Fitting a 3D surface to a dataset of points [R] - r

Question

I have been trying to fit a polynomial surface to a set of point with 3 coordinates.
Let the data be:
DATA <- with(mtcars, as.data.frame(cbind(1:32, wt,disp,mpg)))
I have been trying to draw a surface using:
plot3d from rgl package,
using rsm package,
scatterplot3d package.
For example:
library(scatterplot3d)
attach(mtcars)
DATA <- as.data.frame(cbind(1:32, wt,disp,mpg))
scatterplot3d(wt,disp,mpg, main="3D Scatterplot")
model <- loess(mpg ~wt + disp, data=DATA)
x <-range(DATA$wt)
x <- seq(x[1], x[2], length.out=50)
y <- range(DATA$disp)
y <- seq(y[1], y[2], length.out=50)
z <- outer(x,y,
function(wt,disp)
predict(model, data.frame(wt,disp)))
z
p <- persp(x,y,z, theta=30, phi=30,
col="lightblue",expand = 0.5,shade = 0.2,
xlab="wt", ylab="disp", zlab="mpg")
I have also tried using surf.ls function:
surf.ls(2,DATA[,2],DATA[,3],DATA[,4])
But what I got looks like this:
I don't really know how to transform it to a 3D plot and more importantly, how to get the formula for the best fit surface obtained.
I would really appreciate your help.
PS I have deleted my last post and included more details in this one.

Answer 1

Try this:
attach(mtcars)
DATA <- as.data.frame(cbind(1:32, wt,disp,mpg))
x_wt <- DATA$wt
y_disp <- DATA$disp
z_mpg <- DATA$mpg
fit <- lm(z_mpg ~ poly(x_wt, y_disp, degree = 2), data = DATA)
To plot with rsm, use the following:
library(rsm)
image(fit, y_disp ~ x_wt)
contour(fit, y_disp ~ x_wt)
persp(fit, y_disp ~ x_wt, zlab = "z_mpg")
To plot with ggplot, use the following:
## ggplot
# Use rsm package to create surface model.
library(rsm)
SurfMod <- contour(fit, y_disp ~ x_wt)
# extract list values from rsm Surface Model
Xvals <- SurfMod$`x_wt ~ y_disp`[1]
Yvals <- SurfMod$`x_wt ~ y_disp`[2]
Zvals <- SurfMod$`x_wt ~ y_disp`[3]
# Construct matrix with col and row names
SurfMatrix <- Zvals$z
colnames(SurfMatrix) <- Yvals$y
rownames(SurfMatrix) <- Xvals$x
# Convert matrix to data frame
library(reshape2)
SurfDF <- melt(SurfMatrix)
library(ggplot2)
gg <- ggplot(data = SurfDF) +
geom_tile(data = SurfDF, aes(Var1, Var2,z = value, fill = value)) +
stat_contour(data = SurfDF, aes(Var1, Var2, z = value, color = ..level..)) +
scale_colour_gradient(low = "green", high = "red") +
geom_point(data = DATA, aes(wt, disp, z = mpg, color = mpg)) +
geom_text(data = DATA, aes(wt, disp,label=mpg),hjust=0, vjust=0) +
scale_fill_continuous(name="mpg") +
xlab("x_wt") +
ylab("y_disp")
library(directlabels)
direct.label.ggplot(gg, "angled.endpoints")
To see all of the available direct.label methods, go to http://directlabels.r-forge.r-project.org/docs/index.html