Circular and Spherical random uniform distribution functions

circle_sphere_distributions.R

rcau <- function() {
  angle <- 2 * pi * runif(1)
  radius <- 1 * (runif(1) ^ (1/2))
  
  x <- radius * cos(angle)
  y <- radius * sin(angle)
  
  c(x, y)
}

coord_mat <- matrix(0, nrow = 2000, ncol = 2)
for(i in 1:nrow(coord_mat)) {
  coord_mat[i,] <- rcau()
}

plot(coord_mat)

library(rgl)

rsau <- function() {
  theta <- acos(runif(1) * 2 - 1)
  phi <- 2 * pi * runif(1)
  radius <- 1 * (runif(1) ^ (1/3))
  
  x <- radius * cos(phi) * sin(theta)
  y <- radius * sin(phi) * sin(theta)
  z <- radius * cos(theta)
  
  c(x, y,z)
}


coord_mat <- matrix(0, nrow = 2000, ncol = 3)
for(i in 1:nrow(coord_mat)) {
  coord_mat[i,] <- rsau()
}

points3d(coord_mat)