Rendering 3D surfaces

Question

I've got data representing 3D surfaces (i.e. earthquake fault planes) in xyz point format. I'd like to create a 3D representation of these surfaces. I've had some success using rgl and akima, however it can't really handle geometry that may fold back on itself or have multiple z values at the same x,y point. Alternatively, using geometry (the convhulln function from qhull) I can create convex hulls that show up nicely in rgl but these are closed surfaces where in reality, the objects are open (don't completely enclose the point set). Is there a way to create these surfaces and render them, preferably in rgl?

EDIT

To clarify, the points are in a point cloud that defines the surface. They have varying density of coverage across the surface. However, the main issue is that the surface is one-sided, not closed, and I don't know how to generate a mesh/surface that isn't closed for more complex geometry.

As an example...

require(rgl)
require(akima)
faultdata<-cbind(c(1,1,1,2,2,2),c(1,1,1,2,2,2),c(10,20,-10,10,20,-10))
x <- faultdata[,1]
y <- faultdata[,2]
z <- faultdata[,3]
s <- interp(x,z,y,duplicate="strip")
surface3d(s$x,s$y,s$z,col=a,add=T)

This creates generally what I want. However, for planes that are more complex this doesn't necessarily work. e.g. where the data are:

faultdata<-cbind(c(2,2,2,2,2,2),c(1,1,1,2,2,2),c(10,20,-10,10,20,-10))

I can't use this approach because the points are all vertically co-planar. I also can't use convhulln because of the same issue and in general I don't want a closed hull, I want a surface. I looked at alphashape3d and it looks promising, but I'm not sure how to go about using it for this problem.

Answer 1

How do you determine how the points are connected together as a surface? By distance? That can be one way, and the alphashape3d package might be of use. Otherwise, if you know exactly how they are to be connected, then you can visualize it directly with rgl structures.