R help - Feb 2008 - distances between points in R^3

Dear R helpers,

I'm trying to write a numerical scheme for a boundary integral method  
to solve an electromagnetic problem. This requires the computation of  
the distance between points at the surface of an object (a sphere, in  
my example). Here is my code,
> require(rgl)
> r<-1
> size<-10
> theta<-seq(0,2*pi,length=size*2)
> phi<-seq(0,pi,length=size)
> pc = as.matrix(rbind(expand.grid(theta,phi)))
> x<- r* sin(pc[,2]) * cos(pc[,1])
> y<- r* sin(pc[,2]) * sin(pc[,1])
> z<- r* cos(pc[,2])
>
>   plot3d(x, y, z, col=rainbow(1000), size=2,zlim=c(-1,1)) #  
> scatterplot of points on a sphere
>
> df<- unique(rbind(x,y,z), MARGIN = 2 ) # removes duplicates in  
> cartesian coordinates
> dimension <- dim(df)[1]
> matDistances <- array(data=0,dim=c(dimension,dimension))
>
> norm <- function(a) sqrt(a %*% a)
>
> for (ii in 1:dimension){
> for (jj in ii:dimension){
> matDistances[ii,jj]<- norm( df[,ii] - df[,jj])
> }
> }

This is both inefficient and ugly, I'll welcome any suggestion. In  
particular:

- the location of the points on the sphere is not ideal (understand:  
not uniformly distributed over the area): i looked into delaunayn  
from the geometry package and qhull.com but at best I obtained a  
random set of points on the sphere. It must be a most classical  
problem ?? generating a uniform distribution of points on a sphere??,  
but i've set that problem aside for the moment.

- the double for loop over all the points cries out for a vectorized  
solution, but i can't really think of any.



Many thanks in advance,

baptiste
_____________________________

Baptiste Augui?

Physics Department
University of Exeter
Stocker Road,
Exeter, Devon,
EX4 4QL, UK

Phone: +44 1392 264187

http://newton.ex.ac.uk/research/emag
http://projects.ex.ac.uk/atto

OK, I've come across a partial answer to the for loop problem in the  
use of "dist()". However, my problem not only require to find the  
distances between points, but also to store the vector differences,  
and the normal to each face when i get the delaunay triangulation  
sorted.

As i understand, the dist() function calls a C routine, is there a  
straight-forward way to find / edit / modify it to serve this  
specific purpose?


Thanks,

baptiste

On 3 Feb 2008, at 18:55, baptiste Augui? wrote:
> Dear R helpers,
>
> I'm trying to write a numerical scheme for a boundary integral  
> method to solve an electromagnetic problem. This requires the  
> computation of the distance between points at the surface of an  
> object (a sphere, in my example). Here is my code,
>
>> require(rgl)
>> r<-1
>> size<-10
>> theta<-seq(0,2*pi,length=size*2)
>> phi<-seq(0,pi,length=size)
>> pc = as.matrix(rbind(expand.grid(theta,phi)))
>> x<- r* sin(pc[,2]) * cos(pc[,1])
>> y<- r* sin(pc[,2]) * sin(pc[,1])
>> z<- r* cos(pc[,2])
>>
>>   plot3d(x, y, z, col=rainbow(1000), size=2,zlim=c(-1,1)) #  
>> scatterplot of points on a sphere
>>
>> df<- unique(rbind(x,y,z), MARGIN = 2 ) # removes duplicates in  
>> cartesian coordinates
>> dimension <- dim(df)[1]
>> matDistances <- array(data=0,dim=c(dimension,dimension))
>>
>> norm <- function(a) sqrt(a %*% a)
>>
>> for (ii in 1:dimension){
>> for (jj in ii:dimension){
>> matDistances[ii,jj]<- norm( df[,ii] - df[,jj])
>> }
>> }
>
>
> This is both inefficient and ugly, I'll welcome any suggestion. In  
> particular:
>
> - the location of the points on the sphere is not ideal  
> (understand: not uniformly distributed over the area): i looked  
> into delaunayn from the geometry package and qhull.com but at best  
> I obtained a random set of points on the sphere. It must be a most  
> classical problem ?? generating a uniform distribution of points on  
> a sphere??, but i've set that problem aside for the moment.
>
> - the double for loop over all the points cries out for a  
> vectorized solution, but i can't really think of any.
>
>
>
> Many thanks in advance,
>
> baptiste
> _____________________________
>
> Baptiste Augui?
>
> Physics Department
> University of Exeter
> Stocker Road,
> Exeter, Devon,
> EX4 4QL, UK
>
> Phone: +44 1392 264187
>
> http://newton.ex.ac.uk/research/emag
> http://projects.ex.ac.uk/atto
> ______________________________
>
>
>
>
>
_____________________________

Baptiste Augui?

Physics Department
University of Exeter
Stocker Road,
Exeter, Devon,
EX4 4QL, UK

Phone: +44 1392 264187

http://newton.ex.ac.uk/research/emag
http://projects.ex.ac.uk/atto