Rasterizing a grid of points causes empty raster cells and misalignement between points and raster cells

Question

I have a set of coordinates supposed to be at the centroïds of a grid of 5km x 5km cells and an attached value (subsample provided at the end of this post as a “df” data.frame). I would like to create a 5km raster based on these coordinates.

I tried to do that both with stars and terra packages but I encounter the same problems : the points are not at the centroïd of the raster cells and some empty cells are created where they should be some value.

I’m uncertain about the crs : could be 4326 or 4258 but using one or the other does not change my problems.

library(terra)
library(stars)
library(sf)
library(mapview)
library(leaflet)

Example with terra package

points <- vect(df, crs = "EPSG:4258")
points <- vect(df, crs = "EPSG:4326") # not certain which one is right one
# project in a local metric crs
points <- project(points, "EPSG:31370")


# Create a raster template and rasterize the points
r_template <- rast(ext(points), resolution = 5000, crs = crs(points))
r <- rasterize(points, r_template, field = "value")

# Four of the raster cells are empty while they should not be
# The points are not at the centroid of the cells

# x11(width = 8/2.54, height = 14/2.54)
my_lims <- as.vector(ext(r)) + c(-10000, 10000, -10000, 10000)
plot(r, xlim = my_lims[1:2], ylim = my_lims[3:4])
plot(points, col ="red", add = T, cex = 0.6)

I remember that there was a problem when plotting rasters and points with mapview, however both these code chunks provide similar results

mapview::mapview(r) + mapview::mapview(points)

leaflet() |> 
    addProviderTiles(providers$CartoDB.Positron) |>
    addRasterImage(project(r, "EPSG:3857"), project = FALSE) |> 
    addCircles(data = project(points, "EPSG:4326"))

Maybe the problem comes from the fact that the points are not at the centroïd of the cells but at one of the corners ? I tried to correct that as if it was the bottom left corner but it does not work either

# Shift the coordinates by 2500 meters
tmp <- cbind(df, x = geom(points)[,"x"] - 2500, 
             y = geom(points)[,"y"] - 2500) 
tmp <- tmp[,c("x", "y", "value")]
tmp <- vect(tmp, c("x", "y"), crs = "EPSG:31370")

# Rasterize the variable values
r_template <- rast(ext(tmp), resolution = 5000, crs = crs(tmp))
r <- rasterize(tmp, r_template, field = "value")

# x11(width = 8/2.54, height = 14/2.54)
my_lims <- as.vector(ext(r)) + c(-10000, 10000, -10000, 10000)
plot(r, xlim = my_lims[1:2], ylim = my_lims[3:4])
plot(points, col ="red", add = T, cex = 0.6)

Note that the real distance between points (after projection) is not exactly 5km but rather between 5000 and 5015 meters. Could that be the source of the problem ?

my_dist <- distance(points, points)
my_dist <- my_dist[upper.tri(my_dist)]
my_dist[my_dist<6000] |> round(1) |> table() 
#> 
#> 5000.5 5000.6 5000.7 5000.8 5000.9   5001 5001.1 5001.2 5001.3 5001.4 5001.5 
#>      4     16     29     23     22     32     37     31     34     32     36 
#> 5001.6 5001.7 5001.8 5001.9   5002 5002.1 5002.2 5002.3 5002.4 5002.5 5014.7 
#>     29     35     19     31     22     29     18      9      3      1     10 
#> 5014.8 5014.9   5015 5015.1 5015.2 5015.3 5015.4 5015.5 
#>     54     63     80     74     73     57     49      6

Example with stars and sf packages :

# Create point vector objects and project it in a metric crs (31370 is typical for this area)
points <- st_as_sf(df,  coords = c("lon", "lat"), crs = 4258)
points <- st_transform(points, 31370)

# Create a raster template and rasterize the points
r_template <- st_as_stars(st_bbox(points), values = NA, 
                          dx = 5000, dy = 5000, 
                          crs = st_crs(points))
r <- st_rasterize(points, template = r_template)

# for some reason, I'm not able to add the points on top of the 
# raster despite their crs being the same
# But at least the two empty cells arevisible

# x11(width = 8/2.54, height = 14/2.54)
plot(r)
plot(st_geometry(points), col ="red", add = T, reset = F)

st_crs(r) == st_crs(points)
#> [1] TRUE

mapview::mapview(r) + mapview::mapview(points)

---

Edit : trying to use rast with type = xyz on a regular grid

Based on Robert Hijmans's answer and after finding the right projection to get the original 5km grid

# The original projection used to create the grid seems to be : 
my_proj <- "+proj=lcc +lat_2=50.569898649999999 +lat_1=50.569898649999999 +lon_0=4.553615160000000 +units=m +no_defs +a=6371229.0 +es=0.0"
points <- vect(df, crs = "EPSG:4326") 
points <- project(points, my_proj)

# The distances are then exactly 5000m 
# 
# Small differences were due to the fact that I rounded the long lat values 
# to 7 decimals to save space.
# I have now updated the df dump to keep all the decimals
my_dist <- distance(points, points)
my_dist <- my_dist[upper.tri(my_dist)]
my_dist[my_dist<6000] |> round(1) |> table() 

#> [1] 5000 
#> [2] 958 

# Using type = xyz as we have now a perfectly regular grid
# the problem seems to be that we don't have a square grid so we need to 
# impute NA values which seems impossible 
tmp <- data.frame(geom(points)[,c("x","y")], value = df[,"value"])
rast(tmp, type = "xyz", crs = my_proj, digits = 0)

#> [1] Error in v[cells, ] <- xyz[, -c(1:2)] : 
#> [2]  NAs interdits dans les affectations indicées

---

Sample of the data.frame for this reprex :

df <- 
structure(list(lon = c(5.4191010793597, 5.48833289530293, 5.55756308279838, 
5.62679152130563, 5.41990964531345, 5.48920612673468, 5.55850097514038, 
5.62779406965214, 5.69708528940996, 5.76637451357343, 5.83566162132305, 
5.28199275995389, 5.35135693922935, 5.42071972338989, 5.49008099118482, 
5.55944062137935, 5.62879849275588, 5.69815448411525, 5.76750847427803, 
5.83686034208576, 5.90620996640225, 5.28267452673745, 5.3521036218039, 
5.4215313178346, 5.49095749323822, 5.5603820264394, 5.62980479588006, 
5.69922568002064, 5.76864455734138, 5.83806130634364, 5.9074758055511, 
5.14436558491735, 5.21386215746602, 5.28335757095296, 5.35285170341665, 
5.42234443290906, 5.49183563749693, 5.56132519526307, 5.63081298430763, 
5.70029888274937, 5.76978276872696, 5.83926452040024, 5.90874401595155, 
5.07535680221645, 5.14491958098964, 5.21448131975452, 5.28404189619397, 
5.35360118800314, 5.42315907289072, 5.49271542858026, 5.56227013281143, 
5.63182306334134, 5.70137409794578, 5.77092311442057, 5.84046999058279, 
5.91001460427209, 5.00621755632929, 5.07584654683406, 5.14547461707207, 
5.2151016443705, 5.28472750606753, 5.35435207951369, 5.42397524207311, 
5.49359687112486, 5.56321684406418, 5.63283503830384, 5.7024513312754, 
5.77206560043051, 5.84167772324221, 5.00664280448114, 5.07633721172005, 
5.14603069609593, 5.21572313458991, 5.28541440419422, 5.35510438191345, 
5.42479294476589, 5.49447996978479, 5.56416533401972, 5.63384891453779, 
5.70353058842503, 5.77321023278765, 5.0070688524688, 5.07682879947071, 
5.14658782100352, 5.21634579370107, 5.28610259420827, 5.35585809918252, 
5.42561218529491, 5.49536472923165, 5.56511560769525, 5.63486469740593, 
5.70461187510286, 5.77435701754552, 5.00749570255096, 5.07732131269208, 
5.14714599474825, 5.21696962500464, 5.28679207975758, 5.35661323531593, 
5.42643296800233, 5.49625115415457, 5.56606767012687, 5.63588239229119, 
5.70569519703858, 5.77550596078043, 5.00792335699478, 5.07781475400005, 
5.14770522029463, 5.21759463181373, 5.28748286450379, 5.3573697943238, 
5.42725529724665, 5.4971392492604, 5.56702152636964, 5.6369020045968, 
5.70678055998344, 5.77665706859161, 5.84653140650517, 5.00835181807602, 
5.07830912602036, 5.14826550061836, 5.21822081745395, 5.28817495212235, 
5.35812778023138, 5.42807917740282, 5.49802901927371, 5.5679771814977, 
5.63792353974632, 5.70786796971039, 5.77781034710127, 5.84775054765223, 
5.008781088079, 5.07880443138867, 5.14882683870639, 5.21884818526348, 
5.2888683463026, 5.35888719707909, 5.42890461286231, 5.49892046893693, 
5.56893464060431, 5.63894700318383, 5.70895743201418, 5.77896580245472, 
5.84897198988682, 5.0092111692967, 5.0793006727506, 5.14938923755693, 
5.21947673859308, 5.28956305074781, 5.35964804892264, 5.42973160803316, 
5.49981360301037, 5.56989390880202, 5.63997240037395, 5.71004895271143, 
5.7801234408205, 5.85019573972927, 5.92026572448933, 5.00964206403074, 
5.07979785276178, 5.14995270017957, 5.22010648080621, 5.29025906917526, 
5.36041033983307, 5.43056016734012, 5.50070842627239, 5.57085499122269, 
5.64099973680199, 5.71114253764079, 5.78128326839046, 5.85142180372457, 
5.92155801834023, 5.99169178695944, 5.0100737745915, 5.08029597408789, 
5.15051722959525, 5.22073741527907, 5.29095640531632, 5.36117407389684, 
5.43139029522467, 5.50160494351942, 5.5718178930176, 5.64202901797399, 
5.71223819266298, 5.78244529137992, 5.85265018844247, 5.92285275819194, 
5.99305287499466, 5.01050630329807, 5.08079503940472, 5.15108282883641, 
5.22136954540064, 5.29165506291648, 5.36193925521588, 5.43222199614512, 
5.50250315956605, 5.57278261935757, 5.6430602494169, 5.71333592366095, 
5.78360951602772, 5.8538809004776, 5.92414995099479, 5.99441654158857, 
5.01093965247837, 5.0812950513982, 5.15164950094694, 5.22200287457277, 
5.29235504573544, 5.36270588790771, 5.43305527457669, 5.50340307924517, 
5.57374917543303, 5.64409343667858, 5.71443573653993, 5.78477594859635, 
5.85511394644963, 5.92544960372546, 5.99578279407474, 5.01137382446915, 
5.08179601276448, 5.15221724898234, 5.2226374062102, 5.29305635754718, 
5.36347397610546, 5.4338901350116, 5.50430470740797, 5.57471756645409, 
5.64512858532799, 5.7155376372276, 5.78594459537211, 5.85634933300333, 
5.9267517233871, 5.99715163981458, 5.01180882161605, 5.08229792620993, 
5.15278607600968, 5.22327314374068, 5.29375900214004, 5.36424352395796, 
5.43472658195914, 5.50520804892412, 5.57568779765069, 5.64616570095523, 
5.71664163167414, 5.78711546266514, 5.85758706680872, 5.92805631700947, 
5.99852308619747, 5.01224464627361, 5.08280079445125, 5.15335598510773, 
5.223910090605, 5.29446298331674, 5.36501453562986, 5.43556461994575, 
5.50611310868179, 5.57665987427264, 5.64720478917168, 5.71774772585236, 
5.78828855680961, 5.85882715456118, 5.92936339164907, 5.99989714064088, 
5.01268130080536, 5.08330462021545, 5.15392697936697, 5.22454825025701, 
5.29516830489451, 5.36578701530162, 5.43640425351511, 5.50701989158776, 
5.57763380158975, 5.64824585561006, 5.71885592575784, 5.78946388416379, 
5.86006960298159, 5.93067295438925, 5.01311878758384, 5.08380940623996, 
5.15449906188965, 5.22518762616379, 5.29587497070511, 5.36656096716967, 
5.4372454872282, 5.50792840256751, 5.57860958489191, 5.64928890592458, 
5.71996623740896, 5.79064145111018, 5.86131441881643, 5.93198501234035, 
5.01355710899062, 5.08431515527264, 5.15507223578988, 5.22582822180558, 
5.29658298459492, 5.36733639544643, 5.43808832566342, 5.50883864656533, 
5.57958722948919, 5.65033394579099, 5.72107866684709, 5.79182126405562, 
5.86256160883791, 5.93329957263982, 5.01399626741639, 5.08482187007185, 
5.15564650419364, 5.22647004067596, 5.29729235042501, 5.36811330436042, 
5.43893277341664, 5.50975062854436, 5.58056674071192, 5.65138098090672, 
5.72219322013664, 5.79300332943141, 5.86381117984408, 5.93461664245237, 
5.01443626526097, 5.0853295534065, 5.15622187023888, 5.22711308628184, 
5.29800307207122, 5.3688916981563, 5.4397788351013, 5.51066435348672, 
5.58154812391081, 5.65243001699099, 5.72330990336521, 5.79418765369343, 
5.86506313865899, 5.93593622897005, 5.01487710493335, 5.08583820805609, 
5.15679833707553, 5.22775736214356, 5.2987151534242, 5.369671581095, 
5.44062651534849, 5.51157982639359, 5.58253138445706, 5.65348105978488, 
5.72442872264369, 5.79537424332224, 5.86631749213277, 5.93725833941246, 
5.01531878885177, 5.08634783681076, 5.15737590786561, 5.22840287179493, 
5.29942859838951, 5.37045295745373, 5.44147581880703, 5.51249705228532, 
5.58351652774241, 5.65453411505144, 5.72554968410634, 5.79656310482321, 
5.86757424714178, 5.93858298102681, 5.01576131944373, 5.08685844247134, 
5.15795458578325, 5.22904961878333, 5.30014341088769, 5.37123583152613, 
5.44232675014357, 5.51341603620146, 5.58450355917926, 5.65558918857585, 
5.72667279391097, 5.79775424472667, 5.86883341058873, 5.93991016108809, 
5.01620469914603, 5.08737002784944, 5.15853437401476, 5.22969760666971, 
5.3008595948543, 5.3720202076223, 5.44317931404265, 5.51433678320094, 
5.58549248420081, 5.65664628616544, 5.72779805823897, 5.01664893040486, 
5.08788259576743, 5.15911527575869, 5.23034683902874, 5.30157715424005, 
5.3728060900689, 5.44403351520682, 5.51525929836208, 5.58648330826108, 
5.65770541364986, 5.01709401567579, 5.08839614905856, 5.15969729422588, 
5.2309973194488, 5.30229609301079, 5.37359348320919, 5.44488935835669, 
5.51618358678274, 5.58747603683509, 5.65876657688116, 5.73005507530954, 
5.01753995742386, 5.08891069056698, 5.16028043263955, 5.23164905153211, 
5.30301641514768, 5.3743823914032, 5.44574684823103, 5.51710965358041, 
5.58847067541891, 5.65982978173391, 5.73118684053406, 5.01798675812358, 
5.08942622314776, 5.1608646942353, 5.23230203889475, 5.30373812464718, 
5.3751728190277, 5.44660598958688, 5.51803750389225, 5.58946722952977, 
5.66089503410531, 5.73232078524608, 5.01843442025904, 5.08994274966704, 
5.16145008226124, 5.23295628516672, 5.30446122552118, 5.37596477047637, 
5.44746678719961, 5.51896714287526, 5.59046570470619, 5.66196233991527, 
5.73345691574684, 5.80494929946821, 5.01888294632387, 5.09046027300197, 
5.16203659997799, 5.23361179399208, 5.30518572179704, 5.37675825015982, 
5.44832924586302, 5.51989857570632, 5.59146610650803, 5.66303170510656, 
5.73459523836189, 5.80615657315705, 5.01933233882137, 5.09097879604084, 
5.16262425065878, 5.23426856902891, 5.30591161751768, 5.37755326250573, 
5.44919337038942, 5.52083180758231, 5.59246844051665, 5.66410313564491, 
5.73573575944119, 5.80736617840281, 5.87899425905174, 5.01978260026452, 
5.0914983216831, 5.16321303758949, 5.23492661394948, 5.30663891674166, 
5.37834981195886, 5.45005916560973, 5.5217668437202, 5.59347271233499, 
5.66517663751908, 5.73687848535927, 5.80857812196563, 5.88027541347302, 
5.02023373317599, 5.09201885283943, 5.16380296406873, 5.23558593244026, 
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5.16439403340788, 5.23624652820199, 5.30809774201245, 5.37994754005201, 
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5.16498624893117, 5.23690840494978, 5.45266662402438, 5.52458283017851, 
5.02159238609431, 5.09358650866911, 5.16557961397572, 5.0220470303023, 
5.09411109121486, 5.02250255873967, 5.09463669399833, 5.02295897398849, 
5.09516331999868), lat = c(49.5100149170223, 49.5094694150977, 
49.5088819585021, 49.5082525487942, 49.5549690001112, 49.5544229809136, 
49.5538349672697, 49.553204960742, 49.5525329630038, 49.5518189758405, 
49.5510630011485, 49.6008906614407, 49.6004281971217, 49.5999236957368, 
49.599377158628, 49.598788587249, 49.5981579831653, 49.5974853480543, 
49.5967706837049, 49.5960139920178, 49.5952152750054, 49.6458468599545, 
49.6453839568406, 49.6448789767815, 49.6443319211221, 49.6437427913193, 
49.6431115889421, 49.6424383156713, 49.6417229732999, 49.6409655637327, 
49.6401660889864, 49.6916039473286, 49.6912248422192, 49.6908036178773, 
49.690340275426, 49.6898348161011, 49.6892872412502, 49.6886975523334, 
49.6880657509232, 49.6873918387041, 49.6866758174729, 49.6859176891384, 
49.685117455722, 49.7368993021074, 49.7365619973096, 49.736182532283, 
49.7357609080408, 49.7352971257086, 49.7347911865247, 49.7342430918399, 
49.7336528431175, 49.7330204419332, 49.7323458899753, 49.7316291890444, 
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49.8717773412465, 49.871439074271, 49.8710585268133, 49.8706356998932, 
49.8701705946438, 49.8696632123115, 49.8691135542559, 49.8685216219499, 
49.8678874169795, 49.8672109410442, 49.8664921959563, 49.9170338401996, 
49.916737573276, 49.9163989847777, 49.916018075613, 49.9155948468041, 
49.9151292994867, 49.9146214349097, 49.9140712544357, 49.913478759541, 
49.9128439518149, 49.9121668329606, 49.9114474047945, 49.961994751266, 
49.9616982026555, 49.9613592922342, 49.9609780209126, 49.9605543897151, 
49.9600883997796, 49.9595800523579, 49.9590293488158, 49.9584362906325, 
49.9578008794011, 49.9571231168282, 49.9564030047343, 49.9556405450535, 
50.0069560327083, 50.0066592020601, 50.0063199693149, 50.0059383353853, 
50.0055143012979, 50.0050478681931, 50.0045390373256, 50.0039878100639, 
50.0033941878906, 50.0027581724023, 50.0020797653092, 50.001358968436, 
50.000595783721, 50.0519176571759, 50.0516205441383, 50.0512809886674, 
50.0508989916777, 50.0504745541981, 50.0500076773715, 50.0494983624554, 
50.0489466108212, 50.0483524239549, 50.0477158034564, 50.0470367510399, 
50.0463152685339, 50.0455513578809, 50.0968795972918, 50.0965822015123, 
50.0962423229128, 50.0958599624098, 50.0954351210345, 50.0949677999323, 
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Answer 1

The extent of the raster is not the same of that of the points. You can add 2500 (half a cell size at each side) and then things look pretty good:

library(terra)
# now using the updated coordinate reference system
prj <- "+proj=lcc +lat_2=50.569898649999999 +lat_1=50.569898649999999 +lon_0=4.553615160000000 +units=m +no_defs +a=6371229.0 +es=0.0"
points <- vect(df, crs = "EPSG:4326") |> project(prj)

r_template <- rast(ext(points)+2500, resolution=5000, crs=points)
r <- rasterize(points, r_template, field = "value")

plot(r)
lines(r, col="gray")
points(points, cex=.5, col="red")

Your comment

# project in a local metric crs

suggests that you do not know in which coordinate reference system these points are equally spaced and that may cause the variation in interpoint distances. The variant of the lon/lat crs is probably not very important.

---

With your updated example I can now do the below to get the same result

library(terra)
prj <- "+proj=lcc +lat_2=50.569898649999999 +lat_1=50.569898649999999 +lon_0=4.553615160000000 +units=m +no_defs +a=6371229.0 +es=0.0"
m <- as.matrix(df)
m[,1:2] <- project(m[,1:2], "EPSG:4326", prj) |> round(6)
rr <- rast(m, type="xyz", crs=prj)
rr
#class       : SpatRaster 
#dimensions  : 45, 15, 1  (nrow, ncol, nlyr)
#resolution  : 5000, 5000  (x, y)
#extent      : 30000, 105000, 6215514, 6440514  (xmin, xmax, ymin, ymax)
#coord. ref. : +proj=lcc +lat_0=0 +lon_0=4.55361516 +lat_1=50.56989865 +lat_2=50.56989865 +x_0=0 +y_0=0 +R=6371229 +units=m +no_defs 
#source(s)   : memory
#name        : value 
#min value   :     1 
#max value   :  1360