A Ruby script to calculate Bézier curves.

bezier.rb

require "matrix"
require "pry"

class Integer
	# Method to compute binomial coefficient nCk (where n is this object,
	# and k is some other integer.
	def choose(k)
		# n! / (n-k)!
		top = (((self-k)+1)..(self)).inject(1, &:*)

		# k!
		bottom = (2..k).inject(1, &:*)

		# n! / (n-k)!k!
		top / bottom
	end
end

class Bezier

	attr_accessor :points

	def initialize(points)
		@points = points

		validate_points!
	end

	def calculate(time)
		validate_points!

		@points.each_with_index.map do |point, index|
			# Multiply the point (which should be a Vector)
			# by a scalar, which corresponds to:
			#
			# (Where n is the maximum point index, t is the parametric time,
			# from 0.0 to 1.0, and i is the index of the current point)
			#
			# nCi * ((1 - t)^(n - i)) * (t ^ i).
			point *
				((@points.count - 1).choose(index)) *
				((1 - time) ** (@points.count - 1 - index)) *
				(time ** index)
		end.inject(:+)
	end

	protected

	def validate_points(points)
		point_counts = points.map do |point|
			point.count
		end

		unique_point_counts = point_counts.uniq

		raise RuntimeError, "Not all points are of the same length!" unless unique_point_counts.length == 1
	end

	def validate_points!
		validate_points(@points)
	end

end

bezier = Bezier.new([Vector[0, 0], Vector[0, 2], Vector[1, 2], Vector[1, 0], Vector[2, 0], Vector[2, 2]])

(0.00..1.00).step(0.01) do |t|
	p bezier.calculate t
end