ymax)

# Transform back to lat & long
latlon_te <- project(buff_te, y = "epsg:4326")
ext(latlon_te)
SpatExtent : -78.4997462383223, -78.4638340108377, -0.202955733632546, -0.16680166596275 (xmin, xmax, ymin, ymax)

The coordinates of the projected buffer's bounding box using either sf::st_transform() or terra::project() match those of the coordinates supplied with your custom function.