三角形三角形問題の描画

triangle-triangle.rb

#!/usr/bin/env ruby

# triangle-triangle.rb
#   三角形三角形問題の描画
#   by takehikom

# 要ImageMagick (convertコマンド), フォント (IPAexゴシック)

# ruby triangle-triangle.rb
# env FONT=/full/path/of/ipaexg.ttf ruby triangle-triangle.rb
# ruby triangle-triangle.rb test

module TriangleTriangle
  class Point
    def initialize(x_ = 0.0, y_ = 0.0, label_ = nil)
      @x = x_.to_f
      @y = y_.to_f
      @label = label_
    end
    attr_accessor :x, :y, :label

    def to_s
      s = ""
      s += "[#{label}] " if @label
      s += "(#{@x},#{@y})"
      s
    end

    def internal_division(p2, r1, r2, label_ = nil)
      # http://manapedia.jp/text/293
      raise if (r1 + r2).zero?
      p = Point.new(0, 0, label_)
      p.x = (r2 * self.x + r1 * p2.x) / (r1 + r2)
      p.y = (r2 * self.y + r1 * p2.y) / (r1 + r2)
      p
    end

    def external_division(p2, r1, r2, label_ = nil)
      # http://manapedia.jp/text/293?page=2
      raise if (r1 - r2).zero?
      p = Point.new(0, 0, label_)
      p.x = (-r2 * self.x + r1 * p2.x) / (r1 - r2)
      p.y = (-r2 * self.y + r1 * p2.y) / (r1 - r2)
      p
    end
  end

  class Plane
    def self.internal_division(p1, p2, r1, r2, label_ = nil)
      p1.internal_division(p2, r1, r2, label_)
    end

    def self.external_division(p1, p2, r1, r2, label_ = nil)
      p1.external_division(p2, r1, r2, label_)
    end

    def length(p1, p2)
      d_x = p1.x - p2.x
      d_y = p1.y - p2.y
      Math.sqrt(d_x * d_x + d_y * d_y)
    end

    def self.intersection(p1, p2, q1, q2, label_ = nil)
      a = p2.y - p1.y # (p1, p2) => a * x + b * y = c
      b = p1.x - p2.x
      c = p1.x * p2.y - p2.x * p1.y
      d = q2.y - q1.y # (p1, p2) => d * x + e * y = f
      e = q1.x - q2.x
      f = q1.x * q2.y - q2.x * q1.y

      puts "l1: #{a} x + #{b}y = #{c}" if $debug
      puts "l2: #{d} x + #{e}y = #{f}" if $debug

      raise if (a.zero? && b.zero?) || (d.zero? && e.zero?)
      det = a * e - b * d
      raise if det.zero?

      x = (c * e - b * f) / det
      y = (a * f - c * d) / det

      Point.new(x, y, label_)
    end

    def self.area(p1, p2, p3)
      # http://www004.upp.so-net.ne.jp/s_honma/heron/heron.htm
      p4 = Point.new(p1.x - p3.x, p1.y - p3.y)
      p5 = Point.new(p2.x - p3.x, p2.y - p3.y)

      (p4.x * p5.y - p4.y * p5.x).abs * 0.5
    end

    def self.transform(m, *points)
      points.map do |p|
        Point.new(m[0] * p.x + m[1] * p.y + m[2],
                  m[3] * p.x + m[4] * p.y + m[5],
                  p.label)
      end
    end
  end

  class Drawer
    def initialize(tt_, param = Hash.new)
      @tt_orig = tt_
      @m = param[:matrix] || [1, 0, 0, 0, 1, 0]
      @margin = param[:margin] || 30
      @linewidth = param[:linewidth] || 2
      @extra = param[:extra] || ""
      @fontname = param[:fontname] || ENV["FONT"] || "ipaexg.ttf"
      @fontsize = param[:fontsize] || 24
      @filename = param[:filename] || "triangle-triangle.png"
      if param[:bestfit]
        @tt = @tt_orig.transform2(param[:width] || 300,
                                  param[:height] || 200,
                                  param[:margin] || 30,
                                  param[:flap].nil? ? true : param[:flap])
      else
        @tt = @tt_orig.transform(@m)
      end
      @command = ""
    end
    attr_reader :tt, :tt_orig, :margin, :linewidth, :filename
    attr_reader :fontname, :fontsize, :extra
    attr_reader :command

    def to_s; @command; end

    def set_command
      width = ([@tt.a.x, @tt.b.x, @tt.c.x].max + @margin).to_i
      height = ([@tt.a.y, @tt.b.y, @tt.c.y].max + @margin).to_i
      @command = "convert -size #{width}x#{height} xc:white"

      add_auxline2 if @extra.index("line2")
      if @extra.index("line1")
        if @extra.index("line1") == @extra.index("line1ae")
          add_auxline1ae
        elsif @extra.index("line1+ae")
          add_auxline1
          add_auxline1ae
        else
          add_auxline1
        end
      end
      add_label_abcdef if @extra.index("abcdef")
      add_label_ghi if @extra.index("ghi")
      add_s213 if @extra.index("s213")
      if @extra.index("sabc")
        if @extra.index("sabcabc")
          add_sabcabc
        else
          add_sabc
        end
      end
      add_ratio if @extra.index("ratio")
      add_triangle_triangle

      @command += " -quality 95 #{@filename}"

      self
    end
    alias :start :set_command

    def insert_command(c)
      @command[" -quality"] = c + " -quality"
    end

    def add_triangle_triangle
      @command += " -stroke black -strokewidth #{@linewidth} -fill none"
      @command += " -draw \""
      @command += "line #{@tt.a.x},#{@tt.a.y},#{@tt.b.x},#{@tt.b.y}"
      @command += " line #{@tt.b.x},#{@tt.b.y},#{@tt.c.x},#{@tt.c.y}"
      @command += " line #{@tt.c.x},#{@tt.c.y},#{@tt.a.x},#{@tt.a.y}"
      @command += " line #{@tt.a.x},#{@tt.a.y},#{@tt.f.x},#{@tt.f.y}"
      @command += " line #{@tt.b.x},#{@tt.b.y},#{@tt.d.x},#{@tt.d.y}"
      @command += " line #{@tt.c.x},#{@tt.c.y},#{@tt.e.x},#{@tt.e.y}"
      @command += "\""
    end

    def add_auxline1
      @command += " -stroke blue -strokewidth #{@linewidth} -fill none"
      @command += " -draw \""
      @command += "line #{@tt.a.x},#{@tt.a.y},#{@tt.e.x},#{@tt.e.y}"
      @command += " line #{@tt.b.x},#{@tt.b.y},#{@tt.f.x},#{@tt.f.y}"
      @command += " line #{@tt.c.x},#{@tt.c.y},#{@tt.d.x},#{@tt.d.y}"
      @command += "\""
    end

    def add_auxline2
      @command += " -stroke maroon -strokewidth #{@linewidth} -fill none"
      @command += " -draw \""
      @command += "line #{@tt.f.x},#{@tt.f.y},#{@tt.g.x},#{@tt.g.y}"
      @command += " line #{@tt.d.x},#{@tt.d.y},#{@tt.h.x},#{@tt.h.y}"
      @command += " line #{@tt.e.x},#{@tt.e.y},#{@tt.i.x},#{@tt.i.y}"
      @command += "\""
    end

    def add_auxline1ae
      @command += " -stroke black -strokewidth #{@linewidth} -fill none"
      @command += " -draw \""
      @command += "line #{@tt.a.x},#{@tt.a.y},#{@tt.e.x},#{@tt.e.y}"
      @command += "\""
    end

    # 以下のuの第2・第3引数の値は，デフォルト設定(IPAexゴシック, 24pt)
    # に依存しているため，他のフォントやサイズにすると適切に
    # 表示しない可能性あり
    def add_label_abcdef
      @command += " -font #{@fontname} -pointsize #{@fontsize} -fill black -stroke none"
      @command += " -draw \""
      @command += "text #{u('a', -18, +1)} \'A\'"
      @command += " text #{u('b', -17, -1)} \'B\'"
      @command += " text #{u('c', 1, -1)} \'C\'"
      @command += " text #{u('d', 4, +4)} \'D\'"
      @command += " text #{u('e', -11, -4)} \'E\'"
      @command += " text #{u('f', -8, +24)} \'F\'"
      @command += "\""
    end

    def add_label_ghi
      @command += " -font #{@fontname} -pointsize #{@fontsize} -fill black -stroke none"
      @command += " -draw \""
      @command += "text #{u('g', -9, +22)} \'G\'"
      @command += " text #{u('h', 3, +1)} \'H\'"
      @command += " text #{u('i', -12, -1)} \'I\'"
      @command += "\""
      # tt3.insert_command(" -font #{font} -pointsize 24 -fill black -stroke none -draw \"text #{tt3.u('g', -9, +22)} \'G\' text #{tt3.u('h', 3, +1)} \'H\' text #{tt3.u('i', -12, -1)} \'I\'\"")
    end

    def add_s213
      @command += " -font #{@fontname} -pointsize #{@fontsize * 0.75} -fill green4 -stroke none"
      @command += " -draw \""
      @command += "text #{u('def', -5, +10)} \'s\'"
      @command += " text #{u('ade', -8, +10)} \'2s\'"
      @command += " text #{u('bef', -8, +5)} \'s\'"
      @command += " text #{u('cfd', -8, +10)} \'3s\'"
      @command += " text #{u('eab', -6, +6)} \'2s\'"
      @command += " text #{u('fbc', -5, +6)} \'3s\'"
      @command += " text #{u('dca', -16, +8)} \'6s\'"
      @command += "\""
    end

    def add_sabc
      @command += " -font #{@fontname} -pointsize #{@fontsize * 0.75} -fill green4 -stroke none"
      @command += " -draw \""
      @command += "text #{u('def', -5, +10)} \'s\'"
      @command += " text #{u('ade', -8, +10)} \'as\'"
      @command += " text #{u('bef', -8, +5)} \'bs\'"
      @command += " text #{u('cfd', -8, +10)} \'cs\'"
      @command += "\""
    end

    def add_sabcabc
      @command += " -font #{@fontname} -pointsize #{@fontsize * 0.75} -fill green4 -stroke none"
      @command += " -draw \""
      @command += "text #{u('def', -5, +10)} \'s\'"
      @command += " text #{u('ade', -8, +10)} \'as\'"
      @command += " text #{u('bef', -8, +5)} \'bs\'"
      @command += " text #{u('cfd', -8, +10)} \'cs\'"
      @command += " text #{u('eab', -15, +13)} \'abs\'"
      @command += " text #{u('fbc', -5, +6)} \'bcs\'"
      @command += " text #{u('dca', -16, +8)} \'cas\'"
      @command += "\""
    end

    def add_ratio
      @command += " -font #{@fontname} -pointsize #{@fontsize * 0.75} -stroke none"
      @command += " -fill chocolate"
      @command += " -draw \"text #{u('ai', -33, +0)} \'a+1\' text #{u('bi', -12, -1)} \'b\'\""
      @command += " -fill goldenrod"
      @command += " -draw \"text #{u('bg', -14, +20)} \'b+1\' text #{u('cg', -8, +15)} \'c\'\""
      @command += " -fill IndianRed"
      @command += " -draw \"text #{u('ch', -2, -5)} \'c+1\' text #{u('ah', +5, +2)} \'a\'\""
    end

    def u(points, del_x = 0, del_y = 0, flag_array = false)
      # pointsは1つ以上の点の文字列
      # 1点ならその座標，2点なら中点，3点以上なら重心について
      # del_x，del_yの補正を加え，convertコマンドの座標となる
      # 文字列を返す
      x = y = 0
      points.downcase.each_char do |c|
        x += @tt.send(c.to_sym).x
        y += @tt.send(c.to_sym).y
      end
      x = x / points.length + del_x
      y = y / points.length + del_y
      flag_array ? [x, y] : "#{x},#{y}"
    end
    alias :point :u
    alias :center :u

    def exec_command(opt_print = true)
      puts @command if opt_print
      system @command
    end
  end

  class Calculator
    def initialize(h = Hash.new)
      @a = h["A"]
      @b = h["B"]
      @c = h["C"]
      @ad_df = h["AD_DF"].to_f
      @be_ed = h["BE_ED"].to_f
      @cf_fe = h["CF_FE"].to_f
      puts "AD:DF=#{@ad_df}:1", "BE:ED=#{@be_ed}:1", "CF:FE=#{@cf_fe}:1"
      raise if @ad_df.zero? || @be_ed.zero? || @cf_fe.zero?
      raise if @ad_df.nan? || @be_ed.nan? || @cf_fe.nan?
    end
    attr_accessor :a, :b, :c, :ad_df, :be_ed, :cf_fe
    attr_reader :d, :e, :f, :g, :h, :i

    def print_result
      puts @a, @b, @c
      puts "AD:DF=#{@ad_df}:1", "BE:ED=#{@be_ed}:1", "CF:FE=#{@cf_fe}:1"
      puts @d, @e, @f
      puts @g, @h, @i

      d_ext = Plane.external_division(@b, @e, @be_ed + 1, 1, "Dext")
      e_ext = Plane.external_division(@c, @f, @cf_fe + 1, 1, "Eext")
      f_ext = Plane.external_division(@a, @d, @ad_df + 1, 1, "Fext")
      puts d_ext, e_ext, f_ext

      area_whole = Plane.area(@a, @b, @c)
      area_min = Plane.area(@d, @e, @f)
      puts "ABC = #{area_whole}", "DEF = #{area_min}", "ABC/DEF = #{area_whole / area_min}"
    end

    def transform(m = nil)
      tt = self.dup
      return tt if m.nil?

      tt.a, tt.b, tt.c = Plane.transform(m, @a, @b, @c)
      tt.start
    end

    def transform2(width, height, margin, flag_flip)
      # (0,0)-(width+margin*2, height+margin*2)に描画できるよう変換
      left = [@a.x, @b.x, @c.x].min
      right = [@a.x, @b.x, @c.x].max
      top = [@a.y, @b.y, @c.y].max
      bottom = [@a.y, @b.y, @c.y].min
      raise if (right - left).zero? || (bottom - top).zero?

      a2, b2, c2 = Plane.transform([1, 0, -left, 0, 1, flag_flip ? -top : -bottom], @a, @b, @c)
      a3, b3, c3 = Plane.transform([width / (right - left), 0, 0, 0, height / (top - bottom) * (flag_flip ? -1 : 1), 0], a2, b2, c2)
      a4, b4, c4 = Plane.transform([1, 0, margin, 0, 1, margin], a3, b3, c3)

      tt = self.dup
      tt.a, tt.b, tt.c = a4, b4, c4
      tt.start
    end

    def find_point
      @g = Plane.internal_division(@b, @c, @be_ed + 1, @cf_fe, "G")
      @h = Plane.internal_division(@c, @a, @cf_fe + 1, @ad_df, "H")
      @i = Plane.internal_division(@a, @b, @ad_df + 1, @be_ed, "I")
      @d = Plane.intersection(@a, @g, @b, @h, "D")
      @e = Plane.intersection(@b, @h, @c, @i, "E")
      @f = Plane.intersection(@c, @i, @a, @g, "F")

      self
    end
    alias :start :find_point
  end
end

if __FILE__ == $0
  if ARGV.first == "test"
    include TriangleTriangle

    puts "internal division"
    p1 = Point.new(0, 0)
    p2 = Point.new(3, 0.3)
    r1 = 1.0
    r2 = 2.0
    d = Plane.internal_division(p1, p2, r1, r2)
    puts "#{p1} #{r1}:#{r2} #{p2} => #{d}"
    puts "external division"
    p1 = Point.new(0, 0)
    p2 = Point.new(3, 0.6)
    r1 = 3.0
    r2 = 1.0
    d = Plane.external_division(p1, p2, r1, r2)
    puts "#{p1} #{r1}:#{r2} #{p2} => #{d}"
    puts "intersection"
    p1 = Point.new(0, 0)
    p2 = Point.new(5, 3)
    q1 = Point.new(0, 2)
    q2 = Point.new(2, 0)
    c = Plane.intersection(p1, p2, q1, q2)
    puts "#{p1}-#{p2}, #{q1}-#{q2} => #{c}"

    exit
  end

  include TriangleTriangle
  h = {
    "A" => Point.new(2.3, 4, "A"),
    "B" => Point.new(0, 0, "B"),
    "C" => Point.new(5, 0, "C"),
    "AD_DF" => 2.0,
    "BE_ED" => 1.0,
    "CF_FE" => 3.0
  }
  tt1 = Calculator.new(h).start
  tt1.print_result

  d1 = Drawer.new(tt1, :bestfit => true, :filename => "tritri1.png",
                  :extra => "abcdef").start
  d1.tt.print_result
  d1.exec_command

  d2 = Drawer.new(tt1, :bestfit => true, :filename => "tritri2.png",
                  :extra => "abcdef line1 s213").start
  d2.tt.print_result
  d2.exec_command

  d3 = Drawer.new(tt1, :bestfit => true, :filename => "tritri3.png",
                  :extra => "abcdef line1").start
  d3.tt.print_result
  d3.exec_command

  d4 = Drawer.new(tt1, :bestfit => true, :filename => "tritri4.png",
                  :extra => "abcdef line1 sabc").start
  d4.tt.print_result
  d4.exec_command

  d5 = Drawer.new(tt1, :bestfit => true, :filename => "tritri5.png",
                  :extra => "abcdef line1 sabcabc").start
  d5.tt.print_result
  d5.exec_command

  d6 = Drawer.new(tt1, :bestfit => true, :filename => "tritri6.png",
                  :extra => "abcdef ghi line1 line2").start
  d6.tt.print_result
  d6.exec_command

  d7 = Drawer.new(tt1, :bestfit => true, :filename => "tritri7.png",
                  :extra => "abcdef ghi line1 line2 sabc ratio").start
  d7.tt.print_result
  d7.exec_command

  d8 = Drawer.new(tt1, :bestfit => true, :filename => "tritri1ae.png",
                  :extra => "abcdef line1ae").start
  d8.tt.print_result
  d8.exec_command

  d9 = Drawer.new(tt1, :bestfit => true, :filename => "tritri2ae.png",
                  :extra => "abcdef line1 s213 line1+ae").start
  d9.tt.print_result
  d9.exec_command

  d = Drawer.new(tt1, :bestfit => true, :filename => "tritri_test.png",
                 :extra => "abcdef ghi line1 line2 sabcabc ratio").start
  d.tt.print_result
  d.exec_command
end