randomPointInSphere.lua

function randomPointInSphere(radius)
  radius = radius or 1
  local sx, sy, sz = 0, 0, 0;
  for i = 1, 4 do
    local x, y, z = math.random(), math.random(), math.random()
    sx, sy, sz = sx + x, sy + y, sz + z
    local xc, yc, zc = x - 0.5, y - 0.5, z - 0.5
    if xc * xc + yc * yc + zc * zc <= 0.25 then
      local r2 = radius * 2
      return xc * r2, yc * r2, zc * r2
    end
  end

  sx, sy, sz = sx - 2, sy - 2, sz - 2
  local u = math.random()
  local norm = math.sqrt(0.5 * (math.sqrt(u) + u)/(sx*sx + sy*sy + sz*sz + 1e-25)) * radius
  return sx*norm, sy*norm, sz*norm
end

function randomPointInCircle(radius)
  radius = radius or 1
  local sx, sy = 0, 0
  for i = 1, 4 do
    local x, y = math.random(), math.random()
    sx, sy = sx + x, sy + y
    local xc, yc = x - 0.5, y - 0.5
    if xc * xc + yc * yc <= 0.25 then
      local r2 = radius * 2
      return xc * r2, yc * r2
    end
  end

  sx, sy = sx - 2, sy - 2
  local norm = math.sqrt(math.random()/(sx*sx+sy*sy + 1e-25)) * radius
  return sx*norm, sy*norm
end