I've got 4 vectors with their coordinates at different time steps.
lon <- list(505997.627175236, 505997.627175236, 505997.627175236, 505997.627175236, 505997.064187932, 505997.814896096,
505997.843587834, 505997.880929633, 505996.906012923, 505998.486599226, 505998.075906002, 505998.079921271)
lon <- do.call(rbind.data.frame, lon)
lat <- list(7941821.025438220, 7941821.025438220, 7941821.025438220, 7941821.025438220, 7941819.791667340, 7941821.329316000,
7941821.741379530, 7941821.171989530, 7941819.103811300, 7941821.831421200, 7941822.024924560, 7941822.110412460)
lat <- do.call(rbind.data.frame, lat)
step <- list(1,1,1,1,2,2,2,2,3,3,3,3)
step <- do.call(rbind.data.frame, step)
allbuff <- cbind(lon, lat, step)
colnames(allbuff) <- c("lon", "lat", "STEP")
I've calculated the angles between the four vectors at step, step+1, ..., step+n with this following script:
M_PI <- 3.14159265359
output_angle = NULL
for (i in unique(allbuff$STEP)) {
select = allbuff[allbuff$STEP == i, 1:2]
result1 = atan2((select[1,2] - select[2,2]), (select[1,1] - select[2,1]))*(180/M_PI) # between 1 & 2
result2 = atan2((select[1,2] - select[3,2]), (select[1,1] - select[3,1]))*(180/M_PI) # between 1 & 3
result3 = atan2((select[1,2] - select[4,2]), (select[1,1] - select[4,1]))*(180/M_PI) # between 1 & 4
result4 = atan2((select[2,2] - select[3,2]), (select[2,1] - select[3,1]))*(180/M_PI) # between 2 & 3
result5 = atan2((select[2,2] - select[4,2]), (select[2,1] - select[4,1]))*(180/M_PI) # between 2 & 4
result6 = atan2((select[3,2] - select[4,2]), (select[3,1] - select[4,1]))*(180/M_PI) # between 3 & 4
result <- rbind(result1,result2,result3,result4,result5,result6)
STEP <- c(i,i)
result <- cbind(result, as.data.frame(STEP))
output_angle = rbind(output_angle,result)
}
output_angle <- as.data.frame(output_angle)
It's working and not too long to code with a small number of vectors but with 1000 vectors, this way of coding can be very time consuming.
Therefore, is there a more efficient way (procedurally speaking) to calculate the angles between all the vectors at step n whatever the number of vector in input?
Maybe the base R code below can help a bit
dfout <- do.call(rbind,
c(make.row.names = F,
lapply(split(allbuff,allbuff$STEP), function(v)
data.frame(result = combn(nrow(v),2,function(k) atan2(diff(v[rev(k),2]),diff(v[rev(k),1])) )*(180/M_PI),
STEP = unique(v[3]),
row.names = NULL))))
and you will get
> dfout
result STEP
1 0.00000 1
2 0.00000 1
3 0.00000 1
4 0.00000 1
5 0.00000 1
6 0.00000 1
7 -116.02248 2
8 -111.78912 2
9 -120.61296 2
10 -93.98304 2
11 112.76891 2
12 93.75220 2
13 -120.09129 3
14 -111.82589 3
15 -111.32784 3
16 -25.22807 3
17 -34.45110 3
18 -92.68914 3