def tick args
  args.outputs.background_color = [33, 33, 33]
  args.outputs.lines << bezier(100, 100,
                               100, 620,
                               1180, 620,
                               1180, 100,
                               0)

  args.outputs.lines << bezier(100, 100,
                               100, 620,
                               1180, 620,
                               1180, 100,
                               20)
end


def bezier x1, y1, x2, y2, x3, y3, x4, y4, step
  step ||= 0
  color = [200, 200, 200]
  points = points_for_bezier [x1, y1], [x2, y2], [x3, y3], [x4, y4], step

  points.each_cons(2).map do |p1, p2|
    [p1, p2, color]
  end
end

def points_for_bezier p1, p2, p3, p4, step
  points = []
  if step == 0
    [p1, p2, p3, p4]
  else
    t_step = 1.fdiv(step + 1)
    t = 0
    t += t_step
    points = []
    while t < 1
      points << [
        b_for_t(p1.x, p2.x, p3.x, p4.x, t),
        b_for_t(p1.y, p2.y, p3.y, p4.y, t),
      ]
      t += t_step
    end

    [
      p1,
      *points,
      p4
    ]
  end
end

def b_for_t v0, v1, v2, v3, t
  pow(1 - t, 3) * v0 +
  3 * pow(1 - t, 2) * t * v1 +
  3 * (1 - t) * pow(t, 2) * v2 +
  pow(t, 3) * v3
end

def pow n, to
  n ** to
end