[R] Geometry delaunayn and deldir results, differing results from Octave due to decimal precision?

[Yuen, Kam]

The problem:
I would like to translate the Octave algorithm in griddata.m to R.
Within the griddata algorithm calls are made to the Delaunay function. For the R translation I have found delaunayn within the "geometry" package and also the deldir package.
Both do similar things but give slightly different results depending on the input.
The question is, what is making the results for the R packages different from each other?
And are those differences down to the decimal precision in the latter case of using 9 d.p.?
In the following example I have defined x and y to be small vectors and all three sets of results agree (but are in a different order), i.e. Octave's delaunay, geometry.delaunayn, and deldir.deldir

Octave

x = [0.9554283   0.4695926   0.0769020   0.3033320   0.3553984   0.6051734   0.8661461   0.5511353   0.5214984   0.0061548]

y = [0.851911   0.402087   0.704462   0.687721   0.939775   0.499157   0.077145   0.588351   0.454380   0.193425]

tri = delaunay(x,y)

tri =

    2    7   10

    2    9    7

    6    7    1

    6    9    7

    4    2    9

    4    2   10

    8    5    1

    8    6    1

    8    4    5

    8    6    9

    8    4    9

    3    4   10

    3    4    5


R With deldir package
x <- c(0.9554283,0.4695926,0.0769020,0.3033320,0.3553984,0.6051734,0.8661461,0.5511353,0.5214984,0.0061548)
y <- c(0.851911,0.402087,0.704462,0.687721,0.939775,0.499157,0.077145,0.588351,0.454380,0.193425)
tri <- deldir(x,y)
triMat(tri) =
      [,1] [,2] [,3]
[1,]    1    5    8
[2,]    1    6    7
[3,]    1    6    8
[4,]    2    4   10
[5,]    2    4    9
[6,]    2    7   10
[7,]    2    7    9
[8,]    3    4   10
[9,]    3    4    5
[10,]    4    5    8
[11,]    4    8    9
[12,]    6    7    9
[13,]    6    8    9

R with geometry package

x <- c(0.9554283,0.4695926,0.0769020,0.3033320,0.3553984,0.6051734,0.8661461,0.5511353,0.5214984,0.0061548)

y <- c(0.851911,0.402087,0.704462,0.687721,0.939775,0.499157,0.077145,0.588351,0.454380,0.193425)

library(geometry)

tri <- delaunayn(cbind(x,y))



tri

      [,1] [,2] [,3]

[1,]    2    7   10

[2,]    8    5    1

[3,]    6    7    1

[4,]    6    8    1

[5,]    4    2   10

[6,]    4    3   10

[7,]    4    3    5

[8,]    4    8    5

[9,]    9    6    8

[10,]    9    4    2

[11,]    9    4    8

[12,]    9    2    7

[13,]    9    6    7

As you can see, the results are identical with the exception of ordering.

*However* when I use a slightly larger set of data for input, "geometry.delaunayn" and "deldir.deldir" seems to give results that are off by one in a lot of instances.
The input for the Delaunay function has been exported from Octave to 9 d.p. and then imported into R by using the "foreign" package.

Example data is on the following link. It is a set of variables exported from Octave 'x y tri xiflat yiflat tri_list.mat'
https://pastebin.com/xELkj6r6

the variable tri_list is just the tri_list = search(x,y,tri_deldir,xiflat,yiflat) in Octave


The command history is a as follows:
library(deldir)
library(geometry)
library(foreign)
theData <- read.octave('x y tri xiflat yiflat tri_list.mat')
options(digits = 10)
x <- unlist(theData[1])
y <- unlist(theData[3])
tri_deldir <- triMat(deldir(x,y))
tri_delaunayn <- delaunayn(x,y)
tri_delaunayn <- delaunayn(cbind(x,y))
tri_list_from_deldir <- tsearch(x,y,tri_deldir,xiflat,yiflat)
xiflat <- unlist(theData[7])
yiflat <- unlist(theData[9])
tri_list_from_deldir <- tsearch(x,y,tri_deldir,xiflat,yiflat)
tri_list_from_delaunayn <- tsearch(x,y,tri_delaunayn,xiflat,yiflat)


Kam Yuen
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