Moire (w/ Matrices)

moire.rb

require 'graphics'
require 'matrix'

class Moire < Graphics::Simulation
  include Math
  def initialize(*args, distance:, radius:, frames_per_rotation:)
    super *args
    @fpr          = frames_per_rotation
    @radius       = radius
    @to_center    = translate -w/2, -h/2
    midpoint      = Matrix[[w/2], [h/2], [1]]
    canvas_radius = sqrt 2 * [w/2, h/2].min**2
    num_dots      = (2 * canvas_radius / distance).ceil
    @points       = num_dots.times.flat_map do |x|
      num_dots.times.map do |y|
        translate(x*distance-num_dots*distance/2, y*distance-num_dots*distance/2) * midpoint
      end
    end
  end

  def draw(n)
    clear :white
    transform = @to_center * rotate(n*2*PI/@fpr) * -@to_center
    @points.each { |point| circle *xy(point),             @radius, :black, :fill }
    @points.each { |point| circle *xy(transform * point), @radius, :black, :fill }
  end

  def xy(point)
    return point[0, 0], point[1, 0]
  end

  def translate(x, y)
    Matrix[
      [1, 0, x],
      [0, 1, y],
      [0, 0, 1],
    ]
  end

  def rotate(radians)
    Matrix[
      [cos(radians), -sin(radians), 0],
      [sin(radians),  cos(radians), 0],
      [           0,             0, 1],
    ]
  end
end

Moire.new(500, 500, distance: 10, radius: 2, frames_per_rotation: 250).run