cart2sph.R

cart2sph <- function (x, y, z, x0 = 0, y0 = 0, z0 = 0, units = "rad") {
  # See http://mathworld.wolfram.com/SphericalCoordinates.html and https://en.wikipedia.org/wiki/Spherical_coordinate_system
  # Use ISO convention
  # rho = radial distance
  # theta = polar angle (inclination); default units is radians
  # phi = azimuthal angle; default units is radians
  x <- x - x0
  y <- y - y0
  z <- z - z0
  rho <- sqrt(x^2 + y^2 + z^2)
  theta <- acos(z / rho)
  phi <- atan(y / x)
  if (units == "deg") {
    k <- 180 / pi
    theta <- theta * k
    phi <- phi * k
  }
  data.frame(rho, theta, phi)
}

s <- 3
scale <- 10
df <- data.frame(x1 = round(runif(s) * scale, 1),
                 y1 = round(runif(s) * scale, 1),
                 z1 = round(runif(s) * scale, 1),
                 x2 = round(runif(s) * scale, 1),
                 y2 = round(runif(s) * scale, 1),
                 z2 = 0)
library(magrittr)
library
df %>% mutate(radial = cart2sph(x1, y1, z1, x2, y2, z2, units = "deg")[, "rho"],
              azimuthal = cart2sph(x1, y1, z1, x2, y2, z2, units = "deg")[, "theta"],
              polar = cart2sph(x1, y1, z1, x2, y2, z2, units = "deg")[, "phi"])