trying to fit a thin plate spline to a triangular plot

Hi

Has anyone tried to fit a thin plate spine to a triangular plot before? I'm having trouble working out a piece of code to make it possible with three axes.

I have done it before with two axes. 

I've found a package I prefer that makes triangular plots (plotrix) using the triax.plot() function. An example of some data and the plot follows:

graph.data<-data.frame(a=c(9,6.2, 5.9,8.1,8.9,56.9,50,39.5,62.1,49.9,4.2,3,6,4.1),
                      b=c(1.8,1.2,1.2,1.6,1.8,11.4,10,7.9,12.4,10,4.2,3,6,4.1),
                      c=c(1.8,1.2,1.2,1.6,1.8,11.4,10,7.9,12.4,10,4.2,3,6,4.1),
                      d=c(10,15,16,14,13,18,19,17,20,19,21,22,22,23))

triax.plot(graph.data, main="Title", no.add=F, show.grid=T,tick.labels=list(l=seq(10,90,by=10),r=seq(10,90,by=10),b=seq(10,90,by=10)),
          pch=1,cc.axes=TRUE)

I want to fit the 'd' data as a spline to the plot. 

Any help is greatly appreciated.