r - plotting a curve around a set of points

Question

I have a set of points on a plane. They are partitioned into subsets. I want to plot a closed curve around points that belong to the same subset, so that points that belong to a subset will be inside the curve, and those that aren't will be outside. Therefore simple circles, or a convex hull might not work.

For a starter, let's say I just want to have a smooth curve around a set of point (without the requirement that it excludes other points)

Any ideas how to do that in R?

---added later---

What I'm looking eventually, is something in the spirit of the graphics in here: https://tex.stackexchange.com/questions/1175/drawing-a-hypergraph - although the context is not a hypergraph, but rather a given set of points and a partition of those.

Answer 1

Okay, here's a version of an answer that I think gets close to what you are chasing: It uses the spline.poly function created over at this answer ( https://gis.stackexchange.com/a/24929 ) on the GIS forum.

Here's some example points:

testpts <- 
structure(list(x = c(4.9, 4.2, 4, 4.1, 4.4, 5.8, 5.8, 5.8, 5.8, 
5.5, 4.9, 3.2, 3.2, 3.3, 5.4, 5.4, 5.7, 6.4, 6.7, 6.7, 6, 4.8, 
3.6, 2.8, 3.5, 4.4, 5.1, 4, 3.7, 4.5, 4.9, 5.7), y = c(6.9, 6.2, 
5.3, 4.1, 3.1, 2.9, 2.9, 3.5, 4.2, 4.9, 5.1, 4.9, 4.9, 5.2, 6.9, 
6.9, 5.3, 3.8, 4.2, 5.6, 6.9, 5.8, 1.2, 2.5, 5.3, 6.4, 6.8, 7.6, 
6.9, 5.4, 4.8, 4.4)), .Names = c("x", "y"))

Set up a basic plot

plot(NA,xlim=c(0,10),ylim=c(0,10))
points(testpts,pch=19)
chuld <- lapply(testpts,"[",chull(testpts))
polygon(chuld,lty=2,border="gray")
polygon(spline.poly(as.matrix(as.data.frame(chuld)),100),border="red",lwd=2)

And the result:

EDIT TO ADD A CONCAVE EXAMPLE

This part of the answer uses the alphahull library

# load the required library
library(alphahull)

plot(NA,xlim=c(0,10),ylim=c(0,10))
points(testpts,pch=19)
# remove duplicate points so the ahull function doesn't error out
testptsnodup <- lapply(testpts,"[",which(!duplicated(as.matrix(as.data.frame(testpts)))))

Generate and plot the ahull object - the alpha value seems to be very important in determining the fit of the polygon to the data.

ahull.obj <- ahull(testptsnodup,alpha=2)
plot(ahull.obj,add=TRUE,col="red",wpoints=FALSE)

And the result: