Yet another quadrilateral analyzer & drawer

qpr.rb

#!/usr/bin/env ruby

# qpr.rb : 四角形(Quadrilateral)の2辺の関係に基づき平行(Parallel)・
# 垂直(Right angle)の数を求め，2次元平面上に図形を描画する
#   by takehikom
# see also:
#   青山尚司「平行だけでなく，垂直も観点に加えた四角形の弁別より」,
#   算数授業研究, Vol.137, pp.58-59 (2021). [isbn:9784491046365]

class QPR
  def initialize(hash = {})
    @points = hash[:p] || [[1, 0], [2, 1], [1, 2], [0, 1]]
    @draw_param = hash[:d] || {}
  end

  def start
    @num_parallel = 0
    @num_vertical = 0

    # 平行の数
    [[0, 1, 2, 3],
      [1, 2, 3, 0]].each do |a|
      p1, p2, p3, p4 = a.map { |e| @points[e] }
      if is_parallel(p1, p2, p3, p4)
        puts "#{p_s(p1)}-#{p_s(p2)}, #{p_s(p3)}-#{p_s(p4)}: parallel"
        @num_parallel += 1
      end
    end

    # 垂直の数
    [[0, 1, 1, 2],
      [1, 2, 2, 3],
      [2, 3, 3, 0],
      [3, 0, 0, 1],
      [0, 1, 2, 3],
      [1, 2, 3, 0]].each do |a|
      p1, p2, p3, p4 = a.map { |e| @points[e] }
      if is_vertical(p1, p2, p3, p4)
        puts "#{p_s(p1)}-#{p_s(p2)}, #{p_s(p3)}-#{p_s(p4)}: right angle"
        @num_vertical += 1
      end
    end

    self
  end

  def p_s(xy)
    "(" + xy.join(",") + ")"
  end

  def is_zero(n)
    case n
    when Float
      eps = 1.0e-6
      return -eps < n && n < eps
    when Numeric
      return n.zero?
    else
      raise
    end
  end

  def is_parallel(p1, p2, p3, p4)
    d1 = [p1[0] - p2[0], p1[1] - p2[1]]
    d2 = [p3[0] - p4[0], p3[1] - p4[1]]
    is_zero(d1[0] * d2[1] - d1[1] * d2[0])
  end

  def is_vertical(p1, p2, p3, p4)
    d1 = [p1[0] - p2[0], p1[1] - p2[1]]
    d2 = [p3[0] - p4[0], p3[1] - p4[1]]
    is_zero(d1[0] * d2[0] + d1[1] * d2[1])
  end

  def draw
    @image_filename = @draw_param[:filename] || "rect.png"
    @margin = @draw_param[:margin] || 10
    @side = @draw_param[:side] || 40
    @linewidth = @draw_param[:linewidth] || 2
    @dotradius = @draw_param[:dotradius] || 3
    @linecolor = @draw_param[:linecolor] || "#6666ff"
    @bgcolor = @draw_param[:bgcolor] || "#f0fff0"
    @axiscolor = @draw_param[:axiscolor] || "#666666"
    @axiswidth = @draw_param[:axiswidth] || @linewidth * 0.5
    @x_min = @draw_param[:xmin] || @points.map { |p| p[0] }.min
    @x_max = @draw_param[:xmax] || @points.map { |p| p[0] }.max
    @y_min = @draw_param[:ymin] || @points.map { |p| p[1] }.min
    @y_max = @draw_param[:ymax] || @points.map { |p| p[1] }.max
    @quality = @draw_param[:quality] || ""
    if Numeric === @quality
      @quality = "-quality #{@quality}"
    end
    @print_command = @draw_param[:print]
    @flip = @draw_param[:flip] # 真のとき上下反転(yの値が大きければ上に表示)

    @x_trans = [-@x_min, 0].max
    @y_trans = [-@y_min, 0].max

    image_width = @margin * 2 + (@x_max - @x_min) * @side
    image_height = @margin * 2 + (@y_max - @y_min) * @side

    # 画像を新規作成
    @command = "convert -size #{image_width}x#{image_height} \'xc:#{@bgcolor}\'"

    # 縦目盛り
    @command += " -fill none -stroke \'#{@axiscolor}\' -strokewidth \'#{@axiswidth}\' -draw \""
    @x_min.upto(@x_max) do |x|
      @command += " line #{xy_image_s(x, @y_min)} #{xy_image_s(x, @y_max)}"
    end
    @command += "\""

    # 横目盛り
    @command += " -draw \""
    @y_min.upto(@y_max) do |y|
      @command += " line #{xy_image_s(@x_min, y)} #{xy_image_s(@x_max, y)}"
    end
    @command += "\""

    # 四角形の頂点
    if @dotradius > 0
      @command += " -fill \'#{@linecolor}\' -stroke none -draw \""
      @points.each do |x, y|
        px, py = xy_image(x, y)
        s1 = [px, py].join(',')
        s2 = [px + @dotradius, py].join(',')
        @command += " circle #{s1} #{s2}"
      end
      @command += "\""
    end

    # 四角形の辺
    @command += " -fill none -stroke \'#{@linecolor}\' -strokewidth \'#{@linewidth}\' -draw \"polygon #{@points.map { |xy| xy_image_s(*xy) }.join(' ')}\""

    # ファイル保存
    @command += " #{@quality} #{@image_filename}"

    puts @command if @print_command
    system @command
  end

  def xy_image(x, y)
    px = @margin + (@x_trans + x) * @side
    py = @margin + (@flip ? @y_max - y : @y_trans + y) * @side
    [px, py]
  end

  def xy_image_s(x, y)
    xy_image(x, y).join(",")
  end
end

if __FILE__ == $0
  draw_param_base = {
    :xmin => 0, :xmax => 3, :ymin => 0, :ymax => 3,
    :quality => 92,
    :flip => true,
#    :print => true,
  }

  points_a = [
    [[0, 0], [3, 0], [3, 3], [0, 3]], # q1.png 正方形
    [[0, 0], [2, 0], [2, 3], [0, 3]], # q2.png 長方形
    [[1, 1], [2, 2], [1, 3], [0, 2]], # q3.png ダイヤモンド型(正方形)
    [[0, 0], [1, 0], [3, 3], [2, 3]], # q4.png 平行四辺形
    [[0, 0], [2, 1], [1, 3], [0, 3]], # q5.png 0平行2垂直
    [[0, 0], [2, 2], [1, 3], [0, 3]], # q6.png 0平行2垂直
    [[1, 0], [2, 3], [1, 2], [0, 3]], # q7.png 0平行1垂直(270°)
    [[0, 1], [3, 1], [2, 2], [1, 2]], # q8.png 1平行1垂直
    [[0, 2], [3, 2], [2, 1], [2, 0]], # q9.png 0平行2垂直
  ]
  points_a.each_with_index do |points, i|
    filename = "q#{i + 1}.png"
    draw_param = draw_param_base.dup
    draw_param[:filename] = filename
    puts "==== shape No.#{i + 1} (#{filename}) ===="
    QPR.new(p: points, d: draw_param).start.draw
  end
end