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对于金属，折射进表面的光线的能量会立即被金属中的自由电子吸收，转换成电子的能量，不再可见
对于非金属（电介质或绝缘体），它们往往不是由单一成分构成，而可以认为其中包含了很多折射率不同的微粒，光线遇到这些粒子后发生反射折射，在物质内部不断传播，散射到不同方向，其中一部分会再次穿过表面被观察到,这种现象称为次表面散射(Subsurface Scattering)
根据物质属性和观察尺度的不同，次表面散射会表现出不同的效果
如果光线在物质中传播距离小于观察尺度（绿色区域，可以认为是一个像素区域），我们看到情况如下面的右上图，入射点、反射点、次表面散射的出射点看起来是同一个点。其中反射部分（图中浅棕色出射光）就是我们常说的高光（Specular Light），常聚集在一个方向周围，向这个方向观察该点会看到明显的高光，从其他方向观察该点时高光则比较微弱；次表面散射部分（图中蓝色出射光）是漫射光（Diffuse Light），光线被散射到各个方向。
如果光线在物质中的传播距离大于观察尺度，就需要使用次表面散射算法来建模
BRDF(bidirectional reflectance distribution function),是用来描述反光小平面的反射光和入射光的比例关系的函数，设一个不透明的、不发光的小平面，BRDF的定义为
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测量入射光的设备测量小平面的照度（E）最方便，不用关心方向，而测量出射光则是测量辐射率(L)最方便，用狭长的测光筒
一束光照到平面后，被平面反射到各个方向，其中一个出射方向的光通量只是整个反射光通量极小的一部分，当出射方向立体角趋于0时，
',6)),Q("mjx-container",F,[(m(),a("svg",X,[...T[38]||(T[38]=[t('',1)])])),T[39]||(T[39]=Q("mjx-assistive-mml",{unselectable:"on",display:"block"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[Q("munder",null,[Q("mo",{"data-mjx-texclass":"OP",movablelimits:"true"},"lim"),Q("mrow",{"data-mjx-texclass":"ORD"},[Q("msub",null,[Q("mi",null,"ω"),Q("mi",null,"o")]),Q("mo",{stretchy:"false"},"→"),Q("mn",null,"0")])]),Q("mfrac",null,[Q("mrow",null,[Q("mi",null,"d"),Q("msub",null,[Q("mi",null,"L"),Q("mi",null,"o")])]),Q("msub",null,[Q("mi",null,"L"),Q("mi",null,"i")])]),Q("mo",null,"="),Q("mn",null,"0")])],-1))]),Q("p",null,[T[46]||(T[46]=l("所以在实际计算中使用辐射率和辐射率比值是没有意义的。而如果分母改成表面上接收到的来自光源方向的微分辐照度，",-1)),Q("mjx-container",S,[(m(),a("svg",J,[...T[40]||(T[40]=[t('',1)])])),T[41]||(T[41]=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"d"),Q("mi",null,"E"),Q("mo",null,"="),Q("msub",null,[Q("mi",null,"L"),Q("mi",null,"i")]),Q("mo",{stretchy:"false"},"("),Q("mi",null,"l"),Q("mo",{stretchy:"false"},")"),Q("mi",null,"d"),Q("mi",null,"ω"),Q("mi",null,"cos"),Q("mo",{"data-mjx-texclass":"NONE"},""),Q("msub",null,[Q("mi",null,"θ"),Q("mi",null,"i")])])],-1))]),T[47]||(T[47]=l("，",-1)),Q("mjx-container",G,[(m(),a("svg",N,[...T[42]||(T[42]=[t('',1)])])),T[43]||(T[43]=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"d"),Q("mi",null,"E")])],-1))]),T[48]||(T[48]=l("会小很多，所以比值",-1)),Q("mjx-container",E,[(m(),a("svg",z,[...T[44]||(T[44]=[t('',1)])])),T[45]||(T[45]=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("mi",null,"d"),Q("msub",null,[Q("mi",null,"L"),Q("mi",null,"o")]),Q("mrow",{"data-mjx-texclass":"ORD"},[Q("mo",null,"/")]),Q("mi",null,"d"),Q("msub",null,[Q("mi",null,"E"),Q("mi",null,"i")])])],-1))]),T[49]||(T[49]=l("是有意义的",-1))])])}const q=n(g,[["render",P]]),U=JSON.parse('{"path":"/note/graphics/illumination_model/BRDF/BRDF.html","title":"BRDF(双向反射分布函数)","lang":"zh-CN","frontmatter":{"description":"BRDF(双向反射分布函数) 1. 物体对光的反应 1.1 金属 对于金属，折射进表面的光线的能量会立即被金属中的自由电子吸收，转换成电子的能量，不再可见 1.2 非金属 对于非金属（电介质或绝缘体），它们往往不是由单一成分构成，而可以认为其中包含了很多折射率不同的微粒，光线遇到这些粒子后发生反射折射，在物质内部不断传播，散射到不同方向，其中一部分会再...","head":[["script",{"type":"application/ld+json"},"{\\"@context\\":\\"https://schema.org\\",\\"@type\\":\\"Article\\",\\"headline\\":\\"BRDF(双向反射分布函数)\\",\\"image\\":[\\"\\"],\\"dateModified\\":\\"2025-02-22T14:42:02.000Z\\",\\"author\\":[{\\"@type\\":\\"Person\\",\\"name\\":\\"JinChao\\",\\"url\\":\\"https://thecodeway.com\\"}]}"],["meta",{"property":"og:url","content":"https://thejinchao.github.io/note/graphics/illumination_model/BRDF/BRDF.html"}],["meta",{"property":"og:site_name","content":"我的博客和笔记"}],["meta",{"property":"og:title","content":"BRDF(双向反射分布函数)"}],["meta",{"property":"og:description","content":"BRDF(双向反射分布函数) 1. 物体对光的反应 1.1 金属 对于金属，折射进表面的光线的能量会立即被金属中的自由电子吸收，转换成电子的能量，不再可见 1.2 非金属 对于非金属（电介质或绝缘体），它们往往不是由单一成分构成，而可以认为其中包含了很多折射率不同的微粒，光线遇到这些粒子后发生反射折射，在物质内部不断传播，散射到不同方向，其中一部分会再..."}],["meta",{"property":"og:type","content":"article"}],["meta",{"property":"og:locale","content":"zh-CN"}],["meta",{"property":"og:updated_time","content":"2025-02-22T14:42:02.000Z"}],["meta",{"property":"article:modified_time","content":"2025-02-22T14:42:02.000Z"}]]},"git":{"createdTime":1740235322000,"updatedTime":1740235322000,"contributors":[{"name":"thejinchao","username":"thejinchao","email":"thejinchao@gmail.com","commits":1,"url":"https://github.com/thejinchao"}]},"readingTime":{"minutes":2.94,"words":883},"filePathRelative":"note/graphics/illumination_model/BRDF/BRDF.md","autoDesc":true}');export{q as comp,U as data};