[R] voronoi tessellations

[Thomas Lumley]

On Wed, 19 Jul 2006, binabina at bellsouth.net wrote:

> 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')

plot() changes the axis scales. Use points(x,y)

 	-thomas

> 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
>>
>
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Thomas Lumley			Assoc. Professor, Biostatistics
tlumley at u.washington.edu	University of Washington, Seattle