A Sphere class that can give you random, uniformly distributed coordinates on the surface of a sphere. Default creates a unit sphere. You can set the sphere's radius directly or set it by its known volume ("Assume a spherical cow...")

sphere.rb

# https://www.jasondavies.com/maps/random-points/
require 'rspec'
require 'awesome_print'

class Sphere

  attr_accessor :radius, :units

  def initialize(radius=1.0)
    srand
    @radius = radius*1.0
  end

  # We want φ ∈ [-90°, 90°)
  # φ = cos^(-1)(2x - 1), where x is uniformly distributed and x ∈ [0, 1)
  def random_phi(units = :radians)
    raise StandardError.new("only #{self.class.allowed_angular_units} allowed.") unless self.class.allowed_angular_units.include? units
    x = rand
    # acos returns [ 0 - π )
    rads = Math.acos(2*x - 1) - Math::PI/2
    return rads if units == :radians
    return rads*180/Math::PI
  end


  #  pick λ ∈ [-180°, 180°)
  def random_theta(units = :radians)
    degrees = rand*360 - 180
    raise StandardError.new("only #{self.class.allowed_angular_units} allowed.") unless self.class.allowed_angular_units.include? units
    return degrees if units == :degrees
    return degrees*Math::PI/180
  end

  def random_latitude
    random_phi(:degrees)
  end
  def random_longitude
    random_theta(:degrees) + 360
  end

  def volume
    Math::PI*radius*radius*radius
  end

  def area
    4*Math::PI*radius*radius
  end

  # takes the new volume and sets the radius.
  def volume=(new_volume)
    float_vol = new_volume * 1.0
    self.radius = Math.cbrt(float_vol/Math::PI)
  end

  private
  def self.allowed_angular_units
    [:radians, :degrees]
  end

end

# tests for above.
require 'rspec'
require 'awesome_print'
require './sphere'
sphere = Sphere.new
phis = []
thetas = []
100.times do
  phis << sphere.random_phi(:degrees)
  thetas << sphere.random_theta(:degrees)
  # phis << sphere.random_phi()
  # thetas << sphere.random_theta()
end
ap phi: phis
ap theta: thetas
ap min_phi: phis.min, max_phi: phis.max, avg_phi: phis.reduce(:+)/phis.length,
   min_theta: thetas.min, max_theta: thetas.max, avg_theta: thetas.reduce(:+)/thetas.length


RSpec.describe Sphere do
  let(:sphere) { Sphere.new }
  it "sphere is initialized" do
    expect(sphere.area).to be_within(0.009).of(12.56)
    expect(sphere.volume).to be_within(0.0006).of(3.141)
  end

  it "'s volume can be set'" do
    sphere.volume = 225.00
    expect(sphere.radius).to be_within(0.00004).of(4.1528)
  end

  it "can give a random theta" do
    expect(sphere.random_theta >= Math::PI*-1).to be_truthy
    expect(sphere.random_theta <= Math::PI).to be_truthy
  end
  it "can give a random phi" do
    expect(sphere.random_phi >= Math::PI/-2.0).to be_truthy
    expect(sphere.random_phi <= Math::PI/2.0).to be_truthy
  end

  it "can give a random theta in degrees" do
    expect(sphere.random_theta(:degrees) >= -180.0).to be_truthy
    expect(sphere.random_theta(:degrees) <= 180.0).to be_truthy
  end
  it "can give a random phi" do
    expect(sphere.random_phi(:degrees) >= -90.0).to be_truthy
    expect(sphere.random_phi(:degrees) <= 90.0).to be_truthy
  end

end