{"id":924,"date":"2021-07-11T17:20:26","date_gmt":"2021-07-11T09:20:26","guid":{"rendered":"https:\/\/www.caiqinyi.cn\/?p=924"},"modified":"2022-10-18T19:58:22","modified_gmt":"2022-10-18T11:58:22","slug":"real_projective_plane_and_homogeneous_coordinates2","status":"publish","type":"post","link":"https:\/\/www.caiqinyi.cn\/index.php\/2021\/07\/11\/real_projective_plane_and_homogeneous_coordinates2\/","title":{"rendered":"\u5b9e\u5c04\u5f71\u5e73\u9762\u53ca\u56fe\u5f62\u5b66\u4e2d\u7684\u9f50\u6b21\u5750\u6807(\u4e8c)"},"content":{"rendered":"<p><script type=\"text\/javascript\" async src=\"https:\/\/www.caiqinyi.cn\/wp-content\/MathJax\/MathJax.js?config=TeX-AMS_CHTML\">\n<\/script><br \/>\n<script type=\"text\/x-mathjax-config\">\n    MathJax.Hub.Config({\n        tex2jax: {inlineMath: [['$','$']]},\n        TeX: {equationNumbers: {autoNumber: [\"AMS\"], useLabelIds: true}},\n        \"HTML-CSS\": {linebreaks: {automatic: true}},\n        SVG: {linebreaks: {automatic: true}}\n    });\n<\/script><\/p>\n<p>\u8fd9\u5468\u7684\u52a0\u73ed\u751f\u6d3b\u771f\u7684\u662f\u592a\u7d2f\u4e86, \u6bcf\u5929\u665a\u4e0a\u90fd\u662f10\u70b9\u4ee5\u540e\u4e0b\u73ed, \u6240\u5e78\u4e0b\u5468\u6e38\u620f\u5c31\u548c\u73a9\u5bb6\u89c1\u9762\u4e86, \u5de5\u4f5c\u5f3a\u5ea6\u5e94\u8be5\u4f1a\u51cf\u5c11\u4e00\u4e9b\u4e86,<del datetime=\"2021-07-11T12:06:43+00:00\"> (\u4f46\u613f\u5982\u6b64\u2026\u2026)<\/del> \u8fd9\u5468\u7684\u6587\u7ae0\u7a0d\u5fae\u5077\u4e2a\u61d2, \u8bb0\u5f55\u5185\u5bb9\u4f1a\u7b80\u7565\u4e00\u4e9b, \u4e3b\u8981\u8fd8\u662f\u5361\u5728\u4e86\u5c04\u5f71\u5e73\u9762\u4e0e\u9f50\u6b21\u5750\u6807\u8fd9\u91cc, \u6ca1\u6709\u7406\u6e05\u62d3\u6251\u5b66\u4e2d\u7684\u9f50\u6b21\u5750\u6807\u4e0e\u56fe\u5f62\u5b66\u4e2d\u7684\u9f50\u6b21\u5750\u6807\u4e4b\u95f4\u7684\u8054\u7cfb, \u5728\u9605\u8bfb\u4e86\u5361\u5c14\u52a0\u91cc\u5927\u5b66\u7684\u4e24\u4f4d\u8001\u5e08\u5199\u7684\u9f50\u6b21\u5750\u6807\u8bb2\u4e49(<a href=\"https:\/\/www.caiqinyi.cn\/wp-content\/uploads\/2021\/07\/homocoords.pdf\">homocoords<\/a>) \u4ee5\u540e, \u56f0\u60d1\u4e4b\u5904\u4eff\u4f5b\u51cf\u5c11\u4e86\u8bb8\u591a, \u7279\u6b64\u8bb0\u5f55~ <\/p>\n<p><!--more--><\/p>\n<p>\u5b9e\u9645\u4e0a, \u7531\u4e8e\u4e24\u4f4d\u8001\u5e08\u662f\u8ba1\u7b97\u673a\u79d1\u73ed\u51fa\u8eab\u7684, \u6240\u4ee5\u611f\u89c9\u9f50\u6b21\u5750\u6807\u7684\u5f88\u591a\u5185\u5bb9\u5e76\u6ca1\u6709\u6df1\u5165\u5230\u672c\u8d28, \u6240\u4ee5\u4e5f\u4f1a\u7ed3\u5408\u4e4b\u524d\u5b66\u4e60\u7684\u4e00\u4e9b\u62d3\u6251\u77e5\u8bc6\u6765\u8bb2\u89e3~<br \/>\n$\\\\$ \u5c04\u5f71\u5e73\u9762\u76ee\u524d\u6709\u4e24\u79cd\u5b9a\u4e49\u65b9\u5f0f:<br \/>\n$\\\\$ $\\cdot$ \u5b9e\u5c04\u5f71\u5e73\u9762\u662f\u6b27\u6c0f\u7a7a\u95f4\u4e2d\u6240\u6709\u8fc7\u539f\u70b9\u7684\u76f4\u7ebf\u5f62\u6210\u7684\u7a7a\u95f4.<br \/>\n$\\\\$ $\\cdot$ \u5b9e\u5c04\u5f71\u5e73\u9762\u662f\u53ef\u4ee5\u548c<strong>\u628a<\/strong>$O$\u5f62\u6210\u53cc\u5c04\u7684\u5e73\u9762.<br \/>\n$\\\\$ \u5728\u5b66\u4e60\u4e86\u5c04\u5f71\u548c\u622a\u5f71\u7684\u6982\u5ff5\u4ee5\u540e, \u4f1a\u53d1\u73b0\u4e0a\u8ff0\u4e24\u79cd\u5b9a\u4e49\u662f\u7b49\u4ef7\u7684. \u4e00\u822c\u6765\u8bf4, $n$\u7ef4\u5c04\u5f71\u5e73\u9762\u662f\u65e0\u6cd5\u5d4c\u5165\u5728$n$\u7ef4\u6b27\u5f0f\u7a7a\u95f4\u5f53\u4e2d\u7684, \u53ea\u80fd\u5f80\u66f4\u9ad8\u7ef4\u6570\u7684\u6b27\u6c0f\u7a7a\u95f4\u5d4c\u5165, \u901a\u5e38\u4f1a\u628a$n$\u7ef4\u5c04\u5f71\u5e73\u9762\u5d4c\u5165\u5230$n+1$\u7ef4\u7684\u6b27\u6c0f\u7a7a\u95f4\u5f53\u4e2d. \u4f8b\u5982\u5728\u56fe\u5f62\u5b66\u5f53\u4e2d\u4f1a\u628a$(x, y, z)$\u5199\u6210$(x, y, z, 1)$\u7684\u5f62\u5f0f, \u8fd9\u80cc\u540e\u4fbf\u662f\u5e94\u7528\u4e86\u4e00\u4e2a\u5d4c\u5165\u6620\u5c04\u7684\u7ed3\u679c, \u7531\u5b9a\u4e49\u53ef\u77e5\u8fd9\u540c\u65f6\u4e5f\u662f\u4e00\u4e2a\u540c\u80da\u6620\u5c04, \u80fd\u4fdd\u6301\u62d3\u6251\u6027\u8d28\u4e0d\u53d8.<br \/>\n$\\\\$ \u5728\u4e09\u7ef4\u5c04\u5f71\u7a7a\u95f4\u4e2d\u5904\u7406\u70b9\u4e2a\u4eba\u89c9\u5f97\u4e3b\u8981\u6709\u4e09\u4e2a\u597d\u5904:<br \/>\n$\\\\$ $\\cdot$ \u80fd\u591f\u4f7f\u7528\u77e9\u9635\u4e58\u79ef\u8868\u793a\u4eff\u5c04\u53d8\u6362(\u5982\u5e73\u79fb\u53d8\u6362).<br \/>\n$\\\\$ $\\cdot$ \u5bf9\u4e8e\u70b9\u7684\u5904\u7406\u975e\u5e38\u7075\u6d3b, \u5982$(x, y, z)$\u4e0e$(x\/w, y\/w, z\/w)$\u5728\u4e09\u7ef4\u6b27\u6c0f\u7a7a\u95f4\u4e2d\u662f\u4e0d\u7b49\u4ef7\u7684, \u4f46\u7b49\u4ef7\u5173\u7cfb\u5728\u4e09\u7ef4\u5c04\u5f71\u7a7a\u95f4\u4e2d\u5374\u662f\u6210\u7acb\u7684, \u7528\u7b49\u4ef7\u7c7b\u7684\u8bed\u8a00\u5373\u53ef\u63cf\u8ff0\u4e3a$[(x, y, z)] = [(x\/w, y\/w, z\/w)]$; \u5f53$w $$ = 0$\u65f6$(x\/w, y\/w, z\/w)$\u8868\u793a\u4e00\u4e2a\u65e0\u7a77\u8fdc\u7684\u70b9, \u56e0\u6b64\u5728\u4e09\u7ef4\u5c04\u5f71\u7a7a\u95f4\u4e2d\u8fd8\u53ef\u5bf9\u65e0\u7a77\u8fdc\u70b9\u8fdb\u884c\u5904\u7406.<br \/>\n$\\\\$ $\\cdot$ \u53ef\u4ee5\u4f7f\u7528\u4efb\u4e00\u5d4c\u5165\u6620\u5c04, \u5982$(x, y, z) \\to (x, y, z, w), w \\in R$, \u56e0\u6b64\u5728\u6e32\u67d3\u6d41\u6c34\u7ebf\u8ba1\u7b97\u65f6\u7ecf\u5e38\u4f1a\u53d1\u73b0\u901a\u8fc7\u4e00\u4e2a\u56db\u7ef4\u77e9\u9635\u6539\u53d8\u4e86\u70b9\u7684$w$\u5206\u91cf, \u6709\u4eba\u53ef\u80fd\u4f1a\u95ee\u8fd9\u6ca1\u6709\u5173\u7cfb\u4e48? \u7b54\u6848\u662f\u786e\u5b9e\u6ca1\u6709\u5173\u7cfb, \u7531\u4e8e\u5d4c\u5165\u6620\u5c04\u7684\u540c\u80da\u6027\u8d28, \u5b83\u4f9d\u65e7\u6ca1\u6709\u6539\u53d8\u539f\u6765\u7684\u62d3\u6251\u6027\u8d28.<\/p>\n<p>PS: \u8bb2\u4e49\u4e2d\u8fd8\u4ece\u9f50\u6b21\u5750\u6807\u7684\u89d2\u5ea6\u51fa\u53d1\u53bb\u89e3\u91ca\u91cd\u5fc3\u5750\u6807, \u4e2a\u4eba\u89c9\u5f97\u8fd8\u662f\u5341\u5206\u65b0\u9896\u6709\u8da3\u7684\u89c2\u70b9, \u603b\u800c\u8a00\u4e4b, \u8fd9\u7bc7\u8bb2\u4e49\u8fd8\u662f\u503c\u5f97\u591a\u8bfb\u4e24\u904d\u7684, \u5c24\u5176\u662f\u9f50\u6b21\u5750\u6807\u88c1\u526a\u90a3\u4e00\u90e8\u5206, \u8bf4\u4e0d\u5b9a\u80fd\u5e94\u7528\u5230\u5de5\u4f5c\u4e0a\u6765~<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u8fd9\u5468\u7684\u52a0\u73ed\u751f\u6d3b\u771f\u7684\u662f\u592a\u7d2f\u4e86, \u6bcf\u5929\u665a\u4e0a\u90fd\u662f10\u70b9\u4ee5\u540e\u4e0b\u73ed, \u6240\u5e78\u4e0b\u5468\u6e38\u620f\u5c31\u548c\u73a9\u5bb6\u89c1\u9762\u4e86, \u5de5\u4f5c\u5f3a\u5ea6\u5e94\u8be5\u4f1a\u51cf\u5c11\u4e00 &hellip; <a href=\"https:\/\/www.caiqinyi.cn\/index.php\/2021\/07\/11\/real_projective_plane_and_homogeneous_coordinates2\/\" class=\"more-link\">\u7ee7\u7eed\u9605\u8bfb<span class=\"screen-reader-text\">\u5b9e\u5c04\u5f71\u5e73\u9762\u53ca\u56fe\u5f62\u5b66\u4e2d\u7684\u9f50\u6b21\u5750\u6807(\u4e8c)<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[15,10],"tags":[],"_links":{"self":[{"href":"https:\/\/www.caiqinyi.cn\/index.php\/wp-json\/wp\/v2\/posts\/924"}],"collection":[{"href":"https:\/\/www.caiqinyi.cn\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.caiqinyi.cn\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.caiqinyi.cn\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.caiqinyi.cn\/index.php\/wp-json\/wp\/v2\/comments?post=924"}],"version-history":[{"count":19,"href":"https:\/\/www.caiqinyi.cn\/index.php\/wp-json\/wp\/v2\/posts\/924\/revisions"}],"predecessor-version":[{"id":2549,"href":"https:\/\/www.caiqinyi.cn\/index.php\/wp-json\/wp\/v2\/posts\/924\/revisions\/2549"}],"wp:attachment":[{"href":"https:\/\/www.caiqinyi.cn\/index.php\/wp-json\/wp\/v2\/media?parent=924"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.caiqinyi.cn\/index.php\/wp-json\/wp\/v2\/categories?post=924"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.caiqinyi.cn\/index.php\/wp-json\/wp\/v2\/tags?post=924"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}