[R] rgl: ellipse3d with axes

[Duncan Murdoch]

Michael Friendly wrote:
> Last week I asked about data ellipses with rgl:::ellipse3d() with lines 
> showing the principal axes.
> (The goal is a visual demonstration of PCA as a rotation of variable 
> space to component space.)
> I was trying, unsuccessfully, to use princomp() to generate the PCA axes 
> and plot them using
> segments3d:
>
>   
>>> PC <- princomp(trees)
>>> sdev <- PC$sdev         # component standard deviations
>>> sd <- sqrt(diag(cov))   # variable standard deviations
>>>
>>> # vectors in variable space of principal components
>>> vec <- matrix(mu,3,3, byrow=TRUE) + diag(sd) %*% PC$loadings
>>>
>>> for (j in 1:3) {
>>>  mat <- rbind(mu, vec[j,])
>>>  segments3d(mat, col="red")
>>> }
>>>       
> However, it occurred to me that these axes are just the orthogonal axes 
> of the unit sphere
> that is transformed (using chol()) in ellipse3d, so plotting the axes 
> transformed in the
> same way would give me what I want.
>
> Looking at the result returned by ellipse3d, I see a normals component, 
> but I'm not sure if this
> represents what I want, or, if it is, how to use it to draw the ellipse 
> major axes in the plot.
>
>  > e1 <-ellipse3d(cov, centre=mu, level=0.68)
>  > str(e1)
> List of 6
>  $ vb           : num [1:4, 1:386] 4.95 2.64 2.03 1.00 6.74 ...
>  $ ib           : num [1:4, 1:384] 1 195 99 196 51 197 99 195 27 198 ...
>  $ primitivetype: chr "quad"
>  $ homogeneous  : logi TRUE
>  $ material     : list()
>  $ normals      : num [1:4, 1:386]  0.290 -0.902 -0.320  1.000  0.635 ...
>  - attr(*, "class")= chr "qmesh3d"
>   

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
> -Michael
>
>