Catmull-Rom splines implemented in Ruby.

catmull_rom_splines.rb

# Based on https://github.com/Sojo-Studios/catmull-rom/blob/master/test.js
# This implementation assumes circular splines.

class CatmullRomSplines
  def initialize(points)
    @key_points = points
  end

  def generate(detail)
    points = []

    @key_points.size.times do |i|
      p0, p1, p2, p3 = adjacent_key_points(i)

      detail.times do |d|
        points << interpolate(d / detail.to_f, p0, p1, p2, p3)
      end
    end

    points
  end

  private

  def adjacent_key_points(index)
    [
      key_point(index - 1),
      key_point(index),
      key_point(index + 1),
      key_point(index + 2)
    ]
  end

  def key_point(index)
    @key_points[index % @key_points.size]
  end

  def interpolate(u, p0, p1, p2, p3)
    u3 = u * u * u
    u2 = u * u
    f1 = -0.5 * u3 + u2 - 0.5 * u
    f2 =  1.5 * u3 - 2.5 * u2 + 1.0
    f3 = -1.5 * u3 + 2.0 * u2 + 0.5 * u
    f4 =  0.5 * u3 - 0.5 * u2

    # Handle arbitrary sizes
    p0.zip(p1, p2, p3).map do |x0, x1, x2, x3|
      x0 * f1 + x1 * f2 + x2 * f3 + x3 * f4
    end
  end
end