A quick demo of thin plate regression splines in mgcv

thin_plate_demo.R

library(mgcv)
library(plot3D)

#Set up sample data
set.seed(42)
x <- runif(200, -1,1)
y <- runif(200, -1,1)
z <- exp(-(x^2 + y^2)) + rnorm(200, 0, 0.15)

#Fit 2D thin-plate regression spline
fit <- gam(z ~ s(x,y, bs="tp"), method="REML")

#Predict over a grid
ng = 100
x.pred <- seq(min(x), max(x), length.out = ng)
y.pred <- seq(min(y), max(y), length.out = ng)
xy <- expand.grid( x = x.pred, y = y.pred)
z.pred <- matrix(predict(fit, newdata = xy), 
                 nrow = ng, ncol = ng)

#Fitted points
fitpoints <- predict(fit)

#Show points and surface
scatter3D(x, y, z, pch = 18, cex = 1.5, 
          theta = 60, phi = 20, 
          xlab = "x", ylab = "y", zlab = "f(x,y)",  
          surf = list(x = x.pred, y = y.pred, z = z.pred,  
                      facets = NA, fit = fitpoints),
          main = "Smoothest possible surface under thin-plate constraints")