simply draw Bezier curve and display, with RMagick

bezier-curve.rb

#!/usr/bin/env ruby
require 'RMagick'
include Magick

def tpow (t, pow_a, pow_b) 
  (t ** pow_a) * ((1 - t) ** pow_b)
end


# Bezier curve parameters
p1, p2, p3, p4 = 8, 16, 220, 236

image = Image.new 500, 500
draw = Draw.new
draw.stroke_antialias true

# title
draw.annotate(image, 75, 50, 75, 75, "Bezier Curve")

# axis
draw.line 100, 100, 100, 400
draw.line 100, 400, 400, 400

# linear interpolation
draw.line 100, 400, 355, 145

# Bezier interpolation
draw.fill '#FF0000'
last = 145
(1..255).each do |p|
  t = p / 255.0
  bezier = ((5 * p1 * tpow(t, 1, 4)) + (10 * p2 * tpow(t, 2, 3)) + (10 * p3 * tpow(t, 3, 2)) + (5 * p4 * tpow(t, 4, 1)) + (255 * tpow(t, 5, 0)))
  draw.line (355 - p + 1), last, (355 - p), (bezier + 145)
  last = bezier + 145
end

draw.draw image

image.display