{"id":1295,"date":"2023-12-14T00:55:39","date_gmt":"2023-12-13T15:55:39","guid":{"rendered":"https:\/\/mell0w-5phere.net\/jaded5phere\/?p=1295"},"modified":"2023-12-14T00:59:42","modified_gmt":"2023-12-13T15:59:42","slug":"hexmap-distance","status":"publish","type":"post","link":"https:\/\/mell0w-5phere.net\/jaded5phere\/2023\/12\/14\/hexmap-distance\/","title":{"rendered":"Hexmap\u4e0a\u306e\u8ddd\u96e2(\u3064\u304f\u3070\u8ddd\u96e2\uff1f)\u3092\u8003\u3048\u308b"},"content":{"rendered":"<p>\u3000\u516d\u89d2\u5f62\u306e\u30bf\u30a4\u30eb\u304c\u6577\u304d\u8a70\u3081\u3089\u308c\u305f\u90fd\u5e02\u3067\u3001\u305d\u306e\u30bf\u30a4\u30eb\u306e\u8fba\u306b\u6cbf\u3063\u3066\u79fb\u52d5\u3059\u308b\u3068\u304d\u306e\u8ddd\u96e2(\u4ee5\u4e0b\u3001\u3064\u304f\u3070\u8ddd\u96e2\u3068\u547c\u3076)\u306b\u3064\u3044\u3066\u8003\u3048\u308b\u3002<\/p>\n<blockquote class=\"twitter-tweet\">\n<p lang=\"ja\" dir=\"ltr\">\u300c\u30de\u30f3\u30cf\u30c3\u30bf\u30f3\u8ddd\u96e2\u300d\u3067\u306f\u306a\u304f\u300c\u3064\u304f\u3070\u8ddd\u96e2\u300d\u306f\u5b9a\u7fa9\u3067\u304d\u308b\u304b\u306a\uff1f <a href=\"https:\/\/t.co\/y6MRAct28J\">https:\/\/t.co\/y6MRAct28J<\/a><\/p>\n<p>&mdash; AXION (@AXION_CAVOK) <a href=\"https:\/\/twitter.com\/AXION_CAVOK\/status\/1733373371273105421?ref_src=twsrc%5Etfw\">December 9, 2023<\/a><\/p><\/blockquote>\n<p> <script async src=\"https:\/\/platform.twitter.com\/widgets.js\" charset=\"utf-8\"><\/script> <\/p>\n<h4>\u30fb\u76f4\u611f\u7684\u306a\u7b54\u3048<\/h4>\n<p>\u3000\u516d\u89d2\u5f62\u306e\u30bf\u30a4\u30eb\u3092\u6577\u304d\u8a70\u3081\u305f\u3068\u304d\u3001\u3069\u3053\u306b\u5411\u304b\u3063\u3066\u3082\u305d\u306e\u7d4c\u8def\u306f\u30b8\u30b0\u30b6\u30b0\u306b\u306a\u308b\u304c\u3001\u65b9\u5411\u306b\u3088\u3063\u3066\u305d\u306e\u8ddd\u96e2\u306f\u7570\u306a\u308b\u30021\u8fba\u306e\u9577\u3055\u3092 \\(1\\) \u3068\u3059\u308b\u3068\u3001\u30bf\u30a4\u30eb\u306e\u8fba\u306b\u5e73\u884c\u306a\u65b9\u5411(\u4e0b\u56f3\u306e\u8d64\u7dda)\u306b\u9032\u3080\u3068\u304d\u306f\u3001\u8fba\u306b\u6cbf\u3063\u3066 \\(4\\) \u9032\u3080\u3068\u539f\u70b9\u304b\u3089\u306f \\(3\\) \u96e2\u308c\u308b\u3002\u4e00\u65b9\u3067\u3001\u8fba\u306b\u5782\u76f4\u306a\u65b9\u5411(\u9752\u7dda)\u306b\u9032\u3080\u3068\u304d\u306f\u3001 \u8fba\u306b\u6cbf\u3063\u3066 \\(2\\) \u9032\u3080\u3068\u539f\u70b9\u304b\u3089 \\(\\sqrt3\\) \u96e2\u308c\u308b\u3053\u3068\u306b\u306a\u308b\u3002\u3064\u307e\u308a\u3001\u540c\u3058\u3064\u304f\u3070\u8ddd\u96e2\u3092\u9032\u3093\u3067\u3082\u3001\u5411\u304d\u304c30\u5ea6\u9055\u3046\u3068\u539f\u70b9\u304b\u3089\u306e\u30e6\u30fc\u30af\u30ea\u30c3\u30c9\u8ddd\u96e2\u306f \\(2\/\\sqrt3\\) \u500d\u3060\u3051\u7570\u306a\u308b\u308f\u3051\u3067\u3001\u305d\u306e\u3088\u3046\u306a\u56f3\u5f62(\u201d\u7b49\u3064\u304f\u3070\u8ddd\u96e2\u7dda\u201d\u306e\u5f62)\u3068\u306f\u3001\u6b63\u516d\u89d2\u5f62\u3067\u3042\u308b\u3002<img loading=\"lazy\" src=\"https:\/\/mell0w-5phere.net\/jaded5phere\/wp-content\/uploads\/2023\/12\/tsukuba_fig1-300x275.jpg\" alt=\"\" width=\"300\" height=\"275\" class=\"alignnone size-medium wp-image-1313\" srcset=\"https:\/\/mell0w-5phere.net\/jaded5phere\/wp-content\/uploads\/2023\/12\/tsukuba_fig1-300x275.jpg 300w, https:\/\/mell0w-5phere.net\/jaded5phere\/wp-content\/uploads\/2023\/12\/tsukuba_fig1.jpg 377w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<h4>\u30fb\u3082\u3046\u5c11\u3057\u771f\u9762\u76ee\u306b\u8003\u3048\u3066\u307f\u308b<\/h4>\n<p>\u3000\u76f4\u611f\u7684\u306b\u6b63\u516d\u89d2\u5f62\u3067\u3042\u308a\u305d\u3046\u3060\u3001\u3068\u3044\u3046\u3053\u3068\u306f\u308f\u304b\u3063\u305f\u304c\u3001\u672c\u5f53\u306b\u305d\u3046\u3060\u308d\u3046\u304b\uff1f<\/p>\n<p>\u3000\u307e\u305a\u306f\u30bf\u30a4\u30eb\u306b\u6cbf\u3063\u305f\u5ea7\u6a19\u7cfb\u3092\u8003\u3048\u308b\u5fc5\u8981\u304c\u3042\u308b\u3060\u308d\u3046\u3002\u56f3\u306e\u3088\u3046\u306b60\u5ea6\u306e\u89d2\u5ea6\u3067\u4ea4\u308f\u308b\u8ef8 \\(\\xi, \\eta\\) \u3092\u8003\u3048\u3001\u305d\u308c\u305e\u308c\u306e\u65b9\u5411\u306e\u5358\u4f4d\u30d9\u30af\u30c8\u30eb\u3092 \\(\\boldsymbol i, \\boldsymbol j\\) \u3068\u3057\u3088\u3046\u3002\u3055\u3089\u306b\u3001\\(\\boldsymbol j\\) \u306860\u5ea6\u3092\u306a\u3059\u30d9\u30af\u30c8\u30eb\u3092 \\(\\boldsymbol k\\) \u3068\u3057\u3066\u3001\u305d\u308c\u3089\u9006\u5411\u304d\u306e\u30d9\u30af\u30c8\u30eb\u3092\u3001\u4e0a\u306b\u30d0\u30fc\u3092\u3064\u3051\u3066\u8868\u305d\u3046\u3002<br \/>\n<img loading=\"lazy\" src=\"https:\/\/mell0w-5phere.net\/jaded5phere\/wp-content\/uploads\/2023\/12\/tsukuba_fig2.jpg\" alt=\"\" width=\"849\" height=\"450\" class=\"alignnone size-full wp-image-1314\" srcset=\"https:\/\/mell0w-5phere.net\/jaded5phere\/wp-content\/uploads\/2023\/12\/tsukuba_fig2.jpg 849w, https:\/\/mell0w-5phere.net\/jaded5phere\/wp-content\/uploads\/2023\/12\/tsukuba_fig2-300x159.jpg 300w, https:\/\/mell0w-5phere.net\/jaded5phere\/wp-content\/uploads\/2023\/12\/tsukuba_fig2-768x407.jpg 768w\" sizes=\"(max-width: 849px) 100vw, 849px\" \/><br \/>\n\u3000\u5e73\u9762\u4e0a\u306e\u683c\u5b50\u70b9\u306f\u3001\u5270\u4f59$$\\xi-\\eta \\mod 3$$\u306b\u3088\u3063\u3066\u5206\u985e\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u3002\u3064\u307e\u308a<\/p>\n<ul>\n<li>\u5270\u4f59\u304c0(\u9752) \u2192\\(\\boldsymbol j, \\bar{\\boldsymbol i}, \\bar{\\boldsymbol k}\\) \u65b9\u5411\u306b\u9032\u3081\u308b<\/li>\n<li>\u5270\u4f59\u304c1(\u8d64) \u2192\u9802\u70b9\u3067\u306f\u306a\u3044<\/li>\n<li>\u5270\u4f59\u304c2(\u7d2b) \u2192\\(\\boldsymbol i, \\boldsymbol k, \\bar{\\boldsymbol j}\\) \u65b9\u5411\u306b\u9032\u3081\u308b<\/li>\n<\/ul>\n<p>\u3068\u3044\u3046\u3053\u3068\u3067\u3042\u308b\u3002<\/p>\n<p>\u3000\u3044\u307e\u3001\u30bf\u30a4\u30eb\u306e\u30d1\u30bf\u30fc\u30f3\u306f120\u5ea6\u56de\u8ee2\u5bfe\u79f0\u3067\u3001\u307e\u305f \\(\\xi, \\eta\\) \u8ef8\u306b\u5bfe\u3057\u3066\u93e1\u5bfe\u79f0\u306a\u306e\u3067\u3001\u53f3\u4e0a\u306e60\u5ea6\u306e\u9818\u57df\u306b\u3064\u3044\u3066\u3060\u3051\u8003\u3048\u308c\u3070\u826f\u3044\u3002\u3086\u3048\u306b\u3001\u79fb\u52d5\u3059\u308b\u65b9\u5411\u3082 \\(\\boldsymbol i, \\boldsymbol j, \\boldsymbol k, \\bar{\\boldsymbol k}\\) \u3060\u3051\u3092\u8003\u3048\u308c\u3070\u3088\u3044\u3002<\/p>\n<p>\u3000\u3055\u3066\u3001\u539f\u70b9\u304b\u3089\u8fba\u306b\u6cbf\u3063\u3066 \\(2n\\) \u56de\u79fb\u52d5\u3057\u3066\u5230\u9054\u53ef\u80fd\u306a\u70b9\u306e\u96c6\u5408\u3092\u8003\u3048\u308b\u3002\u96a3\u308a\u5408\u3046\u9802\u70b9\u3068\u306f\u5fc5\u305a\u5270\u4f59\u306e\u5024\u304c\u9055\u3046\u306e\u3067\u3001\u3069\u3093\u306a\u7d4c\u8def\u3092\u901a\u3063\u3066\u3082\u9752\u3068\u7d2b\u306e\u70b9\u3092\u4ea4\u4e92\u306b\u8fbf\u308b\u3053\u3068\u306b\u306a\u308b\u3002\u3057\u305f\u304c\u3063\u3066\u534a\u5206\u306e \\(n\\) \u56de\u306f\u9752\u306e\u70b9\u304b\u3089\u3001\u3082\u3046\u534a\u5206\u306e \\(n\\) \u56de\u306f\u7d2b\u306e\u70b9\u304b\u3089\u79fb\u52d5\u3059\u308b\u3053\u3068\u306b\u306a\u308b\u3002\u7d2b\u306e\u70b9\u304b\u3089 \\(\\boldsymbol i\\) \u65b9\u5411\u306b\u9032\u3080\u3053\u3068\u3092\u9078\u3093\u3060\u56de\u6570\u3092 \\(p\\) \u3068\u304a\u304d\u3001\u9752\u306e\u70b9\u304b\u3089 \\(\\boldsymbol j\\) \u65b9\u5411\u306b\u9032\u3080\u3053\u3068\u3092\u9078\u3093\u3060\u56de\u6570\u3092 \\(q\\) \u3068\u304a\u304f\u3068\u3001\u6700\u7d42\u7684\u306b\u5230\u9054\u3059\u308b\u70b9\u306e\u4f4d\u7f6e\u30d9\u30af\u30c8\u30eb\u306f$$p\\boldsymbol i+q\\boldsymbol j+(n-p) \\boldsymbol k+(n-q)\\bar{\\boldsymbol k}$$<br \/>\n\u3067\u3042\u308b\u3002\u3053\u3053\u306b\u3001$$\\begin{eqnarray*}<br \/>\n\\boldsymbol i &=& (1, 0)\\\\<br \/>\n\\boldsymbol j &=& (0, 1)\\\\<br \/>\n\\boldsymbol k &=& (-1, 1)<br \/>\n\\end{eqnarray*}$$<br \/>\n\u3067\u3042\u308b\u304b\u3089\u3001\u3053\u308c\u3092\u7528\u3044\u3066\u5230\u9054\u70b9\u306e\u6210\u5206\u3092\u66f8\u304d\u4e0b\u3059\u3068$$(2p-q, 2q-p)$$\u3068\u306a\u308b\u3002\\(0\\leq p\\leq n, 0 \\leq q \\leq n\\) \u304b\u3064 \\(\\xi\\geq 0, \\eta\\geq 0\\) \u306e\u7bc4\u56f2\u3067\u3053\u308c\u304c\u53d6\u308a\u3046\u308b\u7bc4\u56f2\u3092 \\(\\xi \\mathrm{-} \\eta\\) \u5e73\u9762\u4e0a\u306b\u56f3\u793a\u3059\u308b\u3068\u3001\u4e0b\u56f3\u306e\u8d64\u3067\u56f2\u3093\u3060\u56db\u8fba\u5f62\u306e\u5185\u5074\u306e\u9818\u57df\u3068\u306a\u308b\u3002\u9818\u57df\u5168\u4f53\u306f\u3064\u304f\u3070\u8ddd\u96e2\u304c\\(0\\) \u4ee5\u4e0a \\(2n\\) \u4ee5\u4e0b\u306e\u70b9\u306e\u96c6\u5408\u306a\u306e\u3067\u3001\u3064\u304f\u3070\u8ddd\u96e2\u304c \\(2n\\) \u306b\u7b49\u3057\u304f\u306a\u308b\u306e\u306f\u5883\u754c\u306e\u3046\u3061\u8ef8\u3068\u5171\u901a\u3067\u306a\u3044\u90e8\u5206\u3068\u306a\u308b\u3002\u3053\u308c\u306f\u6b63\u516d\u89d2\u5f62\u306e1\/6\u3060\u304b\u3089\u3001\u78ba\u304b\u306b\u7b49\u8ddd\u96e2\u7dda\u306e\u5f62\u306f\u6b63\u516d\u89d2\u5f62\u306b\u306a\u308b\u3053\u3068\u304c\u308f\u304b\u308b\u3002<br \/>\n<img loading=\"lazy\" src=\"https:\/\/mell0w-5phere.net\/jaded5phere\/wp-content\/uploads\/2023\/12\/tsukuba_fig3.jpg\" alt=\"\" width=\"396\" height=\"425\" class=\"alignnone size-full wp-image-1315\" srcset=\"https:\/\/mell0w-5phere.net\/jaded5phere\/wp-content\/uploads\/2023\/12\/tsukuba_fig3.jpg 396w, https:\/\/mell0w-5phere.net\/jaded5phere\/wp-content\/uploads\/2023\/12\/tsukuba_fig3-280x300.jpg 280w\" sizes=\"(max-width: 396px) 100vw, 396px\" \/><\/p>\n<h4>\u30fb\u4fe1\u7528\u3067\u304d\u306a\u3044\u306e\u3067\u30d7\u30ed\u30b0\u30e9\u30e0\u3067\u78ba\u304b\u3081\u308b<\/h4>\n<p>\u3000\u5e45\u512a\u5148\u63a2\u7d22\u3067\u5b9f\u969b\u306b\u597d\u304d\u306a\u3064\u304f\u3070\u8ddd\u96e2\u3060\u3051\u96e2\u308c\u305f\u70b9\u306e\u96c6\u5408\u3092\u5217\u6319\u3059\u308b\u30d7\u30ed\u30b0\u30e9\u30e0\u3092\u66f8\u3044\u305f\u3002<a href=\"https:\/\/gist.github.com\/sr8e\/12ed1dfd19abe68f01f4bf8628a72c59\">gist<\/a>\u306b\u7f6e\u3044\u3066\u3042\u308b\u306e\u3067\u6c17\u306b\u306a\u308b\u4eba\u306f\u3069\u3046\u305e\u3002<br \/>\n\u3000\u8ddd\u96e2\u304c\u5c0f\u3055\u3044\u3046\u3061\u306f\u8ddd\u96e2\u304c\u5947\u6570\u3060\u3068\u82e5\u5e72\u975e\u5bfe\u79f0\u306b\u306a\u308a\u6b63\u516d\u89d2\u5f62\u306b\u306f\u306a\u3089\u306a\u3044\u304c\u3001\u8ddd\u96e2\u304c\u5927\u304d\u304f\u306a\u308b\u3068\u6b63\u516d\u89d2\u5f62\u306b\u8fd1\u3065\u304f\u3002\u4ee5\u4e0b\u306b\u8ddd\u96e2\u304c \\(5, 6, 31\\) \u306e\u4f8b\u3092\u793a\u3059\u3002<br \/>\n<img loading=\"lazy\" src=\"https:\/\/mell0w-5phere.net\/jaded5phere\/wp-content\/uploads\/2023\/12\/tsukuba_5-300x225.png\" alt=\"\" width=\"300\" height=\"225\" class=\"alignnone size-medium wp-image-1310\" srcset=\"https:\/\/mell0w-5phere.net\/jaded5phere\/wp-content\/uploads\/2023\/12\/tsukuba_5-300x225.png 300w, https:\/\/mell0w-5phere.net\/jaded5phere\/wp-content\/uploads\/2023\/12\/tsukuba_5.png 640w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><br \/>\n<img loading=\"lazy\" src=\"https:\/\/mell0w-5phere.net\/jaded5phere\/wp-content\/uploads\/2023\/12\/tsukuba_6-300x225.png\" alt=\"\" width=\"300\" height=\"225\" class=\"alignnone size-medium wp-image-1311\" srcset=\"https:\/\/mell0w-5phere.net\/jaded5phere\/wp-content\/uploads\/2023\/12\/tsukuba_6-300x225.png 300w, https:\/\/mell0w-5phere.net\/jaded5phere\/wp-content\/uploads\/2023\/12\/tsukuba_6.png 640w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><br \/>\n<img loading=\"lazy\" src=\"https:\/\/mell0w-5phere.net\/jaded5phere\/wp-content\/uploads\/2023\/12\/tsukuba_31-300x225.png\" alt=\"\" width=\"300\" height=\"225\" class=\"alignnone size-medium wp-image-1312\" srcset=\"https:\/\/mell0w-5phere.net\/jaded5phere\/wp-content\/uploads\/2023\/12\/tsukuba_31-300x225.png 300w, https:\/\/mell0w-5phere.net\/jaded5phere\/wp-content\/uploads\/2023\/12\/tsukuba_31.png 640w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><br \/>\n\u3000\u30e6\u30fc\u30af\u30ea\u30c3\u30c9\u8ddd\u96e2\u3001\u30de\u30f3\u30cf\u30c3\u30bf\u30f3\u8ddd\u96e2\u3068\u306e\u6bd4\u8f03\u3082\u793a\u3059\u3002\u5192\u982d\u3067\u8ff0\u3079\u305f\u901a\u308a\u3001\\(x\\)\u8ef8\u3068\u306e\u4ea4\u70b9\u306f \\(3\/4\\), \\(y\\)\u8ef8\u3068\u306e\u4ea4\u70b9\u306f \\(\\sqrt3\/2\\) \u3067\u3042\u308b\u3002<br \/>\n<img loading=\"lazy\" src=\"https:\/\/mell0w-5phere.net\/jaded5phere\/wp-content\/uploads\/2023\/12\/tsukuba_fig4.png\" alt=\"\" width=\"640\" height=\"480\" class=\"alignnone size-full wp-image-1318\" srcset=\"https:\/\/mell0w-5phere.net\/jaded5phere\/wp-content\/uploads\/2023\/12\/tsukuba_fig4.png 640w, https:\/\/mell0w-5phere.net\/jaded5phere\/wp-content\/uploads\/2023\/12\/tsukuba_fig4-300x225.png 300w\" sizes=\"(max-width: 640px) 100vw, 640px\" \/><\/p>\n<hr \/>\n<p>\u3000\u5b9f\u969b\u306b\u3053\u3093\u306a\u9053\u8def\u304c\u3042\u3063\u305f\u3089\u3081\u3061\u3083\u304f\u3061\u3083\u901a\u308a\u306b\u304f\u3044\u3060\u308d\u3046\u3068\u601d\u3046\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u3000\u516d\u89d2\u5f62\u306e\u30bf\u30a4\u30eb\u304c\u6577\u304d\u8a70\u3081\u3089\u308c\u305f\u90fd\u5e02\u3067\u3001\u305d\u306e\u30bf\u30a4\u30eb\u306e\u8fba\u306b\u6cbf\u3063\u3066\u79fb\u52d5\u3059\u308b\u3068\u304d\u306e\u8ddd\u96e2(\u4ee5\u4e0b\u3001\u3064\u304f\u3070\u8ddd\u96e2\u3068\u547c\u3076)\u306b\u3064\u3044\u3066\u8003\u3048\u308b\u3002 \u300c\u30de\u30f3\u30cf\u30c3\u30bf\u30f3\u8ddd\u96e2\u300d\u3067\u306f\u306a\u304f\u300c\u3064\u304f\u3070\u8ddd\u96e2\u300d\u306f\u5b9a\u7fa9\u3067\u304d\u308b\u304b\u306a\uff1f 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