{"id":80,"date":"2024-03-10T09:54:51","date_gmt":"2024-03-10T09:54:51","guid":{"rendered":"https:\/\/ultserver.com\/blog\/?p=80"},"modified":"2024-03-16T22:02:00","modified_gmt":"2024-03-16T14:02:00","slug":"%e7%ba%af%e6%96%b9%e5%90%91%e5%85%89%e5%9c%a8%e8%b7%af%e5%be%84%e8%bf%bd%e8%b8%aa%e4%b8%ad%e7%9a%84%e5%a4%84%e7%90%86%e6%96%b9%e6%b3%95","status":"publish","type":"post","link":"https:\/\/ultserver.com\/blog\/cg\/%e7%ba%af%e6%96%b9%e5%90%91%e5%85%89%e5%9c%a8%e8%b7%af%e5%be%84%e8%bf%bd%e8%b8%aa%e4%b8%ad%e7%9a%84%e5%a4%84%e7%90%86%e6%96%b9%e6%b3%95\/","title":{"rendered":"\u7eaf\u65b9\u5411\u5149\u5728\u8def\u5f84\u8ffd\u8e2a\u4e2d\u7684\u5904\u7406\u65b9\u6cd5"},"content":{"rendered":"\n<p>\u8fd9\u91cc\u5c06\u7eaf\u65b9\u5411\u5149\u6e90\u5b9a\u4e49\u4e3a\u6765\u81ea\u65e0\u9650\u8fdc\u5904\u3001\u9762\u79ef\u65e0\u9650\u5927\u3001\u4e14\u53d1\u51fa\u7684\u5149\u7ebf\u65b9\u5411\u53ea\u6709\u552f\u4e00\u65b9\u5411\u7684\u5149\u6e90\u3002\u4f8b\u5982\u65e5\u5149\u3002<\/p>\n\n\n\n<p>\u5e38\u89c1\u7684\u8def\u5f84\u8ffd\u8e2a\u7b97\u6cd5\u4e2d\uff0c\u4e3a\u4e86\u907f\u514d\u968f\u673a\u91c7\u6837\u5bfc\u81f4\u5c0f\u5149\u6e90\u96be\u4ee5\u88ab\u5c04\u7ebf\u51fb\u4e2d\u7684\u95ee\u9898\uff0c\u53ef\u4ee5\u4f7f\u7528\u76f4\u63a5\u5149\u6e90\u91c7\u6837\uff08Direct\/explicit light sampling\uff09\u65b9\u6cd5\u3002<\/p>\n\n\n\n<p>\u8fd9\u79cd\u65b9\u6cd5\u5c06\u4e00\u4e2a\u70b9\u7684Radiance\u5206\u7c7b\u8ba8\u8bba\u4e3a\u4e24\u79cd\uff1a<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>\u76f4\u63a5\u5149\u7167\uff0c\u5bf9\u5149\u6e90\u8868\u9762\u8fdb\u884c\u79ef\u5206\uff0c\u76f4\u63a5\u8ba1\u7b97\u51fa\u5149\u6e90\u5bf9Radiance\u7684\u8d21\u732e<\/li>\n\n\n\n<li>\u95f4\u63a5\u5149\u7167\uff0c\u5bf9\u7acb\u4f53\u89d2\u8fdb\u884c\u79ef\u5206\uff0c\u9012\u5f52\u7684\u8ba1\u7b97\u51fa\u975e\u5149\u6e90\u5bf9Radiance\u7684\u8d21\u732e<\/li>\n<\/ol>\n\n\n\n<p>\u901a\u8fc7\u8fd9\u79cd\u65b9\u5f0f\uff0c\u5373\u53ef\u907f\u514d\u5c0f\u5149\u6e90\u96be\u4ee5\u88ab\u547d\u4e2d\u7684\u95ee\u9898\u3002<\/p>\n\n\n\n<p>\u4f46\u662f\u8fd9\u79cd\u65b9\u5f0f\u53ea\u9002\u7528\u4e8e\u9762\u79ef\u6709\u9650\u7684\u975e\u65b9\u5411\u5149\u6e90\uff0c\u800c\u5bf9\u4e8e\u7eaf\u65b9\u5411\u5149\u6e90\u6765\u8bf4\uff0c\u65e0\u6cd5\u901a\u8fc7\u5bf9\u5149\u6e90\u8868\u9762\u8fdb\u884c\u79ef\u5206\u6765\u8fdb\u884c\u8ba1\u7b97\uff08\u56e0\u4e3a\u6b63\u5982\u4e0a\u6587\u6240\u8bf4\uff0c\u7eaf\u65b9\u5411\u5149\u6e90\u662f\u65e0\u9650\u5927\u4e14\u65b9\u5411\u552f\u4e00\u7684\uff09\u3002<\/p>\n\n\n\n<p>\u4e3a\u4e86\u6c42\u89e3\u7eaf\u65b9\u5411\u5149\u6e90\u7684\u76f4\u63a5\u5149\u7167\uff0c\u6211\u4eec\u5148\u6765\u770b\u4e00\u4e0b\u6e32\u67d3\u65b9\u7a0b\u7684\u5b9a\u4e49\uff1a<\/p>\n\n\n\n<p>$$<br>L_r(x, \\omega_o)=\\int_{\\Omega}f_r(x, \\omega_i, \\omega_o)L_i(x, \\omega_i)(\\omega_i\\cdot n)d\\omega_i<br>$$<\/p>\n\n\n\n<p>\u516c\u5f0f\u4e2d\u5404\u9879\u7684\u5b9a\u4e49\u4e0e<a href=\"https:\/\/en.wikipedia.org\/wiki\/Rendering_equation#:~:text=In%20computer%20graphics%2C%20the%20rendering,by%20David%20Immel%20et%20al.\">Wiki<\/a>\u4e00\u81f4\uff08\u672c\u6587\u7701\u7565\u4e86\u6ce2\u957f\u3001\u65f6\u95f4\u7b49\u65e0\u5173\u53d8\u91cf\uff09\u3002<\/p>\n\n\n\n<p>\u5176\u4e2d\uff0cBRDF\u9879\u7684\u5b9a\u4e49\u4e3a\uff1a<\/p>\n\n\n\n<p>$$<br>f_r(x, \\omega_i, \\omega_o) = \\frac {dL_r(x, \\omega_o)} {dE_i(\\omega_i)} = \\frac {dL_r(x, \\omega_o)} {L_i(x, \\omega_i)(\\omega_i\\cdot n)d\\omega_i}<br>$$<\/p>\n\n\n\n<p>\u9700\u8981\u6ce8\u610f\uff0c$dL_r(x, \\omega_o)$\u7684\u5b9a\u4e49\u4e3a$x$\u70b9\u5728$\\omega_o$\u65b9\u5411\u7684Radiance\u5728$\\omega_i$\u4e0a\u7684\u5fae\u5206\uff0c\u56e0\u6b64\u5176\u5fae\u5143\u540c\u6837\u4e3a$d\\omega_i$\u3002<\/p>\n\n\n\n<p>\u7531\u4e8e\u7eaf\u65b9\u5411\u5149\u53ea\u5177\u6709\u552f\u4e00\u65b9\u5411\uff0c\u56e0\u6b64\u53ea\u5728\u8be5\u65b9\u5411\u4e0a\u80fd\u591f\u7ed9$x$\u70b9\u5e26\u6765Radiance\uff0c\u56e0\u6b64$L_i$\u51fd\u6570\u6ee1\u8db3\uff1a<\/p>\n\n\n\n<p>$$<br>\\begin{equation}<br>L_i(x, \\omega_i)=<br>\\begin{cases}<br>0&amp; \\omega_i \\neq \\vec d\\\\<br>k&amp; \\omega_i = \\vec d<br>\\end{cases}<br>\\end{equation}<br>$$<\/p>\n\n\n\n<p>\u5176\u4e2d\uff0c$\\vec d$\u4ee3\u8868\u7eaf\u65b9\u5411\u5149\u6e90\u7684\u65b9\u5411\uff0c$k$\u4e3a\u5e38\u6570\uff0c\u4ee3\u8868\u8be5\u7eaf\u65b9\u5411\u5149\u6e90\u5e26\u6765\u7684Radiance\u3002<\/p>\n\n\n\n<p>\u7136\u540e\u6839\u636e$L_i$\u7684\u5b9a\u4e49\uff0c\u53ef\u4ee5\u5c06\u8fd9\u79cd\u60c5\u51b5\u4e0b\u7684\u6e32\u67d3\u65b9\u7a0b\u8fdb\u884c\u5982\u4e0b\u53d8\u6362\uff08\u4e3b\u8981\u539f\u7406\u4e3a\uff1a\u7531\u4e8e$L_i$\u4ec5\u5728$\\vec d$\u5904\u4e0d\u4e3a0\uff0c\u56e0\u6b64\u53ef\u4ee5\u5c06\u79ef\u5206\u4e2d\u5176\u4ed6\u51fd\u6570\u7684$\\omega_i$\u5e26\u5165\u4e3a$\\vec d$\uff09\uff1a<\/p>\n\n\n\n<p>$$<br>\\begin{eqnarray}<br>L_r(x, \\omega_o)&amp;=&amp;\\int_{\\Omega}f_r(x, \\omega_i, \\omega_o)L_i(x, \\omega_i)(\\omega_i\\cdot n)d\\omega_i \\\\<br>~&amp;=&amp;\\int_{\\Omega}f_r(x, \\vec d, \\omega_o)L_i(x, \\omega_i)(\\vec d\\cdot n)d\\omega_i \\\\<br>~&amp;=&amp;f_r(x, \\vec d, \\omega_o)(\\vec d\\cdot n)\\int_{\\Omega}L_i(x, \\omega_i)d\\omega_i \\\\<br>~&amp;=&amp;f_r(x, \\vec d, \\omega_o)(\\vec d\\cdot n)\\int_{\\Omega}L_i(x, \\omega_i)d\\omega_i<br>\\end{eqnarray}<br>$$<\/p>\n\n\n\n<p>\u540c\u65f6\u7531\u4e8e\u5149\u6e90\u5fc5\u5b9a\u5bf9Radiance\u6709\u8d21\u732e\uff08\u4e0d\u8003\u8651\u906e\u6321\uff09\uff0c\u56e0\u6b64\u5fc5\u6709:<\/p>\n\n\n\n<p>$$<br>L_r(x, \\omega_o)\\neq 0<br>$$<\/p>\n\n\n\n<p>\u8fdb\u4e00\u6b65\u6709\uff1a<\/p>\n\n\n\n<p>$$<br>\\int_{\\Omega}L_i(x, \\omega_i)d\\omega_i \\neq 0<br>$$<\/p>\n\n\n\n<p>\u800c\u7531\u4e8e$L_i$\u4ec5\u5728\u5355\u70b9\u975e0\uff0c\u56e0\u6b64$L_i$\u5728\u8be5\u70b9\u4e3a\u65e0\u7a77\u5927\uff0c\u5373$k=\\infty$\uff0c\u7efc\u4e0a\u53ef\u4ee5\u770b\u5230\uff0c$L_i$\u5b9e\u9645\u4e0a\u662f\u4e00\u4e2a\u5f62\u5f0f\u5982\u4e0b\u7684<a href=\"https:\/\/en.wikipedia.org\/wiki\/Dirac_delta_function\">\u72c4\u62c9\u514b\u03b4\u51fd\u6570<\/a>\uff1a<\/p>\n\n\n\n<p>$$<br>L_i=m\\delta(\\omega_i &#8211; \\vec d)<br>$$<\/p>\n\n\n\n<p>\u6839\u636e\u72c4\u62c9\u514b\u03b4\u51fd\u6570\u7684\u6027\u8d28\u6709\uff1a<\/p>\n\n\n\n<p>$$<br>\\int_{\\Omega}L_i(x, \\omega_i)d\\omega_i = m\\int_{\\Omega}\\delta(\\omega_i &#8211; \\vec d)d\\omega_i = m<br>$$<\/p>\n\n\n\n<p>\u53c8\u7531\u4e8eRadiance\u7684\u5355\u4f4d\u4e3a$\\frac W {m^2 sr}$\uff0c\u7acb\u4f53\u89d2\u7684\u5355\u4f4d\u4e3a$\\frac 1 {sr}$\uff0c\u56e0\u6b64$m$\u7684\u5355\u4f4d\u4e3a$\\frac W {m^2}$\uff0c\u4e0eIrradiance\u76f8\u540c\u3002<\/p>\n\n\n\n<p>\u6700\u7ec8\u5f97\u5230\u7684\u7eaf\u65b9\u5411\u5149\u6e32\u67d3\u65b9\u7a0b\u4e3a\uff1a<\/p>\n\n\n\n<p>$$<br>L_r(x, \\omega_o)=f_r(x, \\vec d, \\omega_o)(\\vec d\\cdot n)m<br>$$<\/p>\n\n\n\n<p>\u8fd9\u91cc$m$\u5373\u4ee3\u8868\u4e86\u5149\u6e90\u5bf9$x$\u70b9\u7684Irradiance\u3002\u9700\u8981\u6ce8\u610f\uff0c\u7531\u4e8eIrradiance\u4e0e\u8ddd\u79bb\u6709\u5173\uff0c\u56e0\u6b64\u5728\u5b9e\u9645\u5b9a\u4e49\u5149\u6e90\u7684Irradiance\u65f6\uff0c\u8fd8\u9700\u8981\u8003\u8651\u5149\u6e90\u5230$x$\u7684\u8ddd\u79bb$l$\uff0c\u4f8b\u5982\u5c06$m$\u5b9a\u4e49\u4e3a\u5149\u6e90\u5728\u5355\u4f4d\u8ddd\u79bb\u4e0a\u7684Irradiance\uff0c\u90a3\u4e48\u5e94\u8be5\u5c06\u516c\u5f0f\u4fee\u6539\u4e3a\uff1a<\/p>\n\n\n\n<p>$$<br>L_r(x, \\omega_o)=f_r(x, \\vec d, \\omega_o)(\\vec d\\cdot n)\\frac m {l^2}<br>$$<\/p>\n\n\n\n<p>\u7efc\u4e0a\uff0c\u4e3a\u4e86\u5904\u7406\u7eaf\u65b9\u5411\u5149\u6e90\uff0c\u8fd9\u91cc\u9700\u8981\u5f15\u5165\u53e6\u4e00\u79cd\u5149\u6e90\u7684\u5b9a\u4e49\u65b9\u5f0f\uff1a\u5373\u901a\u8fc7Irradiance\u5b9a\u4e49\u7eaf\u65b9\u5411\u5149\u6e90\u3002\u800c\u4f53\u79ef\u5149\u6e90\u5219\u901a\u8fc7Radiance\u6765\u5b9a\u4e49\u3002\u5176\u4e2d\uff0c\u524d\u8005\u4f7f\u7528\u672c\u6587\u6700\u540e\u53d8\u6362\u5f97\u5230\u7684\u6e32\u67d3\u65b9\u7a0b\u8fdb\u884c\u8ba1\u7b97\uff0c\u540e\u8005\u901a\u8fc7\u539f\u59cb\u7684\u6e32\u67d3\u65b9\u7a0b\u8fdb\u884c\u8ba1\u7b97\u3002<\/p>\n\n\n\n<p>\u53c2\u8003\u6587\u732e\uff1a<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><a href=\"https:\/\/medium.com\/@2305sakake\/an-introduction-to-the-dirac-delta-function-and-applications-in-physics-2c32e7e6fec7\">An Introduction to the Dirac Delta Function and Applications in Physics<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/stackoverflow.com\/questions\/10612262\/dealing-with-point-lights-and-exact-reflections-in-path-tracing\">Dealing with point lights and exact reflections in path tracing<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/computergraphics.stackexchange.com\/questions\/12455\/how-are-point-and-pure-directional-lights-sampled-in-an-unbiased-path-tracer\">How are point and pure directional lights sampled in an unbiased path tracer?<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/www.zhihu.com\/question\/28476602\/answer\/1935502213\">brdf\u4e3a\u4ec0\u4e48\u8981\u5b9a\u4e49\u4e3a\u4e00\u4e2a\u5355\u4f4d\u662fsr-1\u7684\u91cf\uff1f<\/a><\/li>\n<\/ol>\n","protected":false},"excerpt":{"rendered":"<p>\u672c\u6587\u63a2\u8ba8\u4e86\u7eaf\u65b9\u5411\u5149\u5728\u8def\u5f84\u8ffd\u8e2a\u4e2d\u7684\u5904\u7406\u65b9\u6cd5\uff0c\u5305\u62ec\u5bf9\u4e8e\u6e32\u67d3\u65b9\u7a0b\u7684\u79ef\u5206\u9879\u7684\u4e00\u4e9b\u601d\u8003<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":true,"template":"","format":"standard","meta":{"_uag_custom_page_level_css":"","wikipediapreview_detectlinks":true,"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center 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center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[4],"tags":[5,6],"class_list":["post-80","post","type-post","status-publish","format-standard","hentry","category-cg","tag-5","tag-6"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.6 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>\u7eaf\u65b9\u5411\u5149\u5728\u8def\u5f84\u8ffd\u8e2a\u4e2d\u7684\u5904\u7406\u65b9\u6cd5 - UltBlog<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/ultserver.com\/blog\/cg\/\u7eaf\u65b9\u5411\u5149\u5728\u8def\u5f84\u8ffd\u8e2a\u4e2d\u7684\u5904\u7406\u65b9\u6cd5\/\" \/>\n<meta property=\"og:locale\" content=\"zh_CN\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta 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