[R] rgl: ellipse3d with axes

[Duncan Murdoch]

On 24/09/2008 10:12 AM, Michael Friendly wrote:
> Duncan Murdoch wrote:
>> The normals component contains the surface normals.  It is used to 
>> help in rendering the surface, but isn't much use for your purposes.
>> Unfortunately, I'm not familiar enough with the internals of princomp 
>> to tell you how to get the axes you want.
>>
>> Duncan Murdoch
> 
> OK, then let me repharase it. The axes of the unit  sphere are like
> 
> axes <- matrix(
>     c(0, 0, -1,   0, 0, 1,
>        0, -1, 0,   0, 1,  0,
>        -1, 0, 0,   1, 0, 0),  6, 3, byrow=TRUE)
> taken in pairs.  I'd like to transform these coordinates the same was as 
> in ellipse3d() and add them to the plot.

That's easy, but it doesn't give you the principal axes of the ellipse. 
  Just use

axes %*% chol(cov)

If you start with a unit sphere, this will give you points on its 
surface, but not the ones you want.  For those you need the SVD or 
eigenvectors.  This looks like it does what you want:

axes <- matrix(
     c(0, 0, 0, # added origin
        0, 0, -1,   0, 0, 1,
        0, -1, 0,   0, 1,  0,
        -1, 0, 0,   1, 0, 0),  7, 3, byrow=TRUE)
axes <- axes[c(1,2,1,3,1,4,1,5,1,6,1,7),]  # add the origin before each

cov <- cov(trees)
eigen <- eigen(cov)
shade3d(ellipse3d(cov, t=1, alpha=0.2, col='red'))
segments3d(axes %*% sqrt(diag(eigen$values)) %*% t(eigen$vectors))

Duncan Murdoch