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January 1, 2019 13:42
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Drawing SVG images of a regular icosahedron with "kuku" forms along the sides
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| #!/usr/bin/env ruby | |
| # icosa-drawer.rb : drawing SVG images of a regular icosahedron | |
| # with "kuku" forms along the sides | |
| # by takehikom | |
| module IcosaDrawer | |
| class Triangle | |
| def initialize(param = {}) | |
| @label = param[:label] | |
| @x = param[:x] || 0.0 | |
| @y = param[:y] || 0.0 | |
| @inverted = param[:inv] | |
| @side = param[:side] || 100.0 | |
| @fontstyle = param[:fontstyle] # "font-size:16px; font-family:Serif; font-style:normal; font-weight:normal; fill:#000000; stroke:none;" | |
| @rot0 = param[:rot0] | |
| @rot60 = param[:rot60] | |
| @rot120 = param[:rot120] | |
| @rot180 = param[:rot180] | |
| @rot240 = param[:rot240] | |
| @rot300 = param[:rot300] | |
| end | |
| attr_accessor :label, :x, :y, :inverted, :side, :fontstyle | |
| attr_accessor :rot0, :rot60, :rot120, :rot180, :rot240, :rot300 | |
| def svg_transform(indent_level = 0) | |
| ' ' * indent_level + | |
| '<g transform="translate(%f,%f)%s">' % [@x, @y, @inverted ? " rotate(180)" : ""] + "\n" | |
| end | |
| def svg_center(indent_level = 0) | |
| return "" | |
| ' ' * indent_level + | |
| '<text x="%f" y="%f">%s</text>' % [0, @side * 0.05, @label] + | |
| "\n" | |
| end | |
| def svg_sidetext(rot, indent_level = 0) | |
| text = self.send("rot#{rot}") | |
| return "" if text.nil? | |
| # inverted | |
| # rot180 => rotate(360) | |
| # rot300 => rotate(240) | |
| # rot60 => rotate(120) | |
| # !inverted | |
| # rot0 => rotate(360) | |
| # rot120 => rotate(240) | |
| # rot240 => rotate(120) | |
| ' ' * indent_level + | |
| '<g transform="rotate(%d)">' % [inverted ? (180 - rot) : (360 - rot)] + | |
| '<text x="%f" y="%f">%s</text>' % [0, @side * 0.24, text] + | |
| '</g>' + "\n" | |
| end | |
| def svg_end_transform(indent_level = 0) | |
| ' ' * indent_level + | |
| '</g>' + "\n" | |
| end | |
| end | |
| class Drawer | |
| def initialize(param = {}) | |
| @filename_svg = param[:svg] || "icosa.svg" | |
| # @mode == 0 : 面と頂点に番号 | |
| # @mode == 1 : 同一の辺にはa×bとb×a | |
| # @mode == 2 : 同一の辺には同じ積の九九 | |
| @mode = (param[:mode] || 1).to_i | |
| @margin = 10 | |
| @s = @side = 100 # 正三角形の一辺の長さ | |
| @s_h = @s / 2.0 | |
| @s_r3 = @s.to_f * Math.sqrt(3.0) | |
| @s_r3h = @s_r3 / 2.0 # 正三角形の高さ | |
| end | |
| def start | |
| @width = (@s * 6 + @margin * 2).ceil | |
| @height = (@s_r3h * 3 + @margin * 2).ceil | |
| draw_header | |
| draw_expansion | |
| setup_surfaces | |
| draw_surfaces | |
| draw_footer | |
| save | |
| end | |
| def draw_header | |
| # SVGはじめ | |
| @src = <<EOS | |
| <?xml version="1.0" encoding="UTF-8" standalone="no"?> | |
| <svg xmlns="http://www.w3.org/2000/svg" | |
| width="#{@width}" height="#{@height}" id="icosa#{@mode}"> | |
| <style type="text/css" > | |
| <![CDATA[ | |
| .thinline { fill:none; stroke:black; stroke-width:1; } | |
| .thickline { fill:none; stroke:black; stroke-width:2; } | |
| text { font-size:16px; font-family:Serif; font-style:normal; font-weight:normal; fill:#000000; stroke:none; text-anchor:middle } | |
| ]]> | |
| </style> | |
| <rect x="0" y="0" width="#{@width}" height="#{@height}" fill="white" stroke="none"/> | |
| EOS | |
| end | |
| def draw_expansion | |
| # http://polyhedra.cocolog-nifty.com/blog/2017/11/post-dcc9.html | |
| # http://polyhedra.cocolog-nifty.com/polyhedra20.pdf | |
| # 横線4本 | |
| 0.upto(3) do |i| | |
| x1 = @margin + @s_h * ((i + 1) % 2) | |
| y1 = @margin + @s_r3h * i | |
| x2 = x1 + @s * (i == 1 ? 6 : 5) | |
| y2 = y1 | |
| @src += '<path d="M %f,%f L %f,%f" class="thickline"/>' % [x1, y1, x2, y2] | |
| @src += "\n" | |
| end | |
| # 右下がり斜め線5本 | |
| -1.upto(4) do |i| | |
| x1 = @margin + @s_h + @s * i | |
| y1 = @margin | |
| x2 = x1 + @s * 1.5 | |
| y2 = y1 + @s_r3h * 3 | |
| if i == -1 | |
| x1 += @s * 0.5 | |
| y1 += @s_r3h | |
| elsif i == 4 | |
| x2 -= @s * 0.5 | |
| y2 -= @s_r3h | |
| end | |
| @src += '<path d="M %f,%f L %f,%f" class="thickline"/>' % [x1, y1, x2, y2] | |
| @src += "\n" | |
| end | |
| # 左下がり斜め線7本 | |
| 0.upto(6) do |i| | |
| x1 = @margin + @s_h + @s * i | |
| y1 = @margin | |
| x2 = x1 - @s * 1.5 | |
| y2 = y1 + @s_r3h * 3 | |
| if i == 0 | |
| x2 += @s * 0.5 * 2 | |
| y2 -= @s_r3h * 2 | |
| elsif i == 6 | |
| x1 -= @s * 0.5 | |
| y1 += @s_r3h | |
| end | |
| @src += '<path d="M %f,%f L %f,%f" class="thickline"/>' % [x1, y1, x2, y2] | |
| @src += "\n" | |
| end | |
| # のりしろに◎ | |
| if @mode == 0 | |
| 0.upto(4) do |i| | |
| x0 = @margin + @s_h + @s * i | |
| y0 = @margin + @s_r3h * 2.0 / 3.0 | |
| @src += '<g transform="translate(%f,%f)">' % [x0, y0] | |
| @src += "\n" | |
| @src += '<circle cx="0" cy="0" r="6" class="thinline"/>' + "\n" | |
| @src += '<circle cx="0" cy="0" r="9" class="thinline"/>' + "\n" | |
| @src += '</g>' | |
| @src += "\n" | |
| end | |
| 0.upto(5) do |i| | |
| x0 = @margin + @s + @s * i | |
| y0 = @margin + @s_r3h * (2.0 + 1.0 / 3.0) | |
| if i == 5 | |
| x0 -= @s_h | |
| y0 -= @s_r3h | |
| end | |
| @src += '<g transform="translate(%f,%f)">' % [x0, y0] | |
| @src += "\n" | |
| @src += '<circle cx="0" cy="0" r="6" class="thinline"/>' + "\n" | |
| @src += '<circle cx="0" cy="0" r="9" class="thinline"/>' + "\n" | |
| @src += '</g>' | |
| @src += "\n" | |
| end | |
| end | |
| end | |
| def draw_footer | |
| # SVGおわり | |
| @src += <<EOS | |
| </svg> | |
| EOS | |
| end | |
| def save | |
| open(@filename_svg, "w") do |f_out| | |
| f_out.print @src | |
| end | |
| end | |
| def setup_surfaces | |
| @surf = [] | |
| # 上段の5つ（逆三角形） | |
| 0.upto(4) do |i| | |
| param = {} | |
| param[:label] = i.to_s | |
| param[:x] = @margin + @s * (i + 1) | |
| param[:y] = @margin + @s_r3h / 3.0 | |
| param[:inv] = true | |
| param[:side] = @s | |
| @surf << IcosaDrawer::Triangle.new(param) | |
| end | |
| # 中段の5つ（逆三角形） | |
| 0.upto(4) do |i| | |
| param = {} | |
| param[:label] = (5 + i).to_s | |
| param[:x] = @margin + @s_h + @s * i | |
| param[:y] = @margin + @s_r3h + @s_r3h / 3.0 | |
| param[:inv] = true | |
| param[:side] = @s | |
| @surf << IcosaDrawer::Triangle.new(param) | |
| end | |
| # 中段の5つ（通常の向きの三角形） | |
| 0.upto(4) do |i| | |
| param = {} | |
| param[:label] = (10 + i).to_s | |
| param[:x] = @margin + @s * (i + 1) | |
| param[:y] = @margin + @s_r3h + @s_r3h * 2.0 / 3.0 | |
| param[:side] = @s | |
| @surf << IcosaDrawer::Triangle.new(param) | |
| end | |
| # 下段の5つ（通常の向きの三角形） | |
| 0.upto(4) do |i| | |
| param = {} | |
| param[:label] = (15 + i).to_s | |
| param[:x] = @margin + @s_h + @s * i | |
| param[:y] = @margin + @s_r3h * 2 + @s_r3h * 2.0 / 3.0 | |
| param[:side] = @s | |
| @surf << IcosaDrawer::Triangle.new(param) | |
| end | |
| # 正二十面体で同一になる辺の対応付け | |
| case @mode | |
| when 1 | |
| match_edge_mode1 | |
| when 2 | |
| match_edge_mode2 | |
| else | |
| match_edge_mode0 | |
| end | |
| end | |
| def match_edge_mode0 | |
| # 正二十面体で同一になる辺の対応付け | |
| # 同一の辺にはカッコ書きで同じ番号を記載 | |
| 0.upto(4) do |i| | |
| j = (i + 1) % 5 | |
| @surf[i].rot60 = @surf[5 + j].rot180 = "(#{i + 1})" | |
| @surf[i].rot180 = @surf[j].rot300 = "(#{i + 6})" | |
| @surf[5 + i].rot60 = @surf[10 + i].rot240 = "(#{i + 11})" | |
| @surf[10 + i].rot120 = @surf[5 + j].rot300 = "(#{i + 16})" | |
| @surf[10 + i].rot0 = @surf[15 + j].rot240 = "(#{i + 21})" | |
| @surf[15 + i].rot120 = @surf[15 + j].rot0 = "(#{i + 26})" | |
| end | |
| end | |
| def match_edge_mode1 | |
| # 正二十面体で同一になる辺の対応付け | |
| # 同一の辺にはa×bとb×a | |
| srand(9981) | |
| kuku = (2..8).map {|p| ((p + 1)..9).map {|q| [p, q]}}.inject(:+) | |
| kuku << [1, 8] << [1, 9] | |
| kuku.shuffle! | |
| puts "kuku = #{kuku.inspect}" if $DEBUG | |
| 0.upto(4) do |i| | |
| j = (i + 1) % 5 | |
| @surf[i].rot60, @surf[5 + j].rot180 = kuku_forms(kuku[i]) | |
| @surf[i].rot180, @surf[j].rot300 = kuku_forms(kuku[i + 5]) | |
| @surf[5 + i].rot60, @surf[10 + i].rot240 = kuku_forms(kuku[i + 10]) | |
| @surf[10 + i].rot120, @surf[5 + j].rot300 = kuku_forms(kuku[i + 15]) | |
| @surf[10 + i].rot0, @surf[15 + j].rot240 = kuku_forms(kuku[i + 20]) | |
| @surf[15 + i].rot120, @surf[15 + j].rot0 = kuku_forms(kuku[i + 25]) | |
| end | |
| end | |
| def kuku_forms(param) | |
| a = ["#{param[0]}×#{param[1]}", "#{param[1]}×#{param[0]}"] | |
| if rand(2) == 1 | |
| a.reverse! | |
| end | |
| a | |
| end | |
| def match_edge_mode2 | |
| # 正二十面体で同一になる辺の対応付け | |
| # 同一の辺には同じ積の九九 | |
| srand(9981) | |
| kuku = (1..9).map {|p| (p == 1 ? [4, 6, 8, 9] : (1..9)).map {|q| [p, q]}}.inject(:+) | |
| # kuku = (1..9).map {|p| (1..9).map {|q| [p, q]}}.inject(:+) | |
| product = {} | |
| puts "kuku = #{kuku.inspect}" if $DEBUG | |
| kuku.each do |p, q| | |
| r = p * q | |
| s = "%d×%d" % [p, q] | |
| if product.key?(r) | |
| product[r] << s | |
| else | |
| product[r] = [s] | |
| end | |
| end | |
| kuku_a = [] | |
| product.each_key do |r| | |
| a = product[r].dup | |
| while a.length >= 2 | |
| a.shuffle! | |
| s1 = a.pop | |
| s2 = a.pop | |
| kuku_a << [s1, s2] | |
| end | |
| end | |
| kuku_a.shuffle! | |
| kuku_a = kuku_a[0, 30] | |
| puts "kuku_a = #{kuku_a.inspect}" if $DEBUG | |
| 0.upto(4) do |i| | |
| j = (i + 1) % 5 | |
| @surf[i].rot60, @surf[5 + j].rot180 = kuku_a[i] | |
| @surf[i].rot180, @surf[j].rot300 = kuku_a[i + 5] | |
| @surf[5 + i].rot60, @surf[10 + i].rot240 = kuku_a[i + 10] | |
| @surf[10 + i].rot120, @surf[5 + j].rot300 = kuku_a[i + 15] | |
| @surf[10 + i].rot0, @surf[15 + j].rot240 = kuku_a[i + 20] | |
| @surf[15 + i].rot120, @surf[15 + j].rot0 = kuku_a[i + 25] | |
| end | |
| end | |
| def draw_surfaces | |
| @surf.each_with_index do |t, i| | |
| @src += t.svg_transform | |
| @src += t.svg_center | |
| if t.inverted | |
| @src += t.svg_sidetext(180) | |
| @src += t.svg_sidetext(300) | |
| @src += t.svg_sidetext(60) | |
| else | |
| @src += t.svg_sidetext(0) | |
| @src += t.svg_sidetext(120) | |
| @src += t.svg_sidetext(240) | |
| end | |
| @src += t.svg_end_transform | |
| end | |
| end | |
| end | |
| end | |
| if __FILE__ == $0 | |
| puts "mode 0" | |
| IcosaDrawer::Drawer.new(svg: "icosa-test.svg", mode: 0).start | |
| puts "mode 1" | |
| IcosaDrawer::Drawer.new(svg: "icosa1.svg", mode: 1).start | |
| puts "mode 2" | |
| IcosaDrawer::Drawer.new(svg: "icosa2.svg", mode: 2).start | |
| # IcosaDrawer::Drawer.new.start | |
| end |
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