A calculator of polygonal coordinates

polygon-plotter.rb

#!/usr/bin/env ruby

# polygon-plotter.rb : A calculator of polygonal coordinates
#   by takehikom
# see also:
#   https://takehikom.hateblo.jp/entry/2021/05/14/073039
#   https://takehikom.hateblo.jp/entry/2021/05/15/073040

class PolygonPlotter
  def initialize(opt = {})
    if opt[:polygon]
      @polygon = opt[:polygon]
      raise if !(Array === @polygon) || @polygon.length < 3
    else
      setup_regular_polygon(opt[:regular] || 3)
    end
    @precision = opt[:prec] || 6
  end

  def setup_regular_polygon(number_vertex = 3)
    # 正多角形の座標を@polygonに設定する
    @polygon = number_vertex.times.map { |i|
      angle = 360.0 / number_vertex * i
      [Math.sin(angle / 180.0 * Math::PI), Math.cos(angle / 180.0 * Math::PI)]
    }

    self
  end

  def setup_fake_regular_polygon(number_vertex = 3, type = 1)
    # setup_fake_regular_polygon1またはsetup_fake_regular_polygon2
    # を呼び出す
    if type == 2
      setup_fake_regular_polygon2(number_vertex)
    else
      setup_fake_regular_polygon1(number_vertex)
    end
  end

  def setup_fake_regular_polygon1(number_vertex = 3)
    # すべての辺の長さが等しいが1箇所だけ他と角度が異なる
    # 多角形の座標を@polygonに設定する
    # number_vertex == 4のとき多角形にならない

    # 一辺の長さは正多角形から求める
    setup_regular_polygon(number_vertex)
    side = Math.sqrt((@polygon[1][0] - @polygon[0][0]) ** 2 +
                     (@polygon[1][1] - @polygon[0][1]) ** 2)

    # 始点
    x0 = x = 0.0
    y0 = y = 1.0
    angle = 360.0 / number_vertex * 0.5
    angle_error = 360.0 / number_vertex ** 4 * 2
    @polygon = [[x0, y0]]

    # 残りの点
    1.upto(number_vertex - 1) do |i|
      x += side * Math.cos(angle / 180.0 * Math::PI)
      y -= side * Math.sin(angle / 180.0 * Math::PI)
      @polygon << [x, y]
      angle += 360.0 / number_vertex
      angle += 360.0 / number_vertex if i == number_vertex - 2 # 最後の1つ前だけ角度を変える
    end

    self
  end

  def setup_fake_regular_polygon2(number_vertex = 3)
    # すべての辺の長さが等しいが角度が異なる
    # 多角形の座標を@polygonに設定する

    # 一辺の長さは正多角形から求める
    setup_regular_polygon(number_vertex)
    side = Math.sqrt((@polygon[1][0] - @polygon[0][0]) ** 2 +
                     (@polygon[1][1] - @polygon[0][1]) ** 2)

    # 始点
    x0 = x = 0.0
    y0 = y = 1.0
    angle = 360.0 / number_vertex * 0.5
    angle_error = 360.0 / number_vertex ** 4 * 2
    @polygon = [[x0, y0]]

    # 始点・終点以外
    1.upto(number_vertex - 2) do |i|
      x += side * Math.cos(angle / 180.0 * Math::PI)
      y -= side * Math.sin(angle / 180.0 * Math::PI)
      @polygon << [x, y]
      angle += 360.0 / number_vertex - angle_error * i
    end

    # 終点
    xlast, ylast = find_last_point(x0, y0, x, y, side)
    @polygon << [xlast, ylast]

    self
  end

  def find_last_point(x1, y1, x2, y2, r)
    # 次の条件を満たす[x, y]の1つを返す
    #   [x1, y1]と[x, y]との距離がrと等しい
    #   [x2, y2]と[x, y]との距離がrと等しい
    d = Math.sqrt((x2 - x1) ** 2 + (y2 - y1) ** 2)
    w = d * 0.5
    h = -Math.sqrt(r ** 2 - w ** 2)
    theta = Math.atan2(y2 - y1, x2 - x1)
    x = w * Math.cos(theta) - h * Math.sin(theta) + x1
    y = w * Math.sin(theta) + h * Math.cos(theta) + y1

    [x, y]
  end

  def print_status
    # 多角形の座標を出力する
    puts "point: #{array_to_string(@polygon)}"

    @sides = []
    @polygon.length.times do |i|
      x1, y1 = @polygon[i]
      x2, y2 = @polygon[(i + 1) % @polygon.length]
      d = Math.sqrt((x1 - x2) ** 2 + (y1 - y2) ** 2)
      @sides << d
    end

    # 各辺の長さの出力
    puts "side: #{array_to_string(@sides)}"

    @angles = []
    @polygon.length.times do |i|
      x1, y1 = @polygon[i]
      x2, y2 = @polygon[(i + 1) % @polygon.length]
      x3, y3 = @polygon[(i + 2) % @polygon.length]
      # http://www5d.biglobe.ne.jp/~noocyte/Programming/Geometry/RotationDirection.html#GetAngle
      ax = x1 - x2
      ay = y1 - y2
      bx = x3 - x2
      by = y3 - y2
      t = Math.atan2(ax * by - ay * bx, ax * bx + ay * by)
      a = t / Math::PI * 180.0
      a += 360.0 if a < 0
      @angles << a
    end

    # 角の和が大きい場合はすべて360から引く
    if @angles.sum >= (@polygon.length - 2) * 180.0 * 1.1
      @angles.map! { |a| 360.0 - a }
    end

    # 各頂点の角度の出力
    puts "angle: #{array_to_string(@angles)}: #{@angles.sum}"

    self
  end
  alias :start :print_status

  def array_to_string(a)
    # 小数点以下の桁数を@precisionにし，配列を文字列にする
    a.map { |b|
      if Array === b
        array_to_string(b)
      elsif Numeric === @precision && @precision > 0
        "%.*f" % [@precision, b]
      else
        b
      end
    }.inspect.gsub('"', '')
  end

  def to_svg(io = $stdout, param = {})
    # SVGを出力する
    image_width = (param[:w] || 320).to_i
    image_height = (param[:h] || 320).to_i
    margin = param[:margin] || 10
    line_width = param[:l] || 3
    background_color = param[:bg] || "\#f0fff0"
    stroke = param[:fg] || "black"
    option_exterior = param[:ext] # 真なら外角の線分を出力する

    cx = image_width / 2
    cy = image_height / 2
    mag = [image_width, image_height].min * 0.5 - margin

    io.puts '<?xml version="1.0" encoding="UTF-8" standalone="no"?>'
    io.puts '<svg xmlns="http://www.w3.org/2000/svg" width="%d" height="%d">' % [image_width, image_height]
    io.puts '<rect x="0" y="0" width="%d" height="%d" fill="%s" stroke="none" />' % [image_width, image_height, background_color]
    if option_exterior
      @polygon.length.times do |i|
        p0 = @polygon[i]
        p1 = @polygon[(i + 1) % @polygon.length]
        p2 = [p1[0] + (p1[0] - p0[0]), p1[1] + (p1[1] - p0[1])]
        p1 = [cx + p1[0] * mag, cy - p1[1] * mag]
        p2 = [cx + p2[0] * mag, cy - p2[1] * mag]
        io.puts '<line x1="%f" y1="%f" x2="%f" y2="%f" stroke="%s" stroke-width="%f" />' % (p1 + p2 + [stroke, line_width])
      end
    end
    io.print '<polygon points="' + @polygon.map { |a| "%f %f" % [cx + a[0] * mag, cy - a[1] * mag]}.join(" ")
    io.puts '" fill="none" stroke="%s" stroke-width="%f" />' % [stroke, line_width]
    io.puts '</svg>'

    self
  end

  def self.create_files(param = {})
    prec = param[:prec] || 3
    min = param[:min] || 3
    max = param[:max] || 10

    min.upto(max) do |n|
      puts "==== Regular, n=#{n}, prec=#{prec} ===="
      PolygonPlotter.new(prec: prec, regular: n).start.to_svg(open("polygon#{n}.svg", "w"))
      puts "==== Regular, n=#{n}, prec=#{prec}, with exterior edges ===="
      PolygonPlotter.new(prec: prec, regular: n).start.to_svg(open("polygon#{n}ext.svg", "w"), ext: true)
      puts "==== Fake 1, n=#{n}, prec=#{prec} ===="
      PolygonPlotter.new(prec: prec).setup_fake_regular_polygon(n).start.to_svg(open("polygon#{n}f1.svg", "w"))
      puts "==== Fake 1, n=#{n}, prec=#{prec}, with exterior edges ===="
      PolygonPlotter.new(prec: prec).setup_fake_regular_polygon(n).start.to_svg(open("polygon#{n}f1ext.svg", "w"), ext: true)
      puts "==== Fake 2, n=#{n}, prec=#{prec} ===="
      PolygonPlotter.new(prec: prec).setup_fake_regular_polygon2(n).start.to_svg(open("polygon#{n}f2.svg", "w"))
      puts "==== Fake 2, n=#{n}, prec=#{prec}, with exterior edges ===="
      PolygonPlotter.new(prec: prec).setup_fake_regular_polygon2(n).start.to_svg(open("polygon#{n}f2ext.svg", "w"), ext: true)
    end
  end
end

if __FILE__ == $0
  PolygonPlotter.create_files(min: 3, max: 10, prec: 3)
end