# [R] points on a sphere

Jan de Leeuw deleeuw at stat.ucla.edu
Sat Oct 26 05:17:49 CEST 2002

```This puts n points in R^p "as equally spaced as possible". If
sphere=TRUE
it constrains them to be on the sphere.
============================================================

equidist<-function(n, p, eps=1e-6, itmax=Inf, verbose=TRUE,
sphere=FALSE) {
x<-matrix(rnorm(n*p),n,p); sprev<-0; itel<-1
if (sphere) x<-row.norm(x) else x<-x/sqrt(sum(x^2))
repeat{
s<-sum(d<-eudist(x))
if (verbose) cat(formatC(itel,width=6),
formatC(s,digits=6,width=20,format="f"),"\n")
if ((((s-sprev)/sprev) < eps) || (itel == itmax)) return(x)
diag(d)<-1; e<-1/d; f<-apply(e,1,sum); e<--e; diag(e)<-f
x<-e%*%x
if (sphere) x<-row.norm(x) else x<-x/sqrt(sum(x^2))
sprev<-s; itel<-itel+1
}
}

row.norm<-function(x) x/sqrt(apply(x^2,1,sum))

eudist<-function(x){
c<-crossprod(t(x)); s<-diag(c)
sqrt(outer(s,s,"+")-2*c)
}

bmat<-function(d,delta,w){
}

On Friday, October 25, 2002, at 04:46 PM, Richard Rowe wrote:

> Not an R question directly, but has anyone got a method for placing a
> moderately large number of (near) equi-spaced points on a sphere?  I
> have a nasty feeling platonic solids are needed for exact solutions
> and I'm thinking of samplings involving around 200 - 1000
> regularly-spaced points,
>
> Thanks,
>
> Richard Rowe
>
> Richard Rowe
> Senior Lecturer
> Department of Zoology and Tropical Ecology, James Cook University
> Townsville, Queensland 4811, Australia
> fax (61)7 47 25 1570
> phone (61)7 47 81 4851
> e-mail: Richard.Rowe at jcu.edu.au
> http://www.jcu.edu.au/school/tbiol/zoology/homepage.html
>
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===
Jan de Leeuw; Professor and Chair, UCLA Department of Statistics;
Editor: Journal of Multivariate Analysis, Journal of Statistical
Software
US mail: 9432 Boelter Hall, Box 951554, Los Angeles, CA 90095-1554
phone (310)-825-9550;  fax (310)-206-5658;  email: deleeuw at stat.ucla.edu
homepage: http://gifi.stat.ucla.edu

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