[R] Scatterplot3d model reporting question

[Max]

I've used the scatterplot3d function to graph some data and had it 
graph a "smooth" fit. Is there a way to actualy find out the function 
of the surface? I've looked through the help and figured out how to get 
it to report the following:

Family: gaussian
Link function: identity

Formula:
y ~ s(x, z)

Parametric coefficients:
            Estimate Std. Error t value Pr(>|t|)
(Intercept)  0.20750    0.01223   16.97   <2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Approximate significance of smooth terms:
         edf Est.rank     F  p-value
s(x,z) 8.403       17 9.729 1.76e-14 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

R-sq.(adj) =  0.684   Deviance explained = 70.9%
GCV score = 0.017692   Scale est. = 0.016151  n = 108

But I'm still not really sure what I'm looking at, either that or 
"smooth" means something different than I thought. Any help would be 
great!

thanks,

-Max