On 3/24/2007 1:43 AM, Ranjan Maitra wrote:
> Dear list,
>
> Does anyone have a suggestion (or better still) code for sampling from the
> uniform distribution over the convex hull of a set of points?
Are you talking about two dimensional points, or higher dimensions? The
suggestion below works for any dimension, but the actual code is
2-dimensional. I don't know if there's an equivalent of chull available
for higher dimensions.
Suggestion: Find a rectangular region containing the hull, and sample
uniformly there. Accept points that don't expand the hull of the
original points.
For example:
rhull <- function(n,x) {
boundary <- x[chull(x),]
xlim <- range(boundary[,1])
ylim <- range(boundary[,2])
boundary <- rbind(c(NA,NA), boundary) # add space for new test point
result <- matrix(NA, n, 2)
for (i in 1:n) {
repeat {
boundary[1,1] <- runif(1, xlim[1], xlim[2])
boundary[1,2] <- runif(1, ylim[1], ylim[2])
if ( !(1 %in% chull(boundary)) ) {
result[i,] <- boundary[1,]
break
}
}
}
result
}
x <- matrix(rnorm(20), ncol=2)
plot(x, cex=2, col="red")
sample <- rhull(1000, x)
points(sample)
Duncan Murdoch
______________________________________________
R-help@stat.math.ethz.ch mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.
