[R] Euclidean Distance in 3 Dimensions

William Dunlap wdunlap at tibco.com
Fri Aug 22 17:43:43 CEST 2014

```> This function unfortunately does not work in 3d space.

[I think 'this' is refering to the 'dist' function.]

Can you show how it is not working for you?  I.e., what does it
produce compared to what you want for a given input?

dist() does work on a 3-column (or n-column) matrix or data.frame,
which is how R generally represents 3 dimensional (or n dimensional)
data.  E.g.,

> d <- data.frame(One=1:3, Two=c(3,5,8), Three=c(4,8,16))
> d
One Two Three
1   1   3     4
2   2   5     8
3   3   8    16
> dist(d)
1         2
2  4.582576
3 13.152946  8.602325
> as.matrix(dist(d)) # the matrix format makes further compuations easier
1        2         3
1  0.000000 4.582576 13.152946
2  4.582576 0.000000  8.602325
3 13.152946 8.602325  0.000000
> which(as.matrix(dist(d))>8, arr.ind=TRUE)
row col
3   3   1
3   3   2
1   1   3
2   2   3
> sqrt(sum((d[,2] - d[,3])^2)) # the 2,3 or 3,2 element, by hand
[1] 8.602325

I think it would help if you restated your problem.  I found the original
description confusing.  A small example, with the expected output, would

Bill Dunlap
TIBCO Software
wdunlap tibco.com

On Thu, Aug 21, 2014 at 11:34 AM, Patzelt, Edward <patzelt at g.harvard.edu> wrote:
> This function unfortunately does not work in 3d space.
>
> Thoughts?
>
>
> On Wed, Aug 20, 2014 at 4:57 PM, Don McKenzie <dmck at u.washington.edu> wrote:
>
>> ?dist
>>
>> from the help
>>
>> dist {stats}    R Documentation
>> Distance Matrix Computation
>>
>> Description
>>
>> This function computes and returns the distance matrix computed by using
>> the specified distance measure to compute the distances between the rows of
>> a data matrix.
>>
>> Is this what you want?  Computing on a matrix whose rows are your x, y,
>> and z values?
>>
>>
>> On Aug 20, 2014, at 1:12 PM, Patzelt, Edward <patzelt at g.harvard.edu>
>> wrote:
>>
>> > R Community -
>> >
>> > I am attempting to write a function that will calculate the distance
>> > between points in 3 dimensional space for unique regions (e.g. localized
>> > brain regions such as the frontal lobe).
>> >
>> > For example I'm looking to compare each point in region 45 to every other
>> > region in 45 to establish if they are a distance of 8 or more apart. I
>> can
>> > do this linearly comparing each distance to the previous but this is not
>> > comparing all points.
>> >
>> > structure(list(Cluster.Index = c(46L, 46L, 46L, 46L, 46L, 45L,
>> > 45L, 45L, 45L, 45L, 44L, 44L, 44L, 44L, 44L, 43L, 43L, 43L, 43L,
>> > 43L), Value = c(8.21, 7.96, 7.85, 7.83, 7.8, 5.38, 4.56, 4.5,
>> > 4, 3.99, 5.42, 4.82, 4.21, 4.18, 3.91, 4.79, 4.27, 3.24, 3.06,
>> > 3.04), x = c(33L, 38L, 37L, 36L, 38L, 47L, 42L, 43L, 44L, 42L,
>> > 50L, 41L, 39L, 41L, 44L, 46L, 45L, 45L, 41L, 46L), y = c(15L,
>> > 12L, 12L, 13L, 13L, 91L, 84L, 84L, 95L, 96L, 69L, 70L, 65L, 65L,
>> > 59L, 41L, 40L, 46L, 44L, 47L), z = c(41L, 38L, 41L, 39L, 33L,
>> > 39L, 40L, 42L, 44L, 45L, 34L, 36L, 30L, 35L, 39L, 53L, 47L, 61L,
>> > 52L, 57L), X = c(NA, 6.557438524302, 3.16227766016838, 2.44948974278318,
>> > 6.32455532033676, 78.7464284904401, 8.66025403784439, 2.23606797749979,
>> > 11.2249721603218, 2.44948974278318, 30.2324329156619, 9.2736184954957,
>> > 8.06225774829855, 5.3851648071345, 7.81024967590665, 22.8910462845192,
>> > 6.16441400296898, 15.2315462117278, 10.0498756211209, 7.68114574786861
>> > )), .Names = c("Cluster.Index", "Value", "x", "y", "z", "X"), row.names =
>> > c(NA,
>> > 20L), class = "data.frame")
>> >
>> > mainDat <- data.frame()
>> > for(i in 2:nrow(dat)){
>> > tempDist <- (sqrt((dat\$x[i] - dat\$x[i-1])^2 + (dat\$y[i] - dat\$y[i-1])^2 +
>> > (dat\$z[i] - dat\$z[i-1])^2))
>> > dat\$X[i] <- c(tempDist)
>> > if(dat\$Cluster.Index[i] != dat\$Cluster.Index[i-1]){
>> > mainDat <- rbind(mainDat, dat[i,])
>> > }
>> > if((dat\$Cluster.Index[i] == dat\$Cluster.Index[i-1])) {
>> > if(tempDist > 8){
>> > mainDat <- rbind(mainDat, dat[i,])
>> > }
>> > }
>> > }
>> >
>> >
>> >
>> >
>> > --
>> >
>> > *Edward H Patzelt | Clinical Science PhD StudentPsychology | Harvard
>> > University *
>> >
>> >       [[alternative HTML version deleted]]
>> >
>> > ______________________________________________
>> > R-help at r-project.org mailing list
>> > https://stat.ethz.ch/mailman/listinfo/r-help
>> http://www.R-project.org/posting-guide.html
>> > and provide commented, minimal, self-contained, reproducible code.
>>
>> Don McKenzie
>> Research Ecologist
>> Pacific Wildland Fire Sciences Lab
>> US Forest Service
>>
>> Affiliate Professor
>> School of Environmental and Forest Sciences
>> University of Washington
>> dmck at uw.edu
>>
>>
>>
>>
>>
>
>
> --
>
> *Edward H Patzelt | Clinical Science PhD StudentPsychology | Harvard
> University *
>
>         [[alternative HTML version deleted]]
>
> ______________________________________________
> R-help at r-project.org mailing list
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