plotting a curve around a set of points

问题:

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.

回答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:

回答2:

The ggalt package provides geom_encircle, which is supposed to provide something like this - convex, but smooth:

library(ggplot2)
library(ggalt)  ## v 0.4.0

df <- data.frame(x = rnorm(20), y = rnorm(20),
      z = sample(letters[1:5], 20, replace = TRUE))
ggplot(df, aes(x, y, colour = z)) + geom_point() +
     geom_encircle(aes(fill=z),alpha=0.3)

回答3:

After some googling, I little modify this example Morota ggplot2

EDIT

It uses the chull function with bezier

library(ggplot2)
library(plyr)
library(Hmisc)



df <- data.frame(x = rnorm(20), y = rnorm(20),z = sample(letters[1:5], 20, rep = T))
ggplot(df, aes(x, y, colour = z)) + geom_point()

find_hull <- function(df) {
    res.ch <- df[chull(df$x, df$y), ]
    res <- bezier(res.ch)
    res <- data.frame(x=res$x,y=res$y)
    res$z <- res$z
    res
  }
hulls <- ddply(df, "z", find_hull)
ggplot(df, aes(x, y, colour = z,fill = z)) +
  geom_point() + geom_polygon(data = hulls,alpha = 0.4)

回答4:

Simply:

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"))
x <- do.call('cbind',testpts)
ch<-chull(x)
x[c(ch,ch[1]),]
plot(x,pch=20)
points(x[ch,],pch=20,col='red')
lines(x[c(ch,ch[1]),],lwd=.5)

Plot:

the plot