extensive-intensive.R

library(sf)
library(sfheaders)

# define polygon coords
m <- matrix(
  c(2, -2, 2, 2, -2, 2, -2, -2, 2, -2),
  ncol = 2, byrow = TRUE
) 

# create polygon from matrix
p1 <- sfc_polygon(m)

# overlapping area of 4
m2 <- m + 2
p2 <- sfc_polygon(m2) 
v2 <- 3 # intensive value for polygon

# overlapping area of 1
m3 <- matrix(
  c(
    -1, -3,
    -1, -1,
    -3, -1,
    -3, -3,
    -1, -3
  ), ncol = 2, byrow = TRUE
)
p3 <- sfc_polygon(m3)
v3 <- 12 # intensive value for polygon

# view them all together 
plot(c(p1, p2, p3))

# join candidates
cands <- st_sf(v = c(v2, v3), geometry = c(p2, p3))

# target
tar <- st_sf(geometry = p1)

# intensive interpolation returns 4.8
st_interpolate_aw(cands, tar, FALSE)

# create intersection of overlaps:
overlap <- st_intersection(cands, tar)

# weighted mean where the value is weighted by overlapping area
# divided by the area of the target
weighted.mean(
  cands$v,
  st_area(overlap) / st_area(tar)
)

# to replicate the extensive value
w <- st_area(overlap) / st_area(tar)
sum(cands$v * w) 
st_interpolate_aw(cands, tar, TRUE)


w <- st_area(overlap) / st_area(cands)

sum( cands$v) 

weighted.mean(
  cands$v,
  st_area(overlap) / st_area(cands)
)