spherical.js

function xyz_to_ρ (x, y, z) {
  return Math.sqrt((x * x) + (y * y) + (z * z));
}

function zρ_to_θ (z, ρ) {
  return Math.acos(z / ρ);
}

function yx_to_φ (y, x) {
  return Math.atan(y / x);
}

function xyz_to_ρθφ (x, y, z) {
  const ρ = xyz_to_ρ(x, y, z);
  const θ = zρ_to_θ(z, ρ);
  const φ = yx_to_φ(y, x);
  return [ρ, θ, φ];
}

function ρθφ_to_x (ρ, θ, φ) {
  return ρ * Math.sin(θ) * Math.cos (φ);
}

function ρθφ_to_y (ρ, θ, φ) {
  return ρ * Math.sin(θ) * Math.sin (φ);
}

function ρθ_to_z (ρ, θ) {
  return ρ * Math.cos(θ);
}

function ρθφ_to_xyz (ρ, θ, φ) {
  const x = ρθφ_to_x(ρ, θ, φ);
  const y = ρθφ_to_y(ρ, θ, φ);
  const z = ρθ_to_z(ρ, θ);
  return [x, y, z];
}

module.exports = {
  xyz_to_ρ,
  zρ_to_θ,
  yx_to_φ,
  xyz_to_ρθφ,
  ρθφ_to_x,
  ρθφ_to_y,
  ρθ_to_z,
  ρθφ_to_xyz
};