interlmkdist() (Expand for more details)
  • \(A\): A 3D array containing landmark coordinates for a set of specimens.
  • \(lmks\): A matrix or dataframe of landmark numbers for the start and end points of each linear measurements. See below for specific formatting.



Defining distances

The start and end points of the distance measure required need to be defined manually. This is done with a two-column matrix or dataframe with the column names “start” and “end.” For the sake of this example, we are interested in the distances between landmarks 1:2 and 3:4 respectively:

dists <- matrix(c(1,2,3,4),ncol = 2, byrow = T)
colnames(dists) <- c("start", "end")
dists
##      start end
## [1,]     1   2
## [2,]     3   4



intlmkdist <- interlmkdist(lmk, dists)
intlmkdist
##           [,1]     [,2]
## [1,] 1.0732464 3.965878
## [2,] 0.7904719 3.984135
## [3,] 0.8565340 3.705467
## [4,] 1.2985309 4.029318
## [5,] 0.9468429 3.975509

Each column contains one distance measure for each specimen. In this case, the first column is the distance between landmarks 1 and 2 for each of the 10 specimens in our dataset.

Defining All Pairwise Distances

Calculating interlandmark distances for all possible combinations of landmarks requires a bit more code, but is nonetheless fairly simple:

First, we need to generate a vector of landmark numbers equal to the total number of landmarks in our dataset:

lmkno <- c(1:dim(lmk)[1]) #vector of 1:number of landmarks
lmkno
## [1] 1 2 3 4 5



Next, using the combn function we can generate a matrix of all possible combinations of those landmarks:

alldist <- matrix(combn(lmkno,2, c),ncol = 2, byrow = T) #returns all pairwise combinations of landmark numbers
colnames(alldist) <- c("start", "end")
alldist
##       start end
##  [1,]     1   2
##  [2,]     1   3
##  [3,]     1   4
##  [4,]     1   5
##  [5,]     2   3
##  [6,]     2   4
##  [7,]     2   5
##  [8,]     3   4
##  [9,]     3   5
## [10,]     4   5



Then run the function as normal: 
intlmkdist <- interlmkdist(lmk, alldist)
intlmkdist
##           [,1]     [,2]     [,3]     [,4]     [,5]     [,6]     [,7]     [,8]     [,9]     [,10]
## [1,] 1.0732464 3.360799 7.094816 7.634875 3.977041 7.395026 7.997329 3.965878 4.400389 0.7336264
## [2,] 0.7904719 3.228808 6.953514 7.331036 3.580447 7.040904 7.463865 3.984135 4.261914 0.5788650
## [3,] 0.8565340 3.175094 6.727441 7.008508 3.519829 6.836761 7.186543 3.705467 3.892784 0.6470026
## [4,] 1.2985309 3.528328 7.312307 7.750283 4.018143 7.359630 7.937849 4.029318 4.302592 0.9678678
## [5,] 0.9468429 2.785570 6.606091 7.110076 3.260097 6.790600 7.382265 3.975509 4.378959 0.8621375