what is the easiest way to create random points on a circle of specific radius with noise in R? is there a library that does this kind of things?
- How should the points be distributed ?user1196549– user11965492022-02-15 21:36:30 +00:00Commented Feb 15, 2022 at 21:36
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3 Answers
theta = runif(100, 0,2*pi) x = cos(theta) + rnorm(100, 0, 0.03) y = sin(theta) + rnorm(100, 0, 0.03) plot(x,y, pch=20) 
3 Comments
Gregor Thomas
It seems strange to me that you're drawing the radial noise independently for the x and y components rather than a single
r = rnorm(...). OP didn't specify any particular distribution, but this might introduce something a little weirder than the other way (or at least be a bit harder to make a definitive statement for what the variance of the radius is).
G5W
I see this as two separate random factors - position on the circle and variation from the circle. I don't see how to view it as one dimensional, although if you can describe it as such, that would be interesting.
Mikael Jagan
@GregorThomas I agree, though I'm guessing you mean
r = rlnorm(...). It is strange to introduce three sources of variation (one runif and two rnorm) in a space with two dimensions.It would be more natural to sample:
- the polar angle
thetafrom a uniform distribution supported on[0, 2*pi), - the polar radius
rfrom a lognormal distribution supported on(0, Inf), so thatlog(r)is normally distributed with meanmeanlogand standard deviationsdlog.
So you could try something like this:
set.seed(1L) n <- 100L theta <- runif(n, 0, 2 * pi) r <- rlnorm(n, meanlog = log(2), sdlog = 0.1) plot(r * cos(theta), r * sin(theta), asp = 1) 
And you could generalize to multiple circles like so:
circles <- function(n, mu, sigma) { lr <- Map(rlnorm, n = n, meanlog = mu, sdlog = sigma) N <- length(lr) n <- lengths(lr, FALSE) data.frame(group = rep.int(gl(N, 1L), n), r = unlist(lr, FALSE, FALSE), theta = runif(sum(n), 0, 2 * pi)) } set.seed(1L) d <- circles(n = c(25L, 100L, 400L), mu = log(c(1, 2, 4)), sigma = c(0, 0.05, 0.1)) str(d) ## 'data.frame': 525 obs. of 3 variables: ## $ group: Factor w/ 3 levels "1","2","3": 1 1 1 1 1 1 1 1 1 1 ... ## $ r : num 1 1 1 1 1 1 1 1 1 1 ... ## $ theta: num 3.335 4.303 2.408 6 0.744 ... par(mfrow = c(1L, 2L)) with(d, { plot(r * cos(theta), r * sin(theta), asp = 1, col = group) plot(r * cos(theta), r * sin(theta), asp = 1, col = cut(theta, 0:3 * 2 * pi / 3)) }) 
The function circles is vectorized in n, mu, and sigma, where n is the number of points in a circle and mu and sigma are the mean and standard deviation of the log radius.
Comments
We can use 1i to construct polar coordinates (complex format) and then plot it
set.seed(1) n <- 100 plot(rnorm(n, 1, 0.1) * exp(1i * runif(n, 0, 2 * pi))) 