\u5728\u5149\u7ebf\u8ffd\u8e2a\u4e2d\uff0c\u5047\u8bbe\u76f8\u673a\u662f\u4e2a\u70b9\u800c\u4e0d\u662f\u4e2a\u77e9\u5f62\u3002\u7136\u540e\u5c06\u6bcf\u4e2a\u50cf\u7d20\u548c\u76f8\u673a\u76f8\u8fde\u5e76\u5ef6\u957f\u8fd9\u6761\u7ebf\uff0c\u4f5c\u4e3a\u5149\u7ebf\uff0c\u8fd9\u6761\u7ebf\u88ab\u79f0\u4e3a\u201c\u773c\u775b\u5149\u7ebf\u201d\u3002\u8fd9\u6839\u5149\u7ebf\u4f1a\u548c\u573a\u666f\u4e2d\u7684\u7269\u4f53\u76f8\u4ea4\uff0c\u8bb0\u5f55\u4e0b\u6700\u8fd1\u7684\u4ea4\u70b9\u3002\u5c06\u4ea4\u70b9\u4e0e\u5149\u6e90\u76f8\u8fde\uff0c\u5224\u65ad\u80fd\u5426\u88ab\u5149\u6e90\u76f4\u63a5\u7167\u5230\u3002\u4f7f\u7528\u7740\u8272\u5668\u8fdb\u884c\u7740\u8272\uff0c\u5199\u5165\u8be5\u50cf\u7d20\u70b9\u7684\u989c\u8272\u503c\u3002<\/p>\n\n\n\n<\/figure >\n<\/figure><\/noscript>\n\n\n\nWhitted\u98ce\u683c\u5149\u7ebf\u8ffd\u8e2a<\/h3>\n\n\n\n\u5f53\u5149\u7ebf\u4e0e\u7269\u4f53\u76f8\u4ea4\u65f6\uff0c\u8ba1\u7b97\u8be5\u5149\u7ebf\u7684\u53cd\u5c04\u5149\u3001\u6298\u5c04\u5149\u3002\u540c\u65f6\u4e0d\u65ad\u9012\u5f52\u53cd\u5c04\u5149\u3001\u6298\u5c04\u5149\uff0c\u8ba1\u7b97\u6bcf\u4e00\u4e2a\u53cd\u5c04\u5149\u3001\u6298\u5c04\u5149\u4e0e\u573a\u666f\u7684\u4ea4\u70b9\u3001\u4ea7\u751f\u7684\u53cd\u5c04\u5149\u3001\u6298\u5c04\u5149\uff0c\u5e76\u4e0e\u5149\u6e90\u76f8\u8fde\uff0c\u5224\u65ad\u662f\u5426\u80fd\u88ab\u5149\u6e90\u76f4\u63a5\u7167\u5c04\u5230\u3002\u7136\u540e\u4f7f\u7528\u7740\u8272\u5668\u8fdb\u884c\u7740\u8272\uff0c\u5e76\u5c06\u6700\u540e\u5c06\u5f97\u5230\u7684\u6240\u6709\u989c\u8272\u503c\u76f8\u52a0\u3002<\/p>\n\n\n\n<\/figure >\n<\/figure><\/noscript>\n\n\n\n\u5149\u7ebf\u4e0e\u6a21\u578b\u7684\u4ea4\u70b9<\/h2>\n\n\n\n\u5b9a\u4e49\u5149\u7ebf<\/h3>\n\n\n\n\u5bf9\u4e8e\u4efb\u610f\u4e00\u6761\u5149\u7ebf\uff0c\u53ef\u4ee5\u7528[latex]r(t)=o+td (0 \\le t < \\infty [\/latex]\u6765\u8868\u793a\u3002\u5176\u4e2dr\u4e3a\u5149\u7ebf\uff0ct\u4e3a\u65f6\u95f4\uff0co\u4e3a\u5149\u6e90\uff0cd\u4e3a\u5149\u7ebf\u65b9\u5411\u3002<\/p>\n\n\n\n<\/figure >\n<\/figure><\/noscript>\n\n\n\n\u5149\u7ebf\u4e0e\u7403\u4f53\u7684\u4ea4\u70b9<\/h3>\n\n\n\n\u7403\u4f53p\u7684\u5b9a\u4e49[latex](p-c)^2-R^2=0[\/latex]<\/p>\n\n\n\n <\/figcaption><\/figure >\n <\/figcaption><\/figure><\/noscript>\n\n\n\n\u5c06\u5149\u7ebf\u5e26\u5165\u7403\u4f53\u7684\u516c\u5f0f\u4e2d\uff1a[latex](o+td-c)^2-R^2=0[\/latex][latex]a t^2+b t+c=0, \\text { where }[\/latex][latex]a=\\mathbf{d} \\cdot \\mathbf{d}[\/latex][latex]b=2(\\mathbf{o}-\\mathbf{c}) \\cdot \\mathbf{d}[\/latex][latex]c=(\\mathbf{o}-\\mathbf{c}) \\cdot(\\mathbf{o}-\\mathbf{c})-R^2[\/latex][latex]t=\\frac{-b \\pm \\sqrt{b^2-4 a c}}{2 a}[\/latex]<\/p>\n\n\n\n\u5229\u7528\u25b3\u53ef\u77e5\u4e0e\u7403\u4f53\u7684\u4ea4\u70b9\u4e2a\u6570\uff0c\u7528\u6c42\u6839\u516c\u5f0f\u5373\u53ef\u5f97\u51fa\u4ea4\u70b9<\/p>\n\n\n\n<\/figure >\n<\/figure><\/noscript>\n\n\n\n\u5149\u7ebf\u4e0e\u9690\u5f0f\u8868\u9762\u7684\u4ea4\u70b9<\/h3>\n\n\n\n\u5b9a\u4e49\u9690\u5f0f\u8868\u9762p\uff1a[latex]f(p)=0[\/latex]\u5c06\u5149\u7ebf\u5e26\u5165\u516c\u5f0f[latex]f(o+td)=0[\/latex]\u89e3\u51fa\u65b9\u7a0b\u7684\u6839\u5373\u53ef<\/p>\n\n\n\n\u5149\u7ebf\u4e0e\u663e\u5f0f\u8868\u9762\u7684\u4ea4\u70b9<\/h3>\n\n\n\n\u6c42\u5149\u7ebf\u4e0e\u663e\u5f0f\u8868\u9762\u7684\u4ea4\u70b9\uff0c\u5373\u4e3a\u6c42\u5149\u7ebf\u4e0e\u4e09\u89d2\u5f62\u6c42\u4ea4\u70b9\u3002<\/p>\n\n\n\n\u5b9a\u4e49\u5e73\u9762\uff1a<\/p>\n\n\n\n\u5b9a\u4e49\u5e73\u9762\u7684\u6cd5\u7ebfN\uff0c\u518d\u5b9a\u4e49\u5e73\u9762\u4e0a\u4efb\u610f\u4e00\u70b9[latex]p^{\\prime}[\/latex]\uff0c\u5982\u679c\u6709\u4e00\u70b9\u5728\u5e73\u9762\u5185\uff0c\u8fd9\u4e2a\u70b9\u4e0ep'\u7684\u8fde\u7ebf\u4e0e\u6cd5\u7ebf\u5782\u76f4\u3002<\/p>\n\n\n\n<\/figure >\n<\/figure><\/noscript>\n\n\n\n\u5373\u5e73\u9762p\uff1a [latex](p-p') \\cdot N=0[\/latex]<\/p>\n\n\n\n\u4ee4[latex]p=r(t)[\/latex][latex]\\left(\\mathbf{p}-\\mathbf{p}^{\\prime}\\right) \\cdot \\mathbf{N}=\\left(\\mathbf{o}+t \\mathbf{d}-\\mathbf{p}^{\\prime}\\right) \\cdot \\mathbf{N}=0[\/latex]<\/p>\n\n\n\n\u5373\u53ef\u6c42\u51fat\uff1a[latex]t=\\frac{\\left(\\mathbf{p}^{\\prime}-\\mathbf{o}\\right) \\cdot \\mathbf{N}}{\\mathbf{d} \\cdot \\mathbf{N}}[\/latex][latex]0 \\leq t<\\infty[\/latex]<\/p>\n\n\n\nM\u00f6ller Trumbore\u7b97\u6cd5<\/h3>\n\n\n\n\u8be5\u7b97\u6cd5\u53ef\u4ee5\u5feb\u901f\u6c42\u51fa\u5149\u7ebf\u5728\u4e09\u89d2\u5f62\u5185\u7684\u4ea4\u70b9\u3002<\/p>\n\n\n\n\u5982\u679c\u5149\u7ebf\u4e0e\u5e73\u9762\u7684\u4ea4\u70b9\u5728\u4e09\u89d2\u5f62\u5185\uff0c\u90a3\u8fd9\u4e00\u70b9\u4e5f\u5c31\u80fd\u591f\u7528\u91cd\u5fc3\u5750\u6807\u8868\u793a\uff0c\u5373\uff1a[latex]\\overrightarrow{\\mathbf{O}}+t \\overrightarrow{\\mathbf{D}}=\\left(1-b_1-b_2\\right) \\overrightarrow{\\mathbf{P}}_0+b_1 \\overrightarrow{\\mathbf{P}}_1+b_2 \\overrightarrow{\\mathbf{P}}_2[\/latex]<\/p>\n\n\n\n\u4ee4\uff1a[latex]\\begin{aligned}& \\overrightarrow{\\mathbf{E}}_1=\\overrightarrow{\\mathbf{P}}_1-\\overrightarrow{\\mathbf{P}}_0 \\\\& \\overrightarrow{\\mathbf{E}}_2=\\overrightarrow{\\mathbf{P}}_2-\\overrightarrow{\\mathbf{P}}_0 \\\\& \\overrightarrow{\\mathbf{S}}=\\overrightarrow{\\mathbf{O}}-\\overrightarrow{\\mathbf{P}}_0 \\\\& \\overrightarrow{\\mathbf{S}}_1=\\overrightarrow{\\mathbf{D}} \\times \\overrightarrow{\\mathbf{E}}_2 \\\\& \\overrightarrow{\\mathbf{S}}_2=\\overrightarrow{\\mathbf{S}} \\times \\overrightarrow{\\mathbf{E}}_1\\end{aligned}[\/latex]<\/p>\n\n\n\n\u5229\u7528Cramer \u6cd5\u5219\uff1a[latex]\\left[\\begin{array}{l}t \\\\b_1 \\\\b_2\\end{array}\\right]=\\frac{1}{\\overrightarrow{\\mathbf{S}}_1 \\cdot \\overrightarrow{\\mathbf{E}}_1}\\left[\\begin{array}{c}\\overrightarrow{\\mathbf{S}}_2 \\cdot \\overrightarrow{\\mathbf{E}}_2 \\\\\\overrightarrow{\\mathbf{S}}_1 \\cdot \\overrightarrow{\\mathbf{S}} \\\\\\overrightarrow{\\mathbf{S}}_2 \\cdot \\overrightarrow{\\mathbf{D}}\\end{array}\\right][\/latex]<\/p>\n\n\n\n\u5373\u53ef\u6c42\u51fa\u4e0a\u8ff0\u65b9\u7a0b\u7684\u89e3\uff0c\u5176\u7b97\u529b\u5f00\u9500\u975e\u5e38\u4f4e\u3002<\/p>\n\n\n\n\u52a0\u901f\u7b97\u6cd5<\/h2>\n\n\n\n\u5305\u56f4\u76d2<\/h3>\n\n\n\n\u4f7f\u7528\u5305\u56f4\u76d2\u5c06\u6bcf\u4e00\u4e2a\u6a21\u578b\u5305\u56f4\u8d77\u6765\uff0c\u5982\u679c\u5149\u7ebf\u4e0e\u5305\u56f4\u76d2\u76f8\u4ea4\uff0c\u624d\u8ba1\u7b97\u5149\u7ebf\u548c\u5305\u56f4\u76d2\u5185\u6a21\u578b\u7684\u6bcf\u4e2a\u4e09\u89d2\u5f62\u662f\u5426\u76f8\u4ea4\u3002<\/p>\n\n\n\n\u5c06\u5305\u56f4\u548c\u7406\u89e3\u4e3a3\u7ec4\u5bf9\u9762\u5f62\u6210\u7684\u4ea4\u96c6\uff1a<\/p>\n\n\n\n<\/figure >\n<\/figure><\/noscript>\n\n\n\n\u8f74\u5bf9\u9f50\u5305\u56f4\u76d2AABB<\/h3>\n\n\n\nAxis-Aligned Bounding Box\uff0c\u6bcf\u4e2a\u9762\u90fd\u548c\u5750\u6807\u8f74\u7684\u9762\u5e73\u884c\u3002<\/p>\n\n\n\n\u5728\u4e8c\u7ef4\u4e2d\uff0c\u5224\u65ad\u4e00\u4e2a\u957f\u65b9\u5f62\u548c\u4e00\u6761\u76f4\u7ebf\u662f\u5426\u6709\u4ea4\u96c6\uff0c\u53ef\u4ee5\u5148\u6c42\u51fa\u5176\u548c\u7ebfx0\uff0cx1\u7684\u4e24\u4e2a\u4ea4\u70b9\uff0c\u518d\u6c42\u51fa\u548c\u7ebfy0\uff0cy1\u7684\u4e24\u4e2a\u4ea4\u70b9<\/p>\n\n\n\n<\/figure >\n<\/figure><\/noscript>\n\n\n\n\u56e0\u4e3a\u5f53\u5149\u7ebf\u8fdb\u5165\u5230\u6240\u6709\u7684\u9762\uff0c\u624d\u80fd\u786e\u5b9a\u5149\u8fdb\u5165\u5230\u5305\u56f4\u76d2\u4e2d\uff0c\u800c\u5f53\u5149\u7ebf\u79bb\u5f00\u4efb\u610f\u4e00\u4e2a\u9762\uff0c\u5373\u4e3a\u79bb\u5f00\u5305\u56f4\u76d2\u3002\u6240\u4ee5\u6c42\u51fa\u5176\u4e2d\u6700\u5927\u7684[latex]t_{min}[\/latex]\u548c\u6700\u5c0f\u7684[latex]t_{max}[\/latex]\u5373\u4e3a\u5149\u7ebf\u5b9e\u9645\u8fdb\u5165\u548c\u79bb\u5f00\u76d2\u5b50\u7684\u65f6\u95f4\u3002<\/p>\n\n\n\n<\/figure >\n<\/figure><\/noscript>\n\n\n\n\u5373[latex]t_{enter}=max(t_{min}),t_{exit}=min(t_{max})[\/latex]\u3002\u5728\u4e09\u7ef4\u7a7a\u95f4\u4e2d\u540c\u7406\u3002<\/p>\n\n\n\n\u5982\u679c[latex]t_{enter}<t_{exit}[\/latex]\uff0c\u5373\u4e3a\u5149\u7ebf\u7ecf\u8fc7\u4e86\u5305\u56f4\u76d2\uff08\u5149\u7ebf\u5728\u5305\u56f4\u76d2\u4e2d\u5f85\u4e86\u4e00\u6bb5\u65f6\u95f4\uff09\u3002<\/p>\n\n\n\n\u4f46\u662f\u5149\u7ebf\u662f\u5c04\u7ebf\uff0c\u4e0d\u662f\u76f4\u7ebf\uff0c\u6240\u4ee5\u5f53[latex]t_{exit}<0[\/latex]\uff0c\u8bf4\u660e\u7269\u4f53\u5728\u5149\u7ebf\u7684\u80cc\u540e\uff0c\u5373\u4e0d\u53ef\u80fd\u6709\u4ea4\u70b9\u3002\u5f53[latex]t_{exit}>=0,t_{enter}<0[\/latex]\uff0c\u5373\u5149\u7ebf\u7684\u8d77\u70b9\u5728\u5305\u56f4\u76d2\u5185\u90e8\u3002<\/p>\n\n\n\n\u6240\u4ee5\u5f53\u4e14\u4ec5\u5f53[latex]t_{enter}<t_{exit},t_{exit}\\ge0[\/latex]\u65f6\uff0c\u5149\u7ebf\u7a7f\u8fc7\u5305\u56f4\u76d2\u3002<\/p>\n\n\n\n\u8ba1\u7b97\u5149\u7ebf\u4e0e\u9762\u4f55\u65f6\u76f8\u4ea4\uff1a[latex]t=\\frac{\\left(\\mathbf{p}^{\\prime}-\\mathbf{o}\\right) \\cdot \\mathbf{N}}{\\mathbf{d} \\cdot \\mathbf{N}}[\/latex]\u800c\u8fd9\u91cc\u7684\u9762\u662f\u4e0e\u5750\u6807\u8f74\u5e73\u9762\u5e73\u884c\u7684\uff0c\u6240\u4ee5\u53ef\u4ee5\u7b80\u5316\u8fd0\u7b97\uff1a\u5bf9\u4e8eyz\u5e73\u9762\u5e73\u884c\uff0c\u5373\u4e3a\u5782\u76f4\u4e8ex\u8f74\uff1a[latex]t=\\frac{\\mathbf{p}_x^{\\prime}-\\mathbf{o}_x}{\\mathbf{d}_x}[\/latex]<\/p>\n","protected":false},"excerpt":{"rendered":"\u5149\u7ebf\u8ffd\u8e2a \u5728\u5149\u7ebf\u8ffd\u8e2a\u4e2d\uff0c\u5047\u8bbe\u76f8\u673a\u662f\u4e2a\u70b9\u800c\u4e0d\u662f\u4e2a\u77e9\u5f62\u3002\u7136\u540e\u5c06\u6bcf\u4e2a\u50cf\u7d20\u548c\u76f8\u673a\u76f8\u8fde\u5e76\u5ef6\u957f\u8fd9\u6761\u7ebf\uff0c\u4f5c\u4e3a\u5149\u7ebf\uff0c\u8fd9\u6761\u7ebf\u88ab\u79f0\u4e3a\u201c\u773c\u775b\u5149\u7ebf\u201d\u3002\u8fd9\u6839 …<\/p>","protected":false},"author":1,"featured_media":1141,"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-1140","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\/1140","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=1140"}],"version-history":[{"count":1,"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/posts\/1140\/revisions"}],"predecessor-version":[{"id":1747,"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/posts\/1140\/revisions\/1747"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/media\/1141"}],"wp:attachment":[{"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/media?parent=1140"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/categories?post=1140"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/tags?post=1140"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
\u5f53\u5149\u7ebf\u4e0e\u7269\u4f53\u76f8\u4ea4\u65f6\uff0c\u8ba1\u7b97\u8be5\u5149\u7ebf\u7684\u53cd\u5c04\u5149\u3001\u6298\u5c04\u5149\u3002\u540c\u65f6\u4e0d\u65ad\u9012\u5f52\u53cd\u5c04\u5149\u3001\u6298\u5c04\u5149\uff0c\u8ba1\u7b97\u6bcf\u4e00\u4e2a\u53cd\u5c04\u5149\u3001\u6298\u5c04\u5149\u4e0e\u573a\u666f\u7684\u4ea4\u70b9\u3001\u4ea7\u751f\u7684\u53cd\u5c04\u5149\u3001\u6298\u5c04\u5149\uff0c\u5e76\u4e0e\u5149\u6e90\u76f8\u8fde\uff0c\u5224\u65ad\u662f\u5426\u80fd\u88ab\u5149\u6e90\u76f4\u63a5\u7167\u5c04\u5230\u3002\u7136\u540e\u4f7f\u7528\u7740\u8272\u5668\u8fdb\u884c\u7740\u8272\uff0c\u5e76\u5c06\u6700\u540e\u5c06\u5f97\u5230\u7684\u6240\u6709\u989c\u8272\u503c\u76f8\u52a0\u3002<\/p>\n\n\n\n<\/figure >\n<\/figure><\/noscript>\n\n\n\n\u5149\u7ebf\u4e0e\u6a21\u578b\u7684\u4ea4\u70b9<\/h2>\n\n\n\n\u5b9a\u4e49\u5149\u7ebf<\/h3>\n\n\n\n\u5bf9\u4e8e\u4efb\u610f\u4e00\u6761\u5149\u7ebf\uff0c\u53ef\u4ee5\u7528[latex]r(t)=o+td (0 \\le t < \\infty [\/latex]\u6765\u8868\u793a\u3002\u5176\u4e2dr\u4e3a\u5149\u7ebf\uff0ct\u4e3a\u65f6\u95f4\uff0co\u4e3a\u5149\u6e90\uff0cd\u4e3a\u5149\u7ebf\u65b9\u5411\u3002<\/p>\n\n\n\n<\/figure >\n<\/figure><\/noscript>\n\n\n\n\u5149\u7ebf\u4e0e\u7403\u4f53\u7684\u4ea4\u70b9<\/h3>\n\n\n\n\u7403\u4f53p\u7684\u5b9a\u4e49[latex](p-c)^2-R^2=0[\/latex]<\/p>\n\n\n\n <\/figcaption><\/figure >\n <\/figcaption><\/figure><\/noscript>\n\n\n\n\u5c06\u5149\u7ebf\u5e26\u5165\u7403\u4f53\u7684\u516c\u5f0f\u4e2d\uff1a[latex](o+td-c)^2-R^2=0[\/latex][latex]a t^2+b t+c=0, \\text { where }[\/latex][latex]a=\\mathbf{d} \\cdot \\mathbf{d}[\/latex][latex]b=2(\\mathbf{o}-\\mathbf{c}) \\cdot \\mathbf{d}[\/latex][latex]c=(\\mathbf{o}-\\mathbf{c}) \\cdot(\\mathbf{o}-\\mathbf{c})-R^2[\/latex][latex]t=\\frac{-b \\pm \\sqrt{b^2-4 a c}}{2 a}[\/latex]<\/p>\n\n\n\n\u5229\u7528\u25b3\u53ef\u77e5\u4e0e\u7403\u4f53\u7684\u4ea4\u70b9\u4e2a\u6570\uff0c\u7528\u6c42\u6839\u516c\u5f0f\u5373\u53ef\u5f97\u51fa\u4ea4\u70b9<\/p>\n\n\n\n<\/figure >\n<\/figure><\/noscript>\n\n\n\n\u5149\u7ebf\u4e0e\u9690\u5f0f\u8868\u9762\u7684\u4ea4\u70b9<\/h3>\n\n\n\n\u5b9a\u4e49\u9690\u5f0f\u8868\u9762p\uff1a[latex]f(p)=0[\/latex]\u5c06\u5149\u7ebf\u5e26\u5165\u516c\u5f0f[latex]f(o+td)=0[\/latex]\u89e3\u51fa\u65b9\u7a0b\u7684\u6839\u5373\u53ef<\/p>\n\n\n\n\u5149\u7ebf\u4e0e\u663e\u5f0f\u8868\u9762\u7684\u4ea4\u70b9<\/h3>\n\n\n\n\u6c42\u5149\u7ebf\u4e0e\u663e\u5f0f\u8868\u9762\u7684\u4ea4\u70b9\uff0c\u5373\u4e3a\u6c42\u5149\u7ebf\u4e0e\u4e09\u89d2\u5f62\u6c42\u4ea4\u70b9\u3002<\/p>\n\n\n\n\u5b9a\u4e49\u5e73\u9762\uff1a<\/p>\n\n\n\n\u5b9a\u4e49\u5e73\u9762\u7684\u6cd5\u7ebfN\uff0c\u518d\u5b9a\u4e49\u5e73\u9762\u4e0a\u4efb\u610f\u4e00\u70b9[latex]p^{\\prime}[\/latex]\uff0c\u5982\u679c\u6709\u4e00\u70b9\u5728\u5e73\u9762\u5185\uff0c\u8fd9\u4e2a\u70b9\u4e0ep'\u7684\u8fde\u7ebf\u4e0e\u6cd5\u7ebf\u5782\u76f4\u3002<\/p>\n\n\n\n<\/figure >\n<\/figure><\/noscript>\n\n\n\n\u5373\u5e73\u9762p\uff1a [latex](p-p') \\cdot N=0[\/latex]<\/p>\n\n\n\n\u4ee4[latex]p=r(t)[\/latex][latex]\\left(\\mathbf{p}-\\mathbf{p}^{\\prime}\\right) \\cdot \\mathbf{N}=\\left(\\mathbf{o}+t \\mathbf{d}-\\mathbf{p}^{\\prime}\\right) \\cdot \\mathbf{N}=0[\/latex]<\/p>\n\n\n\n\u5373\u53ef\u6c42\u51fat\uff1a[latex]t=\\frac{\\left(\\mathbf{p}^{\\prime}-\\mathbf{o}\\right) \\cdot \\mathbf{N}}{\\mathbf{d} \\cdot \\mathbf{N}}[\/latex][latex]0 \\leq t<\\infty[\/latex]<\/p>\n\n\n\nM\u00f6ller Trumbore\u7b97\u6cd5<\/h3>\n\n\n\n\u8be5\u7b97\u6cd5\u53ef\u4ee5\u5feb\u901f\u6c42\u51fa\u5149\u7ebf\u5728\u4e09\u89d2\u5f62\u5185\u7684\u4ea4\u70b9\u3002<\/p>\n\n\n\n\u5982\u679c\u5149\u7ebf\u4e0e\u5e73\u9762\u7684\u4ea4\u70b9\u5728\u4e09\u89d2\u5f62\u5185\uff0c\u90a3\u8fd9\u4e00\u70b9\u4e5f\u5c31\u80fd\u591f\u7528\u91cd\u5fc3\u5750\u6807\u8868\u793a\uff0c\u5373\uff1a[latex]\\overrightarrow{\\mathbf{O}}+t \\overrightarrow{\\mathbf{D}}=\\left(1-b_1-b_2\\right) \\overrightarrow{\\mathbf{P}}_0+b_1 \\overrightarrow{\\mathbf{P}}_1+b_2 \\overrightarrow{\\mathbf{P}}_2[\/latex]<\/p>\n\n\n\n\u4ee4\uff1a[latex]\\begin{aligned}& \\overrightarrow{\\mathbf{E}}_1=\\overrightarrow{\\mathbf{P}}_1-\\overrightarrow{\\mathbf{P}}_0 \\\\& \\overrightarrow{\\mathbf{E}}_2=\\overrightarrow{\\mathbf{P}}_2-\\overrightarrow{\\mathbf{P}}_0 \\\\& \\overrightarrow{\\mathbf{S}}=\\overrightarrow{\\mathbf{O}}-\\overrightarrow{\\mathbf{P}}_0 \\\\& \\overrightarrow{\\mathbf{S}}_1=\\overrightarrow{\\mathbf{D}} \\times \\overrightarrow{\\mathbf{E}}_2 \\\\& \\overrightarrow{\\mathbf{S}}_2=\\overrightarrow{\\mathbf{S}} \\times \\overrightarrow{\\mathbf{E}}_1\\end{aligned}[\/latex]<\/p>\n\n\n\n\u5229\u7528Cramer \u6cd5\u5219\uff1a[latex]\\left[\\begin{array}{l}t \\\\b_1 \\\\b_2\\end{array}\\right]=\\frac{1}{\\overrightarrow{\\mathbf{S}}_1 \\cdot \\overrightarrow{\\mathbf{E}}_1}\\left[\\begin{array}{c}\\overrightarrow{\\mathbf{S}}_2 \\cdot \\overrightarrow{\\mathbf{E}}_2 \\\\\\overrightarrow{\\mathbf{S}}_1 \\cdot \\overrightarrow{\\mathbf{S}} \\\\\\overrightarrow{\\mathbf{S}}_2 \\cdot \\overrightarrow{\\mathbf{D}}\\end{array}\\right][\/latex]<\/p>\n\n\n\n\u5373\u53ef\u6c42\u51fa\u4e0a\u8ff0\u65b9\u7a0b\u7684\u89e3\uff0c\u5176\u7b97\u529b\u5f00\u9500\u975e\u5e38\u4f4e\u3002<\/p>\n\n\n\n\u52a0\u901f\u7b97\u6cd5<\/h2>\n\n\n\n\u5305\u56f4\u76d2<\/h3>\n\n\n\n\u4f7f\u7528\u5305\u56f4\u76d2\u5c06\u6bcf\u4e00\u4e2a\u6a21\u578b\u5305\u56f4\u8d77\u6765\uff0c\u5982\u679c\u5149\u7ebf\u4e0e\u5305\u56f4\u76d2\u76f8\u4ea4\uff0c\u624d\u8ba1\u7b97\u5149\u7ebf\u548c\u5305\u56f4\u76d2\u5185\u6a21\u578b\u7684\u6bcf\u4e2a\u4e09\u89d2\u5f62\u662f\u5426\u76f8\u4ea4\u3002<\/p>\n\n\n\n\u5c06\u5305\u56f4\u548c\u7406\u89e3\u4e3a3\u7ec4\u5bf9\u9762\u5f62\u6210\u7684\u4ea4\u96c6\uff1a<\/p>\n\n\n\n<\/figure >\n<\/figure><\/noscript>\n\n\n\n\u8f74\u5bf9\u9f50\u5305\u56f4\u76d2AABB<\/h3>\n\n\n\nAxis-Aligned Bounding Box\uff0c\u6bcf\u4e2a\u9762\u90fd\u548c\u5750\u6807\u8f74\u7684\u9762\u5e73\u884c\u3002<\/p>\n\n\n\n\u5728\u4e8c\u7ef4\u4e2d\uff0c\u5224\u65ad\u4e00\u4e2a\u957f\u65b9\u5f62\u548c\u4e00\u6761\u76f4\u7ebf\u662f\u5426\u6709\u4ea4\u96c6\uff0c\u53ef\u4ee5\u5148\u6c42\u51fa\u5176\u548c\u7ebfx0\uff0cx1\u7684\u4e24\u4e2a\u4ea4\u70b9\uff0c\u518d\u6c42\u51fa\u548c\u7ebfy0\uff0cy1\u7684\u4e24\u4e2a\u4ea4\u70b9<\/p>\n\n\n\n<\/figure >\n<\/figure><\/noscript>\n\n\n\n\u56e0\u4e3a\u5f53\u5149\u7ebf\u8fdb\u5165\u5230\u6240\u6709\u7684\u9762\uff0c\u624d\u80fd\u786e\u5b9a\u5149\u8fdb\u5165\u5230\u5305\u56f4\u76d2\u4e2d\uff0c\u800c\u5f53\u5149\u7ebf\u79bb\u5f00\u4efb\u610f\u4e00\u4e2a\u9762\uff0c\u5373\u4e3a\u79bb\u5f00\u5305\u56f4\u76d2\u3002\u6240\u4ee5\u6c42\u51fa\u5176\u4e2d\u6700\u5927\u7684[latex]t_{min}[\/latex]\u548c\u6700\u5c0f\u7684[latex]t_{max}[\/latex]\u5373\u4e3a\u5149\u7ebf\u5b9e\u9645\u8fdb\u5165\u548c\u79bb\u5f00\u76d2\u5b50\u7684\u65f6\u95f4\u3002<\/p>\n\n\n\n<\/figure >\n<\/figure><\/noscript>\n\n\n\n\u5373[latex]t_{enter}=max(t_{min}),t_{exit}=min(t_{max})[\/latex]\u3002\u5728\u4e09\u7ef4\u7a7a\u95f4\u4e2d\u540c\u7406\u3002<\/p>\n\n\n\n\u5982\u679c[latex]t_{enter}<t_{exit}[\/latex]\uff0c\u5373\u4e3a\u5149\u7ebf\u7ecf\u8fc7\u4e86\u5305\u56f4\u76d2\uff08\u5149\u7ebf\u5728\u5305\u56f4\u76d2\u4e2d\u5f85\u4e86\u4e00\u6bb5\u65f6\u95f4\uff09\u3002<\/p>\n\n\n\n\u4f46\u662f\u5149\u7ebf\u662f\u5c04\u7ebf\uff0c\u4e0d\u662f\u76f4\u7ebf\uff0c\u6240\u4ee5\u5f53[latex]t_{exit}<0[\/latex]\uff0c\u8bf4\u660e\u7269\u4f53\u5728\u5149\u7ebf\u7684\u80cc\u540e\uff0c\u5373\u4e0d\u53ef\u80fd\u6709\u4ea4\u70b9\u3002\u5f53[latex]t_{exit}>=0,t_{enter}<0[\/latex]\uff0c\u5373\u5149\u7ebf\u7684\u8d77\u70b9\u5728\u5305\u56f4\u76d2\u5185\u90e8\u3002<\/p>\n\n\n\n\u6240\u4ee5\u5f53\u4e14\u4ec5\u5f53[latex]t_{enter}<t_{exit},t_{exit}\\ge0[\/latex]\u65f6\uff0c\u5149\u7ebf\u7a7f\u8fc7\u5305\u56f4\u76d2\u3002<\/p>\n\n\n\n\u8ba1\u7b97\u5149\u7ebf\u4e0e\u9762\u4f55\u65f6\u76f8\u4ea4\uff1a[latex]t=\\frac{\\left(\\mathbf{p}^{\\prime}-\\mathbf{o}\\right) \\cdot \\mathbf{N}}{\\mathbf{d} \\cdot \\mathbf{N}}[\/latex]\u800c\u8fd9\u91cc\u7684\u9762\u662f\u4e0e\u5750\u6807\u8f74\u5e73\u9762\u5e73\u884c\u7684\uff0c\u6240\u4ee5\u53ef\u4ee5\u7b80\u5316\u8fd0\u7b97\uff1a\u5bf9\u4e8eyz\u5e73\u9762\u5e73\u884c\uff0c\u5373\u4e3a\u5782\u76f4\u4e8ex\u8f74\uff1a[latex]t=\\frac{\\mathbf{p}_x^{\\prime}-\\mathbf{o}_x}{\\mathbf{d}_x}[\/latex]<\/p>\n","protected":false},"excerpt":{"rendered":"\u5149\u7ebf\u8ffd\u8e2a \u5728\u5149\u7ebf\u8ffd\u8e2a\u4e2d\uff0c\u5047\u8bbe\u76f8\u673a\u662f\u4e2a\u70b9\u800c\u4e0d\u662f\u4e2a\u77e9\u5f62\u3002\u7136\u540e\u5c06\u6bcf\u4e2a\u50cf\u7d20\u548c\u76f8\u673a\u76f8\u8fde\u5e76\u5ef6\u957f\u8fd9\u6761\u7ebf\uff0c\u4f5c\u4e3a\u5149\u7ebf\uff0c\u8fd9\u6761\u7ebf\u88ab\u79f0\u4e3a\u201c\u773c\u775b\u5149\u7ebf\u201d\u3002\u8fd9\u6839 …<\/p>","protected":false},"author":1,"featured_media":1141,"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-1140","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\/1140","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=1140"}],"version-history":[{"count":1,"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/posts\/1140\/revisions"}],"predecessor-version":[{"id":1747,"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/posts\/1140\/revisions\/1747"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/media\/1141"}],"wp:attachment":[{"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/media?parent=1140"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/categories?post=1140"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/tags?post=1140"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
\u5bf9\u4e8e\u4efb\u610f\u4e00\u6761\u5149\u7ebf\uff0c\u53ef\u4ee5\u7528[latex]r(t)=o+td (0 \\le t < \\infty [\/latex]\u6765\u8868\u793a\u3002\u5176\u4e2dr\u4e3a\u5149\u7ebf\uff0ct\u4e3a\u65f6\u95f4\uff0co\u4e3a\u5149\u6e90\uff0cd\u4e3a\u5149\u7ebf\u65b9\u5411\u3002<\/p>\n\n\n\n<\/figure >\n<\/figure><\/noscript>\n\n\n\n\u5149\u7ebf\u4e0e\u7403\u4f53\u7684\u4ea4\u70b9<\/h3>\n\n\n\n\u7403\u4f53p\u7684\u5b9a\u4e49[latex](p-c)^2-R^2=0[\/latex]<\/p>\n\n\n\n <\/figcaption><\/figure >\n <\/figcaption><\/figure><\/noscript>\n\n\n\n\u5c06\u5149\u7ebf\u5e26\u5165\u7403\u4f53\u7684\u516c\u5f0f\u4e2d\uff1a[latex](o+td-c)^2-R^2=0[\/latex][latex]a t^2+b t+c=0, \\text { where }[\/latex][latex]a=\\mathbf{d} \\cdot \\mathbf{d}[\/latex][latex]b=2(\\mathbf{o}-\\mathbf{c}) \\cdot \\mathbf{d}[\/latex][latex]c=(\\mathbf{o}-\\mathbf{c}) \\cdot(\\mathbf{o}-\\mathbf{c})-R^2[\/latex][latex]t=\\frac{-b \\pm \\sqrt{b^2-4 a c}}{2 a}[\/latex]<\/p>\n\n\n\n\u5229\u7528\u25b3\u53ef\u77e5\u4e0e\u7403\u4f53\u7684\u4ea4\u70b9\u4e2a\u6570\uff0c\u7528\u6c42\u6839\u516c\u5f0f\u5373\u53ef\u5f97\u51fa\u4ea4\u70b9<\/p>\n\n\n\n<\/figure >\n<\/figure><\/noscript>\n\n\n\n\u5149\u7ebf\u4e0e\u9690\u5f0f\u8868\u9762\u7684\u4ea4\u70b9<\/h3>\n\n\n\n\u5b9a\u4e49\u9690\u5f0f\u8868\u9762p\uff1a[latex]f(p)=0[\/latex]\u5c06\u5149\u7ebf\u5e26\u5165\u516c\u5f0f[latex]f(o+td)=0[\/latex]\u89e3\u51fa\u65b9\u7a0b\u7684\u6839\u5373\u53ef<\/p>\n\n\n\n\u5149\u7ebf\u4e0e\u663e\u5f0f\u8868\u9762\u7684\u4ea4\u70b9<\/h3>\n\n\n\n\u6c42\u5149\u7ebf\u4e0e\u663e\u5f0f\u8868\u9762\u7684\u4ea4\u70b9\uff0c\u5373\u4e3a\u6c42\u5149\u7ebf\u4e0e\u4e09\u89d2\u5f62\u6c42\u4ea4\u70b9\u3002<\/p>\n\n\n\n\u5b9a\u4e49\u5e73\u9762\uff1a<\/p>\n\n\n\n\u5b9a\u4e49\u5e73\u9762\u7684\u6cd5\u7ebfN\uff0c\u518d\u5b9a\u4e49\u5e73\u9762\u4e0a\u4efb\u610f\u4e00\u70b9[latex]p^{\\prime}[\/latex]\uff0c\u5982\u679c\u6709\u4e00\u70b9\u5728\u5e73\u9762\u5185\uff0c\u8fd9\u4e2a\u70b9\u4e0ep'\u7684\u8fde\u7ebf\u4e0e\u6cd5\u7ebf\u5782\u76f4\u3002<\/p>\n\n\n\n<\/figure >\n<\/figure><\/noscript>\n\n\n\n\u5373\u5e73\u9762p\uff1a [latex](p-p') \\cdot N=0[\/latex]<\/p>\n\n\n\n\u4ee4[latex]p=r(t)[\/latex][latex]\\left(\\mathbf{p}-\\mathbf{p}^{\\prime}\\right) \\cdot \\mathbf{N}=\\left(\\mathbf{o}+t \\mathbf{d}-\\mathbf{p}^{\\prime}\\right) \\cdot \\mathbf{N}=0[\/latex]<\/p>\n\n\n\n\u5373\u53ef\u6c42\u51fat\uff1a[latex]t=\\frac{\\left(\\mathbf{p}^{\\prime}-\\mathbf{o}\\right) \\cdot \\mathbf{N}}{\\mathbf{d} \\cdot \\mathbf{N}}[\/latex][latex]0 \\leq t<\\infty[\/latex]<\/p>\n\n\n\nM\u00f6ller Trumbore\u7b97\u6cd5<\/h3>\n\n\n\n\u8be5\u7b97\u6cd5\u53ef\u4ee5\u5feb\u901f\u6c42\u51fa\u5149\u7ebf\u5728\u4e09\u89d2\u5f62\u5185\u7684\u4ea4\u70b9\u3002<\/p>\n\n\n\n\u5982\u679c\u5149\u7ebf\u4e0e\u5e73\u9762\u7684\u4ea4\u70b9\u5728\u4e09\u89d2\u5f62\u5185\uff0c\u90a3\u8fd9\u4e00\u70b9\u4e5f\u5c31\u80fd\u591f\u7528\u91cd\u5fc3\u5750\u6807\u8868\u793a\uff0c\u5373\uff1a[latex]\\overrightarrow{\\mathbf{O}}+t \\overrightarrow{\\mathbf{D}}=\\left(1-b_1-b_2\\right) \\overrightarrow{\\mathbf{P}}_0+b_1 \\overrightarrow{\\mathbf{P}}_1+b_2 \\overrightarrow{\\mathbf{P}}_2[\/latex]<\/p>\n\n\n\n\u4ee4\uff1a[latex]\\begin{aligned}& \\overrightarrow{\\mathbf{E}}_1=\\overrightarrow{\\mathbf{P}}_1-\\overrightarrow{\\mathbf{P}}_0 \\\\& \\overrightarrow{\\mathbf{E}}_2=\\overrightarrow{\\mathbf{P}}_2-\\overrightarrow{\\mathbf{P}}_0 \\\\& \\overrightarrow{\\mathbf{S}}=\\overrightarrow{\\mathbf{O}}-\\overrightarrow{\\mathbf{P}}_0 \\\\& \\overrightarrow{\\mathbf{S}}_1=\\overrightarrow{\\mathbf{D}} \\times \\overrightarrow{\\mathbf{E}}_2 \\\\& \\overrightarrow{\\mathbf{S}}_2=\\overrightarrow{\\mathbf{S}} \\times \\overrightarrow{\\mathbf{E}}_1\\end{aligned}[\/latex]<\/p>\n\n\n\n\u5229\u7528Cramer \u6cd5\u5219\uff1a[latex]\\left[\\begin{array}{l}t \\\\b_1 \\\\b_2\\end{array}\\right]=\\frac{1}{\\overrightarrow{\\mathbf{S}}_1 \\cdot \\overrightarrow{\\mathbf{E}}_1}\\left[\\begin{array}{c}\\overrightarrow{\\mathbf{S}}_2 \\cdot \\overrightarrow{\\mathbf{E}}_2 \\\\\\overrightarrow{\\mathbf{S}}_1 \\cdot \\overrightarrow{\\mathbf{S}} \\\\\\overrightarrow{\\mathbf{S}}_2 \\cdot \\overrightarrow{\\mathbf{D}}\\end{array}\\right][\/latex]<\/p>\n\n\n\n\u5373\u53ef\u6c42\u51fa\u4e0a\u8ff0\u65b9\u7a0b\u7684\u89e3\uff0c\u5176\u7b97\u529b\u5f00\u9500\u975e\u5e38\u4f4e\u3002<\/p>\n\n\n\n\u52a0\u901f\u7b97\u6cd5<\/h2>\n\n\n\n\u5305\u56f4\u76d2<\/h3>\n\n\n\n\u4f7f\u7528\u5305\u56f4\u76d2\u5c06\u6bcf\u4e00\u4e2a\u6a21\u578b\u5305\u56f4\u8d77\u6765\uff0c\u5982\u679c\u5149\u7ebf\u4e0e\u5305\u56f4\u76d2\u76f8\u4ea4\uff0c\u624d\u8ba1\u7b97\u5149\u7ebf\u548c\u5305\u56f4\u76d2\u5185\u6a21\u578b\u7684\u6bcf\u4e2a\u4e09\u89d2\u5f62\u662f\u5426\u76f8\u4ea4\u3002<\/p>\n\n\n\n\u5c06\u5305\u56f4\u548c\u7406\u89e3\u4e3a3\u7ec4\u5bf9\u9762\u5f62\u6210\u7684\u4ea4\u96c6\uff1a<\/p>\n\n\n\n<\/figure >\n<\/figure><\/noscript>\n\n\n\n\u8f74\u5bf9\u9f50\u5305\u56f4\u76d2AABB<\/h3>\n\n\n\nAxis-Aligned Bounding Box\uff0c\u6bcf\u4e2a\u9762\u90fd\u548c\u5750\u6807\u8f74\u7684\u9762\u5e73\u884c\u3002<\/p>\n\n\n\n\u5728\u4e8c\u7ef4\u4e2d\uff0c\u5224\u65ad\u4e00\u4e2a\u957f\u65b9\u5f62\u548c\u4e00\u6761\u76f4\u7ebf\u662f\u5426\u6709\u4ea4\u96c6\uff0c\u53ef\u4ee5\u5148\u6c42\u51fa\u5176\u548c\u7ebfx0\uff0cx1\u7684\u4e24\u4e2a\u4ea4\u70b9\uff0c\u518d\u6c42\u51fa\u548c\u7ebfy0\uff0cy1\u7684\u4e24\u4e2a\u4ea4\u70b9<\/p>\n\n\n\n<\/figure >\n<\/figure><\/noscript>\n\n\n\n\u56e0\u4e3a\u5f53\u5149\u7ebf\u8fdb\u5165\u5230\u6240\u6709\u7684\u9762\uff0c\u624d\u80fd\u786e\u5b9a\u5149\u8fdb\u5165\u5230\u5305\u56f4\u76d2\u4e2d\uff0c\u800c\u5f53\u5149\u7ebf\u79bb\u5f00\u4efb\u610f\u4e00\u4e2a\u9762\uff0c\u5373\u4e3a\u79bb\u5f00\u5305\u56f4\u76d2\u3002\u6240\u4ee5\u6c42\u51fa\u5176\u4e2d\u6700\u5927\u7684[latex]t_{min}[\/latex]\u548c\u6700\u5c0f\u7684[latex]t_{max}[\/latex]\u5373\u4e3a\u5149\u7ebf\u5b9e\u9645\u8fdb\u5165\u548c\u79bb\u5f00\u76d2\u5b50\u7684\u65f6\u95f4\u3002<\/p>\n\n\n\n<\/figure >\n<\/figure><\/noscript>\n\n\n\n\u5373[latex]t_{enter}=max(t_{min}),t_{exit}=min(t_{max})[\/latex]\u3002\u5728\u4e09\u7ef4\u7a7a\u95f4\u4e2d\u540c\u7406\u3002<\/p>\n\n\n\n\u5982\u679c[latex]t_{enter}<t_{exit}[\/latex]\uff0c\u5373\u4e3a\u5149\u7ebf\u7ecf\u8fc7\u4e86\u5305\u56f4\u76d2\uff08\u5149\u7ebf\u5728\u5305\u56f4\u76d2\u4e2d\u5f85\u4e86\u4e00\u6bb5\u65f6\u95f4\uff09\u3002<\/p>\n\n\n\n\u4f46\u662f\u5149\u7ebf\u662f\u5c04\u7ebf\uff0c\u4e0d\u662f\u76f4\u7ebf\uff0c\u6240\u4ee5\u5f53[latex]t_{exit}<0[\/latex]\uff0c\u8bf4\u660e\u7269\u4f53\u5728\u5149\u7ebf\u7684\u80cc\u540e\uff0c\u5373\u4e0d\u53ef\u80fd\u6709\u4ea4\u70b9\u3002\u5f53[latex]t_{exit}>=0,t_{enter}<0[\/latex]\uff0c\u5373\u5149\u7ebf\u7684\u8d77\u70b9\u5728\u5305\u56f4\u76d2\u5185\u90e8\u3002<\/p>\n\n\n\n\u6240\u4ee5\u5f53\u4e14\u4ec5\u5f53[latex]t_{enter}<t_{exit},t_{exit}\\ge0[\/latex]\u65f6\uff0c\u5149\u7ebf\u7a7f\u8fc7\u5305\u56f4\u76d2\u3002<\/p>\n\n\n\n\u8ba1\u7b97\u5149\u7ebf\u4e0e\u9762\u4f55\u65f6\u76f8\u4ea4\uff1a[latex]t=\\frac{\\left(\\mathbf{p}^{\\prime}-\\mathbf{o}\\right) \\cdot \\mathbf{N}}{\\mathbf{d} \\cdot \\mathbf{N}}[\/latex]\u800c\u8fd9\u91cc\u7684\u9762\u662f\u4e0e\u5750\u6807\u8f74\u5e73\u9762\u5e73\u884c\u7684\uff0c\u6240\u4ee5\u53ef\u4ee5\u7b80\u5316\u8fd0\u7b97\uff1a\u5bf9\u4e8eyz\u5e73\u9762\u5e73\u884c\uff0c\u5373\u4e3a\u5782\u76f4\u4e8ex\u8f74\uff1a[latex]t=\\frac{\\mathbf{p}_x^{\\prime}-\\mathbf{o}_x}{\\mathbf{d}_x}[\/latex]<\/p>\n","protected":false},"excerpt":{"rendered":"\u5149\u7ebf\u8ffd\u8e2a \u5728\u5149\u7ebf\u8ffd\u8e2a\u4e2d\uff0c\u5047\u8bbe\u76f8\u673a\u662f\u4e2a\u70b9\u800c\u4e0d\u662f\u4e2a\u77e9\u5f62\u3002\u7136\u540e\u5c06\u6bcf\u4e2a\u50cf\u7d20\u548c\u76f8\u673a\u76f8\u8fde\u5e76\u5ef6\u957f\u8fd9\u6761\u7ebf\uff0c\u4f5c\u4e3a\u5149\u7ebf\uff0c\u8fd9\u6761\u7ebf\u88ab\u79f0\u4e3a\u201c\u773c\u775b\u5149\u7ebf\u201d\u3002\u8fd9\u6839 …<\/p>","protected":false},"author":1,"featured_media":1141,"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-1140","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\/1140","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=1140"}],"version-history":[{"count":1,"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/posts\/1140\/revisions"}],"predecessor-version":[{"id":1747,"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/posts\/1140\/revisions\/1747"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/media\/1141"}],"wp:attachment":[{"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/media?parent=1140"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/categories?post=1140"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/tags?post=1140"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
\u7403\u4f53p\u7684\u5b9a\u4e49[latex](p-c)^2-R^2=0[\/latex]<\/p>\n\n\n\n <\/figcaption><\/figure >\n <\/figcaption><\/figure><\/noscript>\n\n\n\n\u5c06\u5149\u7ebf\u5e26\u5165\u7403\u4f53\u7684\u516c\u5f0f\u4e2d\uff1a[latex](o+td-c)^2-R^2=0[\/latex][latex]a t^2+b t+c=0, \\text { where }[\/latex][latex]a=\\mathbf{d} \\cdot \\mathbf{d}[\/latex][latex]b=2(\\mathbf{o}-\\mathbf{c}) \\cdot \\mathbf{d}[\/latex][latex]c=(\\mathbf{o}-\\mathbf{c}) \\cdot(\\mathbf{o}-\\mathbf{c})-R^2[\/latex][latex]t=\\frac{-b \\pm \\sqrt{b^2-4 a c}}{2 a}[\/latex]<\/p>\n\n\n\n\u5229\u7528\u25b3\u53ef\u77e5\u4e0e\u7403\u4f53\u7684\u4ea4\u70b9\u4e2a\u6570\uff0c\u7528\u6c42\u6839\u516c\u5f0f\u5373\u53ef\u5f97\u51fa\u4ea4\u70b9<\/p>\n\n\n\n<\/figure >\n<\/figure><\/noscript>\n\n\n\n\u5149\u7ebf\u4e0e\u9690\u5f0f\u8868\u9762\u7684\u4ea4\u70b9<\/h3>\n\n\n\n\u5b9a\u4e49\u9690\u5f0f\u8868\u9762p\uff1a[latex]f(p)=0[\/latex]\u5c06\u5149\u7ebf\u5e26\u5165\u516c\u5f0f[latex]f(o+td)=0[\/latex]\u89e3\u51fa\u65b9\u7a0b\u7684\u6839\u5373\u53ef<\/p>\n\n\n\n\u5149\u7ebf\u4e0e\u663e\u5f0f\u8868\u9762\u7684\u4ea4\u70b9<\/h3>\n\n\n\n\u6c42\u5149\u7ebf\u4e0e\u663e\u5f0f\u8868\u9762\u7684\u4ea4\u70b9\uff0c\u5373\u4e3a\u6c42\u5149\u7ebf\u4e0e\u4e09\u89d2\u5f62\u6c42\u4ea4\u70b9\u3002<\/p>\n\n\n\n\u5b9a\u4e49\u5e73\u9762\uff1a<\/p>\n\n\n\n\u5b9a\u4e49\u5e73\u9762\u7684\u6cd5\u7ebfN\uff0c\u518d\u5b9a\u4e49\u5e73\u9762\u4e0a\u4efb\u610f\u4e00\u70b9[latex]p^{\\prime}[\/latex]\uff0c\u5982\u679c\u6709\u4e00\u70b9\u5728\u5e73\u9762\u5185\uff0c\u8fd9\u4e2a\u70b9\u4e0ep'\u7684\u8fde\u7ebf\u4e0e\u6cd5\u7ebf\u5782\u76f4\u3002<\/p>\n\n\n\n<\/figure >\n<\/figure><\/noscript>\n\n\n\n\u5373\u5e73\u9762p\uff1a [latex](p-p') \\cdot N=0[\/latex]<\/p>\n\n\n\n\u4ee4[latex]p=r(t)[\/latex][latex]\\left(\\mathbf{p}-\\mathbf{p}^{\\prime}\\right) \\cdot \\mathbf{N}=\\left(\\mathbf{o}+t \\mathbf{d}-\\mathbf{p}^{\\prime}\\right) \\cdot \\mathbf{N}=0[\/latex]<\/p>\n\n\n\n\u5373\u53ef\u6c42\u51fat\uff1a[latex]t=\\frac{\\left(\\mathbf{p}^{\\prime}-\\mathbf{o}\\right) \\cdot \\mathbf{N}}{\\mathbf{d} \\cdot \\mathbf{N}}[\/latex][latex]0 \\leq t<\\infty[\/latex]<\/p>\n\n\n\nM\u00f6ller Trumbore\u7b97\u6cd5<\/h3>\n\n\n\n\u8be5\u7b97\u6cd5\u53ef\u4ee5\u5feb\u901f\u6c42\u51fa\u5149\u7ebf\u5728\u4e09\u89d2\u5f62\u5185\u7684\u4ea4\u70b9\u3002<\/p>\n\n\n\n\u5982\u679c\u5149\u7ebf\u4e0e\u5e73\u9762\u7684\u4ea4\u70b9\u5728\u4e09\u89d2\u5f62\u5185\uff0c\u90a3\u8fd9\u4e00\u70b9\u4e5f\u5c31\u80fd\u591f\u7528\u91cd\u5fc3\u5750\u6807\u8868\u793a\uff0c\u5373\uff1a[latex]\\overrightarrow{\\mathbf{O}}+t \\overrightarrow{\\mathbf{D}}=\\left(1-b_1-b_2\\right) \\overrightarrow{\\mathbf{P}}_0+b_1 \\overrightarrow{\\mathbf{P}}_1+b_2 \\overrightarrow{\\mathbf{P}}_2[\/latex]<\/p>\n\n\n\n\u4ee4\uff1a[latex]\\begin{aligned}& \\overrightarrow{\\mathbf{E}}_1=\\overrightarrow{\\mathbf{P}}_1-\\overrightarrow{\\mathbf{P}}_0 \\\\& \\overrightarrow{\\mathbf{E}}_2=\\overrightarrow{\\mathbf{P}}_2-\\overrightarrow{\\mathbf{P}}_0 \\\\& \\overrightarrow{\\mathbf{S}}=\\overrightarrow{\\mathbf{O}}-\\overrightarrow{\\mathbf{P}}_0 \\\\& \\overrightarrow{\\mathbf{S}}_1=\\overrightarrow{\\mathbf{D}} \\times \\overrightarrow{\\mathbf{E}}_2 \\\\& \\overrightarrow{\\mathbf{S}}_2=\\overrightarrow{\\mathbf{S}} \\times \\overrightarrow{\\mathbf{E}}_1\\end{aligned}[\/latex]<\/p>\n\n\n\n\u5229\u7528Cramer \u6cd5\u5219\uff1a[latex]\\left[\\begin{array}{l}t \\\\b_1 \\\\b_2\\end{array}\\right]=\\frac{1}{\\overrightarrow{\\mathbf{S}}_1 \\cdot \\overrightarrow{\\mathbf{E}}_1}\\left[\\begin{array}{c}\\overrightarrow{\\mathbf{S}}_2 \\cdot \\overrightarrow{\\mathbf{E}}_2 \\\\\\overrightarrow{\\mathbf{S}}_1 \\cdot \\overrightarrow{\\mathbf{S}} \\\\\\overrightarrow{\\mathbf{S}}_2 \\cdot \\overrightarrow{\\mathbf{D}}\\end{array}\\right][\/latex]<\/p>\n\n\n\n\u5373\u53ef\u6c42\u51fa\u4e0a\u8ff0\u65b9\u7a0b\u7684\u89e3\uff0c\u5176\u7b97\u529b\u5f00\u9500\u975e\u5e38\u4f4e\u3002<\/p>\n\n\n\n\u52a0\u901f\u7b97\u6cd5<\/h2>\n\n\n\n\u5305\u56f4\u76d2<\/h3>\n\n\n\n\u4f7f\u7528\u5305\u56f4\u76d2\u5c06\u6bcf\u4e00\u4e2a\u6a21\u578b\u5305\u56f4\u8d77\u6765\uff0c\u5982\u679c\u5149\u7ebf\u4e0e\u5305\u56f4\u76d2\u76f8\u4ea4\uff0c\u624d\u8ba1\u7b97\u5149\u7ebf\u548c\u5305\u56f4\u76d2\u5185\u6a21\u578b\u7684\u6bcf\u4e2a\u4e09\u89d2\u5f62\u662f\u5426\u76f8\u4ea4\u3002<\/p>\n\n\n\n\u5c06\u5305\u56f4\u548c\u7406\u89e3\u4e3a3\u7ec4\u5bf9\u9762\u5f62\u6210\u7684\u4ea4\u96c6\uff1a<\/p>\n\n\n\n<\/figure >\n<\/figure><\/noscript>\n\n\n\n\u8f74\u5bf9\u9f50\u5305\u56f4\u76d2AABB<\/h3>\n\n\n\nAxis-Aligned Bounding Box\uff0c\u6bcf\u4e2a\u9762\u90fd\u548c\u5750\u6807\u8f74\u7684\u9762\u5e73\u884c\u3002<\/p>\n\n\n\n\u5728\u4e8c\u7ef4\u4e2d\uff0c\u5224\u65ad\u4e00\u4e2a\u957f\u65b9\u5f62\u548c\u4e00\u6761\u76f4\u7ebf\u662f\u5426\u6709\u4ea4\u96c6\uff0c\u53ef\u4ee5\u5148\u6c42\u51fa\u5176\u548c\u7ebfx0\uff0cx1\u7684\u4e24\u4e2a\u4ea4\u70b9\uff0c\u518d\u6c42\u51fa\u548c\u7ebfy0\uff0cy1\u7684\u4e24\u4e2a\u4ea4\u70b9<\/p>\n\n\n\n<\/figure >\n<\/figure><\/noscript>\n\n\n\n\u56e0\u4e3a\u5f53\u5149\u7ebf\u8fdb\u5165\u5230\u6240\u6709\u7684\u9762\uff0c\u624d\u80fd\u786e\u5b9a\u5149\u8fdb\u5165\u5230\u5305\u56f4\u76d2\u4e2d\uff0c\u800c\u5f53\u5149\u7ebf\u79bb\u5f00\u4efb\u610f\u4e00\u4e2a\u9762\uff0c\u5373\u4e3a\u79bb\u5f00\u5305\u56f4\u76d2\u3002\u6240\u4ee5\u6c42\u51fa\u5176\u4e2d\u6700\u5927\u7684[latex]t_{min}[\/latex]\u548c\u6700\u5c0f\u7684[latex]t_{max}[\/latex]\u5373\u4e3a\u5149\u7ebf\u5b9e\u9645\u8fdb\u5165\u548c\u79bb\u5f00\u76d2\u5b50\u7684\u65f6\u95f4\u3002<\/p>\n\n\n\n<\/figure >\n<\/figure><\/noscript>\n\n\n\n\u5373[latex]t_{enter}=max(t_{min}),t_{exit}=min(t_{max})[\/latex]\u3002\u5728\u4e09\u7ef4\u7a7a\u95f4\u4e2d\u540c\u7406\u3002<\/p>\n\n\n\n\u5982\u679c[latex]t_{enter}<t_{exit}[\/latex]\uff0c\u5373\u4e3a\u5149\u7ebf\u7ecf\u8fc7\u4e86\u5305\u56f4\u76d2\uff08\u5149\u7ebf\u5728\u5305\u56f4\u76d2\u4e2d\u5f85\u4e86\u4e00\u6bb5\u65f6\u95f4\uff09\u3002<\/p>\n\n\n\n\u4f46\u662f\u5149\u7ebf\u662f\u5c04\u7ebf\uff0c\u4e0d\u662f\u76f4\u7ebf\uff0c\u6240\u4ee5\u5f53[latex]t_{exit}<0[\/latex]\uff0c\u8bf4\u660e\u7269\u4f53\u5728\u5149\u7ebf\u7684\u80cc\u540e\uff0c\u5373\u4e0d\u53ef\u80fd\u6709\u4ea4\u70b9\u3002\u5f53[latex]t_{exit}>=0,t_{enter}<0[\/latex]\uff0c\u5373\u5149\u7ebf\u7684\u8d77\u70b9\u5728\u5305\u56f4\u76d2\u5185\u90e8\u3002<\/p>\n\n\n\n\u6240\u4ee5\u5f53\u4e14\u4ec5\u5f53[latex]t_{enter}<t_{exit},t_{exit}\\ge0[\/latex]\u65f6\uff0c\u5149\u7ebf\u7a7f\u8fc7\u5305\u56f4\u76d2\u3002<\/p>\n\n\n\n\u8ba1\u7b97\u5149\u7ebf\u4e0e\u9762\u4f55\u65f6\u76f8\u4ea4\uff1a[latex]t=\\frac{\\left(\\mathbf{p}^{\\prime}-\\mathbf{o}\\right) \\cdot \\mathbf{N}}{\\mathbf{d} \\cdot \\mathbf{N}}[\/latex]\u800c\u8fd9\u91cc\u7684\u9762\u662f\u4e0e\u5750\u6807\u8f74\u5e73\u9762\u5e73\u884c\u7684\uff0c\u6240\u4ee5\u53ef\u4ee5\u7b80\u5316\u8fd0\u7b97\uff1a\u5bf9\u4e8eyz\u5e73\u9762\u5e73\u884c\uff0c\u5373\u4e3a\u5782\u76f4\u4e8ex\u8f74\uff1a[latex]t=\\frac{\\mathbf{p}_x^{\\prime}-\\mathbf{o}_x}{\\mathbf{d}_x}[\/latex]<\/p>\n","protected":false},"excerpt":{"rendered":"\u5149\u7ebf\u8ffd\u8e2a \u5728\u5149\u7ebf\u8ffd\u8e2a\u4e2d\uff0c\u5047\u8bbe\u76f8\u673a\u662f\u4e2a\u70b9\u800c\u4e0d\u662f\u4e2a\u77e9\u5f62\u3002\u7136\u540e\u5c06\u6bcf\u4e2a\u50cf\u7d20\u548c\u76f8\u673a\u76f8\u8fde\u5e76\u5ef6\u957f\u8fd9\u6761\u7ebf\uff0c\u4f5c\u4e3a\u5149\u7ebf\uff0c\u8fd9\u6761\u7ebf\u88ab\u79f0\u4e3a\u201c\u773c\u775b\u5149\u7ebf\u201d\u3002\u8fd9\u6839 …<\/p>","protected":false},"author":1,"featured_media":1141,"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-1140","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\/1140","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=1140"}],"version-history":[{"count":1,"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/posts\/1140\/revisions"}],"predecessor-version":[{"id":1747,"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/posts\/1140\/revisions\/1747"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/media\/1141"}],"wp:attachment":[{"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/media?parent=1140"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/categories?post=1140"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/tags?post=1140"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
\u5c06\u5149\u7ebf\u5e26\u5165\u7403\u4f53\u7684\u516c\u5f0f\u4e2d\uff1a[latex](o+td-c)^2-R^2=0[\/latex][latex]a t^2+b t+c=0, \\text { where }[\/latex][latex]a=\\mathbf{d} \\cdot \\mathbf{d}[\/latex][latex]b=2(\\mathbf{o}-\\mathbf{c}) \\cdot \\mathbf{d}[\/latex][latex]c=(\\mathbf{o}-\\mathbf{c}) \\cdot(\\mathbf{o}-\\mathbf{c})-R^2[\/latex][latex]t=\\frac{-b \\pm \\sqrt{b^2-4 a c}}{2 a}[\/latex]<\/p>\n\n\n\n
\u5229\u7528\u25b3\u53ef\u77e5\u4e0e\u7403\u4f53\u7684\u4ea4\u70b9\u4e2a\u6570\uff0c\u7528\u6c42\u6839\u516c\u5f0f\u5373\u53ef\u5f97\u51fa\u4ea4\u70b9<\/p>\n\n\n\n<\/figure >\n<\/figure><\/noscript>\n\n\n\n\u5149\u7ebf\u4e0e\u9690\u5f0f\u8868\u9762\u7684\u4ea4\u70b9<\/h3>\n\n\n\n\u5b9a\u4e49\u9690\u5f0f\u8868\u9762p\uff1a[latex]f(p)=0[\/latex]\u5c06\u5149\u7ebf\u5e26\u5165\u516c\u5f0f[latex]f(o+td)=0[\/latex]\u89e3\u51fa\u65b9\u7a0b\u7684\u6839\u5373\u53ef<\/p>\n\n\n\n\u5149\u7ebf\u4e0e\u663e\u5f0f\u8868\u9762\u7684\u4ea4\u70b9<\/h3>\n\n\n\n\u6c42\u5149\u7ebf\u4e0e\u663e\u5f0f\u8868\u9762\u7684\u4ea4\u70b9\uff0c\u5373\u4e3a\u6c42\u5149\u7ebf\u4e0e\u4e09\u89d2\u5f62\u6c42\u4ea4\u70b9\u3002<\/p>\n\n\n\n\u5b9a\u4e49\u5e73\u9762\uff1a<\/p>\n\n\n\n\u5b9a\u4e49\u5e73\u9762\u7684\u6cd5\u7ebfN\uff0c\u518d\u5b9a\u4e49\u5e73\u9762\u4e0a\u4efb\u610f\u4e00\u70b9[latex]p^{\\prime}[\/latex]\uff0c\u5982\u679c\u6709\u4e00\u70b9\u5728\u5e73\u9762\u5185\uff0c\u8fd9\u4e2a\u70b9\u4e0ep'\u7684\u8fde\u7ebf\u4e0e\u6cd5\u7ebf\u5782\u76f4\u3002<\/p>\n\n\n\n<\/figure >\n<\/figure><\/noscript>\n\n\n\n\u5373\u5e73\u9762p\uff1a [latex](p-p') \\cdot N=0[\/latex]<\/p>\n\n\n\n\u4ee4[latex]p=r(t)[\/latex][latex]\\left(\\mathbf{p}-\\mathbf{p}^{\\prime}\\right) \\cdot \\mathbf{N}=\\left(\\mathbf{o}+t \\mathbf{d}-\\mathbf{p}^{\\prime}\\right) \\cdot \\mathbf{N}=0[\/latex]<\/p>\n\n\n\n\u5373\u53ef\u6c42\u51fat\uff1a[latex]t=\\frac{\\left(\\mathbf{p}^{\\prime}-\\mathbf{o}\\right) \\cdot \\mathbf{N}}{\\mathbf{d} \\cdot \\mathbf{N}}[\/latex][latex]0 \\leq t<\\infty[\/latex]<\/p>\n\n\n\nM\u00f6ller Trumbore\u7b97\u6cd5<\/h3>\n\n\n\n\u8be5\u7b97\u6cd5\u53ef\u4ee5\u5feb\u901f\u6c42\u51fa\u5149\u7ebf\u5728\u4e09\u89d2\u5f62\u5185\u7684\u4ea4\u70b9\u3002<\/p>\n\n\n\n\u5982\u679c\u5149\u7ebf\u4e0e\u5e73\u9762\u7684\u4ea4\u70b9\u5728\u4e09\u89d2\u5f62\u5185\uff0c\u90a3\u8fd9\u4e00\u70b9\u4e5f\u5c31\u80fd\u591f\u7528\u91cd\u5fc3\u5750\u6807\u8868\u793a\uff0c\u5373\uff1a[latex]\\overrightarrow{\\mathbf{O}}+t \\overrightarrow{\\mathbf{D}}=\\left(1-b_1-b_2\\right) \\overrightarrow{\\mathbf{P}}_0+b_1 \\overrightarrow{\\mathbf{P}}_1+b_2 \\overrightarrow{\\mathbf{P}}_2[\/latex]<\/p>\n\n\n\n\u4ee4\uff1a[latex]\\begin{aligned}& \\overrightarrow{\\mathbf{E}}_1=\\overrightarrow{\\mathbf{P}}_1-\\overrightarrow{\\mathbf{P}}_0 \\\\& \\overrightarrow{\\mathbf{E}}_2=\\overrightarrow{\\mathbf{P}}_2-\\overrightarrow{\\mathbf{P}}_0 \\\\& \\overrightarrow{\\mathbf{S}}=\\overrightarrow{\\mathbf{O}}-\\overrightarrow{\\mathbf{P}}_0 \\\\& \\overrightarrow{\\mathbf{S}}_1=\\overrightarrow{\\mathbf{D}} \\times \\overrightarrow{\\mathbf{E}}_2 \\\\& \\overrightarrow{\\mathbf{S}}_2=\\overrightarrow{\\mathbf{S}} \\times \\overrightarrow{\\mathbf{E}}_1\\end{aligned}[\/latex]<\/p>\n\n\n\n\u5229\u7528Cramer \u6cd5\u5219\uff1a[latex]\\left[\\begin{array}{l}t \\\\b_1 \\\\b_2\\end{array}\\right]=\\frac{1}{\\overrightarrow{\\mathbf{S}}_1 \\cdot \\overrightarrow{\\mathbf{E}}_1}\\left[\\begin{array}{c}\\overrightarrow{\\mathbf{S}}_2 \\cdot \\overrightarrow{\\mathbf{E}}_2 \\\\\\overrightarrow{\\mathbf{S}}_1 \\cdot \\overrightarrow{\\mathbf{S}} \\\\\\overrightarrow{\\mathbf{S}}_2 \\cdot \\overrightarrow{\\mathbf{D}}\\end{array}\\right][\/latex]<\/p>\n\n\n\n\u5373\u53ef\u6c42\u51fa\u4e0a\u8ff0\u65b9\u7a0b\u7684\u89e3\uff0c\u5176\u7b97\u529b\u5f00\u9500\u975e\u5e38\u4f4e\u3002<\/p>\n\n\n\n\u52a0\u901f\u7b97\u6cd5<\/h2>\n\n\n\n\u5305\u56f4\u76d2<\/h3>\n\n\n\n\u4f7f\u7528\u5305\u56f4\u76d2\u5c06\u6bcf\u4e00\u4e2a\u6a21\u578b\u5305\u56f4\u8d77\u6765\uff0c\u5982\u679c\u5149\u7ebf\u4e0e\u5305\u56f4\u76d2\u76f8\u4ea4\uff0c\u624d\u8ba1\u7b97\u5149\u7ebf\u548c\u5305\u56f4\u76d2\u5185\u6a21\u578b\u7684\u6bcf\u4e2a\u4e09\u89d2\u5f62\u662f\u5426\u76f8\u4ea4\u3002<\/p>\n\n\n\n\u5c06\u5305\u56f4\u548c\u7406\u89e3\u4e3a3\u7ec4\u5bf9\u9762\u5f62\u6210\u7684\u4ea4\u96c6\uff1a<\/p>\n\n\n\n<\/figure >\n<\/figure><\/noscript>\n\n\n\n\u8f74\u5bf9\u9f50\u5305\u56f4\u76d2AABB<\/h3>\n\n\n\nAxis-Aligned Bounding Box\uff0c\u6bcf\u4e2a\u9762\u90fd\u548c\u5750\u6807\u8f74\u7684\u9762\u5e73\u884c\u3002<\/p>\n\n\n\n\u5728\u4e8c\u7ef4\u4e2d\uff0c\u5224\u65ad\u4e00\u4e2a\u957f\u65b9\u5f62\u548c\u4e00\u6761\u76f4\u7ebf\u662f\u5426\u6709\u4ea4\u96c6\uff0c\u53ef\u4ee5\u5148\u6c42\u51fa\u5176\u548c\u7ebfx0\uff0cx1\u7684\u4e24\u4e2a\u4ea4\u70b9\uff0c\u518d\u6c42\u51fa\u548c\u7ebfy0\uff0cy1\u7684\u4e24\u4e2a\u4ea4\u70b9<\/p>\n\n\n\n<\/figure >\n<\/figure><\/noscript>\n\n\n\n\u56e0\u4e3a\u5f53\u5149\u7ebf\u8fdb\u5165\u5230\u6240\u6709\u7684\u9762\uff0c\u624d\u80fd\u786e\u5b9a\u5149\u8fdb\u5165\u5230\u5305\u56f4\u76d2\u4e2d\uff0c\u800c\u5f53\u5149\u7ebf\u79bb\u5f00\u4efb\u610f\u4e00\u4e2a\u9762\uff0c\u5373\u4e3a\u79bb\u5f00\u5305\u56f4\u76d2\u3002\u6240\u4ee5\u6c42\u51fa\u5176\u4e2d\u6700\u5927\u7684[latex]t_{min}[\/latex]\u548c\u6700\u5c0f\u7684[latex]t_{max}[\/latex]\u5373\u4e3a\u5149\u7ebf\u5b9e\u9645\u8fdb\u5165\u548c\u79bb\u5f00\u76d2\u5b50\u7684\u65f6\u95f4\u3002<\/p>\n\n\n\n<\/figure >\n<\/figure><\/noscript>\n\n\n\n\u5373[latex]t_{enter}=max(t_{min}),t_{exit}=min(t_{max})[\/latex]\u3002\u5728\u4e09\u7ef4\u7a7a\u95f4\u4e2d\u540c\u7406\u3002<\/p>\n\n\n\n\u5982\u679c[latex]t_{enter}<t_{exit}[\/latex]\uff0c\u5373\u4e3a\u5149\u7ebf\u7ecf\u8fc7\u4e86\u5305\u56f4\u76d2\uff08\u5149\u7ebf\u5728\u5305\u56f4\u76d2\u4e2d\u5f85\u4e86\u4e00\u6bb5\u65f6\u95f4\uff09\u3002<\/p>\n\n\n\n\u4f46\u662f\u5149\u7ebf\u662f\u5c04\u7ebf\uff0c\u4e0d\u662f\u76f4\u7ebf\uff0c\u6240\u4ee5\u5f53[latex]t_{exit}<0[\/latex]\uff0c\u8bf4\u660e\u7269\u4f53\u5728\u5149\u7ebf\u7684\u80cc\u540e\uff0c\u5373\u4e0d\u53ef\u80fd\u6709\u4ea4\u70b9\u3002\u5f53[latex]t_{exit}>=0,t_{enter}<0[\/latex]\uff0c\u5373\u5149\u7ebf\u7684\u8d77\u70b9\u5728\u5305\u56f4\u76d2\u5185\u90e8\u3002<\/p>\n\n\n\n\u6240\u4ee5\u5f53\u4e14\u4ec5\u5f53[latex]t_{enter}<t_{exit},t_{exit}\\ge0[\/latex]\u65f6\uff0c\u5149\u7ebf\u7a7f\u8fc7\u5305\u56f4\u76d2\u3002<\/p>\n\n\n\n\u8ba1\u7b97\u5149\u7ebf\u4e0e\u9762\u4f55\u65f6\u76f8\u4ea4\uff1a[latex]t=\\frac{\\left(\\mathbf{p}^{\\prime}-\\mathbf{o}\\right) \\cdot \\mathbf{N}}{\\mathbf{d} \\cdot \\mathbf{N}}[\/latex]\u800c\u8fd9\u91cc\u7684\u9762\u662f\u4e0e\u5750\u6807\u8f74\u5e73\u9762\u5e73\u884c\u7684\uff0c\u6240\u4ee5\u53ef\u4ee5\u7b80\u5316\u8fd0\u7b97\uff1a\u5bf9\u4e8eyz\u5e73\u9762\u5e73\u884c\uff0c\u5373\u4e3a\u5782\u76f4\u4e8ex\u8f74\uff1a[latex]t=\\frac{\\mathbf{p}_x^{\\prime}-\\mathbf{o}_x}{\\mathbf{d}_x}[\/latex]<\/p>\n","protected":false},"excerpt":{"rendered":"\u5149\u7ebf\u8ffd\u8e2a \u5728\u5149\u7ebf\u8ffd\u8e2a\u4e2d\uff0c\u5047\u8bbe\u76f8\u673a\u662f\u4e2a\u70b9\u800c\u4e0d\u662f\u4e2a\u77e9\u5f62\u3002\u7136\u540e\u5c06\u6bcf\u4e2a\u50cf\u7d20\u548c\u76f8\u673a\u76f8\u8fde\u5e76\u5ef6\u957f\u8fd9\u6761\u7ebf\uff0c\u4f5c\u4e3a\u5149\u7ebf\uff0c\u8fd9\u6761\u7ebf\u88ab\u79f0\u4e3a\u201c\u773c\u775b\u5149\u7ebf\u201d\u3002\u8fd9\u6839 …<\/p>","protected":false},"author":1,"featured_media":1141,"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-1140","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\/1140","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=1140"}],"version-history":[{"count":1,"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/posts\/1140\/revisions"}],"predecessor-version":[{"id":1747,"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/posts\/1140\/revisions\/1747"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/media\/1141"}],"wp:attachment":[{"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/media?parent=1140"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/categories?post=1140"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/tags?post=1140"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
\u5b9a\u4e49\u9690\u5f0f\u8868\u9762p\uff1a[latex]f(p)=0[\/latex]\u5c06\u5149\u7ebf\u5e26\u5165\u516c\u5f0f[latex]f(o+td)=0[\/latex]\u89e3\u51fa\u65b9\u7a0b\u7684\u6839\u5373\u53ef<\/p>\n\n\n\n
\u6c42\u5149\u7ebf\u4e0e\u663e\u5f0f\u8868\u9762\u7684\u4ea4\u70b9\uff0c\u5373\u4e3a\u6c42\u5149\u7ebf\u4e0e\u4e09\u89d2\u5f62\u6c42\u4ea4\u70b9\u3002<\/p>\n\n\n\n
\u5b9a\u4e49\u5e73\u9762\uff1a<\/p>\n\n\n\n
\u5b9a\u4e49\u5e73\u9762\u7684\u6cd5\u7ebfN\uff0c\u518d\u5b9a\u4e49\u5e73\u9762\u4e0a\u4efb\u610f\u4e00\u70b9[latex]p^{\\prime}[\/latex]\uff0c\u5982\u679c\u6709\u4e00\u70b9\u5728\u5e73\u9762\u5185\uff0c\u8fd9\u4e2a\u70b9\u4e0ep'\u7684\u8fde\u7ebf\u4e0e\u6cd5\u7ebf\u5782\u76f4\u3002<\/p>\n\n\n\n<\/figure >\n<\/figure><\/noscript>\n\n\n\n\u5373\u5e73\u9762p\uff1a [latex](p-p') \\cdot N=0[\/latex]<\/p>\n\n\n\n\u4ee4[latex]p=r(t)[\/latex][latex]\\left(\\mathbf{p}-\\mathbf{p}^{\\prime}\\right) \\cdot \\mathbf{N}=\\left(\\mathbf{o}+t \\mathbf{d}-\\mathbf{p}^{\\prime}\\right) \\cdot \\mathbf{N}=0[\/latex]<\/p>\n\n\n\n\u5373\u53ef\u6c42\u51fat\uff1a[latex]t=\\frac{\\left(\\mathbf{p}^{\\prime}-\\mathbf{o}\\right) \\cdot \\mathbf{N}}{\\mathbf{d} \\cdot \\mathbf{N}}[\/latex][latex]0 \\leq t<\\infty[\/latex]<\/p>\n\n\n\nM\u00f6ller Trumbore\u7b97\u6cd5<\/h3>\n\n\n\n\u8be5\u7b97\u6cd5\u53ef\u4ee5\u5feb\u901f\u6c42\u51fa\u5149\u7ebf\u5728\u4e09\u89d2\u5f62\u5185\u7684\u4ea4\u70b9\u3002<\/p>\n\n\n\n\u5982\u679c\u5149\u7ebf\u4e0e\u5e73\u9762\u7684\u4ea4\u70b9\u5728\u4e09\u89d2\u5f62\u5185\uff0c\u90a3\u8fd9\u4e00\u70b9\u4e5f\u5c31\u80fd\u591f\u7528\u91cd\u5fc3\u5750\u6807\u8868\u793a\uff0c\u5373\uff1a[latex]\\overrightarrow{\\mathbf{O}}+t \\overrightarrow{\\mathbf{D}}=\\left(1-b_1-b_2\\right) \\overrightarrow{\\mathbf{P}}_0+b_1 \\overrightarrow{\\mathbf{P}}_1+b_2 \\overrightarrow{\\mathbf{P}}_2[\/latex]<\/p>\n\n\n\n\u4ee4\uff1a[latex]\\begin{aligned}& \\overrightarrow{\\mathbf{E}}_1=\\overrightarrow{\\mathbf{P}}_1-\\overrightarrow{\\mathbf{P}}_0 \\\\& \\overrightarrow{\\mathbf{E}}_2=\\overrightarrow{\\mathbf{P}}_2-\\overrightarrow{\\mathbf{P}}_0 \\\\& \\overrightarrow{\\mathbf{S}}=\\overrightarrow{\\mathbf{O}}-\\overrightarrow{\\mathbf{P}}_0 \\\\& \\overrightarrow{\\mathbf{S}}_1=\\overrightarrow{\\mathbf{D}} \\times \\overrightarrow{\\mathbf{E}}_2 \\\\& \\overrightarrow{\\mathbf{S}}_2=\\overrightarrow{\\mathbf{S}} \\times \\overrightarrow{\\mathbf{E}}_1\\end{aligned}[\/latex]<\/p>\n\n\n\n\u5229\u7528Cramer \u6cd5\u5219\uff1a[latex]\\left[\\begin{array}{l}t \\\\b_1 \\\\b_2\\end{array}\\right]=\\frac{1}{\\overrightarrow{\\mathbf{S}}_1 \\cdot \\overrightarrow{\\mathbf{E}}_1}\\left[\\begin{array}{c}\\overrightarrow{\\mathbf{S}}_2 \\cdot \\overrightarrow{\\mathbf{E}}_2 \\\\\\overrightarrow{\\mathbf{S}}_1 \\cdot \\overrightarrow{\\mathbf{S}} \\\\\\overrightarrow{\\mathbf{S}}_2 \\cdot \\overrightarrow{\\mathbf{D}}\\end{array}\\right][\/latex]<\/p>\n\n\n\n\u5373\u53ef\u6c42\u51fa\u4e0a\u8ff0\u65b9\u7a0b\u7684\u89e3\uff0c\u5176\u7b97\u529b\u5f00\u9500\u975e\u5e38\u4f4e\u3002<\/p>\n\n\n\n\u52a0\u901f\u7b97\u6cd5<\/h2>\n\n\n\n\u5305\u56f4\u76d2<\/h3>\n\n\n\n\u4f7f\u7528\u5305\u56f4\u76d2\u5c06\u6bcf\u4e00\u4e2a\u6a21\u578b\u5305\u56f4\u8d77\u6765\uff0c\u5982\u679c\u5149\u7ebf\u4e0e\u5305\u56f4\u76d2\u76f8\u4ea4\uff0c\u624d\u8ba1\u7b97\u5149\u7ebf\u548c\u5305\u56f4\u76d2\u5185\u6a21\u578b\u7684\u6bcf\u4e2a\u4e09\u89d2\u5f62\u662f\u5426\u76f8\u4ea4\u3002<\/p>\n\n\n\n\u5c06\u5305\u56f4\u548c\u7406\u89e3\u4e3a3\u7ec4\u5bf9\u9762\u5f62\u6210\u7684\u4ea4\u96c6\uff1a<\/p>\n\n\n\n<\/figure >\n<\/figure><\/noscript>\n\n\n\n\u8f74\u5bf9\u9f50\u5305\u56f4\u76d2AABB<\/h3>\n\n\n\nAxis-Aligned Bounding Box\uff0c\u6bcf\u4e2a\u9762\u90fd\u548c\u5750\u6807\u8f74\u7684\u9762\u5e73\u884c\u3002<\/p>\n\n\n\n\u5728\u4e8c\u7ef4\u4e2d\uff0c\u5224\u65ad\u4e00\u4e2a\u957f\u65b9\u5f62\u548c\u4e00\u6761\u76f4\u7ebf\u662f\u5426\u6709\u4ea4\u96c6\uff0c\u53ef\u4ee5\u5148\u6c42\u51fa\u5176\u548c\u7ebfx0\uff0cx1\u7684\u4e24\u4e2a\u4ea4\u70b9\uff0c\u518d\u6c42\u51fa\u548c\u7ebfy0\uff0cy1\u7684\u4e24\u4e2a\u4ea4\u70b9<\/p>\n\n\n\n<\/figure >\n<\/figure><\/noscript>\n\n\n\n\u56e0\u4e3a\u5f53\u5149\u7ebf\u8fdb\u5165\u5230\u6240\u6709\u7684\u9762\uff0c\u624d\u80fd\u786e\u5b9a\u5149\u8fdb\u5165\u5230\u5305\u56f4\u76d2\u4e2d\uff0c\u800c\u5f53\u5149\u7ebf\u79bb\u5f00\u4efb\u610f\u4e00\u4e2a\u9762\uff0c\u5373\u4e3a\u79bb\u5f00\u5305\u56f4\u76d2\u3002\u6240\u4ee5\u6c42\u51fa\u5176\u4e2d\u6700\u5927\u7684[latex]t_{min}[\/latex]\u548c\u6700\u5c0f\u7684[latex]t_{max}[\/latex]\u5373\u4e3a\u5149\u7ebf\u5b9e\u9645\u8fdb\u5165\u548c\u79bb\u5f00\u76d2\u5b50\u7684\u65f6\u95f4\u3002<\/p>\n\n\n\n<\/figure >\n<\/figure><\/noscript>\n\n\n\n\u5373[latex]t_{enter}=max(t_{min}),t_{exit}=min(t_{max})[\/latex]\u3002\u5728\u4e09\u7ef4\u7a7a\u95f4\u4e2d\u540c\u7406\u3002<\/p>\n\n\n\n\u5982\u679c[latex]t_{enter}<t_{exit}[\/latex]\uff0c\u5373\u4e3a\u5149\u7ebf\u7ecf\u8fc7\u4e86\u5305\u56f4\u76d2\uff08\u5149\u7ebf\u5728\u5305\u56f4\u76d2\u4e2d\u5f85\u4e86\u4e00\u6bb5\u65f6\u95f4\uff09\u3002<\/p>\n\n\n\n\u4f46\u662f\u5149\u7ebf\u662f\u5c04\u7ebf\uff0c\u4e0d\u662f\u76f4\u7ebf\uff0c\u6240\u4ee5\u5f53[latex]t_{exit}<0[\/latex]\uff0c\u8bf4\u660e\u7269\u4f53\u5728\u5149\u7ebf\u7684\u80cc\u540e\uff0c\u5373\u4e0d\u53ef\u80fd\u6709\u4ea4\u70b9\u3002\u5f53[latex]t_{exit}>=0,t_{enter}<0[\/latex]\uff0c\u5373\u5149\u7ebf\u7684\u8d77\u70b9\u5728\u5305\u56f4\u76d2\u5185\u90e8\u3002<\/p>\n\n\n\n\u6240\u4ee5\u5f53\u4e14\u4ec5\u5f53[latex]t_{enter}<t_{exit},t_{exit}\\ge0[\/latex]\u65f6\uff0c\u5149\u7ebf\u7a7f\u8fc7\u5305\u56f4\u76d2\u3002<\/p>\n\n\n\n\u8ba1\u7b97\u5149\u7ebf\u4e0e\u9762\u4f55\u65f6\u76f8\u4ea4\uff1a[latex]t=\\frac{\\left(\\mathbf{p}^{\\prime}-\\mathbf{o}\\right) \\cdot \\mathbf{N}}{\\mathbf{d} \\cdot \\mathbf{N}}[\/latex]\u800c\u8fd9\u91cc\u7684\u9762\u662f\u4e0e\u5750\u6807\u8f74\u5e73\u9762\u5e73\u884c\u7684\uff0c\u6240\u4ee5\u53ef\u4ee5\u7b80\u5316\u8fd0\u7b97\uff1a\u5bf9\u4e8eyz\u5e73\u9762\u5e73\u884c\uff0c\u5373\u4e3a\u5782\u76f4\u4e8ex\u8f74\uff1a[latex]t=\\frac{\\mathbf{p}_x^{\\prime}-\\mathbf{o}_x}{\\mathbf{d}_x}[\/latex]<\/p>\n","protected":false},"excerpt":{"rendered":"\u5149\u7ebf\u8ffd\u8e2a \u5728\u5149\u7ebf\u8ffd\u8e2a\u4e2d\uff0c\u5047\u8bbe\u76f8\u673a\u662f\u4e2a\u70b9\u800c\u4e0d\u662f\u4e2a\u77e9\u5f62\u3002\u7136\u540e\u5c06\u6bcf\u4e2a\u50cf\u7d20\u548c\u76f8\u673a\u76f8\u8fde\u5e76\u5ef6\u957f\u8fd9\u6761\u7ebf\uff0c\u4f5c\u4e3a\u5149\u7ebf\uff0c\u8fd9\u6761\u7ebf\u88ab\u79f0\u4e3a\u201c\u773c\u775b\u5149\u7ebf\u201d\u3002\u8fd9\u6839 …<\/p>","protected":false},"author":1,"featured_media":1141,"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-1140","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\/1140","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=1140"}],"version-history":[{"count":1,"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/posts\/1140\/revisions"}],"predecessor-version":[{"id":1747,"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/posts\/1140\/revisions\/1747"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/media\/1141"}],"wp:attachment":[{"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/media?parent=1140"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/categories?post=1140"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/tags?post=1140"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
\u5373\u5e73\u9762p\uff1a [latex](p-p') \\cdot N=0[\/latex]<\/p>\n\n\n\n
\u4ee4[latex]p=r(t)[\/latex][latex]\\left(\\mathbf{p}-\\mathbf{p}^{\\prime}\\right) \\cdot \\mathbf{N}=\\left(\\mathbf{o}+t \\mathbf{d}-\\mathbf{p}^{\\prime}\\right) \\cdot \\mathbf{N}=0[\/latex]<\/p>\n\n\n\n
\u5373\u53ef\u6c42\u51fat\uff1a[latex]t=\\frac{\\left(\\mathbf{p}^{\\prime}-\\mathbf{o}\\right) \\cdot \\mathbf{N}}{\\mathbf{d} \\cdot \\mathbf{N}}[\/latex][latex]0 \\leq t<\\infty[\/latex]<\/p>\n\n\n\n
\u8be5\u7b97\u6cd5\u53ef\u4ee5\u5feb\u901f\u6c42\u51fa\u5149\u7ebf\u5728\u4e09\u89d2\u5f62\u5185\u7684\u4ea4\u70b9\u3002<\/p>\n\n\n\n
\u5982\u679c\u5149\u7ebf\u4e0e\u5e73\u9762\u7684\u4ea4\u70b9\u5728\u4e09\u89d2\u5f62\u5185\uff0c\u90a3\u8fd9\u4e00\u70b9\u4e5f\u5c31\u80fd\u591f\u7528\u91cd\u5fc3\u5750\u6807\u8868\u793a\uff0c\u5373\uff1a[latex]\\overrightarrow{\\mathbf{O}}+t \\overrightarrow{\\mathbf{D}}=\\left(1-b_1-b_2\\right) \\overrightarrow{\\mathbf{P}}_0+b_1 \\overrightarrow{\\mathbf{P}}_1+b_2 \\overrightarrow{\\mathbf{P}}_2[\/latex]<\/p>\n\n\n\n
\u4ee4\uff1a[latex]\\begin{aligned}& \\overrightarrow{\\mathbf{E}}_1=\\overrightarrow{\\mathbf{P}}_1-\\overrightarrow{\\mathbf{P}}_0 \\\\& \\overrightarrow{\\mathbf{E}}_2=\\overrightarrow{\\mathbf{P}}_2-\\overrightarrow{\\mathbf{P}}_0 \\\\& \\overrightarrow{\\mathbf{S}}=\\overrightarrow{\\mathbf{O}}-\\overrightarrow{\\mathbf{P}}_0 \\\\& \\overrightarrow{\\mathbf{S}}_1=\\overrightarrow{\\mathbf{D}} \\times \\overrightarrow{\\mathbf{E}}_2 \\\\& \\overrightarrow{\\mathbf{S}}_2=\\overrightarrow{\\mathbf{S}} \\times \\overrightarrow{\\mathbf{E}}_1\\end{aligned}[\/latex]<\/p>\n\n\n\n
\u5229\u7528Cramer \u6cd5\u5219\uff1a[latex]\\left[\\begin{array}{l}t \\\\b_1 \\\\b_2\\end{array}\\right]=\\frac{1}{\\overrightarrow{\\mathbf{S}}_1 \\cdot \\overrightarrow{\\mathbf{E}}_1}\\left[\\begin{array}{c}\\overrightarrow{\\mathbf{S}}_2 \\cdot \\overrightarrow{\\mathbf{E}}_2 \\\\\\overrightarrow{\\mathbf{S}}_1 \\cdot \\overrightarrow{\\mathbf{S}} \\\\\\overrightarrow{\\mathbf{S}}_2 \\cdot \\overrightarrow{\\mathbf{D}}\\end{array}\\right][\/latex]<\/p>\n\n\n\n
\u5373\u53ef\u6c42\u51fa\u4e0a\u8ff0\u65b9\u7a0b\u7684\u89e3\uff0c\u5176\u7b97\u529b\u5f00\u9500\u975e\u5e38\u4f4e\u3002<\/p>\n\n\n\n
\u4f7f\u7528\u5305\u56f4\u76d2\u5c06\u6bcf\u4e00\u4e2a\u6a21\u578b\u5305\u56f4\u8d77\u6765\uff0c\u5982\u679c\u5149\u7ebf\u4e0e\u5305\u56f4\u76d2\u76f8\u4ea4\uff0c\u624d\u8ba1\u7b97\u5149\u7ebf\u548c\u5305\u56f4\u76d2\u5185\u6a21\u578b\u7684\u6bcf\u4e2a\u4e09\u89d2\u5f62\u662f\u5426\u76f8\u4ea4\u3002<\/p>\n\n\n\n
\u5c06\u5305\u56f4\u548c\u7406\u89e3\u4e3a3\u7ec4\u5bf9\u9762\u5f62\u6210\u7684\u4ea4\u96c6\uff1a<\/p>\n\n\n\n<\/figure >\n<\/figure><\/noscript>\n\n\n\n\u8f74\u5bf9\u9f50\u5305\u56f4\u76d2AABB<\/h3>\n\n\n\nAxis-Aligned Bounding Box\uff0c\u6bcf\u4e2a\u9762\u90fd\u548c\u5750\u6807\u8f74\u7684\u9762\u5e73\u884c\u3002<\/p>\n\n\n\n\u5728\u4e8c\u7ef4\u4e2d\uff0c\u5224\u65ad\u4e00\u4e2a\u957f\u65b9\u5f62\u548c\u4e00\u6761\u76f4\u7ebf\u662f\u5426\u6709\u4ea4\u96c6\uff0c\u53ef\u4ee5\u5148\u6c42\u51fa\u5176\u548c\u7ebfx0\uff0cx1\u7684\u4e24\u4e2a\u4ea4\u70b9\uff0c\u518d\u6c42\u51fa\u548c\u7ebfy0\uff0cy1\u7684\u4e24\u4e2a\u4ea4\u70b9<\/p>\n\n\n\n<\/figure >\n<\/figure><\/noscript>\n\n\n\n\u56e0\u4e3a\u5f53\u5149\u7ebf\u8fdb\u5165\u5230\u6240\u6709\u7684\u9762\uff0c\u624d\u80fd\u786e\u5b9a\u5149\u8fdb\u5165\u5230\u5305\u56f4\u76d2\u4e2d\uff0c\u800c\u5f53\u5149\u7ebf\u79bb\u5f00\u4efb\u610f\u4e00\u4e2a\u9762\uff0c\u5373\u4e3a\u79bb\u5f00\u5305\u56f4\u76d2\u3002\u6240\u4ee5\u6c42\u51fa\u5176\u4e2d\u6700\u5927\u7684[latex]t_{min}[\/latex]\u548c\u6700\u5c0f\u7684[latex]t_{max}[\/latex]\u5373\u4e3a\u5149\u7ebf\u5b9e\u9645\u8fdb\u5165\u548c\u79bb\u5f00\u76d2\u5b50\u7684\u65f6\u95f4\u3002<\/p>\n\n\n\n<\/figure >\n<\/figure><\/noscript>\n\n\n\n\u5373[latex]t_{enter}=max(t_{min}),t_{exit}=min(t_{max})[\/latex]\u3002\u5728\u4e09\u7ef4\u7a7a\u95f4\u4e2d\u540c\u7406\u3002<\/p>\n\n\n\n\u5982\u679c[latex]t_{enter}<t_{exit}[\/latex]\uff0c\u5373\u4e3a\u5149\u7ebf\u7ecf\u8fc7\u4e86\u5305\u56f4\u76d2\uff08\u5149\u7ebf\u5728\u5305\u56f4\u76d2\u4e2d\u5f85\u4e86\u4e00\u6bb5\u65f6\u95f4\uff09\u3002<\/p>\n\n\n\n\u4f46\u662f\u5149\u7ebf\u662f\u5c04\u7ebf\uff0c\u4e0d\u662f\u76f4\u7ebf\uff0c\u6240\u4ee5\u5f53[latex]t_{exit}<0[\/latex]\uff0c\u8bf4\u660e\u7269\u4f53\u5728\u5149\u7ebf\u7684\u80cc\u540e\uff0c\u5373\u4e0d\u53ef\u80fd\u6709\u4ea4\u70b9\u3002\u5f53[latex]t_{exit}>=0,t_{enter}<0[\/latex]\uff0c\u5373\u5149\u7ebf\u7684\u8d77\u70b9\u5728\u5305\u56f4\u76d2\u5185\u90e8\u3002<\/p>\n\n\n\n\u6240\u4ee5\u5f53\u4e14\u4ec5\u5f53[latex]t_{enter}<t_{exit},t_{exit}\\ge0[\/latex]\u65f6\uff0c\u5149\u7ebf\u7a7f\u8fc7\u5305\u56f4\u76d2\u3002<\/p>\n\n\n\n\u8ba1\u7b97\u5149\u7ebf\u4e0e\u9762\u4f55\u65f6\u76f8\u4ea4\uff1a[latex]t=\\frac{\\left(\\mathbf{p}^{\\prime}-\\mathbf{o}\\right) \\cdot \\mathbf{N}}{\\mathbf{d} \\cdot \\mathbf{N}}[\/latex]\u800c\u8fd9\u91cc\u7684\u9762\u662f\u4e0e\u5750\u6807\u8f74\u5e73\u9762\u5e73\u884c\u7684\uff0c\u6240\u4ee5\u53ef\u4ee5\u7b80\u5316\u8fd0\u7b97\uff1a\u5bf9\u4e8eyz\u5e73\u9762\u5e73\u884c\uff0c\u5373\u4e3a\u5782\u76f4\u4e8ex\u8f74\uff1a[latex]t=\\frac{\\mathbf{p}_x^{\\prime}-\\mathbf{o}_x}{\\mathbf{d}_x}[\/latex]<\/p>\n","protected":false},"excerpt":{"rendered":"\u5149\u7ebf\u8ffd\u8e2a \u5728\u5149\u7ebf\u8ffd\u8e2a\u4e2d\uff0c\u5047\u8bbe\u76f8\u673a\u662f\u4e2a\u70b9\u800c\u4e0d\u662f\u4e2a\u77e9\u5f62\u3002\u7136\u540e\u5c06\u6bcf\u4e2a\u50cf\u7d20\u548c\u76f8\u673a\u76f8\u8fde\u5e76\u5ef6\u957f\u8fd9\u6761\u7ebf\uff0c\u4f5c\u4e3a\u5149\u7ebf\uff0c\u8fd9\u6761\u7ebf\u88ab\u79f0\u4e3a\u201c\u773c\u775b\u5149\u7ebf\u201d\u3002\u8fd9\u6839 …<\/p>","protected":false},"author":1,"featured_media":1141,"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-1140","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\/1140","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=1140"}],"version-history":[{"count":1,"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/posts\/1140\/revisions"}],"predecessor-version":[{"id":1747,"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/posts\/1140\/revisions\/1747"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/media\/1141"}],"wp:attachment":[{"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/media?parent=1140"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/categories?post=1140"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/tags?post=1140"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
Axis-Aligned Bounding Box\uff0c\u6bcf\u4e2a\u9762\u90fd\u548c\u5750\u6807\u8f74\u7684\u9762\u5e73\u884c\u3002<\/p>\n\n\n\n
\u5728\u4e8c\u7ef4\u4e2d\uff0c\u5224\u65ad\u4e00\u4e2a\u957f\u65b9\u5f62\u548c\u4e00\u6761\u76f4\u7ebf\u662f\u5426\u6709\u4ea4\u96c6\uff0c\u53ef\u4ee5\u5148\u6c42\u51fa\u5176\u548c\u7ebfx0\uff0cx1\u7684\u4e24\u4e2a\u4ea4\u70b9\uff0c\u518d\u6c42\u51fa\u548c\u7ebfy0\uff0cy1\u7684\u4e24\u4e2a\u4ea4\u70b9<\/p>\n\n\n\n<\/figure >\n<\/figure><\/noscript>\n\n\n\n\u56e0\u4e3a\u5f53\u5149\u7ebf\u8fdb\u5165\u5230\u6240\u6709\u7684\u9762\uff0c\u624d\u80fd\u786e\u5b9a\u5149\u8fdb\u5165\u5230\u5305\u56f4\u76d2\u4e2d\uff0c\u800c\u5f53\u5149\u7ebf\u79bb\u5f00\u4efb\u610f\u4e00\u4e2a\u9762\uff0c\u5373\u4e3a\u79bb\u5f00\u5305\u56f4\u76d2\u3002\u6240\u4ee5\u6c42\u51fa\u5176\u4e2d\u6700\u5927\u7684[latex]t_{min}[\/latex]\u548c\u6700\u5c0f\u7684[latex]t_{max}[\/latex]\u5373\u4e3a\u5149\u7ebf\u5b9e\u9645\u8fdb\u5165\u548c\u79bb\u5f00\u76d2\u5b50\u7684\u65f6\u95f4\u3002<\/p>\n\n\n\n<\/figure >\n<\/figure><\/noscript>\n\n\n\n\u5373[latex]t_{enter}=max(t_{min}),t_{exit}=min(t_{max})[\/latex]\u3002\u5728\u4e09\u7ef4\u7a7a\u95f4\u4e2d\u540c\u7406\u3002<\/p>\n\n\n\n\u5982\u679c[latex]t_{enter}<t_{exit}[\/latex]\uff0c\u5373\u4e3a\u5149\u7ebf\u7ecf\u8fc7\u4e86\u5305\u56f4\u76d2\uff08\u5149\u7ebf\u5728\u5305\u56f4\u76d2\u4e2d\u5f85\u4e86\u4e00\u6bb5\u65f6\u95f4\uff09\u3002<\/p>\n\n\n\n\u4f46\u662f\u5149\u7ebf\u662f\u5c04\u7ebf\uff0c\u4e0d\u662f\u76f4\u7ebf\uff0c\u6240\u4ee5\u5f53[latex]t_{exit}<0[\/latex]\uff0c\u8bf4\u660e\u7269\u4f53\u5728\u5149\u7ebf\u7684\u80cc\u540e\uff0c\u5373\u4e0d\u53ef\u80fd\u6709\u4ea4\u70b9\u3002\u5f53[latex]t_{exit}>=0,t_{enter}<0[\/latex]\uff0c\u5373\u5149\u7ebf\u7684\u8d77\u70b9\u5728\u5305\u56f4\u76d2\u5185\u90e8\u3002<\/p>\n\n\n\n\u6240\u4ee5\u5f53\u4e14\u4ec5\u5f53[latex]t_{enter}<t_{exit},t_{exit}\\ge0[\/latex]\u65f6\uff0c\u5149\u7ebf\u7a7f\u8fc7\u5305\u56f4\u76d2\u3002<\/p>\n\n\n\n\u8ba1\u7b97\u5149\u7ebf\u4e0e\u9762\u4f55\u65f6\u76f8\u4ea4\uff1a[latex]t=\\frac{\\left(\\mathbf{p}^{\\prime}-\\mathbf{o}\\right) \\cdot \\mathbf{N}}{\\mathbf{d} \\cdot \\mathbf{N}}[\/latex]\u800c\u8fd9\u91cc\u7684\u9762\u662f\u4e0e\u5750\u6807\u8f74\u5e73\u9762\u5e73\u884c\u7684\uff0c\u6240\u4ee5\u53ef\u4ee5\u7b80\u5316\u8fd0\u7b97\uff1a\u5bf9\u4e8eyz\u5e73\u9762\u5e73\u884c\uff0c\u5373\u4e3a\u5782\u76f4\u4e8ex\u8f74\uff1a[latex]t=\\frac{\\mathbf{p}_x^{\\prime}-\\mathbf{o}_x}{\\mathbf{d}_x}[\/latex]<\/p>\n","protected":false},"excerpt":{"rendered":"\u5149\u7ebf\u8ffd\u8e2a \u5728\u5149\u7ebf\u8ffd\u8e2a\u4e2d\uff0c\u5047\u8bbe\u76f8\u673a\u662f\u4e2a\u70b9\u800c\u4e0d\u662f\u4e2a\u77e9\u5f62\u3002\u7136\u540e\u5c06\u6bcf\u4e2a\u50cf\u7d20\u548c\u76f8\u673a\u76f8\u8fde\u5e76\u5ef6\u957f\u8fd9\u6761\u7ebf\uff0c\u4f5c\u4e3a\u5149\u7ebf\uff0c\u8fd9\u6761\u7ebf\u88ab\u79f0\u4e3a\u201c\u773c\u775b\u5149\u7ebf\u201d\u3002\u8fd9\u6839 …<\/p>","protected":false},"author":1,"featured_media":1141,"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-1140","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\/1140","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=1140"}],"version-history":[{"count":1,"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/posts\/1140\/revisions"}],"predecessor-version":[{"id":1747,"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/posts\/1140\/revisions\/1747"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/media\/1141"}],"wp:attachment":[{"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/media?parent=1140"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/categories?post=1140"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/tags?post=1140"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
\u56e0\u4e3a\u5f53\u5149\u7ebf\u8fdb\u5165\u5230\u6240\u6709\u7684\u9762\uff0c\u624d\u80fd\u786e\u5b9a\u5149\u8fdb\u5165\u5230\u5305\u56f4\u76d2\u4e2d\uff0c\u800c\u5f53\u5149\u7ebf\u79bb\u5f00\u4efb\u610f\u4e00\u4e2a\u9762\uff0c\u5373\u4e3a\u79bb\u5f00\u5305\u56f4\u76d2\u3002\u6240\u4ee5\u6c42\u51fa\u5176\u4e2d\u6700\u5927\u7684[latex]t_{min}[\/latex]\u548c\u6700\u5c0f\u7684[latex]t_{max}[\/latex]\u5373\u4e3a\u5149\u7ebf\u5b9e\u9645\u8fdb\u5165\u548c\u79bb\u5f00\u76d2\u5b50\u7684\u65f6\u95f4\u3002<\/p>\n\n\n\n<\/figure >\n<\/figure><\/noscript>\n\n\n\n\u5373[latex]t_{enter}=max(t_{min}),t_{exit}=min(t_{max})[\/latex]\u3002\u5728\u4e09\u7ef4\u7a7a\u95f4\u4e2d\u540c\u7406\u3002<\/p>\n\n\n\n\u5982\u679c[latex]t_{enter}<t_{exit}[\/latex]\uff0c\u5373\u4e3a\u5149\u7ebf\u7ecf\u8fc7\u4e86\u5305\u56f4\u76d2\uff08\u5149\u7ebf\u5728\u5305\u56f4\u76d2\u4e2d\u5f85\u4e86\u4e00\u6bb5\u65f6\u95f4\uff09\u3002<\/p>\n\n\n\n\u4f46\u662f\u5149\u7ebf\u662f\u5c04\u7ebf\uff0c\u4e0d\u662f\u76f4\u7ebf\uff0c\u6240\u4ee5\u5f53[latex]t_{exit}<0[\/latex]\uff0c\u8bf4\u660e\u7269\u4f53\u5728\u5149\u7ebf\u7684\u80cc\u540e\uff0c\u5373\u4e0d\u53ef\u80fd\u6709\u4ea4\u70b9\u3002\u5f53[latex]t_{exit}>=0,t_{enter}<0[\/latex]\uff0c\u5373\u5149\u7ebf\u7684\u8d77\u70b9\u5728\u5305\u56f4\u76d2\u5185\u90e8\u3002<\/p>\n\n\n\n\u6240\u4ee5\u5f53\u4e14\u4ec5\u5f53[latex]t_{enter}<t_{exit},t_{exit}\\ge0[\/latex]\u65f6\uff0c\u5149\u7ebf\u7a7f\u8fc7\u5305\u56f4\u76d2\u3002<\/p>\n\n\n\n\u8ba1\u7b97\u5149\u7ebf\u4e0e\u9762\u4f55\u65f6\u76f8\u4ea4\uff1a[latex]t=\\frac{\\left(\\mathbf{p}^{\\prime}-\\mathbf{o}\\right) \\cdot \\mathbf{N}}{\\mathbf{d} \\cdot \\mathbf{N}}[\/latex]\u800c\u8fd9\u91cc\u7684\u9762\u662f\u4e0e\u5750\u6807\u8f74\u5e73\u9762\u5e73\u884c\u7684\uff0c\u6240\u4ee5\u53ef\u4ee5\u7b80\u5316\u8fd0\u7b97\uff1a\u5bf9\u4e8eyz\u5e73\u9762\u5e73\u884c\uff0c\u5373\u4e3a\u5782\u76f4\u4e8ex\u8f74\uff1a[latex]t=\\frac{\\mathbf{p}_x^{\\prime}-\\mathbf{o}_x}{\\mathbf{d}_x}[\/latex]<\/p>\n","protected":false},"excerpt":{"rendered":"\u5149\u7ebf\u8ffd\u8e2a \u5728\u5149\u7ebf\u8ffd\u8e2a\u4e2d\uff0c\u5047\u8bbe\u76f8\u673a\u662f\u4e2a\u70b9\u800c\u4e0d\u662f\u4e2a\u77e9\u5f62\u3002\u7136\u540e\u5c06\u6bcf\u4e2a\u50cf\u7d20\u548c\u76f8\u673a\u76f8\u8fde\u5e76\u5ef6\u957f\u8fd9\u6761\u7ebf\uff0c\u4f5c\u4e3a\u5149\u7ebf\uff0c\u8fd9\u6761\u7ebf\u88ab\u79f0\u4e3a\u201c\u773c\u775b\u5149\u7ebf\u201d\u3002\u8fd9\u6839 …<\/p>","protected":false},"author":1,"featured_media":1141,"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-1140","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\/1140","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=1140"}],"version-history":[{"count":1,"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/posts\/1140\/revisions"}],"predecessor-version":[{"id":1747,"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/posts\/1140\/revisions\/1747"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/media\/1141"}],"wp:attachment":[{"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/media?parent=1140"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/categories?post=1140"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/tags?post=1140"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
\u5373[latex]t_{enter}=max(t_{min}),t_{exit}=min(t_{max})[\/latex]\u3002\u5728\u4e09\u7ef4\u7a7a\u95f4\u4e2d\u540c\u7406\u3002<\/p>\n\n\n\n
\u5982\u679c[latex]t_{enter}<t_{exit}[\/latex]\uff0c\u5373\u4e3a\u5149\u7ebf\u7ecf\u8fc7\u4e86\u5305\u56f4\u76d2\uff08\u5149\u7ebf\u5728\u5305\u56f4\u76d2\u4e2d\u5f85\u4e86\u4e00\u6bb5\u65f6\u95f4\uff09\u3002<\/p>\n\n\n\n
\u4f46\u662f\u5149\u7ebf\u662f\u5c04\u7ebf\uff0c\u4e0d\u662f\u76f4\u7ebf\uff0c\u6240\u4ee5\u5f53[latex]t_{exit}<0[\/latex]\uff0c\u8bf4\u660e\u7269\u4f53\u5728\u5149\u7ebf\u7684\u80cc\u540e\uff0c\u5373\u4e0d\u53ef\u80fd\u6709\u4ea4\u70b9\u3002\u5f53[latex]t_{exit}>=0,t_{enter}<0[\/latex]\uff0c\u5373\u5149\u7ebf\u7684\u8d77\u70b9\u5728\u5305\u56f4\u76d2\u5185\u90e8\u3002<\/p>\n\n\n\n
\u6240\u4ee5\u5f53\u4e14\u4ec5\u5f53[latex]t_{enter}<t_{exit},t_{exit}\\ge0[\/latex]\u65f6\uff0c\u5149\u7ebf\u7a7f\u8fc7\u5305\u56f4\u76d2\u3002<\/p>\n\n\n\n
\u8ba1\u7b97\u5149\u7ebf\u4e0e\u9762\u4f55\u65f6\u76f8\u4ea4\uff1a[latex]t=\\frac{\\left(\\mathbf{p}^{\\prime}-\\mathbf{o}\\right) \\cdot \\mathbf{N}}{\\mathbf{d} \\cdot \\mathbf{N}}[\/latex]\u800c\u8fd9\u91cc\u7684\u9762\u662f\u4e0e\u5750\u6807\u8f74\u5e73\u9762\u5e73\u884c\u7684\uff0c\u6240\u4ee5\u53ef\u4ee5\u7b80\u5316\u8fd0\u7b97\uff1a\u5bf9\u4e8eyz\u5e73\u9762\u5e73\u884c\uff0c\u5373\u4e3a\u5782\u76f4\u4e8ex\u8f74\uff1a[latex]t=\\frac{\\mathbf{p}_x^{\\prime}-\\mathbf{o}_x}{\\mathbf{d}_x}[\/latex]<\/p>\n","protected":false},"excerpt":{"rendered":"
\u5149\u7ebf\u8ffd\u8e2a \u5728\u5149\u7ebf\u8ffd\u8e2a\u4e2d\uff0c\u5047\u8bbe\u76f8\u673a\u662f\u4e2a\u70b9\u800c\u4e0d\u662f\u4e2a\u77e9\u5f62\u3002\u7136\u540e\u5c06\u6bcf\u4e2a\u50cf\u7d20\u548c\u76f8\u673a\u76f8\u8fde\u5e76\u5ef6\u957f\u8fd9\u6761\u7ebf\uff0c\u4f5c\u4e3a\u5149\u7ebf\uff0c\u8fd9\u6761\u7ebf\u88ab\u79f0\u4e3a\u201c\u773c\u775b\u5149\u7ebf\u201d\u3002\u8fd9\u6839 …<\/p>","protected":false},"author":1,"featured_media":1141,"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-1140","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\/1140","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=1140"}],"version-history":[{"count":1,"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/posts\/1140\/revisions"}],"predecessor-version":[{"id":1747,"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/posts\/1140\/revisions\/1747"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/media\/1141"}],"wp:attachment":[{"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/media?parent=1140"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/categories?post=1140"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/tags?post=1140"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
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