#!/usr/bin/Rscript
polar <- function(points)
{
	r <- sqrt(points[,1])*sqrt(1/pi)
	p <- points[,2]*2*pi
	points[,1] <- r*cos(p)
	points[,2] <- r*sin(p)
	return(points)
}

points <- runif(10000)
dim(points) <- c(5000,2)
square <- points
circle <- polar(points)
square.distances <- apply(square, 1, function(x) sqrt(sum(x^2)))
circle.distances <- apply(circle, 1, function(x) sqrt(sum(x^2)))

par(mfrow=c(2,2))
plot(square)
qqnorm(square.distances)
plot(circle)
qqnorm(circle.distances)