Contour plots on a sphere surface

Question

I have acquired some data at a fixed distance R and for various theta (from the vertical axis) and phi (from the x axis) angles so to obtain a 3D representation of the quantity of interest. Please note that while phi spans 360°, theta only spans from 70° to 90°.

I know how to generate a 3D plot with the plot3D package (namely, the persp3D function) or a contour plot, but I would like to draw such contours over a sphere using the theta and phi angles information.

Would you please point me to the appropriate online resource where I can find a suitable solution?

Many thanks and kind regards

Nicola

Answer 1

This isn't exactly a 3d representation (e.g. in rgl), but maybe it gets you started:

library(maps)
library(mapproj)        
library(akima)

set.seed(11)
n <- 500
x <- runif(n, min=-180,max=180)
y <- runif(n, min=-90,max=90)
z <- x^2+y^3

PARAM <- NULL
PROJ <- "orthographic"
ORIENT <- c(45,15,0)
XLIM <- c(-180, 180)
YLIM <- c(-90, 90)

nlevels=20
pal <- colorRampPalette(
  c("purple4", "blue", "cyan", "yellow", "red", "pink"))
map("world", col=NA, param=PARAM, proj=PROJ, orient=ORIENT, xlim=XLIM, ylim=YLIM)
P <- mapproject(x,y)
incl <- which(!is.na(P$x))
Field <- interp(P$x[incl],P$y[incl],z[incl],
  xo=seq(min(P$x[incl]), max(P$x[incl]), length = 100),
  yo=seq(min(P$y[incl]), max(P$y[incl]), length = 100)
)
image(Field, add=TRUE, col=pal(nlevels))
points(P$x, P$y, pch=".", cex=2, col=4)
Cont <- contour(Field, add=TRUE, n=nlevels, col="white")
lines(sin(seq(0,2*pi,,100)), cos(seq(0,2*pi,,100)), lwd=3)