\u76f8\u673a\u7684\u4f4d\u7f6e[latex]\\overrightarrow{e}[\/latex]<\/p>\n\n\n\n
\u76f8\u673a\u7684\u89c6\u7ebf[latex]\\widehat{g}[\/latex]<\/p>\n\n\n\n
\u76f8\u673a\u5411\u4e0a\u65b9\u5411[latex]\\widehat{t}[\/latex]<\/p>\n\n\n\n
\u5c06\u6240\u6709\u7269\u54c1\u548c\u76f8\u673a\u8fdb\u884c\u79fb\u52a8\uff0c\u4f7f\u5f97\u76f8\u673a\u79fb\u52a8\u5230\u6807\u51c6\u4f4d\uff1a\u76f8\u673a\u5904\u4e8e\u539f\u70b9\uff0c\u5411-Z\u65b9\u5411\u770b\uff0c\u5411\u4e0a\u65b9\u5411\u4e3aY<\/p>\n\n\n\n<\/figure >\n<\/figure><\/noscript>\n\n\n\n\u5148\u5c06 [latex]\\overrightarrow{e}[\/latex] \u5e73\u79fb\u5230\u539f\u70b9\uff0c\u518d\u5c06 [latex]\\widehat{g}[\/latex] \u65cb\u8f6c\u5230 -Z \u65b9\u5411\uff0c\u518d\u5c06 [latex]\\widehat{t}[\/latex] \u65cb\u8f6c\u5230 Y \u65b9\u5411\uff0c\u6700\u540e\u5c06 [latex](g \\times t)[\/latex] \u65cb\u8f6c\u5230 X \u65b9\u5411\u3002<\/p>\n\n\n\n<\/figure >\n<\/figure><\/noscript>\n\n\n\n[latex]M_{\\text {view }}=R_{\\text {view }} T_{\\text {view }}[\/latex]<\/p>\n\n\n\n1.\u5e73\u79fb [latex]\\overrightarrow{e}[\/latex] \u5230\u539f\u70b9[latex]T_{\\text {view }}=\\begin{bmatrix}1 & 0 & 0 & -x_e \\\\0 & 1 & 0 & -y_e \\\\0 & 0 & 1 & -z_e \\\\0 & 0 & 0 & 1\\end{bmatrix}[\/latex]<\/p>\n\n\n\n2. \u65cb\u8f6c [latex]\\widehat{g}[\/latex] \u5230 -Z \u65b9\u5411\uff0c\u65cb\u8f6c [latex]\\widehat{t}[\/latex] \u5230 Y \u65b9\u5411\uff0c\u65cb\u8f6c [latex](g \\times t)[\/latex] \u5230 X \u65b9\u5411\u3002 [latex]R_{\\text {view }}=\\begin{bmatrix}x_{\\hat{g} \\times \\hat{t}} & y_{\\hat{g} \\times \\hat{t}} & z_{\\hat{g} \\times \\hat{t}} & 0 \\\\x_t & y_t & z_t & 0 \\\\x_{-g} & y_{-g} & z_{-g} & 0 \\\\0 & 0 & 0 & 1\\end{bmatrix}[\/latex]<\/p>\n\n\n\n\u6295\u5f71<\/h2>\n\n\n\n\u6295\u5f71\u5206\u4e3a\u6b63\u4ea4\u6295\u5f71\u548c\u900f\u89c6\u6295\u5f71<\/p>\n\n\n\n<\/figure >\n<\/figure><\/noscript>\n\n\n\n\u89c6\u666f\u4f53<\/h3>\n\n\n\n\u89c6\u666f\u4f53\u662f\u6307\u7531\u6444\u50cf\u673a\u6216\u89c2\u5bdf\u8005\u6240\u770b\u5230\u7684\u573a\u666f\u7684\u51e0\u4f55\u5f62\u72b6\uff0c\u5b83\u662f\u75316\u4e2a\u5e73\u9762\u786e\u5b9a\u7684\u533a\u57df\uff0c\u8fd96\u4e2a\u5e73\u9762\u5206\u522b\u4e3a\u4e0a\u5e73\u9762\uff08up\uff09\u3001\u4e0b\u5e73\u9762\uff08down\uff09\u3001\u5de6\u5e73\u9762\uff08left\uff09\u3001\u53f3\u5e73\u9762\uff08right\uff09\u3001\u8fdc\u5e73\u9762\uff08far\uff09\u548c\u8fd1\u5e73\u9762\uff08near\uff09\u3002\u89c6\u666f\u4f53\u5185\u7684\u7269\u4f53\u53ef\u4ee5\u88ab\u6295\u5f71\u5230\u8fd1\u5e73\u9762\u4e0a\uff0c\u800c\u89c6\u666f\u4f53\u5916\u9762\u7684\u7269\u4f53\u5219\u4f1a\u88ab\u88c1\u526a\u6389\u3002<\/p>\n\n\n\nl\uff08left\uff09\uff1a\u89c6\u666f\u4f53\u5de6\u4fa7\u76f8\u5bf9\u4e8e\u76f8\u673a\u7684\u8ddd\u79bb\u3002r\uff08right\uff09\uff1a\u89c6\u666f\u4f53\u53f3\u4fa7\u76f8\u5bf9\u4e8e\u76f8\u673a\u7684\u8ddd\u79bb\u3002n\uff08near\uff09\uff1a\u89c6\u666f\u4f53\u8fd1\u7aef\u76f8\u5bf9\u4e8e\u76f8\u673a\u7684\u8ddd\u79bb\u3002f\uff08far\uff09\uff1a\u89c6\u666f\u4f53\u8fdc\u7aef\u76f8\u5bf9\u4e8e\u76f8\u673a\u7684\u8ddd\u79bb\u3002t\uff08top\uff09\uff1a\u89c6\u666f\u4f53\u4e0a\u4fa7\u76f8\u5bf9\u4e8e\u76f8\u673a\u7684\u8ddd\u79bb\u3002b\uff08bottom\uff09\uff1a\u89c6\u666f\u4f53\u4e0b\u4fa7\u76f8\u5bf9\u4e8e\u76f8\u673a\u7684\u8ddd\u79bb\u3002<\/p>\n\n\n\n\u6b63\u4ea4\u6295\u5f71<\/h3>\n\n\n\n1.\u5b9a\u4e49\u4e00\u4e2a\u7acb\u65b9\u4f53\uff0c\u5373\u89c6\u666f\u4f53[latex][l,r]\\times[b,t]\\times[f,n][\/latex]2.\u5c06\u89c6\u666f\u4f53\u7684\u4e2d\u5fc3\u79fb\u52a8\u5230\u539f\u70b93.\u5c06\u89c6\u666f\u4f53\u7684\u8fb9\u957f\u62c9\u5347\u6210[latex][-1,1]^3[\/latex]4.\u5f97\u5230\u4e00\u4e2aCanonical\uff08\u6b63\u5219\u3001\u89c4\u8303\u3001\u6807\u51c6\uff09\u7acb\u65b9\u4f53<\/p>\n\n\n\n\u5224\u65ad\u8fdc\u8fd1\uff1a\u4f7f\u7528\u539f\u7acb\u65b9\u4f53\u7684z\u5750\u6807 [latex][f,n][\/latex]\uff0c\u7531\u4e8e\u662f\u770b\u5411-Z\u65b9\u5411\uff0c\u6240\u4ee5\u5f53Z\u5750\u6807\u503c\u8d8a\u5927\uff0c\u79bb\u76f8\u673a\u8d8a\u8fd1\uff0cZ\u5750\u6807\u503c\u8d8a\u5c0f\uff0c\u79bb\u76f8\u673a\u8d8a\u8fdc <\/p>\n\n\n\n\u6570\u5b66\u8868\u8fbe\uff1a\u5148\u5c06\u4e2d\u5fc3\u5e73\u79fb\u5230\u539f\u70b9\u4e0a\uff0c\u7136\u540e\u8fdb\u884c\u7f29\u653e[latex]M_{\\text {ortho }}=\\begin{bmatrix}\\frac{2}{r-l} & 0 & 0 & 0 \\\\0 & \\frac{2}{t-b} & 0 & 0 \\\\0 & 0 & \\frac{2}{n-f} & 0 \\\\0 & 0 & 0 & 1\\end{bmatrix}\\begin{bmatrix}1 & 0 & 0 & -\\frac{r+l}{2} \\\\0 & 1 & 0 & -\\frac{t+b}{2} \\\\0 & 0 & 1 & -\\frac{n+f}{2} \\\\0 & 0 & 0 & 1\\end{bmatrix}[\/latex]<\/p>\n\n\n\n\u4f46\u7531\u4e8e\u6709\u4e4b\u524d\u7684\u89c6\u56fe\u53d8\u6362\uff0c\u89c6\u666f\u4f53n\u3001f\u5e73\u9762\u7684\u4e2d\u5fc3\u5c31\u5728Z\u8f74\u4e0a\uff0c\u6240\u4ee5\u5e73\u79fb\u65f6\u53ea\u9700\u8981\u5c06\u89c6\u666f\u4f53\u6cbfZ\u8f74\u5e73\u79fb\u4f7f\u4e2d\u5fc3\u5728\u5750\u6807\u539f\u70b9\u4e0a\u3002\u5e76\u4e14\u6709[latex]r=-l[\/latex]\uff0c[latex]b=-t[\/latex]\u3002\u6240\u4ee5\u516c\u5f0f\u53ef\u4ee5\u8fdb\u884c\u7b80\u5316 [latex]M_{\\text {ortho }}=\\begin{bmatrix}\\frac{2}{r-l} & 0 & 0 & 0 \\\\0 & \\frac{2}{t-b} & 0 & 0 \\\\0 & 0 & \\frac{2}{n-f} & 0 \\\\0 & 0 & 0 & 1\\end{bmatrix}\\begin{bmatrix}1 & 0 & 0 & 0 \\\\0 & 1 & 0 & 0 \\\\0 & 0 & 1 & -\\frac{n+f}{2} \\\\0 & 0 & 0 & 1\\end{bmatrix}[\/latex]<\/p>\n\n\n\n<\/figure >\n<\/figure><\/noscript>\n\n\n\n \u900f\u89c6\u6295\u5f71<\/h3>\n\n\n\n\u6839\u636e\u9f50\u6b21\u5750\u6807\u7684\u5b9a\u4e49 [latex]\\begin{bmatrix}x \/ w \\\\y \/ w \\\\z \/ w \\\\1\\end{bmatrix}, w \\neq 0[\/latex] \u53ef\u77e5\uff0c\u5c06\u91cc\u9762\u6bcf\u4e2a\u5143\u7d20\u4e58\u4ee5[latex]k(k\\ne 0)[\/latex]\u540e\uff0c\u8868\u793a\u7684\u662f\u540c\u4e00\u5411\u91cf\u3002<\/p>\n\n\n\n<\/figure >\n<\/figure><\/noscript>\n\n\n\n\u5728\u8fdb\u884c\u900f\u89c6\u6295\u5f71\u65f6\uff0c\u5148\u5c06\u900f\u89c6\u6295\u5f71\u7684\u68f1\u53f0\u8fdb\u884c\u6324\u538b\uff0c\u76f4\u5230\u53d8\u6210\u89c6\u666f\u4f53\uff0c\u5373\u4e00\u4e2a\u957f\u65b9\u4f53\uff0c\u7136\u540e\u518d\u8fdb\u884c\u6b63\u4ea4\u6295\u5f71<\/p>\n\n\n\n\u5728\u6324\u538b\u65f6\uff0c\u8981\u9075\u5faa\uff1a1.\u8fd1\u5e73\u9762\u6324\u538b\u540e\u4e0d\u53d82.\u8fdc\u5e73\u9762\u6324\u538b\u540eZ\u503c\u4e0d\u53d83.\u8fdc\u5e73\u9762\u7684\u4e2d\u5fc3\u6324\u538b\u540e\u4ecd\u7136\u4e3a\u4e2d\u5fc3<\/p>\n\n\n\n<\/figure >\n<\/figure><\/noscript>\n\n\n\n\u5bf9\u4e8e\u70b9[latex](x,y,z)[\/latex]\u88ab\u6324\u538b\u540e\u5f97\u5230[latex](x^{\\prime},y^{\\prime}, z^{\\prime})[\/latex] \uff0c\u6839\u636e\u76f8\u4f3c\u4e09\u89d2\u5f62\u53ef\u5f97\uff1a[latex]x^{\\prime}=\\frac{n}{z} x[\/latex][latex]y^{\\prime}=\\frac{n}{z} y[\/latex]<\/p>\n\n\n\n\u5199\u4f5c\u9f50\u6b21\u5750\u6807\u4e3a\uff1a[latex]\\begin{bmatrix}x \\\\y \\\\z \\\\1\\end{bmatrix}\\Rightarrow\\begin{bmatrix}n x \/ z \\\\n y \/ z \\\\\\text { unknown } \\\\1\\end{bmatrix}\\stackrel{\\text { mult. by z }}{==}\\begin{bmatrix}n x \\\\n y \\\\\\text { still unknown } \\\\z\\end{bmatrix}[\/latex]<\/p>\n\n\n\n\u4e8e\u662f\u53ef\u4ee5\u5f97\u51fa[latex]M_{\\text {persp } \\rightarrow \\text { ortho }}[\/latex]\u4e3a\uff1a[latex]M_{\\text {persp } \\rightarrow \\text { ortho }}=\\begin{bmatrix}n & 0 & 0 & 0 \\\\0 & n & 0 & 0 \\\\? & ? & ? & ? \\\\0 & 0 & 1 & 0\\end{bmatrix}[\/latex]<\/p>\n\n\n\n\u73b0\u5728\u9700\u8981\u6c42\u51faZ\u5750\u6807\uff0c\u4e5f\u5c31\u662f\u4e0a\u8ff0\u77e9\u9635\u7684\u7b2c\u4e09\u884c\u3002<\/p>\n\n\n\n\u6839\u636e\u4ee5\u4e0a\u538b\u7f29\u65f6\u9075\u5faa\u7684\u4e09\u4e2a\u539f\u5219\u7684\u7b2c\u4e00\u70b9\uff0c\u8fd1\u5e73\u9762\u6324\u538b\u540e\u4e0d\u53d8\uff0c\u53ef\u4ee5\u5199\u51fa\u4ee5\u4e0b\u65b9\u7a0b[latex]\\begin{bmatrix}x \\\\y \\\\n \\\\1\\end{bmatrix}\\Rightarrow\\begin{bmatrix}x \\\\y \\\\n \\\\1\\end{bmatrix}==\\begin{bmatrix}n x \\\\n y \\\\n^2 \\\\n\\end{bmatrix}[\/latex]<\/p>\n\n\n\n\u56e0\u6b64\uff0c\u7b2c\u4e09\u884c\u7684\u5f62\u5f0f\u4e3a[latex]\\begin{bmatrix}0 &0 &A &B\\end{bmatrix}[\/latex][latex]\\begin{bmatrix}0 &0 &A &B\\end{bmatrix}\\begin{bmatrix}0\\\\ 0\\\\ A\\\\ B\\end{bmatrix}=n^2[\/latex]<\/p>\n\n\n\n\u5373[latex]A n+B=n^2[\/latex]<\/p>\n\n\n\n\u6839\u636e\u4ee5\u4e0a\u539f\u5219\u7684\u7b2c\u4e8c\u70b9\uff0c\u8fdc\u5e73\u9762\u6324\u538b\u540eZ\u503c\u4e0d\u53d8\uff0c\u53ef\u4ee5\u5199\u51fa\u4ee5\u4e0b\u65b9\u7a0b [latex]\\begin{bmatrix}0 \\\\0 \\\\f \\\\1\\end{bmatrix}\\Rightarrow\\begin{bmatrix}0 \\\\0 \\\\f \\\\1\\end{bmatrix}==\\begin{bmatrix}0 \\\\0 \\\\f^2 \\\\f\\end{bmatrix}[\/latex]<\/p>\n\n\n\n\u5373[latex]A f+B=f^2[\/latex]<\/p>\n\n\n\n\u8054\u7acb2\u4e2a\u65b9\u7a0b\uff0c\u53ef\u4ee5\u89e3\u51faA\u3001B[latex]\\begin{aligned}& A=n+f \\\\& B=-n f\\end{aligned}[\/latex]<\/p>\n\n\n\n\u7efc\u4e0a\uff0c\u53ef\u4ee5\u5f97\u51fa[latex]M_{\\text {persp } \\rightarrow \\text { ortho }}[\/latex]\u4e3a\uff1a[latex]M_{\\text {persp } \\rightarrow \\text { ortho }}=\\begin{bmatrix}n & 0 & 0 & 0 \\\\0 & n & 0 & 0 \\\\0 & 0 & n+f & -nf \\\\0 & 0 & 1 & 0\\end{bmatrix}[\/latex]<\/p>\n","protected":false},"excerpt":{"rendered":"\u89c6\u56fe\u53d8\u6362 \u76f8\u673a \u76f8\u673a\u7684\u4f4d\u7f6e[latex]\\overrightarrow{e}[\/latex] \u76f8\u673a\u7684\u89c6\u7ebf[latex]\\wideh …<\/p>","protected":false},"author":1,"featured_media":766,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[18,14,30,3],"tags":[17,15,16,12,22],"class_list":["post-765","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-games","category-games101","category-30","category-3","tag-games","tag-games101","tag-16","tag-12","tag-22"],"_links":{"self":[{"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/posts\/765","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/comments?post=765"}],"version-history":[{"count":1,"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/posts\/765\/revisions"}],"predecessor-version":[{"id":1760,"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/posts\/765\/revisions\/1760"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/media\/766"}],"wp:attachment":[{"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/media?parent=765"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/categories?post=765"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/tags?post=765"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
\u5148\u5c06 [latex]\\overrightarrow{e}[\/latex] \u5e73\u79fb\u5230\u539f\u70b9\uff0c\u518d\u5c06 [latex]\\widehat{g}[\/latex] \u65cb\u8f6c\u5230 -Z \u65b9\u5411\uff0c\u518d\u5c06 [latex]\\widehat{t}[\/latex] \u65cb\u8f6c\u5230 Y \u65b9\u5411\uff0c\u6700\u540e\u5c06 [latex](g \\times t)[\/latex] \u65cb\u8f6c\u5230 X \u65b9\u5411\u3002<\/p>\n\n\n\n<\/figure >\n<\/figure><\/noscript>\n\n\n\n[latex]M_{\\text {view }}=R_{\\text {view }} T_{\\text {view }}[\/latex]<\/p>\n\n\n\n1.\u5e73\u79fb [latex]\\overrightarrow{e}[\/latex] \u5230\u539f\u70b9[latex]T_{\\text {view }}=\\begin{bmatrix}1 & 0 & 0 & -x_e \\\\0 & 1 & 0 & -y_e \\\\0 & 0 & 1 & -z_e \\\\0 & 0 & 0 & 1\\end{bmatrix}[\/latex]<\/p>\n\n\n\n2. \u65cb\u8f6c [latex]\\widehat{g}[\/latex] \u5230 -Z \u65b9\u5411\uff0c\u65cb\u8f6c [latex]\\widehat{t}[\/latex] \u5230 Y \u65b9\u5411\uff0c\u65cb\u8f6c [latex](g \\times t)[\/latex] \u5230 X \u65b9\u5411\u3002 [latex]R_{\\text {view }}=\\begin{bmatrix}x_{\\hat{g} \\times \\hat{t}} & y_{\\hat{g} \\times \\hat{t}} & z_{\\hat{g} \\times \\hat{t}} & 0 \\\\x_t & y_t & z_t & 0 \\\\x_{-g} & y_{-g} & z_{-g} & 0 \\\\0 & 0 & 0 & 1\\end{bmatrix}[\/latex]<\/p>\n\n\n\n\u6295\u5f71<\/h2>\n\n\n\n\u6295\u5f71\u5206\u4e3a\u6b63\u4ea4\u6295\u5f71\u548c\u900f\u89c6\u6295\u5f71<\/p>\n\n\n\n<\/figure >\n<\/figure><\/noscript>\n\n\n\n\u89c6\u666f\u4f53<\/h3>\n\n\n\n\u89c6\u666f\u4f53\u662f\u6307\u7531\u6444\u50cf\u673a\u6216\u89c2\u5bdf\u8005\u6240\u770b\u5230\u7684\u573a\u666f\u7684\u51e0\u4f55\u5f62\u72b6\uff0c\u5b83\u662f\u75316\u4e2a\u5e73\u9762\u786e\u5b9a\u7684\u533a\u57df\uff0c\u8fd96\u4e2a\u5e73\u9762\u5206\u522b\u4e3a\u4e0a\u5e73\u9762\uff08up\uff09\u3001\u4e0b\u5e73\u9762\uff08down\uff09\u3001\u5de6\u5e73\u9762\uff08left\uff09\u3001\u53f3\u5e73\u9762\uff08right\uff09\u3001\u8fdc\u5e73\u9762\uff08far\uff09\u548c\u8fd1\u5e73\u9762\uff08near\uff09\u3002\u89c6\u666f\u4f53\u5185\u7684\u7269\u4f53\u53ef\u4ee5\u88ab\u6295\u5f71\u5230\u8fd1\u5e73\u9762\u4e0a\uff0c\u800c\u89c6\u666f\u4f53\u5916\u9762\u7684\u7269\u4f53\u5219\u4f1a\u88ab\u88c1\u526a\u6389\u3002<\/p>\n\n\n\nl\uff08left\uff09\uff1a\u89c6\u666f\u4f53\u5de6\u4fa7\u76f8\u5bf9\u4e8e\u76f8\u673a\u7684\u8ddd\u79bb\u3002r\uff08right\uff09\uff1a\u89c6\u666f\u4f53\u53f3\u4fa7\u76f8\u5bf9\u4e8e\u76f8\u673a\u7684\u8ddd\u79bb\u3002n\uff08near\uff09\uff1a\u89c6\u666f\u4f53\u8fd1\u7aef\u76f8\u5bf9\u4e8e\u76f8\u673a\u7684\u8ddd\u79bb\u3002f\uff08far\uff09\uff1a\u89c6\u666f\u4f53\u8fdc\u7aef\u76f8\u5bf9\u4e8e\u76f8\u673a\u7684\u8ddd\u79bb\u3002t\uff08top\uff09\uff1a\u89c6\u666f\u4f53\u4e0a\u4fa7\u76f8\u5bf9\u4e8e\u76f8\u673a\u7684\u8ddd\u79bb\u3002b\uff08bottom\uff09\uff1a\u89c6\u666f\u4f53\u4e0b\u4fa7\u76f8\u5bf9\u4e8e\u76f8\u673a\u7684\u8ddd\u79bb\u3002<\/p>\n\n\n\n\u6b63\u4ea4\u6295\u5f71<\/h3>\n\n\n\n1.\u5b9a\u4e49\u4e00\u4e2a\u7acb\u65b9\u4f53\uff0c\u5373\u89c6\u666f\u4f53[latex][l,r]\\times[b,t]\\times[f,n][\/latex]2.\u5c06\u89c6\u666f\u4f53\u7684\u4e2d\u5fc3\u79fb\u52a8\u5230\u539f\u70b93.\u5c06\u89c6\u666f\u4f53\u7684\u8fb9\u957f\u62c9\u5347\u6210[latex][-1,1]^3[\/latex]4.\u5f97\u5230\u4e00\u4e2aCanonical\uff08\u6b63\u5219\u3001\u89c4\u8303\u3001\u6807\u51c6\uff09\u7acb\u65b9\u4f53<\/p>\n\n\n\n\u5224\u65ad\u8fdc\u8fd1\uff1a\u4f7f\u7528\u539f\u7acb\u65b9\u4f53\u7684z\u5750\u6807 [latex][f,n][\/latex]\uff0c\u7531\u4e8e\u662f\u770b\u5411-Z\u65b9\u5411\uff0c\u6240\u4ee5\u5f53Z\u5750\u6807\u503c\u8d8a\u5927\uff0c\u79bb\u76f8\u673a\u8d8a\u8fd1\uff0cZ\u5750\u6807\u503c\u8d8a\u5c0f\uff0c\u79bb\u76f8\u673a\u8d8a\u8fdc <\/p>\n\n\n\n\u6570\u5b66\u8868\u8fbe\uff1a\u5148\u5c06\u4e2d\u5fc3\u5e73\u79fb\u5230\u539f\u70b9\u4e0a\uff0c\u7136\u540e\u8fdb\u884c\u7f29\u653e[latex]M_{\\text {ortho }}=\\begin{bmatrix}\\frac{2}{r-l} & 0 & 0 & 0 \\\\0 & \\frac{2}{t-b} & 0 & 0 \\\\0 & 0 & \\frac{2}{n-f} & 0 \\\\0 & 0 & 0 & 1\\end{bmatrix}\\begin{bmatrix}1 & 0 & 0 & -\\frac{r+l}{2} \\\\0 & 1 & 0 & -\\frac{t+b}{2} \\\\0 & 0 & 1 & -\\frac{n+f}{2} \\\\0 & 0 & 0 & 1\\end{bmatrix}[\/latex]<\/p>\n\n\n\n\u4f46\u7531\u4e8e\u6709\u4e4b\u524d\u7684\u89c6\u56fe\u53d8\u6362\uff0c\u89c6\u666f\u4f53n\u3001f\u5e73\u9762\u7684\u4e2d\u5fc3\u5c31\u5728Z\u8f74\u4e0a\uff0c\u6240\u4ee5\u5e73\u79fb\u65f6\u53ea\u9700\u8981\u5c06\u89c6\u666f\u4f53\u6cbfZ\u8f74\u5e73\u79fb\u4f7f\u4e2d\u5fc3\u5728\u5750\u6807\u539f\u70b9\u4e0a\u3002\u5e76\u4e14\u6709[latex]r=-l[\/latex]\uff0c[latex]b=-t[\/latex]\u3002\u6240\u4ee5\u516c\u5f0f\u53ef\u4ee5\u8fdb\u884c\u7b80\u5316 [latex]M_{\\text {ortho }}=\\begin{bmatrix}\\frac{2}{r-l} & 0 & 0 & 0 \\\\0 & \\frac{2}{t-b} & 0 & 0 \\\\0 & 0 & \\frac{2}{n-f} & 0 \\\\0 & 0 & 0 & 1\\end{bmatrix}\\begin{bmatrix}1 & 0 & 0 & 0 \\\\0 & 1 & 0 & 0 \\\\0 & 0 & 1 & -\\frac{n+f}{2} \\\\0 & 0 & 0 & 1\\end{bmatrix}[\/latex]<\/p>\n\n\n\n<\/figure >\n<\/figure><\/noscript>\n\n\n\n \u900f\u89c6\u6295\u5f71<\/h3>\n\n\n\n\u6839\u636e\u9f50\u6b21\u5750\u6807\u7684\u5b9a\u4e49 [latex]\\begin{bmatrix}x \/ w \\\\y \/ w \\\\z \/ w \\\\1\\end{bmatrix}, w \\neq 0[\/latex] \u53ef\u77e5\uff0c\u5c06\u91cc\u9762\u6bcf\u4e2a\u5143\u7d20\u4e58\u4ee5[latex]k(k\\ne 0)[\/latex]\u540e\uff0c\u8868\u793a\u7684\u662f\u540c\u4e00\u5411\u91cf\u3002<\/p>\n\n\n\n<\/figure >\n<\/figure><\/noscript>\n\n\n\n\u5728\u8fdb\u884c\u900f\u89c6\u6295\u5f71\u65f6\uff0c\u5148\u5c06\u900f\u89c6\u6295\u5f71\u7684\u68f1\u53f0\u8fdb\u884c\u6324\u538b\uff0c\u76f4\u5230\u53d8\u6210\u89c6\u666f\u4f53\uff0c\u5373\u4e00\u4e2a\u957f\u65b9\u4f53\uff0c\u7136\u540e\u518d\u8fdb\u884c\u6b63\u4ea4\u6295\u5f71<\/p>\n\n\n\n\u5728\u6324\u538b\u65f6\uff0c\u8981\u9075\u5faa\uff1a1.\u8fd1\u5e73\u9762\u6324\u538b\u540e\u4e0d\u53d82.\u8fdc\u5e73\u9762\u6324\u538b\u540eZ\u503c\u4e0d\u53d83.\u8fdc\u5e73\u9762\u7684\u4e2d\u5fc3\u6324\u538b\u540e\u4ecd\u7136\u4e3a\u4e2d\u5fc3<\/p>\n\n\n\n<\/figure >\n<\/figure><\/noscript>\n\n\n\n\u5bf9\u4e8e\u70b9[latex](x,y,z)[\/latex]\u88ab\u6324\u538b\u540e\u5f97\u5230[latex](x^{\\prime},y^{\\prime}, z^{\\prime})[\/latex] \uff0c\u6839\u636e\u76f8\u4f3c\u4e09\u89d2\u5f62\u53ef\u5f97\uff1a[latex]x^{\\prime}=\\frac{n}{z} x[\/latex][latex]y^{\\prime}=\\frac{n}{z} y[\/latex]<\/p>\n\n\n\n\u5199\u4f5c\u9f50\u6b21\u5750\u6807\u4e3a\uff1a[latex]\\begin{bmatrix}x \\\\y \\\\z \\\\1\\end{bmatrix}\\Rightarrow\\begin{bmatrix}n x \/ z \\\\n y \/ z \\\\\\text { unknown } \\\\1\\end{bmatrix}\\stackrel{\\text { mult. by z }}{==}\\begin{bmatrix}n x \\\\n y \\\\\\text { still unknown } \\\\z\\end{bmatrix}[\/latex]<\/p>\n\n\n\n\u4e8e\u662f\u53ef\u4ee5\u5f97\u51fa[latex]M_{\\text {persp } \\rightarrow \\text { ortho }}[\/latex]\u4e3a\uff1a[latex]M_{\\text {persp } \\rightarrow \\text { ortho }}=\\begin{bmatrix}n & 0 & 0 & 0 \\\\0 & n & 0 & 0 \\\\? & ? & ? & ? \\\\0 & 0 & 1 & 0\\end{bmatrix}[\/latex]<\/p>\n\n\n\n\u73b0\u5728\u9700\u8981\u6c42\u51faZ\u5750\u6807\uff0c\u4e5f\u5c31\u662f\u4e0a\u8ff0\u77e9\u9635\u7684\u7b2c\u4e09\u884c\u3002<\/p>\n\n\n\n\u6839\u636e\u4ee5\u4e0a\u538b\u7f29\u65f6\u9075\u5faa\u7684\u4e09\u4e2a\u539f\u5219\u7684\u7b2c\u4e00\u70b9\uff0c\u8fd1\u5e73\u9762\u6324\u538b\u540e\u4e0d\u53d8\uff0c\u53ef\u4ee5\u5199\u51fa\u4ee5\u4e0b\u65b9\u7a0b[latex]\\begin{bmatrix}x \\\\y \\\\n \\\\1\\end{bmatrix}\\Rightarrow\\begin{bmatrix}x \\\\y \\\\n \\\\1\\end{bmatrix}==\\begin{bmatrix}n x \\\\n y \\\\n^2 \\\\n\\end{bmatrix}[\/latex]<\/p>\n\n\n\n\u56e0\u6b64\uff0c\u7b2c\u4e09\u884c\u7684\u5f62\u5f0f\u4e3a[latex]\\begin{bmatrix}0 &0 &A &B\\end{bmatrix}[\/latex][latex]\\begin{bmatrix}0 &0 &A &B\\end{bmatrix}\\begin{bmatrix}0\\\\ 0\\\\ A\\\\ B\\end{bmatrix}=n^2[\/latex]<\/p>\n\n\n\n\u5373[latex]A n+B=n^2[\/latex]<\/p>\n\n\n\n\u6839\u636e\u4ee5\u4e0a\u539f\u5219\u7684\u7b2c\u4e8c\u70b9\uff0c\u8fdc\u5e73\u9762\u6324\u538b\u540eZ\u503c\u4e0d\u53d8\uff0c\u53ef\u4ee5\u5199\u51fa\u4ee5\u4e0b\u65b9\u7a0b [latex]\\begin{bmatrix}0 \\\\0 \\\\f \\\\1\\end{bmatrix}\\Rightarrow\\begin{bmatrix}0 \\\\0 \\\\f \\\\1\\end{bmatrix}==\\begin{bmatrix}0 \\\\0 \\\\f^2 \\\\f\\end{bmatrix}[\/latex]<\/p>\n\n\n\n\u5373[latex]A f+B=f^2[\/latex]<\/p>\n\n\n\n\u8054\u7acb2\u4e2a\u65b9\u7a0b\uff0c\u53ef\u4ee5\u89e3\u51faA\u3001B[latex]\\begin{aligned}& A=n+f \\\\& B=-n f\\end{aligned}[\/latex]<\/p>\n\n\n\n\u7efc\u4e0a\uff0c\u53ef\u4ee5\u5f97\u51fa[latex]M_{\\text {persp } \\rightarrow \\text { ortho }}[\/latex]\u4e3a\uff1a[latex]M_{\\text {persp } \\rightarrow \\text { ortho }}=\\begin{bmatrix}n & 0 & 0 & 0 \\\\0 & n & 0 & 0 \\\\0 & 0 & n+f & -nf \\\\0 & 0 & 1 & 0\\end{bmatrix}[\/latex]<\/p>\n","protected":false},"excerpt":{"rendered":"\u89c6\u56fe\u53d8\u6362 \u76f8\u673a \u76f8\u673a\u7684\u4f4d\u7f6e[latex]\\overrightarrow{e}[\/latex] \u76f8\u673a\u7684\u89c6\u7ebf[latex]\\wideh …<\/p>","protected":false},"author":1,"featured_media":766,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[18,14,30,3],"tags":[17,15,16,12,22],"class_list":["post-765","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-games","category-games101","category-30","category-3","tag-games","tag-games101","tag-16","tag-12","tag-22"],"_links":{"self":[{"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/posts\/765","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/comments?post=765"}],"version-history":[{"count":1,"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/posts\/765\/revisions"}],"predecessor-version":[{"id":1760,"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/posts\/765\/revisions\/1760"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/media\/766"}],"wp:attachment":[{"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/media?parent=765"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/categories?post=765"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/tags?post=765"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
[latex]M_{\\text {view }}=R_{\\text {view }} T_{\\text {view }}[\/latex]<\/p>\n\n\n\n
1.\u5e73\u79fb [latex]\\overrightarrow{e}[\/latex] \u5230\u539f\u70b9[latex]T_{\\text {view }}=\\begin{bmatrix}1 & 0 & 0 & -x_e \\\\0 & 1 & 0 & -y_e \\\\0 & 0 & 1 & -z_e \\\\0 & 0 & 0 & 1\\end{bmatrix}[\/latex]<\/p>\n\n\n\n
2. \u65cb\u8f6c [latex]\\widehat{g}[\/latex] \u5230 -Z \u65b9\u5411\uff0c\u65cb\u8f6c [latex]\\widehat{t}[\/latex] \u5230 Y \u65b9\u5411\uff0c\u65cb\u8f6c [latex](g \\times t)[\/latex] \u5230 X \u65b9\u5411\u3002 [latex]R_{\\text {view }}=\\begin{bmatrix}x_{\\hat{g} \\times \\hat{t}} & y_{\\hat{g} \\times \\hat{t}} & z_{\\hat{g} \\times \\hat{t}} & 0 \\\\x_t & y_t & z_t & 0 \\\\x_{-g} & y_{-g} & z_{-g} & 0 \\\\0 & 0 & 0 & 1\\end{bmatrix}[\/latex]<\/p>\n\n\n\n
\u6295\u5f71\u5206\u4e3a\u6b63\u4ea4\u6295\u5f71\u548c\u900f\u89c6\u6295\u5f71<\/p>\n\n\n\n<\/figure >\n<\/figure><\/noscript>\n\n\n\n\u89c6\u666f\u4f53<\/h3>\n\n\n\n\u89c6\u666f\u4f53\u662f\u6307\u7531\u6444\u50cf\u673a\u6216\u89c2\u5bdf\u8005\u6240\u770b\u5230\u7684\u573a\u666f\u7684\u51e0\u4f55\u5f62\u72b6\uff0c\u5b83\u662f\u75316\u4e2a\u5e73\u9762\u786e\u5b9a\u7684\u533a\u57df\uff0c\u8fd96\u4e2a\u5e73\u9762\u5206\u522b\u4e3a\u4e0a\u5e73\u9762\uff08up\uff09\u3001\u4e0b\u5e73\u9762\uff08down\uff09\u3001\u5de6\u5e73\u9762\uff08left\uff09\u3001\u53f3\u5e73\u9762\uff08right\uff09\u3001\u8fdc\u5e73\u9762\uff08far\uff09\u548c\u8fd1\u5e73\u9762\uff08near\uff09\u3002\u89c6\u666f\u4f53\u5185\u7684\u7269\u4f53\u53ef\u4ee5\u88ab\u6295\u5f71\u5230\u8fd1\u5e73\u9762\u4e0a\uff0c\u800c\u89c6\u666f\u4f53\u5916\u9762\u7684\u7269\u4f53\u5219\u4f1a\u88ab\u88c1\u526a\u6389\u3002<\/p>\n\n\n\nl\uff08left\uff09\uff1a\u89c6\u666f\u4f53\u5de6\u4fa7\u76f8\u5bf9\u4e8e\u76f8\u673a\u7684\u8ddd\u79bb\u3002r\uff08right\uff09\uff1a\u89c6\u666f\u4f53\u53f3\u4fa7\u76f8\u5bf9\u4e8e\u76f8\u673a\u7684\u8ddd\u79bb\u3002n\uff08near\uff09\uff1a\u89c6\u666f\u4f53\u8fd1\u7aef\u76f8\u5bf9\u4e8e\u76f8\u673a\u7684\u8ddd\u79bb\u3002f\uff08far\uff09\uff1a\u89c6\u666f\u4f53\u8fdc\u7aef\u76f8\u5bf9\u4e8e\u76f8\u673a\u7684\u8ddd\u79bb\u3002t\uff08top\uff09\uff1a\u89c6\u666f\u4f53\u4e0a\u4fa7\u76f8\u5bf9\u4e8e\u76f8\u673a\u7684\u8ddd\u79bb\u3002b\uff08bottom\uff09\uff1a\u89c6\u666f\u4f53\u4e0b\u4fa7\u76f8\u5bf9\u4e8e\u76f8\u673a\u7684\u8ddd\u79bb\u3002<\/p>\n\n\n\n\u6b63\u4ea4\u6295\u5f71<\/h3>\n\n\n\n1.\u5b9a\u4e49\u4e00\u4e2a\u7acb\u65b9\u4f53\uff0c\u5373\u89c6\u666f\u4f53[latex][l,r]\\times[b,t]\\times[f,n][\/latex]2.\u5c06\u89c6\u666f\u4f53\u7684\u4e2d\u5fc3\u79fb\u52a8\u5230\u539f\u70b93.\u5c06\u89c6\u666f\u4f53\u7684\u8fb9\u957f\u62c9\u5347\u6210[latex][-1,1]^3[\/latex]4.\u5f97\u5230\u4e00\u4e2aCanonical\uff08\u6b63\u5219\u3001\u89c4\u8303\u3001\u6807\u51c6\uff09\u7acb\u65b9\u4f53<\/p>\n\n\n\n\u5224\u65ad\u8fdc\u8fd1\uff1a\u4f7f\u7528\u539f\u7acb\u65b9\u4f53\u7684z\u5750\u6807 [latex][f,n][\/latex]\uff0c\u7531\u4e8e\u662f\u770b\u5411-Z\u65b9\u5411\uff0c\u6240\u4ee5\u5f53Z\u5750\u6807\u503c\u8d8a\u5927\uff0c\u79bb\u76f8\u673a\u8d8a\u8fd1\uff0cZ\u5750\u6807\u503c\u8d8a\u5c0f\uff0c\u79bb\u76f8\u673a\u8d8a\u8fdc <\/p>\n\n\n\n\u6570\u5b66\u8868\u8fbe\uff1a\u5148\u5c06\u4e2d\u5fc3\u5e73\u79fb\u5230\u539f\u70b9\u4e0a\uff0c\u7136\u540e\u8fdb\u884c\u7f29\u653e[latex]M_{\\text {ortho }}=\\begin{bmatrix}\\frac{2}{r-l} & 0 & 0 & 0 \\\\0 & \\frac{2}{t-b} & 0 & 0 \\\\0 & 0 & \\frac{2}{n-f} & 0 \\\\0 & 0 & 0 & 1\\end{bmatrix}\\begin{bmatrix}1 & 0 & 0 & -\\frac{r+l}{2} \\\\0 & 1 & 0 & -\\frac{t+b}{2} \\\\0 & 0 & 1 & -\\frac{n+f}{2} \\\\0 & 0 & 0 & 1\\end{bmatrix}[\/latex]<\/p>\n\n\n\n\u4f46\u7531\u4e8e\u6709\u4e4b\u524d\u7684\u89c6\u56fe\u53d8\u6362\uff0c\u89c6\u666f\u4f53n\u3001f\u5e73\u9762\u7684\u4e2d\u5fc3\u5c31\u5728Z\u8f74\u4e0a\uff0c\u6240\u4ee5\u5e73\u79fb\u65f6\u53ea\u9700\u8981\u5c06\u89c6\u666f\u4f53\u6cbfZ\u8f74\u5e73\u79fb\u4f7f\u4e2d\u5fc3\u5728\u5750\u6807\u539f\u70b9\u4e0a\u3002\u5e76\u4e14\u6709[latex]r=-l[\/latex]\uff0c[latex]b=-t[\/latex]\u3002\u6240\u4ee5\u516c\u5f0f\u53ef\u4ee5\u8fdb\u884c\u7b80\u5316 [latex]M_{\\text {ortho }}=\\begin{bmatrix}\\frac{2}{r-l} & 0 & 0 & 0 \\\\0 & \\frac{2}{t-b} & 0 & 0 \\\\0 & 0 & \\frac{2}{n-f} & 0 \\\\0 & 0 & 0 & 1\\end{bmatrix}\\begin{bmatrix}1 & 0 & 0 & 0 \\\\0 & 1 & 0 & 0 \\\\0 & 0 & 1 & -\\frac{n+f}{2} \\\\0 & 0 & 0 & 1\\end{bmatrix}[\/latex]<\/p>\n\n\n\n<\/figure >\n<\/figure><\/noscript>\n\n\n\n \u900f\u89c6\u6295\u5f71<\/h3>\n\n\n\n\u6839\u636e\u9f50\u6b21\u5750\u6807\u7684\u5b9a\u4e49 [latex]\\begin{bmatrix}x \/ w \\\\y \/ w \\\\z \/ w \\\\1\\end{bmatrix}, w \\neq 0[\/latex] \u53ef\u77e5\uff0c\u5c06\u91cc\u9762\u6bcf\u4e2a\u5143\u7d20\u4e58\u4ee5[latex]k(k\\ne 0)[\/latex]\u540e\uff0c\u8868\u793a\u7684\u662f\u540c\u4e00\u5411\u91cf\u3002<\/p>\n\n\n\n<\/figure >\n<\/figure><\/noscript>\n\n\n\n\u5728\u8fdb\u884c\u900f\u89c6\u6295\u5f71\u65f6\uff0c\u5148\u5c06\u900f\u89c6\u6295\u5f71\u7684\u68f1\u53f0\u8fdb\u884c\u6324\u538b\uff0c\u76f4\u5230\u53d8\u6210\u89c6\u666f\u4f53\uff0c\u5373\u4e00\u4e2a\u957f\u65b9\u4f53\uff0c\u7136\u540e\u518d\u8fdb\u884c\u6b63\u4ea4\u6295\u5f71<\/p>\n\n\n\n\u5728\u6324\u538b\u65f6\uff0c\u8981\u9075\u5faa\uff1a1.\u8fd1\u5e73\u9762\u6324\u538b\u540e\u4e0d\u53d82.\u8fdc\u5e73\u9762\u6324\u538b\u540eZ\u503c\u4e0d\u53d83.\u8fdc\u5e73\u9762\u7684\u4e2d\u5fc3\u6324\u538b\u540e\u4ecd\u7136\u4e3a\u4e2d\u5fc3<\/p>\n\n\n\n<\/figure >\n<\/figure><\/noscript>\n\n\n\n\u5bf9\u4e8e\u70b9[latex](x,y,z)[\/latex]\u88ab\u6324\u538b\u540e\u5f97\u5230[latex](x^{\\prime},y^{\\prime}, z^{\\prime})[\/latex] \uff0c\u6839\u636e\u76f8\u4f3c\u4e09\u89d2\u5f62\u53ef\u5f97\uff1a[latex]x^{\\prime}=\\frac{n}{z} x[\/latex][latex]y^{\\prime}=\\frac{n}{z} y[\/latex]<\/p>\n\n\n\n\u5199\u4f5c\u9f50\u6b21\u5750\u6807\u4e3a\uff1a[latex]\\begin{bmatrix}x \\\\y \\\\z \\\\1\\end{bmatrix}\\Rightarrow\\begin{bmatrix}n x \/ z \\\\n y \/ z \\\\\\text { unknown } \\\\1\\end{bmatrix}\\stackrel{\\text { mult. by z }}{==}\\begin{bmatrix}n x \\\\n y \\\\\\text { still unknown } \\\\z\\end{bmatrix}[\/latex]<\/p>\n\n\n\n\u4e8e\u662f\u53ef\u4ee5\u5f97\u51fa[latex]M_{\\text {persp } \\rightarrow \\text { ortho }}[\/latex]\u4e3a\uff1a[latex]M_{\\text {persp } \\rightarrow \\text { ortho }}=\\begin{bmatrix}n & 0 & 0 & 0 \\\\0 & n & 0 & 0 \\\\? & ? & ? & ? \\\\0 & 0 & 1 & 0\\end{bmatrix}[\/latex]<\/p>\n\n\n\n\u73b0\u5728\u9700\u8981\u6c42\u51faZ\u5750\u6807\uff0c\u4e5f\u5c31\u662f\u4e0a\u8ff0\u77e9\u9635\u7684\u7b2c\u4e09\u884c\u3002<\/p>\n\n\n\n\u6839\u636e\u4ee5\u4e0a\u538b\u7f29\u65f6\u9075\u5faa\u7684\u4e09\u4e2a\u539f\u5219\u7684\u7b2c\u4e00\u70b9\uff0c\u8fd1\u5e73\u9762\u6324\u538b\u540e\u4e0d\u53d8\uff0c\u53ef\u4ee5\u5199\u51fa\u4ee5\u4e0b\u65b9\u7a0b[latex]\\begin{bmatrix}x \\\\y \\\\n \\\\1\\end{bmatrix}\\Rightarrow\\begin{bmatrix}x \\\\y \\\\n \\\\1\\end{bmatrix}==\\begin{bmatrix}n x \\\\n y \\\\n^2 \\\\n\\end{bmatrix}[\/latex]<\/p>\n\n\n\n\u56e0\u6b64\uff0c\u7b2c\u4e09\u884c\u7684\u5f62\u5f0f\u4e3a[latex]\\begin{bmatrix}0 &0 &A &B\\end{bmatrix}[\/latex][latex]\\begin{bmatrix}0 &0 &A &B\\end{bmatrix}\\begin{bmatrix}0\\\\ 0\\\\ A\\\\ B\\end{bmatrix}=n^2[\/latex]<\/p>\n\n\n\n\u5373[latex]A n+B=n^2[\/latex]<\/p>\n\n\n\n\u6839\u636e\u4ee5\u4e0a\u539f\u5219\u7684\u7b2c\u4e8c\u70b9\uff0c\u8fdc\u5e73\u9762\u6324\u538b\u540eZ\u503c\u4e0d\u53d8\uff0c\u53ef\u4ee5\u5199\u51fa\u4ee5\u4e0b\u65b9\u7a0b [latex]\\begin{bmatrix}0 \\\\0 \\\\f \\\\1\\end{bmatrix}\\Rightarrow\\begin{bmatrix}0 \\\\0 \\\\f \\\\1\\end{bmatrix}==\\begin{bmatrix}0 \\\\0 \\\\f^2 \\\\f\\end{bmatrix}[\/latex]<\/p>\n\n\n\n\u5373[latex]A f+B=f^2[\/latex]<\/p>\n\n\n\n\u8054\u7acb2\u4e2a\u65b9\u7a0b\uff0c\u53ef\u4ee5\u89e3\u51faA\u3001B[latex]\\begin{aligned}& A=n+f \\\\& B=-n f\\end{aligned}[\/latex]<\/p>\n\n\n\n\u7efc\u4e0a\uff0c\u53ef\u4ee5\u5f97\u51fa[latex]M_{\\text {persp } \\rightarrow \\text { ortho }}[\/latex]\u4e3a\uff1a[latex]M_{\\text {persp } \\rightarrow \\text { ortho }}=\\begin{bmatrix}n & 0 & 0 & 0 \\\\0 & n & 0 & 0 \\\\0 & 0 & n+f & -nf \\\\0 & 0 & 1 & 0\\end{bmatrix}[\/latex]<\/p>\n","protected":false},"excerpt":{"rendered":"\u89c6\u56fe\u53d8\u6362 \u76f8\u673a \u76f8\u673a\u7684\u4f4d\u7f6e[latex]\\overrightarrow{e}[\/latex] \u76f8\u673a\u7684\u89c6\u7ebf[latex]\\wideh …<\/p>","protected":false},"author":1,"featured_media":766,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[18,14,30,3],"tags":[17,15,16,12,22],"class_list":["post-765","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-games","category-games101","category-30","category-3","tag-games","tag-games101","tag-16","tag-12","tag-22"],"_links":{"self":[{"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/posts\/765","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/comments?post=765"}],"version-history":[{"count":1,"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/posts\/765\/revisions"}],"predecessor-version":[{"id":1760,"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/posts\/765\/revisions\/1760"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/media\/766"}],"wp:attachment":[{"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/media?parent=765"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/categories?post=765"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/tags?post=765"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
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l\uff08left\uff09\uff1a\u89c6\u666f\u4f53\u5de6\u4fa7\u76f8\u5bf9\u4e8e\u76f8\u673a\u7684\u8ddd\u79bb\u3002r\uff08right\uff09\uff1a\u89c6\u666f\u4f53\u53f3\u4fa7\u76f8\u5bf9\u4e8e\u76f8\u673a\u7684\u8ddd\u79bb\u3002n\uff08near\uff09\uff1a\u89c6\u666f\u4f53\u8fd1\u7aef\u76f8\u5bf9\u4e8e\u76f8\u673a\u7684\u8ddd\u79bb\u3002f\uff08far\uff09\uff1a\u89c6\u666f\u4f53\u8fdc\u7aef\u76f8\u5bf9\u4e8e\u76f8\u673a\u7684\u8ddd\u79bb\u3002t\uff08top\uff09\uff1a\u89c6\u666f\u4f53\u4e0a\u4fa7\u76f8\u5bf9\u4e8e\u76f8\u673a\u7684\u8ddd\u79bb\u3002b\uff08bottom\uff09\uff1a\u89c6\u666f\u4f53\u4e0b\u4fa7\u76f8\u5bf9\u4e8e\u76f8\u673a\u7684\u8ddd\u79bb\u3002<\/p>\n\n\n\n
1.\u5b9a\u4e49\u4e00\u4e2a\u7acb\u65b9\u4f53\uff0c\u5373\u89c6\u666f\u4f53[latex][l,r]\\times[b,t]\\times[f,n][\/latex]2.\u5c06\u89c6\u666f\u4f53\u7684\u4e2d\u5fc3\u79fb\u52a8\u5230\u539f\u70b93.\u5c06\u89c6\u666f\u4f53\u7684\u8fb9\u957f\u62c9\u5347\u6210[latex][-1,1]^3[\/latex]4.\u5f97\u5230\u4e00\u4e2aCanonical\uff08\u6b63\u5219\u3001\u89c4\u8303\u3001\u6807\u51c6\uff09\u7acb\u65b9\u4f53<\/p>\n\n\n\n
\u5224\u65ad\u8fdc\u8fd1\uff1a\u4f7f\u7528\u539f\u7acb\u65b9\u4f53\u7684z\u5750\u6807 [latex][f,n][\/latex]\uff0c\u7531\u4e8e\u662f\u770b\u5411-Z\u65b9\u5411\uff0c\u6240\u4ee5\u5f53Z\u5750\u6807\u503c\u8d8a\u5927\uff0c\u79bb\u76f8\u673a\u8d8a\u8fd1\uff0cZ\u5750\u6807\u503c\u8d8a\u5c0f\uff0c\u79bb\u76f8\u673a\u8d8a\u8fdc <\/p>\n\n\n\n
\u6570\u5b66\u8868\u8fbe\uff1a\u5148\u5c06\u4e2d\u5fc3\u5e73\u79fb\u5230\u539f\u70b9\u4e0a\uff0c\u7136\u540e\u8fdb\u884c\u7f29\u653e[latex]M_{\\text {ortho }}=\\begin{bmatrix}\\frac{2}{r-l} & 0 & 0 & 0 \\\\0 & \\frac{2}{t-b} & 0 & 0 \\\\0 & 0 & \\frac{2}{n-f} & 0 \\\\0 & 0 & 0 & 1\\end{bmatrix}\\begin{bmatrix}1 & 0 & 0 & -\\frac{r+l}{2} \\\\0 & 1 & 0 & -\\frac{t+b}{2} \\\\0 & 0 & 1 & -\\frac{n+f}{2} \\\\0 & 0 & 0 & 1\\end{bmatrix}[\/latex]<\/p>\n\n\n\n
\u4f46\u7531\u4e8e\u6709\u4e4b\u524d\u7684\u89c6\u56fe\u53d8\u6362\uff0c\u89c6\u666f\u4f53n\u3001f\u5e73\u9762\u7684\u4e2d\u5fc3\u5c31\u5728Z\u8f74\u4e0a\uff0c\u6240\u4ee5\u5e73\u79fb\u65f6\u53ea\u9700\u8981\u5c06\u89c6\u666f\u4f53\u6cbfZ\u8f74\u5e73\u79fb\u4f7f\u4e2d\u5fc3\u5728\u5750\u6807\u539f\u70b9\u4e0a\u3002\u5e76\u4e14\u6709[latex]r=-l[\/latex]\uff0c[latex]b=-t[\/latex]\u3002\u6240\u4ee5\u516c\u5f0f\u53ef\u4ee5\u8fdb\u884c\u7b80\u5316 [latex]M_{\\text {ortho }}=\\begin{bmatrix}\\frac{2}{r-l} & 0 & 0 & 0 \\\\0 & \\frac{2}{t-b} & 0 & 0 \\\\0 & 0 & \\frac{2}{n-f} & 0 \\\\0 & 0 & 0 & 1\\end{bmatrix}\\begin{bmatrix}1 & 0 & 0 & 0 \\\\0 & 1 & 0 & 0 \\\\0 & 0 & 1 & -\\frac{n+f}{2} \\\\0 & 0 & 0 & 1\\end{bmatrix}[\/latex]<\/p>\n\n\n\n<\/figure >\n<\/figure><\/noscript>\n\n\n\n \u900f\u89c6\u6295\u5f71<\/h3>\n\n\n\n\u6839\u636e\u9f50\u6b21\u5750\u6807\u7684\u5b9a\u4e49 [latex]\\begin{bmatrix}x \/ w \\\\y \/ w \\\\z \/ w \\\\1\\end{bmatrix}, w \\neq 0[\/latex] \u53ef\u77e5\uff0c\u5c06\u91cc\u9762\u6bcf\u4e2a\u5143\u7d20\u4e58\u4ee5[latex]k(k\\ne 0)[\/latex]\u540e\uff0c\u8868\u793a\u7684\u662f\u540c\u4e00\u5411\u91cf\u3002<\/p>\n\n\n\n<\/figure >\n<\/figure><\/noscript>\n\n\n\n\u5728\u8fdb\u884c\u900f\u89c6\u6295\u5f71\u65f6\uff0c\u5148\u5c06\u900f\u89c6\u6295\u5f71\u7684\u68f1\u53f0\u8fdb\u884c\u6324\u538b\uff0c\u76f4\u5230\u53d8\u6210\u89c6\u666f\u4f53\uff0c\u5373\u4e00\u4e2a\u957f\u65b9\u4f53\uff0c\u7136\u540e\u518d\u8fdb\u884c\u6b63\u4ea4\u6295\u5f71<\/p>\n\n\n\n\u5728\u6324\u538b\u65f6\uff0c\u8981\u9075\u5faa\uff1a1.\u8fd1\u5e73\u9762\u6324\u538b\u540e\u4e0d\u53d82.\u8fdc\u5e73\u9762\u6324\u538b\u540eZ\u503c\u4e0d\u53d83.\u8fdc\u5e73\u9762\u7684\u4e2d\u5fc3\u6324\u538b\u540e\u4ecd\u7136\u4e3a\u4e2d\u5fc3<\/p>\n\n\n\n<\/figure >\n<\/figure><\/noscript>\n\n\n\n\u5bf9\u4e8e\u70b9[latex](x,y,z)[\/latex]\u88ab\u6324\u538b\u540e\u5f97\u5230[latex](x^{\\prime},y^{\\prime}, z^{\\prime})[\/latex] \uff0c\u6839\u636e\u76f8\u4f3c\u4e09\u89d2\u5f62\u53ef\u5f97\uff1a[latex]x^{\\prime}=\\frac{n}{z} x[\/latex][latex]y^{\\prime}=\\frac{n}{z} y[\/latex]<\/p>\n\n\n\n\u5199\u4f5c\u9f50\u6b21\u5750\u6807\u4e3a\uff1a[latex]\\begin{bmatrix}x \\\\y \\\\z \\\\1\\end{bmatrix}\\Rightarrow\\begin{bmatrix}n x \/ z \\\\n y \/ z \\\\\\text { unknown } \\\\1\\end{bmatrix}\\stackrel{\\text { mult. by z }}{==}\\begin{bmatrix}n x \\\\n y \\\\\\text { still unknown } \\\\z\\end{bmatrix}[\/latex]<\/p>\n\n\n\n\u4e8e\u662f\u53ef\u4ee5\u5f97\u51fa[latex]M_{\\text {persp } \\rightarrow \\text { ortho }}[\/latex]\u4e3a\uff1a[latex]M_{\\text {persp } \\rightarrow \\text { ortho }}=\\begin{bmatrix}n & 0 & 0 & 0 \\\\0 & n & 0 & 0 \\\\? & ? & ? & ? \\\\0 & 0 & 1 & 0\\end{bmatrix}[\/latex]<\/p>\n\n\n\n\u73b0\u5728\u9700\u8981\u6c42\u51faZ\u5750\u6807\uff0c\u4e5f\u5c31\u662f\u4e0a\u8ff0\u77e9\u9635\u7684\u7b2c\u4e09\u884c\u3002<\/p>\n\n\n\n\u6839\u636e\u4ee5\u4e0a\u538b\u7f29\u65f6\u9075\u5faa\u7684\u4e09\u4e2a\u539f\u5219\u7684\u7b2c\u4e00\u70b9\uff0c\u8fd1\u5e73\u9762\u6324\u538b\u540e\u4e0d\u53d8\uff0c\u53ef\u4ee5\u5199\u51fa\u4ee5\u4e0b\u65b9\u7a0b[latex]\\begin{bmatrix}x \\\\y \\\\n \\\\1\\end{bmatrix}\\Rightarrow\\begin{bmatrix}x \\\\y \\\\n \\\\1\\end{bmatrix}==\\begin{bmatrix}n x \\\\n y \\\\n^2 \\\\n\\end{bmatrix}[\/latex]<\/p>\n\n\n\n\u56e0\u6b64\uff0c\u7b2c\u4e09\u884c\u7684\u5f62\u5f0f\u4e3a[latex]\\begin{bmatrix}0 &0 &A &B\\end{bmatrix}[\/latex][latex]\\begin{bmatrix}0 &0 &A &B\\end{bmatrix}\\begin{bmatrix}0\\\\ 0\\\\ A\\\\ B\\end{bmatrix}=n^2[\/latex]<\/p>\n\n\n\n\u5373[latex]A n+B=n^2[\/latex]<\/p>\n\n\n\n\u6839\u636e\u4ee5\u4e0a\u539f\u5219\u7684\u7b2c\u4e8c\u70b9\uff0c\u8fdc\u5e73\u9762\u6324\u538b\u540eZ\u503c\u4e0d\u53d8\uff0c\u53ef\u4ee5\u5199\u51fa\u4ee5\u4e0b\u65b9\u7a0b [latex]\\begin{bmatrix}0 \\\\0 \\\\f \\\\1\\end{bmatrix}\\Rightarrow\\begin{bmatrix}0 \\\\0 \\\\f \\\\1\\end{bmatrix}==\\begin{bmatrix}0 \\\\0 \\\\f^2 \\\\f\\end{bmatrix}[\/latex]<\/p>\n\n\n\n\u5373[latex]A f+B=f^2[\/latex]<\/p>\n\n\n\n\u8054\u7acb2\u4e2a\u65b9\u7a0b\uff0c\u53ef\u4ee5\u89e3\u51faA\u3001B[latex]\\begin{aligned}& A=n+f \\\\& B=-n f\\end{aligned}[\/latex]<\/p>\n\n\n\n\u7efc\u4e0a\uff0c\u53ef\u4ee5\u5f97\u51fa[latex]M_{\\text {persp } \\rightarrow \\text { ortho }}[\/latex]\u4e3a\uff1a[latex]M_{\\text {persp } \\rightarrow \\text { ortho }}=\\begin{bmatrix}n & 0 & 0 & 0 \\\\0 & n & 0 & 0 \\\\0 & 0 & n+f & -nf \\\\0 & 0 & 1 & 0\\end{bmatrix}[\/latex]<\/p>\n","protected":false},"excerpt":{"rendered":"\u89c6\u56fe\u53d8\u6362 \u76f8\u673a \u76f8\u673a\u7684\u4f4d\u7f6e[latex]\\overrightarrow{e}[\/latex] \u76f8\u673a\u7684\u89c6\u7ebf[latex]\\wideh …<\/p>","protected":false},"author":1,"featured_media":766,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[18,14,30,3],"tags":[17,15,16,12,22],"class_list":["post-765","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-games","category-games101","category-30","category-3","tag-games","tag-games101","tag-16","tag-12","tag-22"],"_links":{"self":[{"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/posts\/765","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/comments?post=765"}],"version-history":[{"count":1,"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/posts\/765\/revisions"}],"predecessor-version":[{"id":1760,"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/posts\/765\/revisions\/1760"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/media\/766"}],"wp:attachment":[{"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/media?parent=765"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/categories?post=765"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/tags?post=765"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
\u6839\u636e\u9f50\u6b21\u5750\u6807\u7684\u5b9a\u4e49 [latex]\\begin{bmatrix}x \/ w \\\\y \/ w \\\\z \/ w \\\\1\\end{bmatrix}, w \\neq 0[\/latex] \u53ef\u77e5\uff0c\u5c06\u91cc\u9762\u6bcf\u4e2a\u5143\u7d20\u4e58\u4ee5[latex]k(k\\ne 0)[\/latex]\u540e\uff0c\u8868\u793a\u7684\u662f\u540c\u4e00\u5411\u91cf\u3002<\/p>\n\n\n\n<\/figure >\n<\/figure><\/noscript>\n\n\n\n\u5728\u8fdb\u884c\u900f\u89c6\u6295\u5f71\u65f6\uff0c\u5148\u5c06\u900f\u89c6\u6295\u5f71\u7684\u68f1\u53f0\u8fdb\u884c\u6324\u538b\uff0c\u76f4\u5230\u53d8\u6210\u89c6\u666f\u4f53\uff0c\u5373\u4e00\u4e2a\u957f\u65b9\u4f53\uff0c\u7136\u540e\u518d\u8fdb\u884c\u6b63\u4ea4\u6295\u5f71<\/p>\n\n\n\n\u5728\u6324\u538b\u65f6\uff0c\u8981\u9075\u5faa\uff1a1.\u8fd1\u5e73\u9762\u6324\u538b\u540e\u4e0d\u53d82.\u8fdc\u5e73\u9762\u6324\u538b\u540eZ\u503c\u4e0d\u53d83.\u8fdc\u5e73\u9762\u7684\u4e2d\u5fc3\u6324\u538b\u540e\u4ecd\u7136\u4e3a\u4e2d\u5fc3<\/p>\n\n\n\n<\/figure >\n<\/figure><\/noscript>\n\n\n\n\u5bf9\u4e8e\u70b9[latex](x,y,z)[\/latex]\u88ab\u6324\u538b\u540e\u5f97\u5230[latex](x^{\\prime},y^{\\prime}, z^{\\prime})[\/latex] \uff0c\u6839\u636e\u76f8\u4f3c\u4e09\u89d2\u5f62\u53ef\u5f97\uff1a[latex]x^{\\prime}=\\frac{n}{z} x[\/latex][latex]y^{\\prime}=\\frac{n}{z} y[\/latex]<\/p>\n\n\n\n\u5199\u4f5c\u9f50\u6b21\u5750\u6807\u4e3a\uff1a[latex]\\begin{bmatrix}x \\\\y \\\\z \\\\1\\end{bmatrix}\\Rightarrow\\begin{bmatrix}n x \/ z \\\\n y \/ z \\\\\\text { unknown } \\\\1\\end{bmatrix}\\stackrel{\\text { mult. by z }}{==}\\begin{bmatrix}n x \\\\n y \\\\\\text { still unknown } \\\\z\\end{bmatrix}[\/latex]<\/p>\n\n\n\n\u4e8e\u662f\u53ef\u4ee5\u5f97\u51fa[latex]M_{\\text {persp } \\rightarrow \\text { ortho }}[\/latex]\u4e3a\uff1a[latex]M_{\\text {persp } \\rightarrow \\text { ortho }}=\\begin{bmatrix}n & 0 & 0 & 0 \\\\0 & n & 0 & 0 \\\\? & ? & ? & ? \\\\0 & 0 & 1 & 0\\end{bmatrix}[\/latex]<\/p>\n\n\n\n\u73b0\u5728\u9700\u8981\u6c42\u51faZ\u5750\u6807\uff0c\u4e5f\u5c31\u662f\u4e0a\u8ff0\u77e9\u9635\u7684\u7b2c\u4e09\u884c\u3002<\/p>\n\n\n\n\u6839\u636e\u4ee5\u4e0a\u538b\u7f29\u65f6\u9075\u5faa\u7684\u4e09\u4e2a\u539f\u5219\u7684\u7b2c\u4e00\u70b9\uff0c\u8fd1\u5e73\u9762\u6324\u538b\u540e\u4e0d\u53d8\uff0c\u53ef\u4ee5\u5199\u51fa\u4ee5\u4e0b\u65b9\u7a0b[latex]\\begin{bmatrix}x \\\\y \\\\n \\\\1\\end{bmatrix}\\Rightarrow\\begin{bmatrix}x \\\\y \\\\n \\\\1\\end{bmatrix}==\\begin{bmatrix}n x \\\\n y \\\\n^2 \\\\n\\end{bmatrix}[\/latex]<\/p>\n\n\n\n\u56e0\u6b64\uff0c\u7b2c\u4e09\u884c\u7684\u5f62\u5f0f\u4e3a[latex]\\begin{bmatrix}0 &0 &A &B\\end{bmatrix}[\/latex][latex]\\begin{bmatrix}0 &0 &A &B\\end{bmatrix}\\begin{bmatrix}0\\\\ 0\\\\ A\\\\ B\\end{bmatrix}=n^2[\/latex]<\/p>\n\n\n\n\u5373[latex]A n+B=n^2[\/latex]<\/p>\n\n\n\n\u6839\u636e\u4ee5\u4e0a\u539f\u5219\u7684\u7b2c\u4e8c\u70b9\uff0c\u8fdc\u5e73\u9762\u6324\u538b\u540eZ\u503c\u4e0d\u53d8\uff0c\u53ef\u4ee5\u5199\u51fa\u4ee5\u4e0b\u65b9\u7a0b [latex]\\begin{bmatrix}0 \\\\0 \\\\f \\\\1\\end{bmatrix}\\Rightarrow\\begin{bmatrix}0 \\\\0 \\\\f \\\\1\\end{bmatrix}==\\begin{bmatrix}0 \\\\0 \\\\f^2 \\\\f\\end{bmatrix}[\/latex]<\/p>\n\n\n\n\u5373[latex]A f+B=f^2[\/latex]<\/p>\n\n\n\n\u8054\u7acb2\u4e2a\u65b9\u7a0b\uff0c\u53ef\u4ee5\u89e3\u51faA\u3001B[latex]\\begin{aligned}& A=n+f \\\\& B=-n f\\end{aligned}[\/latex]<\/p>\n\n\n\n\u7efc\u4e0a\uff0c\u53ef\u4ee5\u5f97\u51fa[latex]M_{\\text {persp } \\rightarrow \\text { ortho }}[\/latex]\u4e3a\uff1a[latex]M_{\\text {persp } \\rightarrow \\text { ortho }}=\\begin{bmatrix}n & 0 & 0 & 0 \\\\0 & n & 0 & 0 \\\\0 & 0 & n+f & -nf \\\\0 & 0 & 1 & 0\\end{bmatrix}[\/latex]<\/p>\n","protected":false},"excerpt":{"rendered":"\u89c6\u56fe\u53d8\u6362 \u76f8\u673a \u76f8\u673a\u7684\u4f4d\u7f6e[latex]\\overrightarrow{e}[\/latex] \u76f8\u673a\u7684\u89c6\u7ebf[latex]\\wideh …<\/p>","protected":false},"author":1,"featured_media":766,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[18,14,30,3],"tags":[17,15,16,12,22],"class_list":["post-765","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-games","category-games101","category-30","category-3","tag-games","tag-games101","tag-16","tag-12","tag-22"],"_links":{"self":[{"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/posts\/765","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/comments?post=765"}],"version-history":[{"count":1,"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/posts\/765\/revisions"}],"predecessor-version":[{"id":1760,"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/posts\/765\/revisions\/1760"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/media\/766"}],"wp:attachment":[{"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/media?parent=765"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/categories?post=765"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/tags?post=765"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
\u5728\u8fdb\u884c\u900f\u89c6\u6295\u5f71\u65f6\uff0c\u5148\u5c06\u900f\u89c6\u6295\u5f71\u7684\u68f1\u53f0\u8fdb\u884c\u6324\u538b\uff0c\u76f4\u5230\u53d8\u6210\u89c6\u666f\u4f53\uff0c\u5373\u4e00\u4e2a\u957f\u65b9\u4f53\uff0c\u7136\u540e\u518d\u8fdb\u884c\u6b63\u4ea4\u6295\u5f71<\/p>\n\n\n\n
\u5728\u6324\u538b\u65f6\uff0c\u8981\u9075\u5faa\uff1a1.\u8fd1\u5e73\u9762\u6324\u538b\u540e\u4e0d\u53d82.\u8fdc\u5e73\u9762\u6324\u538b\u540eZ\u503c\u4e0d\u53d83.\u8fdc\u5e73\u9762\u7684\u4e2d\u5fc3\u6324\u538b\u540e\u4ecd\u7136\u4e3a\u4e2d\u5fc3<\/p>\n\n\n\n<\/figure >\n<\/figure><\/noscript>\n\n\n\n\u5bf9\u4e8e\u70b9[latex](x,y,z)[\/latex]\u88ab\u6324\u538b\u540e\u5f97\u5230[latex](x^{\\prime},y^{\\prime}, z^{\\prime})[\/latex] \uff0c\u6839\u636e\u76f8\u4f3c\u4e09\u89d2\u5f62\u53ef\u5f97\uff1a[latex]x^{\\prime}=\\frac{n}{z} x[\/latex][latex]y^{\\prime}=\\frac{n}{z} y[\/latex]<\/p>\n\n\n\n\u5199\u4f5c\u9f50\u6b21\u5750\u6807\u4e3a\uff1a[latex]\\begin{bmatrix}x \\\\y \\\\z \\\\1\\end{bmatrix}\\Rightarrow\\begin{bmatrix}n x \/ z \\\\n y \/ z \\\\\\text { unknown } \\\\1\\end{bmatrix}\\stackrel{\\text { mult. by z }}{==}\\begin{bmatrix}n x \\\\n y \\\\\\text { still unknown } \\\\z\\end{bmatrix}[\/latex]<\/p>\n\n\n\n\u4e8e\u662f\u53ef\u4ee5\u5f97\u51fa[latex]M_{\\text {persp } \\rightarrow \\text { ortho }}[\/latex]\u4e3a\uff1a[latex]M_{\\text {persp } \\rightarrow \\text { ortho }}=\\begin{bmatrix}n & 0 & 0 & 0 \\\\0 & n & 0 & 0 \\\\? & ? & ? & ? \\\\0 & 0 & 1 & 0\\end{bmatrix}[\/latex]<\/p>\n\n\n\n\u73b0\u5728\u9700\u8981\u6c42\u51faZ\u5750\u6807\uff0c\u4e5f\u5c31\u662f\u4e0a\u8ff0\u77e9\u9635\u7684\u7b2c\u4e09\u884c\u3002<\/p>\n\n\n\n\u6839\u636e\u4ee5\u4e0a\u538b\u7f29\u65f6\u9075\u5faa\u7684\u4e09\u4e2a\u539f\u5219\u7684\u7b2c\u4e00\u70b9\uff0c\u8fd1\u5e73\u9762\u6324\u538b\u540e\u4e0d\u53d8\uff0c\u53ef\u4ee5\u5199\u51fa\u4ee5\u4e0b\u65b9\u7a0b[latex]\\begin{bmatrix}x \\\\y \\\\n \\\\1\\end{bmatrix}\\Rightarrow\\begin{bmatrix}x \\\\y \\\\n \\\\1\\end{bmatrix}==\\begin{bmatrix}n x \\\\n y \\\\n^2 \\\\n\\end{bmatrix}[\/latex]<\/p>\n\n\n\n\u56e0\u6b64\uff0c\u7b2c\u4e09\u884c\u7684\u5f62\u5f0f\u4e3a[latex]\\begin{bmatrix}0 &0 &A &B\\end{bmatrix}[\/latex][latex]\\begin{bmatrix}0 &0 &A &B\\end{bmatrix}\\begin{bmatrix}0\\\\ 0\\\\ A\\\\ B\\end{bmatrix}=n^2[\/latex]<\/p>\n\n\n\n\u5373[latex]A n+B=n^2[\/latex]<\/p>\n\n\n\n\u6839\u636e\u4ee5\u4e0a\u539f\u5219\u7684\u7b2c\u4e8c\u70b9\uff0c\u8fdc\u5e73\u9762\u6324\u538b\u540eZ\u503c\u4e0d\u53d8\uff0c\u53ef\u4ee5\u5199\u51fa\u4ee5\u4e0b\u65b9\u7a0b [latex]\\begin{bmatrix}0 \\\\0 \\\\f \\\\1\\end{bmatrix}\\Rightarrow\\begin{bmatrix}0 \\\\0 \\\\f \\\\1\\end{bmatrix}==\\begin{bmatrix}0 \\\\0 \\\\f^2 \\\\f\\end{bmatrix}[\/latex]<\/p>\n\n\n\n\u5373[latex]A f+B=f^2[\/latex]<\/p>\n\n\n\n\u8054\u7acb2\u4e2a\u65b9\u7a0b\uff0c\u53ef\u4ee5\u89e3\u51faA\u3001B[latex]\\begin{aligned}& A=n+f \\\\& B=-n f\\end{aligned}[\/latex]<\/p>\n\n\n\n\u7efc\u4e0a\uff0c\u53ef\u4ee5\u5f97\u51fa[latex]M_{\\text {persp } \\rightarrow \\text { ortho }}[\/latex]\u4e3a\uff1a[latex]M_{\\text {persp } \\rightarrow \\text { ortho }}=\\begin{bmatrix}n & 0 & 0 & 0 \\\\0 & n & 0 & 0 \\\\0 & 0 & n+f & -nf \\\\0 & 0 & 1 & 0\\end{bmatrix}[\/latex]<\/p>\n","protected":false},"excerpt":{"rendered":"\u89c6\u56fe\u53d8\u6362 \u76f8\u673a \u76f8\u673a\u7684\u4f4d\u7f6e[latex]\\overrightarrow{e}[\/latex] \u76f8\u673a\u7684\u89c6\u7ebf[latex]\\wideh …<\/p>","protected":false},"author":1,"featured_media":766,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[18,14,30,3],"tags":[17,15,16,12,22],"class_list":["post-765","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-games","category-games101","category-30","category-3","tag-games","tag-games101","tag-16","tag-12","tag-22"],"_links":{"self":[{"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/posts\/765","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/comments?post=765"}],"version-history":[{"count":1,"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/posts\/765\/revisions"}],"predecessor-version":[{"id":1760,"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/posts\/765\/revisions\/1760"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/media\/766"}],"wp:attachment":[{"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/media?parent=765"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/categories?post=765"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/tags?post=765"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
\u5bf9\u4e8e\u70b9[latex](x,y,z)[\/latex]\u88ab\u6324\u538b\u540e\u5f97\u5230[latex](x^{\\prime},y^{\\prime}, z^{\\prime})[\/latex] \uff0c\u6839\u636e\u76f8\u4f3c\u4e09\u89d2\u5f62\u53ef\u5f97\uff1a[latex]x^{\\prime}=\\frac{n}{z} x[\/latex][latex]y^{\\prime}=\\frac{n}{z} y[\/latex]<\/p>\n\n\n\n
\u5199\u4f5c\u9f50\u6b21\u5750\u6807\u4e3a\uff1a[latex]\\begin{bmatrix}x \\\\y \\\\z \\\\1\\end{bmatrix}\\Rightarrow\\begin{bmatrix}n x \/ z \\\\n y \/ z \\\\\\text { unknown } \\\\1\\end{bmatrix}\\stackrel{\\text { mult. by z }}{==}\\begin{bmatrix}n x \\\\n y \\\\\\text { still unknown } \\\\z\\end{bmatrix}[\/latex]<\/p>\n\n\n\n
\u4e8e\u662f\u53ef\u4ee5\u5f97\u51fa[latex]M_{\\text {persp } \\rightarrow \\text { ortho }}[\/latex]\u4e3a\uff1a[latex]M_{\\text {persp } \\rightarrow \\text { ortho }}=\\begin{bmatrix}n & 0 & 0 & 0 \\\\0 & n & 0 & 0 \\\\? & ? & ? & ? \\\\0 & 0 & 1 & 0\\end{bmatrix}[\/latex]<\/p>\n\n\n\n
\u73b0\u5728\u9700\u8981\u6c42\u51faZ\u5750\u6807\uff0c\u4e5f\u5c31\u662f\u4e0a\u8ff0\u77e9\u9635\u7684\u7b2c\u4e09\u884c\u3002<\/p>\n\n\n\n
\u6839\u636e\u4ee5\u4e0a\u538b\u7f29\u65f6\u9075\u5faa\u7684\u4e09\u4e2a\u539f\u5219\u7684\u7b2c\u4e00\u70b9\uff0c\u8fd1\u5e73\u9762\u6324\u538b\u540e\u4e0d\u53d8\uff0c\u53ef\u4ee5\u5199\u51fa\u4ee5\u4e0b\u65b9\u7a0b[latex]\\begin{bmatrix}x \\\\y \\\\n \\\\1\\end{bmatrix}\\Rightarrow\\begin{bmatrix}x \\\\y \\\\n \\\\1\\end{bmatrix}==\\begin{bmatrix}n x \\\\n y \\\\n^2 \\\\n\\end{bmatrix}[\/latex]<\/p>\n\n\n\n
\u56e0\u6b64\uff0c\u7b2c\u4e09\u884c\u7684\u5f62\u5f0f\u4e3a[latex]\\begin{bmatrix}0 &0 &A &B\\end{bmatrix}[\/latex][latex]\\begin{bmatrix}0 &0 &A &B\\end{bmatrix}\\begin{bmatrix}0\\\\ 0\\\\ A\\\\ B\\end{bmatrix}=n^2[\/latex]<\/p>\n\n\n\n
\u5373[latex]A n+B=n^2[\/latex]<\/p>\n\n\n\n
\u6839\u636e\u4ee5\u4e0a\u539f\u5219\u7684\u7b2c\u4e8c\u70b9\uff0c\u8fdc\u5e73\u9762\u6324\u538b\u540eZ\u503c\u4e0d\u53d8\uff0c\u53ef\u4ee5\u5199\u51fa\u4ee5\u4e0b\u65b9\u7a0b [latex]\\begin{bmatrix}0 \\\\0 \\\\f \\\\1\\end{bmatrix}\\Rightarrow\\begin{bmatrix}0 \\\\0 \\\\f \\\\1\\end{bmatrix}==\\begin{bmatrix}0 \\\\0 \\\\f^2 \\\\f\\end{bmatrix}[\/latex]<\/p>\n\n\n\n
\u5373[latex]A f+B=f^2[\/latex]<\/p>\n\n\n\n
\u8054\u7acb2\u4e2a\u65b9\u7a0b\uff0c\u53ef\u4ee5\u89e3\u51faA\u3001B[latex]\\begin{aligned}& A=n+f \\\\& B=-n f\\end{aligned}[\/latex]<\/p>\n\n\n\n
\u7efc\u4e0a\uff0c\u53ef\u4ee5\u5f97\u51fa[latex]M_{\\text {persp } \\rightarrow \\text { ortho }}[\/latex]\u4e3a\uff1a[latex]M_{\\text {persp } \\rightarrow \\text { ortho }}=\\begin{bmatrix}n & 0 & 0 & 0 \\\\0 & n & 0 & 0 \\\\0 & 0 & n+f & -nf \\\\0 & 0 & 1 & 0\\end{bmatrix}[\/latex]<\/p>\n","protected":false},"excerpt":{"rendered":"
\u89c6\u56fe\u53d8\u6362 \u76f8\u673a \u76f8\u673a\u7684\u4f4d\u7f6e[latex]\\overrightarrow{e}[\/latex] \u76f8\u673a\u7684\u89c6\u7ebf[latex]\\wideh …<\/p>","protected":false},"author":1,"featured_media":766,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[18,14,30,3],"tags":[17,15,16,12,22],"class_list":["post-765","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-games","category-games101","category-30","category-3","tag-games","tag-games101","tag-16","tag-12","tag-22"],"_links":{"self":[{"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/posts\/765","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/comments?post=765"}],"version-history":[{"count":1,"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/posts\/765\/revisions"}],"predecessor-version":[{"id":1760,"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/posts\/765\/revisions\/1760"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/media\/766"}],"wp:attachment":[{"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/media?parent=765"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/categories?post=765"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/tags?post=765"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
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