Perhaps a terra approach with glaring deviations from your presented data that might not serve your workflow, and in this case will result in an approximation of 'buffered'. In either case below, the difference in dim must be addressed:
library(terra)
x1a = seq(1,10, by =.01) # first glaring deviation
y1a = seq(1,10, by =.01) # and second
z1a = outer(x1a,y1a)
x1b = seq(1,10,by = 1)
y1b = seq(1,10,by = 1)
z1b = outer(x1b,y1b)
x2 = seq(7,12, by =.01)
y2 = seq(5,12, by =.01)
z2 = outer(x2,y2, FUN = "*")
z1a_apply <- apply(z1a, 2, FUN = 'rev') # get value gradients reversed
z2_apply <- apply(z2, 2, FUN = 'rev') # get value gradients reversed
z1a_rast <- rast(z1a_apply)
z2_rast <- rast(z2_apply)
# these leave origins at (0,0) which is not the case
ext(z2_rast) <- c(701, 1402, 501, 1002)
z1a_z2_crop_ext <- ext(crop(z1a_rast, z2_rast))
z1a_crop <- crop(z1a_rast, z1a_z2_crop_ext)
z2_crop <- crop(z2_rast, z1a_z2_crop_ext)
z1a_z2_mean <- app(c(z1a_crop, z2_crop), mean)
z_sprc <- sprc(z1a_z2_mean, z1a_rast, z2_rast)
z_merge <- merge(z_sprc)
plot(z_merge)
And as will be seen, my fontconfig is broken. So, a partial approach so far.
# picking up with z1b
x1b = seq(1,10,by = 1)
y1b = seq(1,10,by = 1)
z1b = outer(x1b,y1b)
z1b_rast <- rast(z1b)
dim(z1b_rast) <- c(1000, 1000)
# z1b_rast has lost all values
values(z1b_rast) <- outer(c(1:1000),c(1:1000))
# but here the gradient is wrong with high values lower right
z1b_flip <- flip(z1b_rast)
# a picture of a cat might not survive this treatment
# extent, resolution, and origin also have to be adjusted
ext(z1b_flip) <- c(0,1000,0,1000)
res(z1b_flip) <- c(1,1)
origin(z1b_flip) <- c(0.5, 0.5)# should have been done on z2
The subtleties in the 'polygon' approach via line seqments to be addressed next. To better approximate your plot above, points are inset from your segments above by -50.
library(sf)
# using your segments
pts1 <- matrix(c(min(x2),min(y2),max(x1a),min(y2)), nrow = 2, byrow = TRUE)*100
pts2 <- matrix(c(max(x1a),min(y2),max(x1a),max(y1a)), nrow = 2, byrow = TRUE)*100
pts3 <- matrix(c(max(x1a),max(y1a),min(x2),max(y1a)),nrow =2, byrow = TRUE)*100
pts4 <- matrix(c(min(x2),max(y1a),min(x2),min(y2)),nrow = 2, byrow=TRUE)*100
# one point from each line, all inset by 50
pts1_2 <- pts1[2, ] -50
pts2_2 <- pts2[2, ] -50
pts3_2 <- pts3[2, ] -50
pts4_2 <- pts4[2, ] -50
We later find this isn't actually useful compensation as the resulting poly falls outsize our z2_rast, and to avoid general madness it is better to have a poly that is within both rast(s) to pull our mean.
And so adjust out points...
pts1_2[2] <- pts1_2[2] + 75
pts4_2 <- pts4_2 + 75
pts3_2[1] <- pts3_2[1] + 75
poly4 <- st_cast(c(st_point(pts1_2), st_point(pts2_2), st_point(pts3_2), st_point(pts4_2)), 'POLYGON')
#make poly4 a SpatVector
poly4_vect <- vect(poly4)
z1b_poly4_crop <- crop(z1b_flip, poly4_vect)
z2_poly4_crop <- crop(z2_rast, poly4_vect)
#check for damages
all.equal(dim(z1b_poly4_crop), dim(z2_poly4_crop))
[1] TRUE
# Oh, hurray!, But
z1b_z2_poly4_mean <- app(c(z1b_poly4_crop, z2_poly4_crop), mean)
Error in h(simpleError(msg, call)) :
error in evaluating the argument 'x' in selecting a method for function 'app': [rast] extents do not match
ext(z1b_poly4_crop)
SpatExtent : 725.5, 950.5, 525.5, 950.5 (xmin, xmax, ymin, ymax)
ext(z2_poly4_crop)
SpatExtent : 725, 950, 525, 950 (xmin, xmax, ymin, ymax)
# so adjust origin on z2_poly4_crop, or better, on z2 before...
origin(z2_rast)
[1] 0 0
origin(z2_rast) <- c(0.5, 0.5)
z2_poly4_crop <- crop(z2_rast, poly4_vect)
ext(z2_poly4_crop)
SpatExtent : 725.5, 950.5, 525.5, 950.5 (xmin, xmax, ymin, ymax)
# and now can pull mean
z1b_z2_poly4_mean <- app(c(z1b_poly4_crop, z2_poly4_crop), mean)
###
mean_z1b_flip_z2 <- sprc(z1b_z2_poly4_mean, z1b_flip, z2_rast)
mean_z1b_flip_z2_sprc <- sprc(z1b_z2_poly4_mean, z1b_flip, z2_rast)
mean_flip_z2_merge <- merge(mean_z1b_flip_z2_sprc)
# or mosaic - mean goes last and plot
Lots of good fun and rabbit holes to stub one's toes on. There are likely much more compact approaches that others might offer. I imagine that much of this could also be approached through magick.
