[R] voronoi tessellations

[binabina at bellsouth.net]

Okay, been working with tripack, seems the most mature package for this.  Got it to work well with their test data set - data(tritest).  When i tried random numbers to explore further, i am getting some results that don't reconcile.  

example run this:

library(tripack)
y <- runif(100)
x <- runif(100)
vm <- voronoi.mosaic(x,y)
plot(vm)
par(new=T)
plot(x,y,col='blue')

when you look at the plot of the mosaic overlayed with the raw data, the mosaic should have each  data point in 1 cell, however that is not the case - any help would be appreciated.  

However if you run

data(tritest)
x <- tritest$x
y <- tritest$y
vm <- voronoi.mosaic(x,y)
plot(vm)
par(new=T)
plot(x,y,col='blue')

it looks at it should.

-zubin


> 
> From: Prof Brian Ripley <ripley at stats.ox.ac.uk>
> Date: 2006/07/19 Wed AM 03:15:51 EDT
> To: Don MacQueen <macq at llnl.gov>
> CC: zubin <binabina at bellsouth.net>,  r-help at stat.math.ethz.ch
> Subject: Re: [R] voronoi tessellations
> 
> On Tue, 18 Jul 2006, Don MacQueen wrote:
> 
> > I'll suggest going to the CRAN packages page and doing a search for "voronoi".
> 
> The problem here is that `Voronoi tessellation' is a secondary name.  The 
> concept has many names, including Dirichlet tessellation and Thiessen 
> polygons, and Dirichlet has priority over Voronoi.
> 
> > Also, search for 'triangulation', since that is one of the uses of them.
> 
> I know of packages deldir, tripack and perhaps geometry.
> 
> > -Don
> > 
> > At 11:46 PM -0400 7/18/06, zubin wrote:
> > >Hello, looking to draw a voronoi tessellations in R - can anyone
> > >recommend a package that has tackled this?
> > >
> > >some background:
> > >
> > >i have a economic data set and created a sammons projection, like to now
> > >overlay a voronoi tessellation over the sammons 2-D solution for a slick
> > >visual, and potentially color each tessellation element based on a metric.
> > >
> > >home.u <- unique(home1)
> > >home.dist <- dist(home.u)
> > >home.sam <- sammon(home.dist,k=2)
> > >plot(home.sam$points)
> 
> Wait a minute.  If this is sammon() from MASS (uncredited), it is not a 
> projection, and there is no relevant concept of distance between points in 
> the mapped space apart from between the supplied points.
> 
> I suggest Zubin reads carefully the reference whose support software he 
> appears to be using.  (It would also have answered his question.)
> 
> -- 
> Brian D. Ripley,                  ripley at stats.ox.ac.uk
> Professor of Applied Statistics,  http://www.stats.ox.ac.uk/~ripley/
> University of Oxford,             Tel:  +44 1865 272861 (self)
> 1 South Parks Road,                     +44 1865 272866 (PA)
> Oxford OX1 3TG, UK                Fax:  +44 1865 272595
>