Michael Friendly <friendly <at> yorku.ca> writes:
>
> For a paper dealing with generalized ellipsoids, I want to illustrate in
> 3D an ellipsoid that is unbounded
> in one dimension, having the shape of an infinite cylinder along, say,
> z, but whose cross-section in (x,y)
> is an ellipse, say, given by the 2x2 matrix cov(x,y).
>
> I've looked at rgl:::cylinder3d, but don't see any way to make it
> accomplish this. Does anyone have
> any ideas?
>
I haven't quite got this in the form you want, but maybe it's
a start (I started from the ellipsoid3d() function in demo("shapes3d") ...
cyl3d <- function(rx=1,ry=1,n=30,ctr=c(0,0,0),
zmax=1,
qmesh=FALSE,
trans = par3d("userMatrix"),...) {
if (missing(trans) && !rgl.cur()) trans <- diag(4)
degvec <- seq(0,2*pi,length=n)
zvec <- seq(0,zmax,length=n)
ecoord2 <- function(p) {
c(rx*cos(p[1]),ry*sin(p[1]),p[2])
}
v <- apply(expand.grid(degvec,zvec),1,ecoord2)
if (qmesh) v <- rbind(v,rep(1,ncol(v))) ## homogeneous
e <- expand.grid(1:(n-1),1:n)
i1 <- apply(e,1,function(z)z[1]+n*(z[2]-1))
i2 <- i1+1
i3 <- (i1+n-1) %% n^2 + 1
i4 <- (i2+n-1) %% n^2 + 1
i <- rbind(i1,i2,i4,i3)
if (!qmesh)
quads3d(v[1,i],v[2,i],v[3,i],...)
else return(rotate3d(qmesh3d(v,i,material=...),matrix=trans))
}
cyl3d(rx=1,ry=2,zmax=5,col="blue")
cyl3d(rx=3,ry=2,zmax=5,col="red",alpha=0.3,ctr=c(2,1,0),
trans=rotationMatrix(pi/6,0,0,1))
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