[R] is there a way to visualize 3D normal distributions?

[Ben Bolker]

   In response to your last question --

   Duncan already gave you the answer in his last e-mail -- to give
an explicit example, for a particular set of means and
variance-covariance matrix:

library(rgl)
demo(shapes3d)
rgl.clear()
sphere <- ellipsoid3d(2,2,2,qmesh=TRUE)
means <- c(0,0,0)
S <- matrix(c(3,1,-1,1,2,-1,-1,-1,2),nrow=3)
ellipsoid <- translate3d(rotate3d(sphere,matrix=chol(S)*qnorm(0.975)),
                                     means[1],means[2],means[3])
shade3d(ellipsoid)
axis3d()


Duncan Murdoch wrote:
> On 2/2/2006 5:01 PM, Michael wrote:
> 
>> shape3d only gives rigid sphere... not the free form ellipsoid that I
>> want...
> 
> 
> ? If you run the demo, you'll see ellipsoids...
> 
> You just need to work out the appropriate transform to apply to a sphere 
> to get the ellipsoid you want.  I imagine something like this:
> 
> sphere <- ellipsoid3d(2,2,2, qmesh=TRUE)
> ellipsoid <- translate3d(rotate3d(sphere, matrix=chol(S)), xbar, ybar, 
> zbar)
> 
> shade3d(ellipsoid)
> 
> is what you want, where S is the covariance matrix, and xbar,ybar,zbar 
> have the obvious meaning.  (rotate3d() is used with a matrix that isn't 
> a rotation matrix; it may not be obvious that this is allowed, but it is.)
> 
> Duncan Murdoch
> 
> 
>>
>> On 2/2/06, Ben Bolker <bolker at ufl.edu> wrote:
>>
>>> Duncan Murdoch <murdoch <at> stats.uwo.ca> writes:
>>>
>>>> On 2/2/2006 3:39 AM, Michael wrote:
>>>>
>>>>> Hi all,
>>>>>
>>>>> How do I visualize a contour of a tri-variate normal distribution?
>>>>>
>>>>> I just like to see the ellipsoid very much. I hope there is a easy way
>>>
>>> or
>>>
>>>>> existing method in R.
>>>>
>>>> The misc3d package includes a function for 3d contour plots; that 
>>>> should
>>>> do what you want.
>>>>
>>>   is contour3d really necessary or could you just plot ellipsoids?
>>> (library(rgl); demo(shapes3d)) -- still a little bit of figuring
>>> to do, but this should get you most of the way there.
>>>
>>>   Ben Bolker
>>>
>>> ______________________________________________
>>> R-help at stat.math.ethz.ch mailing list
>>> https://stat.ethz.ch/mailman/listinfo/r-help
>>> PLEASE do read the posting guide!
>>> http://www.R-project.org/posting-guide.html
>>>
>>
>>     [[alternative HTML version deleted]]
>>
>> ______________________________________________
>> R-help at stat.math.ethz.ch mailing list
>> https://stat.ethz.ch/mailman/listinfo/r-help
>> PLEASE do read the posting guide! 
>> http://www.R-project.org/posting-guide.html


-- 
620B Bartram Hall                            bolker at zoo.ufl.edu
Zoology Department, University of Florida    http://www.zoo.ufl.edu/bolker
Box 118525                                   (ph)  352-392-5697
Gainesville, FL 32611-8525                   (fax) 352-392-3704