2 lines
73 KiB
JavaScript
2 lines
73 KiB
JavaScript
import{_ as x,c,a,b as m,d as s,o as j}from"./app-DCgfI_Ar.js";const e="/assets/reflectance_equation-CS7cZbpx.jpg",i={};function t(n,l){return j(),c("div",null,l[0]||(l[0]=[a('<h1 id="渲染方程-一" tabindex="-1"><a class="header-anchor" href="#渲染方程-一"><span>渲染方程（一）</span></a></h1><hr><h2 id="_1-定义" tabindex="-1"><a class="header-anchor" href="#_1-定义"><span>1. 定义</span></a></h2><h3 id="_1-1-反射方程" tabindex="-1"><a class="header-anchor" href="#_1-1-反射方程"><span>1.1 反射方程</span></a></h3>',4),m("p",null,[s("计算反射表面反射到"),m("mjx-container",{class:"MathJax",jax:"CHTML",style:{position:"relative"}},[m("mjx-math",{class:"MJX-TEX","aria-hidden":"true"},[m("mjx-TeXAtom",{texclass:"ORD"},[m("mjx-mover",null,[m("mjx-over",{style:{"padding-bottom":"0.105em","padding-left":"0.524em","margin-bottom":"-0.516em"}},[m("mjx-mo",{class:"mjx-n",style:{width:"0","margin-left":"-0.25em"}},[m("mjx-c",{class:"mjx-c20D7 TEX-V"})])]),m("mjx-base",null,[m("mjx-msub",null,[m("mjx-mi",{class:"mjx-i"},[m("mjx-c",{class:"mjx-c1D714 TEX-I"})]),m("mjx-script",{style:{"vertical-align":"-0.15em"}},[m("mjx-mi",{class:"mjx-i",size:"s"},[m("mjx-c",{class:"mjx-c1D45C TEX-I"})])])])])])])]),m("mjx-assistive-mml",{unselectable:"on",display:"inline"},[m("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[m("mrow",{"data-mjx-texclass":"ORD"},[m("mover",null,[m("msub",null,[m("mi",null,"ω"),m("mi",null,"o")]),m("mo",{stretchy:"false"},"→")])])])])]),s("方向上的来自于上半球所有方向入射光的辐射率")],-1),m("figure",null,[m("img",{src:e,alt:"",tabindex:"0",loading:"lazy"}),m("figcaption")],-1),m("mjx-container",{class:"MathJax",jax:"CHTML",display:"true",style:{position:"relative"}},[m("mjx-math",{display:"true",style:{"margin-left":"0","margin-right":"0"},class:"MJX-TEX","aria-hidden":"true"},[m("mjx-msub",null,[m("mjx-mi",{class:"mjx-i"},[m("mjx-c",{class:"mjx-c1D43F TEX-I"})]),m("mjx-script",{style:{"vertical-align":"-0.15em"}},[m("mjx-mi",{class:"mjx-i",size:"s"},[m("mjx-c",{class:"mjx-c1D45C TEX-I"})])])]),m("mjx-mo",{class:"mjx-n"},[m("mjx-c",{class:"mjx-c28"})]),m("mjx-TeXAtom",{texclass:"ORD"},[m("mjx-mover",null,[m("mjx-over",{style:{"padding-bottom":"0.105em","padding-left":"0.524em","margin-bottom":"-0.516em"}},[m("mjx-mo",{class:"mjx-n",style:{width:"0","margin-left":"-0.25em"}},[m("mjx-c",{class:"mjx-c20D7 TEX-V"})])]),m("mjx-base",null,[m("mjx-msub",null,[m("mjx-mi",{class:"mjx-i"},[m("mjx-c",{class:"mjx-c1D714 TEX-I"})]),m("mjx-script",{style:{"vertical-align":"-0.15em"}},[m("mjx-mi",{class:"mjx-i",size:"s"},[m("mjx-c",{class:"mjx-c1D45C TEX-I"})])])])])])]),m("mjx-mo",{class:"mjx-n"},[m("mjx-c",{class:"mjx-c29"})]),m("mjx-mo",{class:"mjx-n",space:"4"},[m("mjx-c",{class:"mjx-c3D"})]),m("mjx-msub",{space:"4"},[m("mjx-mo",{class:"mjx-lop"},[m("mjx-c",{class:"mjx-c222B TEX-S2"})]),m("mjx-script",{style:{"vertical-align":"-0.896em","margin-left":"-0.388em"}},[m("mjx-TeXAtom",{size:"s",texclass:"ORD"},[m("mjx-mi",{class:"mjx-n"},[m("mjx-c",{class:"mjx-c3A9"})])])])]),m("mjx-mi",{class:"mjx-i",space:"2"},[m("mjx-c",{class:"mjx-c1D453 TEX-I"})]),m("mjx-mo",{class:"mjx-n"},[m("mjx-c",{class:"mjx-c28"})]),m("mjx-TeXAtom",{texclass:"ORD"},[m("mjx-mover",null,[m("mjx-over",{style:{"padding-bottom":"0.105em","padding-left":"0.474em","margin-bottom":"-0.516em"}},[m("mjx-mo",{class:"mjx-n",style:{width:"0","margin-left":"-0.25em"}},[m("mjx-c",{class:"mjx-c20D7 TEX-V"})])]),m("mjx-base",null,[m("mjx-msub",null,[m("mjx-mi",{class:"mjx-i"},[m("mjx-c",{class:"mjx-c1D714 TEX-I"})]),m("mjx-script",{style:{"vertical-align":"-0.15em"}},[m("mjx-mi",{class:"mjx-i",size:"s"},[m("mjx-c",{class:"mjx-c1D456 TEX-I"})])])])])])]),m("mjx-mo",{class:"mjx-n"},[m("mjx-c",{class:"mjx-c2C"})]),m("mjx-TeXAtom",{space:"2",texclass:"ORD"},[m("mjx-mover",null,[m("mjx-over",{style:{"padding-bottom":"0.105em","padding-left":"0.524em","margin-bottom":"-0.516em"}},[m("mjx-mo",{class:"mjx-n",style:{width:"0","margin-left":"-0.25em"}},[m("mjx-c",{class:"mjx-c20D7 TEX-V"})])]),m("mjx-base",null,[m("mjx-msub",null,[m("mjx-mi",{class:"mjx-i"},[m("mjx-c",{class:"mjx-c1D714 TEX-I"})]),m("mjx-script",{style:{"vertical-align":"-0.15em"}},[m("mjx-mi",{class:"mjx-i",size:"s"},[m("mjx-c",{class:"mjx-c1D45C TEX-I"})])])])])])]),m("mjx-mo",{class:"mjx-n"},[m("mjx-c",{class:"mjx-c29"})]),m("mjx-msub",null,[m("mjx-mi",{class:"mjx-i"},[m("mjx-c",{class:"mjx-c1D43F TEX-I"})]),m("mjx-script",{style:{"vertical-align":"-0.15em"}},[m("mjx-mi",{class:"mjx-i",size:"s"},[m("mjx-c",{class:"mjx-c1D456 TEX-I"})])])]),m("mjx-mo",{class:"mjx-n"},[m("mjx-c",{class:"mjx-c28"})]),m("mjx-TeXAtom",{texclass:"ORD"},[m("mjx-mover",null,[m("mjx-over",{style:{"padding-bottom":"0.105em","padding-left":"0.474em","margin-bottom":"-0.516em"}},[m("mjx-mo",{class:"mjx-n",style:{width:"0","margin-left":"-0.25em"}},[m("mjx-c",{class:"mjx-c20D7 TEX-V"})])]),m("mjx-base",null,[m("mjx-msub",null,[m("mjx-mi",{class:"mjx-i"},[m("mjx-c",{class:"mjx-c1D714 TEX-I"})]),m("mjx-script",{style:{"vertical-align":"-0.15em"}},[m("mjx-mi",{class:"mjx-i",size:"s"},[m("mjx-c",{class:"mjx-c1D456 TEX-I"})])])])])])]),m("mjx-mo",{class:"mjx-n"},[m("mjx-c",{class:"mjx-c29"})]),m("mjx-mi",{class:"mjx-n",space:"2"},[m("mjx-c",{class:"mjx-c63"}),m("mjx-c",{class:"mjx-c6F"}),m("mjx-c",{class:"mjx-c73"})]),m("mjx-mo",{class:"mjx-n"},[m("mjx-c",{class:"mjx-c2061"})]),m("mjx-msub",{space:"2"},[m("mjx-mi",{class:"mjx-i"},[m("mjx-c",{class:"mjx-c1D703 TEX-I"})]),m("mjx-script",{style:{"vertical-align":"-0.15em"}},[m("mjx-mi",{class:"mjx-i",size:"s"},[m("mjx-c",{class:"mjx-c1D456 TEX-I"})])])]),m("mjx-mi",{class:"mjx-i"},[m("mjx-c",{class:"mjx-c1D451 TEX-I"})]),m("mjx-msub",null,[m("mjx-mi",{class:"mjx-i"},[m("mjx-c",{class:"mjx-c1D714 TEX-I"})]),m("mjx-script",{style:{"vertical-align":"-0.15em"}},[m("mjx-mi",{class:"mjx-i",size:"s"},[m("mjx-c",{class:"mjx-c1D456 TEX-I"})])])])]),m("mjx-assistive-mml",{unselectable:"on",display:"block"},[m("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[m("msub",null,[m("mi",null,"L"),m("mi",null,"o")]),m("mo",{stretchy:"false"},"("),m("mrow",{"data-mjx-texclass":"ORD"},[m("mover",null,[m("msub",null,[m("mi",null,"ω"),m("mi",null,"o")]),m("mo",{stretchy:"false"},"→")])]),m("mo",{stretchy:"false"},")"),m("mo",null,"="),m("msub",null,[m("mo",{"data-mjx-texclass":"OP"},"∫"),m("mrow",{"data-mjx-texclass":"ORD"},[m("mi",{mathvariant:"normal"},"Ω")])]),m("mi",null,"f"),m("mo",{stretchy:"false"},"("),m("mrow",{"data-mjx-texclass":"ORD"},[m("mover",null,[m("msub",null,[m("mi",null,"ω"),m("mi",null,"i")]),m("mo",{stretchy:"false"},"→")])]),m("mo",null,","),m("mrow",{"data-mjx-texclass":"ORD"},[m("mover",null,[m("msub",null,[m("mi",null,"ω"),m("mi",null,"o")]),m("mo",{stretchy:"false"},"→")])]),m("mo",{stretchy:"false"},")"),m("msub",null,[m("mi",null,"L"),m("mi",null,"i")]),m("mo",{stretchy:"false"},"("),m("mrow",{"data-mjx-texclass":"ORD"},[m("mover",null,[m("msub",null,[m("mi",null,"ω"),m("mi",null,"i")]),m("mo",{stretchy:"false"},"→")])]),m("mo",{stretchy:"false"},")"),m("mi",null,"cos"),m("mo",{"data-mjx-texclass":"NONE"},""),m("msub",null,[m("mi",null,"θ"),m("mi",null,"i")]),m("mi",null,"d"),m("msub",null,[m("mi",null,"ω"),m("mi",null,"i")])])])],-1),m("p",null,"上式称为反射方程（Reflectance Equation），用来计算表面反射辐射率",-1),m("h3",{id:"_1-2-渲染方程",tabindex:"-1"},[m("a",{class:"header-anchor",href:"#_1-2-渲染方程"},[m("span",null,"1.2 渲染方程")])],-1),m("p",null,[s("将反射方程增加上自发光因素，可以得到渲染方程("),m("a",{href:"https://en.wikipedia.org/wiki/Rendering_equation",target:"_blank",rel:"noopener noreferrer"},"Rendering equation"),s(")")],-1),m("mjx-container",{class:"MathJax",jax:"CHTML",display:"true",style:{position:"relative"}},[m("mjx-math",{display:"true",style:{"margin-left":"0","margin-right":"0"},class:"MJX-TEX","aria-hidden":"true"},[m("mjx-msub",null,[m("mjx-mi",{class:"mjx-i"},[m("mjx-c",{class:"mjx-c1D43F TEX-I"})]),m("mjx-script",{style:{"vertical-align":"-0.15em"}},[m("mjx-TeXAtom",{size:"s",texclass:"ORD"},[m("mjx-mi",{class:"mjx-i"},[m("mjx-c",{class:"mjx-c1D45C TEX-I"})])])])]),m("mjx-mo",{class:"mjx-n"},[m("mjx-c",{class:"mjx-c28"})]),m("mjx-TeXAtom",{texclass:"ORD"},[m("mjx-mover",null,[m("mjx-over",{style:{"padding-bottom":"0.105em","padding-left":"0.524em","margin-bottom":"-0.516em"}},[m("mjx-mo",{class:"mjx-n",style:{width:"0","margin-left":"-0.25em"}},[m("mjx-c",{class:"mjx-c20D7 TEX-V"})])]),m("mjx-base",null,[m("mjx-msub",null,[m("mjx-mi",{class:"mjx-i"},[m("mjx-c",{class:"mjx-c1D714 TEX-I"})]),m("mjx-script",{style:{"vertical-align":"-0.15em"}},[m("mjx-mi",{class:"mjx-i",size:"s"},[m("mjx-c",{class:"mjx-c1D45C TEX-I"})])])])])])]),m("mjx-mo",{class:"mjx-n"},[m("mjx-c",{class:"mjx-c29"})]),m("mjx-mo",{class:"mjx-n",space:"4"},[m("mjx-c",{class:"mjx-c3D"})]),m("mjx-msub",{space:"4"},[m("mjx-mi",{class:"mjx-i"},[m("mjx-c",{class:"mjx-c1D43F TEX-I"})]),m("mjx-script",{style:{"vertical-align":"-0.15em"}},[m("mjx-TeXAtom",{size:"s",texclass:"ORD"},[m("mjx-mi",{class:"mjx-i"},[m("mjx-c",{class:"mjx-c1D452 TEX-I"})])])])]),m("mjx-mo",{class:"mjx-n"},[m("mjx-c",{class:"mjx-c28"})]),m("mjx-TeXAtom",{texclass:"ORD"},[m("mjx-mover",null,[m("mjx-over",{style:{"padding-bottom":"0.105em","padding-left":"0.524em","margin-bottom":"-0.516em"}},[m("mjx-mo",{class:"mjx-n",style:{width:"0","margin-left":"-0.25em"}},[m("mjx-c",{class:"mjx-c20D7 TEX-V"})])]),m("mjx-base",null,[m("mjx-msub",null,[m("mjx-mi",{class:"mjx-i"},[m("mjx-c",{class:"mjx-c1D714 TEX-I"})]),m("mjx-script",{style:{"vertical-align":"-0.15em"}},[m("mjx-mi",{class:"mjx-i",size:"s"},[m("mjx-c",{class:"mjx-c1D45C TEX-I"})])])])])])]),m("mjx-mo",{class:"mjx-n"},[m("mjx-c",{class:"mjx-c29"})]),m("mjx-mo",{class:"mjx-n",space:"3"},[m("mjx-c",{class:"mjx-c2B"})]),m("mjx-msub",{space:"3"},[m("mjx-mo",{class:"mjx-lop"},[m("mjx-c",{class:"mjx-c222B TEX-S2"})]),m("mjx-script",{style:{"vertical-align":"-0.896em","margin-left":"-0.388em"}},[m("mjx-TeXAtom",{size:"s",texclass:"ORD"},[m("mjx-mi",{class:"mjx-n"},[m("mjx-c",{class:"mjx-c3A9"})])])])]),m("mjx-mi",{class:"mjx-i",space:"2"},[m("mjx-c",{class:"mjx-c1D453 TEX-I"})]),m("mjx-mo",{class:"mjx-n"},[m("mjx-c",{class:"mjx-c28"})]),m("mjx-TeXAtom",{texclass:"ORD"},[m("mjx-mover",null,[m("mjx-over",{style:{"padding-bottom":"0.105em","padding-left":"0.474em","margin-bottom":"-0.516em"}},[m("mjx-mo",{class:"mjx-n",style:{width:"0","margin-left":"-0.25em"}},[m("mjx-c",{class:"mjx-c20D7 TEX-V"})])]),m("mjx-base",null,[m("mjx-msub",null,[m("mjx-mi",{class:"mjx-i"},[m("mjx-c",{class:"mjx-c1D714 TEX-I"})]),m("mjx-script",{style:{"vertical-align":"-0.15em"}},[m("mjx-mi",{class:"mjx-i",size:"s"},[m("mjx-c",{class:"mjx-c1D456 TEX-I"})])])])])])]),m("mjx-mo",{class:"mjx-n"},[m("mjx-c",{class:"mjx-c2C"})]),m("mjx-TeXAtom",{space:"2",texclass:"ORD"},[m("mjx-mover",null,[m("mjx-over",{style:{"padding-bottom":"0.105em","padding-left":"0.524em","margin-bottom":"-0.516em"}},[m("mjx-mo",{class:"mjx-n",style:{width:"0","margin-left":"-0.25em"}},[m("mjx-c",{class:"mjx-c20D7 TEX-V"})])]),m("mjx-base",null,[m("mjx-msub",null,[m("mjx-mi",{class:"mjx-i"},[m("mjx-c",{class:"mjx-c1D714 TEX-I"})]),m("mjx-script",{style:{"vertical-align":"-0.15em"}},[m("mjx-mi",{class:"mjx-i",size:"s"},[m("mjx-c",{class:"mjx-c1D45C TEX-I"})])])])])])]),m("mjx-mo",{class:"mjx-n"},[m("mjx-c",{class:"mjx-c29"})]),m("mjx-msub",null,[m("mjx-mi",{class:"mjx-i"},[m("mjx-c",{class:"mjx-c1D43F TEX-I"})]),m("mjx-script",{style:{"vertical-align":"-0.15em"}},[m("mjx-mi",{class:"mjx-i",size:"s"},[m("mjx-c",{class:"mjx-c1D456 TEX-I"})])])]),m("mjx-mo",{class:"mjx-n"},[m("mjx-c",{class:"mjx-c28"})]),m("mjx-TeXAtom",{texclass:"ORD"},[m("mjx-mover",null,[m("mjx-over",{style:{"padding-bottom":"0.105em","padding-left":"0.474em","margin-bottom":"-0.516em"}},[m("mjx-mo",{class:"mjx-n",style:{width:"0","margin-left":"-0.25em"}},[m("mjx-c",{class:"mjx-c20D7 TEX-V"})])]),m("mjx-base",null,[m("mjx-msub",null,[m("mjx-mi",{class:"mjx-i"},[m("mjx-c",{class:"mjx-c1D714 TEX-I"})]),m("mjx-script",{style:{"vertical-align":"-0.15em"}},[m("mjx-mi",{class:"mjx-i",size:"s"},[m("mjx-c",{class:"mjx-c1D456 TEX-I"})])])])])])]),m("mjx-mo",{class:"mjx-n"},[m("mjx-c",{class:"mjx-c29"})]),m("mjx-mi",{class:"mjx-n",space:"2"},[m("mjx-c",{class:"mjx-c63"}),m("mjx-c",{class:"mjx-c6F"}),m("mjx-c",{class:"mjx-c73"})]),m("mjx-mo",{class:"mjx-n"},[m("mjx-c",{class:"mjx-c2061"})]),m("mjx-msub",{space:"2"},[m("mjx-mi",{class:"mjx-i"},[m("mjx-c",{class:"mjx-c1D703 TEX-I"})]),m("mjx-script",{style:{"vertical-align":"-0.15em"}},[m("mjx-mi",{class:"mjx-i",size:"s"},[m("mjx-c",{class:"mjx-c1D456 TEX-I"})])])]),m("mjx-mi",{class:"mjx-i"},[m("mjx-c",{class:"mjx-c1D451 TEX-I"})]),m("mjx-msub",null,[m("mjx-mi",{class:"mjx-i"},[m("mjx-c",{class:"mjx-c1D714 TEX-I"})]),m("mjx-script",{style:{"vertical-align":"-0.15em"}},[m("mjx-mi",{class:"mjx-i",size:"s"},[m("mjx-c",{class:"mjx-c1D456 TEX-I"})])])])]),m("mjx-assistive-mml",{unselectable:"on",display:"block"},[m("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[m("msub",null,[m("mi",null,"L"),m("mrow",{"data-mjx-texclass":"ORD"},[m("mi",null,"o")])]),m("mo",{stretchy:"false"},"("),m("mrow",{"data-mjx-texclass":"ORD"},[m("mover",null,[m("msub",null,[m("mi",null,"ω"),m("mi",null,"o")]),m("mo",{stretchy:"false"},"→")])]),m("mo",{stretchy:"false"},")"),m("mo",null,"="),m("msub",null,[m("mi",null,"L"),m("mrow",{"data-mjx-texclass":"ORD"},[m("mi",null,"e")])]),m("mo",{stretchy:"false"},"("),m("mrow",{"data-mjx-texclass":"ORD"},[m("mover",null,[m("msub",null,[m("mi",null,"ω"),m("mi",null,"o")]),m("mo",{stretchy:"false"},"→")])]),m("mo",{stretchy:"false"},")"),m("mo",null,"+"),m("msub",null,[m("mo",{"data-mjx-texclass":"OP"},"∫"),m("mrow",{"data-mjx-texclass":"ORD"},[m("mi",{mathvariant:"normal"},"Ω")])]),m("mi",null,"f"),m("mo",{stretchy:"false"},"("),m("mrow",{"data-mjx-texclass":"ORD"},[m("mover",null,[m("msub",null,[m("mi",null,"ω"),m("mi",null,"i")]),m("mo",{stretchy:"false"},"→")])]),m("mo",null,","),m("mrow",{"data-mjx-texclass":"ORD"},[m("mover",null,[m("msub",null,[m("mi",null,"ω"),m("mi",null,"o")]),m("mo",{stretchy:"false"},"→")])]),m("mo",{stretchy:"false"},")"),m("msub",null,[m("mi",null,"L"),m("mi",null,"i")]),m("mo",{stretchy:"false"},"("),m("mrow",{"data-mjx-texclass":"ORD"},[m("mover",null,[m("msub",null,[m("mi",null,"ω"),m("mi",null,"i")]),m("mo",{stretchy:"false"},"→")])]),m("mo",{stretchy:"false"},")"),m("mi",null,"cos"),m("mo",{"data-mjx-texclass":"NONE"},""),m("msub",null,[m("mi",null,"θ"),m("mi",null,"i")]),m("mi",null,"d"),m("msub",null,[m("mi",null,"ω"),m("mi",null,"i")])])])],-1),m("p",null,"完整形式的渲染方程，需要考虑到反射平面所处的位置、时间，光的波长这些因素，具体形式为",-1),m("mjx-container",{class:"MathJax",jax:"CHTML",display:"true",style:{position:"relative"}},[m("mjx-math",{display:"true",style:{"margin-left":"0","margin-right":"0"},class:"MJX-TEX","aria-hidden":"true"},[m("mjx-msub",null,[m("mjx-mi",{class:"mjx-i"},[m("mjx-c",{class:"mjx-c1D43F TEX-I"})]),m("mjx-script",{style:{"vertical-align":"-0.15em"}},[m("mjx-mi",{class:"mjx-i",size:"s"},[m("mjx-c",{class:"mjx-c1D45C TEX-I"})])])]),m("mjx-mo",{class:"mjx-n"},[m("mjx-c",{class:"mjx-c28"})]),m("mjx-TeXAtom",{texclass:"ORD"},[m("mjx-mi",{class:"mjx-b"},[m("mjx-c",{class:"mjx-c1D431 TEX-B"})])]),m("mjx-mo",{class:"mjx-n"},[m("mjx-c",{class:"mjx-c2C"})]),m("mjx-TeXAtom",{space:"2",texclass:"ORD"},[m("mjx-mover",null,[m("mjx-over",{style:{"padding-bottom":"0.105em","padding-left":"0.524em","margin-bottom":"-0.516em"}},[m("mjx-mo",{class:"mjx-n",style:{width:"0","margin-left":"-0.25em"}},[m("mjx-c",{class:"mjx-c20D7 TEX-V"})])]),m("mjx-base",null,[m("mjx-msub",null,[m("mjx-mi",{class:"mjx-i"},[m("mjx-c",{class:"mjx-c1D714 TEX-I"})]),m("mjx-script",{style:{"vertical-align":"-0.15em"}},[m("mjx-mi",{class:"mjx-i",size:"s"},[m("mjx-c",{class:"mjx-c1D45C TEX-I"})])])])])])]),m("mjx-mo",{class:"mjx-n"},[m("mjx-c",{class:"mjx-c2C"})]),m("mjx-mi",{class:"mjx-i",space:"2"},[m("mjx-c",{class:"mjx-c1D706 TEX-I"})]),m("mjx-mo",{class:"mjx-n"},[m("mjx-c",{class:"mjx-c2C"})]),m("mjx-mi",{class:"mjx-i",space:"2"},[m("mjx-c",{class:"mjx-c1D461 TEX-I"})]),m("mjx-mo",{class:"mjx-n"},[m("mjx-c",{class:"mjx-c29"})]),m("mjx-mo",{class:"mjx-n",space:"4"},[m("mjx-c",{class:"mjx-c3D"})]),m("mjx-msub",{space:"4"},[m("mjx-mi",{class:"mjx-i"},[m("mjx-c",{class:"mjx-c1D43F TEX-I"})]),m("mjx-script",{style:{"vertical-align":"-0.15em"}},[m("mjx-mi",{class:"mjx-i",size:"s"},[m("mjx-c",{class:"mjx-c1D452 TEX-I"})])])]),m("mjx-mo",{class:"mjx-n"},[m("mjx-c",{class:"mjx-c28"})]),m("mjx-TeXAtom",{texclass:"ORD"},[m("mjx-mi",{class:"mjx-b"},[m("mjx-c",{class:"mjx-c1D431 TEX-B"})])]),m("mjx-mo",{class:"mjx-n"},[m("mjx-c",{class:"mjx-c2C"})]),m("mjx-TeXAtom",{space:"2",texclass:"ORD"},[m("mjx-mover",null,[m("mjx-over",{style:{"padding-bottom":"0.105em","padding-left":"0.524em","margin-bottom":"-0.516em"}},[m("mjx-mo",{class:"mjx-n",style:{width:"0","margin-left":"-0.25em"}},[m("mjx-c",{class:"mjx-c20D7 TEX-V"})])]),m("mjx-base",null,[m("mjx-msub",null,[m("mjx-mi",{class:"mjx-i"},[m("mjx-c",{class:"mjx-c1D714 TEX-I"})]),m("mjx-script",{style:{"vertical-align":"-0.15em"}},[m("mjx-mi",{class:"mjx-i",size:"s"},[m("mjx-c",{class:"mjx-c1D45C TEX-I"})])])])])])]),m("mjx-mo",{class:"mjx-n"},[m("mjx-c",{class:"mjx-c2C"})]),m("mjx-mi",{class:"mjx-i",space:"2"},[m("mjx-c",{class:"mjx-c1D706 TEX-I"})]),m("mjx-mo",{class:"mjx-n"},[m("mjx-c",{class:"mjx-c2C"})]),m("mjx-mi",{class:"mjx-i",space:"2"},[m("mjx-c",{class:"mjx-c1D461 TEX-I"})]),m("mjx-mo",{class:"mjx-n"},[m("mjx-c",{class:"mjx-c29"})]),m("mjx-mo",{class:"mjx-n",space:"3"},[m("mjx-c",{class:"mjx-c2B"})]),m("mjx-msub",{space:"3"},[m("mjx-mo",{class:"mjx-lop"},[m("mjx-c",{class:"mjx-c222B TEX-S2"})]),m("mjx-script",{style:{"vertical-align":"-0.896em","margin-left":"-0.388em"}},[m("mjx-TeXAtom",{size:"s",texclass:"ORD"},[m("mjx-mi",{class:"mjx-n"},[m("mjx-c",{class:"mjx-c3A9"})])])])]),m("mjx-mi",{class:"mjx-i",space:"2"},[m("mjx-c",{class:"mjx-c1D453 TEX-I"})]),m("mjx-mo",{class:"mjx-n"},[m("mjx-c",{class:"mjx-c28"})]),m("mjx-TeXAtom",{texclass:"ORD"},[m("mjx-mi",{class:"mjx-b"},[m("mjx-c",{class:"mjx-c1D431 TEX-B"})])]),m("mjx-mo",{class:"mjx-n"},[m("mjx-c",{class:"mjx-c2C"})]),m("mjx-TeXAtom",{space:"2",texclass:"ORD"},[m("mjx-mover",null,[m("mjx-over",{style:{"padding-bottom":"0.105em","padding-left":"0.474em","margin-bottom":"-0.516em"}},[m("mjx-mo",{class:"mjx-n",style:{width:"0","margin-left":"-0.25em"}},[m("mjx-c",{class:"mjx-c20D7 TEX-V"})])]),m("mjx-base",null,[m("mjx-msub",null,[m("mjx-mi",{class:"mjx-i"},[m("mjx-c",{class:"mjx-c1D714 TEX-I"})]),m("mjx-script",{style:{"vertical-align":"-0.15em"}},[m("mjx-mi",{class:"mjx-i",size:"s"},[m("mjx-c",{class:"mjx-c1D456 TEX-I"})])])])])])]),m("mjx-mo",{class:"mjx-n"},[m("mjx-c",{class:"mjx-c2C"})]),m("mjx-TeXAtom",{space:"2",texclass:"ORD"},[m("mjx-mover",null,[m("mjx-over",{style:{"padding-bottom":"0.105em","padding-left":"0.524em","margin-bottom":"-0.516em"}},[m("mjx-mo",{class:"mjx-n",style:{width:"0","margin-left":"-0.25em"}},[m("mjx-c",{class:"mjx-c20D7 TEX-V"})])]),m("mjx-base",null,[m("mjx-msub",null,[m("mjx-mi",{class:"mjx-i"},[m("mjx-c",{class:"mjx-c1D714 TEX-I"})]),m("mjx-script",{style:{"vertical-align":"-0.15em"}},[m("mjx-mi",{class:"mjx-i",size:"s"},[m("mjx-c",{class:"mjx-c1D45C TEX-I"})])])])])])]),m("mjx-mo",{class:"mjx-n"},[m("mjx-c",{class:"mjx-c2C"})]),m("mjx-mi",{class:"mjx-i",space:"2"},[m("mjx-c",{class:"mjx-c1D706 TEX-I"})]),m("mjx-mo",{class:"mjx-n"},[m("mjx-c",{class:"mjx-c2C"})]),m("mjx-mi",{class:"mjx-i",space:"2"},[m("mjx-c",{class:"mjx-c1D461 TEX-I"})]),m("mjx-mo",{class:"mjx-n"},[m("mjx-c",{class:"mjx-c29"})]),m("mjx-msub",null,[m("mjx-mi",{class:"mjx-i"},[m("mjx-c",{class:"mjx-c1D43F TEX-I"})]),m("mjx-script",{style:{"vertical-align":"-0.15em"}},[m("mjx-mi",{class:"mjx-i",size:"s"},[m("mjx-c",{class:"mjx-c1D456 TEX-I"})])])]),m("mjx-mo",{class:"mjx-n"},[m("mjx-c",{class:"mjx-c28"})]),m("mjx-TeXAtom",{texclass:"ORD"},[m("mjx-mi",{class:"mjx-b"},[m("mjx-c",{class:"mjx-c1D431 TEX-B"})])]),m("mjx-mo",{class:"mjx-n"},[m("mjx-c",{class:"mjx-c2C"})]),m("mjx-TeXAtom",{space:"2",texclass:"ORD"},[m("mjx-mover",null,[m("mjx-over",{style:{"padding-bottom":"0.105em","padding-left":"0.474em","margin-bottom":"-0.516em"}},[m("mjx-mo",{class:"mjx-n",style:{width:"0","margin-left":"-0.25em"}},[m("mjx-c",{class:"mjx-c20D7 TEX-V"})])]),m("mjx-base",null,[m("mjx-msub",null,[m("mjx-mi",{class:"mjx-i"},[m("mjx-c",{class:"mjx-c1D714 TEX-I"})]),m("mjx-script",{style:{"vertical-align":"-0.15em"}},[m("mjx-mi",{class:"mjx-i",size:"s"},[m("mjx-c",{class:"mjx-c1D456 TEX-I"})])])])])])]),m("mjx-mo",{class:"mjx-n"},[m("mjx-c",{class:"mjx-c2C"})]),m("mjx-mi",{class:"mjx-i",space:"2"},[m("mjx-c",{class:"mjx-c1D706 TEX-I"})]),m("mjx-mo",{class:"mjx-n"},[m("mjx-c",{class:"mjx-c2C"})]),m("mjx-mi",{class:"mjx-i",space:"2"},[m("mjx-c",{class:"mjx-c1D461 TEX-I"})]),m("mjx-mo",{class:"mjx-n"},[m("mjx-c",{class:"mjx-c29"})]),m("mjx-mo",{class:"mjx-n"},[m("mjx-c",{class:"mjx-c28"})]),m("mjx-TeXAtom",{texclass:"ORD"},[m("mjx-mover",null,[m("mjx-over",{style:{"padding-bottom":"0.105em","padding-left":"0.474em","margin-bottom":"-0.516em"}},[m("mjx-mo",{class:"mjx-n",style:{width:"0","margin-left":"-0.25em"}},[m("mjx-c",{class:"mjx-c20D7 TEX-V"})])]),m("mjx-base",null,[m("mjx-msub",null,[m("mjx-mi",{class:"mjx-i"},[m("mjx-c",{class:"mjx-c1D714 TEX-I"})]),m("mjx-script",{style:{"vertical-align":"-0.15em"}},[m("mjx-mi",{class:"mjx-i",size:"s"},[m("mjx-c",{class:"mjx-c1D456 TEX-I"})])])])])])]),m("mjx-mo",{class:"mjx-n",space:"3"},[m("mjx-c",{class:"mjx-c22C5"})]),m("mjx-TeXAtom",{space:"3",texclass:"ORD"},[m("mjx-mover",null,[m("mjx-over",{style:{"padding-bottom":"0.105em","padding-left":"0.32em","margin-bottom":"-0.516em"}},[m("mjx-mo",{class:"mjx-n",style:{width:"0","margin-left":"-0.25em"}},[m("mjx-c",{class:"mjx-c20D7 TEX-V"})])]),m("mjx-base",null,[m("mjx-TeXAtom",{texclass:"ORD"},[m("mjx-mi",{class:"mjx-b"},[m("mjx-c",{class:"mjx-c1D427 TEX-B"})])])])])]),m("mjx-mo",{class:"mjx-n"},[m("mjx-c",{class:"mjx-c29"})]),m("mjx-mi",{class:"mjx-i"},[m("mjx-c",{class:"mjx-c1D451 TEX-I"})]),m("mjx-msub",null,[m("mjx-mi",{class:"mjx-i"},[m("mjx-c",{class:"mjx-c1D714 TEX-I"})]),m("mjx-script",{style:{"vertical-align":"-0.15em"}},[m("mjx-mi",{class:"mjx-i",size:"s"},[m("mjx-c",{class:"mjx-c1D456 TEX-I"})])])])]),m("mjx-assistive-mml",{unselectable:"on",display:"block"},[m("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[m("msub",null,[m("mi",null,"L"),m("mi",null,"o")]),m("mo",{stretchy:"false"},"("),m("mrow",{"data-mjx-texclass":"ORD"},[m("mi",{mathvariant:"bold"},"x")]),m("mo",null,","),m("mrow",{"data-mjx-texclass":"ORD"},[m("mover",null,[m("msub",null,[m("mi",null,"ω"),m("mi",null,"o")]),m("mo",{stretchy:"false"},"→")])]),m("mo",null,","),m("mi",null,"λ"),m("mo",null,","),m("mi",null,"t"),m("mo",{stretchy:"false"},")"),m("mo",null,"="),m("msub",null,[m("mi",null,"L"),m("mi",null,"e")]),m("mo",{stretchy:"false"},"("),m("mrow",{"data-mjx-texclass":"ORD"},[m("mi",{mathvariant:"bold"},"x")]),m("mo",null,","),m("mrow",{"data-mjx-texclass":"ORD"},[m("mover",null,[m("msub",null,[m("mi",null,"ω"),m("mi",null,"o")]),m("mo",{stretchy:"false"},"→")])]),m("mo",null,","),m("mi",null,"λ"),m("mo",null,","),m("mi",null,"t"),m("mo",{stretchy:"false"},")"),m("mo",null,"+"),m("msub",null,[m("mo",{"data-mjx-texclass":"OP"},"∫"),m("mrow",{"data-mjx-texclass":"ORD"},[m("mi",{mathvariant:"normal"},"Ω")])]),m("mi",null,"f"),m("mo",{stretchy:"false"},"("),m("mrow",{"data-mjx-texclass":"ORD"},[m("mi",{mathvariant:"bold"},"x")]),m("mo",null,","),m("mrow",{"data-mjx-texclass":"ORD"},[m("mover",null,[m("msub",null,[m("mi",null,"ω"),m("mi",null,"i")]),m("mo",{stretchy:"false"},"→")])]),m("mo",null,","),m("mrow",{"data-mjx-texclass":"ORD"},[m("mover",null,[m("msub",null,[m("mi",null,"ω"),m("mi",null,"o")]),m("mo",{stretchy:"false"},"→")])]),m("mo",null,","),m("mi",null,"λ"),m("mo",null,","),m("mi",null,"t"),m("mo",{stretchy:"false"},")"),m("msub",null,[m("mi",null,"L"),m("mi",null,"i")]),m("mo",{stretchy:"false"},"("),m("mrow",{"data-mjx-texclass":"ORD"},[m("mi",{mathvariant:"bold"},"x")]),m("mo",null,","),m("mrow",{"data-mjx-texclass":"ORD"},[m("mover",null,[m("msub",null,[m("mi",null,"ω"),m("mi",null,"i")]),m("mo",{stretchy:"false"},"→")])]),m("mo",null,","),m("mi",null,"λ"),m("mo",null,","),m("mi",null,"t"),m("mo",{stretchy:"false"},")"),m("mo",{stretchy:"false"},"("),m("mrow",{"data-mjx-texclass":"ORD"},[m("mover",null,[m("msub",null,[m("mi",null,"ω"),m("mi",null,"i")]),m("mo",{stretchy:"false"},"→")])]),m("mo",null,"⋅"),m("mrow",{"data-mjx-texclass":"ORD"},[m("mover",null,[m("mrow",{"data-mjx-texclass":"ORD"},[m("mi",{mathvariant:"bold"},"n")]),m("mo",{stretchy:"false"},"→")])]),m("mo",{stretchy:"false"},")"),m("mi",null,"d"),m("msub",null,[m("mi",null,"ω"),m("mi",null,"i")])])])],-1),m("h2",{id:"_2-反射方程分解",tabindex:"-1"},[m("a",{class:"header-anchor",href:"#_2-反射方程分解"},[m("span",null,"2. 反射方程分解")])],-1),m("p",null,[s("根据前面的微表面理论分析，入射光能量在材质表面分解为两部分，高光反射部分，比例为"),m("mjx-container",{class:"MathJax",jax:"CHTML",style:{position:"relative"}},[m("mjx-math",{class:"MJX-TEX","aria-hidden":"true"},[m("mjx-msub",null,[m("mjx-mi",{class:"mjx-i"},[m("mjx-c",{class:"mjx-c1D458 TEX-I"})]),m("mjx-script",{style:{"vertical-align":"-0.15em"}},[m("mjx-mi",{class:"mjx-i",size:"s"},[m("mjx-c",{class:"mjx-c1D460 TEX-I"})])])]),m("mjx-mo",{class:"mjx-n",space:"4"},[m("mjx-c",{class:"mjx-c3D"})]),m("mjx-mi",{class:"mjx-i",space:"4"},[m("mjx-c",{class:"mjx-c1D439 TEX-I"})])]),m("mjx-assistive-mml",{unselectable:"on",display:"inline"},[m("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[m("msub",null,[m("mi",null,"k"),m("mi",null,"s")]),m("mo",null,"="),m("mi",null,"F")])])]),s("，折射到材质内部的部分，比例为"),m("mjx-container",{class:"MathJax",jax:"CHTML",style:{position:"relative"}},[m("mjx-math",{class:"MJX-TEX","aria-hidden":"true"},[m("mjx-mn",{class:"mjx-n"},[m("mjx-c",{class:"mjx-c31"})]),m("mjx-mo",{class:"mjx-n",space:"3"},[m("mjx-c",{class:"mjx-c2212"})]),m("mjx-mi",{class:"mjx-i",space:"3"},[m("mjx-c",{class:"mjx-c1D439 TEX-I"})])]),m("mjx-assistive-mml",{unselectable:"on",display:"inline"},[m("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[m("mn",null,"1"),m("mo",null,"−"),m("mi",null,"F")])])]),s("，这部分能量一部分在材质内部转换为其他能量消失掉（对于金属材质为全部），一部分重新从表面发射出去，称为漫反射，所以漫反射的比例为"),m("mjx-container",{class:"MathJax",jax:"CHTML",style:{position:"relative"}},[m("mjx-math",{class:"MJX-TEX","aria-hidden":"true"},[m("mjx-msub",null,[m("mjx-mi",{class:"mjx-i"},[m("mjx-c",{class:"mjx-c1D458 TEX-I"})]),m("mjx-script",{style:{"vertical-align":"-0.15em"}},[m("mjx-mi",{class:"mjx-i",size:"s"},[m("mjx-c",{class:"mjx-c1D460 TEX-I"})])])]),m("mjx-mo",{class:"mjx-n",space:"4"},[m("mjx-c",{class:"mjx-c3D"})]),m("mjx-mo",{class:"mjx-n",space:"4"},[m("mjx-c",{class:"mjx-c28"})]),m("mjx-mn",{class:"mjx-n"},[m("mjx-c",{class:"mjx-c31"})]),m("mjx-mo",{class:"mjx-n",space:"3"},[m("mjx-c",{class:"mjx-c2212"})]),m("mjx-mi",{class:"mjx-i",space:"3"},[m("mjx-c",{class:"mjx-c1D439 TEX-I"})]),m("mjx-mo",{class:"mjx-n"},[m("mjx-c",{class:"mjx-c29"})]),m("mjx-mo",{class:"mjx-n"},[m("mjx-c",{class:"mjx-c28"})]),m("mjx-mn",{class:"mjx-n"},[m("mjx-c",{class:"mjx-c31"})]),m("mjx-mo",{class:"mjx-n",space:"3"},[m("mjx-c",{class:"mjx-c2212"})]),m("mjx-mi",{class:"mjx-i",space:"3"},[m("mjx-c",{class:"mjx-c1D440 TEX-I"})]),m("mjx-mo",{class:"mjx-n"},[m("mjx-c",{class:"mjx-c29"})])]),m("mjx-assistive-mml",{unselectable:"on",display:"inline"},[m("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[m("msub",null,[m("mi",null,"k"),m("mi",null,"s")]),m("mo",null,"="),m("mo",{stretchy:"false"},"("),m("mn",null,"1"),m("mo",null,"−"),m("mi",null,"F"),m("mo",{stretchy:"false"},")"),m("mo",{stretchy:"false"},"("),m("mn",null,"1"),m("mo",null,"−"),m("mi",null,"M"),m("mo",{stretchy:"false"},")")])])]),s("，其中"),m("mjx-container",{class:"MathJax",jax:"CHTML",style:{position:"relative"}},[m("mjx-math",{class:"MJX-TEX","aria-hidden":"true"},[m("mjx-mi",{class:"mjx-i"},[m("mjx-c",{class:"mjx-c1D440 TEX-I"})])]),m("mjx-assistive-mml",{unselectable:"on",display:"inline"},[m("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[m("mi",null,"M")])])]),s("表示金属度，范围从0到1，所以可以将反射方程中的BRDF分解为两部分")],-1),m("mjx-container",{class:"MathJax",jax:"CHTML",display:"true",style:{position:"relative"}},[m("mjx-math",{display:"true",style:{"margin-left":"0","margin-right":"0"},class:"MJX-TEX","aria-hidden":"true"},[m("mjx-mi",{class:"mjx-i"},[m("mjx-c",{class:"mjx-c1D453 TEX-I"})]),m("mjx-mo",{class:"mjx-n"},[m("mjx-c",{class:"mjx-c28"})]),m("mjx-TeXAtom",{texclass:"ORD"},[m("mjx-mover",null,[m("mjx-over",{style:{"padding-bottom":"0.105em","padding-left":"0.474em","margin-bottom":"-0.516em"}},[m("mjx-mo",{class:"mjx-n",style:{width:"0","margin-left":"-0.25em"}},[m("mjx-c",{class:"mjx-c20D7 TEX-V"})])]),m("mjx-base",null,[m("mjx-msub",null,[m("mjx-mi",{class:"mjx-i"},[m("mjx-c",{class:"mjx-c1D714 TEX-I"})]),m("mjx-script",{style:{"vertical-align":"-0.15em"}},[m("mjx-mi",{class:"mjx-i",size:"s"},[m("mjx-c",{class:"mjx-c1D456 TEX-I"})])])])])])]),m("mjx-mo",{class:"mjx-n"},[m("mjx-c",{class:"mjx-c2C"})]),m("mjx-TeXAtom",{space:"2",texclass:"ORD"},[m("mjx-mover",null,[m("mjx-over",{style:{"padding-bottom":"0.105em","padding-left":"0.524em","margin-bottom":"-0.516em"}},[m("mjx-mo",{class:"mjx-n",style:{width:"0","margin-left":"-0.25em"}},[m("mjx-c",{class:"mjx-c20D7 TEX-V"})])]),m("mjx-base",null,[m("mjx-msub",null,[m("mjx-mi",{class:"mjx-i"},[m("mjx-c",{class:"mjx-c1D714 TEX-I"})]),m("mjx-script",{style:{"vertical-align":"-0.15em"}},[m("mjx-mi",{class:"mjx-i",size:"s"},[m("mjx-c",{class:"mjx-c1D45C TEX-I"})])])])])])]),m("mjx-mo",{class:"mjx-n"},[m("mjx-c",{class:"mjx-c29"})]),m("mjx-mo",{class:"mjx-n",space:"4"},[m("mjx-c",{class:"mjx-c3D"})]),m("mjx-msub",{space:"4"},[m("mjx-mi",{class:"mjx-i"},[m("mjx-c",{class:"mjx-c1D458 TEX-I"})]),m("mjx-script",{style:{"vertical-align":"-0.15em"}},[m("mjx-mi",{class:"mjx-i",size:"s"},[m("mjx-c",{class:"mjx-c1D451 TEX-I"})])])]),m("mjx-msub",null,[m("mjx-mi",{class:"mjx-i"},[m("mjx-c",{class:"mjx-c1D453 TEX-I"})]),m("mjx-script",{style:{"vertical-align":"-0.15em","margin-left":"-0.06em"}},[m("mjx-mi",{class:"mjx-i",size:"s"},[m("mjx-c",{class:"mjx-c1D451 TEX-I"})])])]),m("mjx-mo",{class:"mjx-n"},[m("mjx-c",{class:"mjx-c28"})]),m("mjx-TeXAtom",{texclass:"ORD"},[m("mjx-mover",null,[m("mjx-over",{style:{"padding-bottom":"0.105em","padding-left":"0.474em","margin-bottom":"-0.516em"}},[m("mjx-mo",{class:"mjx-n",style:{width:"0","margin-left":"-0.25em"}},[m("mjx-c",{class:"mjx-c20D7 TEX-V"})])]),m("mjx-base",null,[m("mjx-msub",null,[m("mjx-mi",{class:"mjx-i"},[m("mjx-c",{class:"mjx-c1D714 TEX-I"})]),m("mjx-script",{style:{"vertical-align":"-0.15em"}},[m("mjx-mi",{class:"mjx-i",size:"s"},[m("mjx-c",{class:"mjx-c1D456 TEX-I"})])])])])])]),m("mjx-mo",{class:"mjx-n"},[m("mjx-c",{class:"mjx-c2C"})]),m("mjx-TeXAtom",{space:"2",texclass:"ORD"},[m("mjx-mover",null,[m("mjx-over",{style:{"padding-bottom":"0.105em","padding-left":"0.524em","margin-bottom":"-0.516em"}},[m("mjx-mo",{class:"mjx-n",style:{width:"0","margin-left":"-0.25em"}},[m("mjx-c",{class:"mjx-c20D7 TEX-V"})])]),m("mjx-base",null,[m("mjx-msub",null,[m("mjx-mi",{class:"mjx-i"},[m("mjx-c",{class:"mjx-c1D714 TEX-I"})]),m("mjx-script",{style:{"vertical-align":"-0.15em"}},[m("mjx-mi",{class:"mjx-i",size:"s"},[m("mjx-c",{class:"mjx-c1D45C TEX-I"})])])])])])]),m("mjx-mo",{class:"mjx-n"},[m("mjx-c",{class:"mjx-c29"})]),m("mjx-mo",{class:"mjx-n",space:"3"},[m("mjx-c",{class:"mjx-c2B"})]),m("mjx-msub",{space:"3"},[m("mjx-mi",{class:"mjx-i"},[m("mjx-c",{class:"mjx-c1D458 TEX-I"})]),m("mjx-script",{style:{"vertical-align":"-0.15em"}},[m("mjx-mi",{class:"mjx-i",size:"s"},[m("mjx-c",{class:"mjx-c1D460 TEX-I"})])])]),m("mjx-msub",null,[m("mjx-mi",{class:"mjx-i"},[m("mjx-c",{class:"mjx-c1D453 TEX-I"})]),m("mjx-script",{style:{"vertical-align":"-0.15em","margin-left":"-0.06em"}},[m("mjx-mi",{class:"mjx-i",size:"s"},[m("mjx-c",{class:"mjx-c1D460 TEX-I"})])])]),m("mjx-mo",{class:"mjx-n"},[m("mjx-c",{class:"mjx-c28"})]),m("mjx-TeXAtom",{texclass:"ORD"},[m("mjx-mover",null,[m("mjx-over",{style:{"padding-bottom":"0.105em","padding-left":"0.474em","margin-bottom":"-0.516em"}},[m("mjx-mo",{class:"mjx-n",style:{width:"0","margin-left":"-0.25em"}},[m("mjx-c",{class:"mjx-c20D7 TEX-V"})])]),m("mjx-base",null,[m("mjx-msub",null,[m("mjx-mi",{class:"mjx-i"},[m("mjx-c",{class:"mjx-c1D714 TEX-I"})]),m("mjx-script",{style:{"vertical-align":"-0.15em"}},[m("mjx-mi",{class:"mjx-i",size:"s"},[m("mjx-c",{class:"mjx-c1D456 TEX-I"})])])])])])]),m("mjx-mo",{class:"mjx-n"},[m("mjx-c",{class:"mjx-c2C"})]),m("mjx-TeXAtom",{space:"2",texclass:"ORD"},[m("mjx-mover",null,[m("mjx-over",{style:{"padding-bottom":"0.105em","padding-left":"0.524em","margin-bottom":"-0.516em"}},[m("mjx-mo",{class:"mjx-n",style:{width:"0","margin-left":"-0.25em"}},[m("mjx-c",{class:"mjx-c20D7 TEX-V"})])]),m("mjx-base",null,[m("mjx-msub",null,[m("mjx-mi",{class:"mjx-i"},[m("mjx-c",{class:"mjx-c1D714 TEX-I"})]),m("mjx-script",{style:{"vertical-align":"-0.15em"}},[m("mjx-mi",{class:"mjx-i",size:"s"},[m("mjx-c",{class:"mjx-c1D45C TEX-I"})])])])])])]),m("mjx-mo",{class:"mjx-n"},[m("mjx-c",{class:"mjx-c29"})])]),m("mjx-assistive-mml",{unselectable:"on",display:"block"},[m("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[m("mi",null,"f"),m("mo",{stretchy:"false"},"("),m("mrow",{"data-mjx-texclass":"ORD"},[m("mover",null,[m("msub",null,[m("mi",null,"ω"),m("mi",null,"i")]),m("mo",{stretchy:"false"},"→")])]),m("mo",null,","),m("mrow",{"data-mjx-texclass":"ORD"},[m("mover",null,[m("msub",null,[m("mi",null,"ω"),m("mi",null,"o")]),m("mo",{stretchy:"false"},"→")])]),m("mo",{stretchy:"false"},")"),m("mo",null,"="),m("msub",null,[m("mi",null,"k"),m("mi",null,"d")]),m("msub",null,[m("mi",null,"f"),m("mi",null,"d")]),m("mo",{stretchy:"false"},"("),m("mrow",{"data-mjx-texclass":"ORD"},[m("mover",null,[m("msub",null,[m("mi",null,"ω"),m("mi",null,"i")]),m("mo",{stretchy:"false"},"→")])]),m("mo",null,","),m("mrow",{"data-mjx-texclass":"ORD"},[m("mover",null,[m("msub",null,[m("mi",null,"ω"),m("mi",null,"o")]),m("mo",{stretchy:"false"},"→")])]),m("mo",{stretchy:"false"},")"),m("mo",null,"+"),m("msub",null,[m("mi",null,"k"),m("mi",null,"s")]),m("msub",null,[m("mi",null,"f"),m("mi",null,"s")]),m("mo",{stretchy:"false"},"("),m("mrow",{"data-mjx-texclass":"ORD"},[m("mover",null,[m("msub",null,[m("mi",null,"ω"),m("mi",null,"i")]),m("mo",{stretchy:"false"},"→")])]),m("mo",null,","),m("mrow",{"data-mjx-texclass":"ORD"},[m("mover",null,[m("msub",null,[m("mi",null,"ω"),m("mi",null,"o")]),m("mo",{stretchy:"false"},"→")])]),m("mo",{stretchy:"false"},")")])])],-1),m("h2",{id:"_3-lambert漫反射模型",tabindex:"-1"},[m("a",{class:"header-anchor",href:"#_3-lambert漫反射模型"},[m("span",null,"3. Lambert漫反射模型")])],-1),m("p",null,[m("a",{href:"https://zhuanlan.zhihu.com/p/21489591",target:"_blank",rel:"noopener noreferrer"},"参考"),s(" Lambert模型认为，材质的漫反射是均匀发射到所有方向的，所以"),m("mjx-container",{class:"MathJax",jax:"CHTML",style:{position:"relative"}},[m("mjx-math",{class:"MJX-TEX","aria-hidden":"true"},[m("mjx-msub",null,[m("mjx-mi",{class:"mjx-i"},[m("mjx-c",{class:"mjx-c1D453 TEX-I"})]),m("mjx-script",{style:{"vertical-align":"-0.15em","margin-left":"-0.06em"}},[m("mjx-mi",{class:"mjx-i",size:"s"},[m("mjx-c",{class:"mjx-c1D451 TEX-I"})])])])]),m("mjx-assistive-mml",{unselectable:"on",display:"inline"},[m("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[m("msub",null,[m("mi",null,"f"),m("mi",null,"d")])])])]),s("是一个常数，先设想一个最简单的情况，材质只有漫反射，也就是"),m("mjx-container",{class:"MathJax",jax:"CHTML",style:{position:"relative"}},[m("mjx-math",{class:"MJX-TEX","aria-hidden":"true"},[m("mjx-msub",null,[m("mjx-mi",{class:"mjx-i"},[m("mjx-c",{class:"mjx-c1D458 TEX-I"})]),m("mjx-script",{style:{"vertical-align":"-0.15em"}},[m("mjx-mi",{class:"mjx-i",size:"s"},[m("mjx-c",{class:"mjx-c1D451 TEX-I"})])])]),m("mjx-mo",{class:"mjx-n",space:"4"},[m("mjx-c",{class:"mjx-c3D"})]),m("mjx-mn",{class:"mjx-n",space:"4"},[m("mjx-c",{class:"mjx-c31"})]),m("mjx-mo",{class:"mjx-n"},[m("mjx-c",{class:"mjx-c2C"})]),m("mjx-msub",{space:"2"},[m("mjx-mi",{class:"mjx-i"},[m("mjx-c",{class:"mjx-c1D458 TEX-I"})]),m("mjx-script",{style:{"vertical-align":"-0.15em"}},[m("mjx-mi",{class:"mjx-i",size:"s"},[m("mjx-c",{class:"mjx-c1D460 TEX-I"})])])]),m("mjx-mo",{class:"mjx-n",space:"4"},[m("mjx-c",{class:"mjx-c3D"})]),m("mjx-mn",{class:"mjx-n",space:"4"},[m("mjx-c",{class:"mjx-c30"})])]),m("mjx-assistive-mml",{unselectable:"on",display:"inline"},[m("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[m("msub",null,[m("mi",null,"k"),m("mi",null,"d")]),m("mo",null,"="),m("mn",null,"1"),m("mo",null,","),m("msub",null,[m("mi",null,"k"),m("mi",null,"s")]),m("mo",null,"="),m("mn",null,"0")])])]),s(",入射光均匀遍布所有的方向，而且每个方向的亮度都是相同的常数。因为这样"),m("mjx-container",{class:"MathJax",jax:"CHTML",style:{position:"relative"}},[m("mjx-math",{class:"MJX-TEX","aria-hidden":"true"},[m("mjx-msub",null,[m("mjx-mi",{class:"mjx-i"},[m("mjx-c",{class:"mjx-c1D453 TEX-I"})]),m("mjx-script",{style:{"vertical-align":"-0.15em","margin-left":"-0.06em"}},[m("mjx-mi",{class:"mjx-i",size:"s"},[m("mjx-c",{class:"mjx-c1D451 TEX-I"})])])])]),m("mjx-assistive-mml",{unselectable:"on",display:"inline"},[m("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[m("msub",null,[m("mi",null,"f"),m("mi",null,"d")])])])]),s("和"),m("mjx-container",{class:"MathJax",jax:"CHTML",style:{position:"relative"}},[m("mjx-math",{class:"MJX-TEX","aria-hidden":"true"},[m("mjx-msub",null,[m("mjx-mi",{class:"mjx-i"},[m("mjx-c",{class:"mjx-c1D43F TEX-I"})]),m("mjx-script",{style:{"vertical-align":"-0.15em"}},[m("mjx-mi",{class:"mjx-i",size:"s"},[m("mjx-c",{class:"mjx-c1D456 TEX-I"})])])])]),m("mjx-assistive-mml",{unselectable:"on",display:"inline"},[m("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[m("msub",null,[m("mi",null,"L"),m("mi",null,"i")])])])]),s("都是常数，可以提到积分外面。反射方程变成")],-1),m("mjx-container",{class:"MathJax",jax:"CHTML",display:"true",style:{position:"relative"}},[m("mjx-math",{display:"true",style:{"margin-left":"0","margin-right":"0"},class:"MJX-TEX","aria-hidden":"true"},[m("mjx-msub",null,[m("mjx-mi",{class:"mjx-i"},[m("mjx-c",{class:"mjx-c1D43F TEX-I"})]),m("mjx-script",{style:{"vertical-align":"-0.15em"}},[m("mjx-mi",{class:"mjx-i",size:"s"},[m("mjx-c",{class:"mjx-c1D45C TEX-I"})])])]),m("mjx-mo",{class:"mjx-n",space:"4"},[m("mjx-c",{class:"mjx-c3D"})]),m("mjx-msub",{space:"4"},[m("mjx-mi",{class:"mjx-i"},[m("mjx-c",{class:"mjx-c1D453 TEX-I"})]),m("mjx-script",{style:{"vertical-align":"-0.15em","margin-left":"-0.06em"}},[m("mjx-mi",{class:"mjx-i",size:"s"},[m("mjx-c",{class:"mjx-c1D451 TEX-I"})])])]),m("mjx-msub",null,[m("mjx-mi",{class:"mjx-i"},[m("mjx-c",{class:"mjx-c1D43F TEX-I"})]),m("mjx-script",{style:{"vertical-align":"-0.15em"}},[m("mjx-mi",{class:"mjx-i",size:"s"},[m("mjx-c",{class:"mjx-c1D456 TEX-I"})])])]),m("mjx-msub",{space:"2"},[m("mjx-mo",{class:"mjx-lop"},[m("mjx-c",{class:"mjx-c222B TEX-S2"})]),m("mjx-script",{style:{"vertical-align":"-0.896em","margin-left":"-0.388em"}},[m("mjx-TeXAtom",{size:"s",texclass:"ORD"},[m("mjx-mi",{class:"mjx-n"},[m("mjx-c",{class:"mjx-c3A9"})])])])]),m("mjx-mi",{class:"mjx-n",space:"2"},[m("mjx-c",{class:"mjx-c63"}),m("mjx-c",{class:"mjx-c6F"}),m("mjx-c",{class:"mjx-c73"})]),m("mjx-mo",{class:"mjx-n"},[m("mjx-c",{class:"mjx-c2061"})]),m("mjx-msub",{space:"2"},[m("mjx-mi",{class:"mjx-i"},[m("mjx-c",{class:"mjx-c1D703 TEX-I"})]),m("mjx-script",{style:{"vertical-align":"-0.15em"}},[m("mjx-mi",{class:"mjx-i",size:"s"},[m("mjx-c",{class:"mjx-c1D456 TEX-I"})])])]),m("mjx-mi",{class:"mjx-i"},[m("mjx-c",{class:"mjx-c1D451 TEX-I"})]),m("mjx-msub",null,[m("mjx-mi",{class:"mjx-i"},[m("mjx-c",{class:"mjx-c1D714 TEX-I"})]),m("mjx-script",{style:{"vertical-align":"-0.15em"}},[m("mjx-mi",{class:"mjx-i",size:"s"},[m("mjx-c",{class:"mjx-c1D456 TEX-I"})])])])]),m("mjx-assistive-mml",{unselectable:"on",display:"block"},[m("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[m("msub",null,[m("mi",null,"L"),m("mi",null,"o")]),m("mo",null,"="),m("msub",null,[m("mi",null,"f"),m("mi",null,"d")]),m("msub",null,[m("mi",null,"L"),m("mi",null,"i")]),m("msub",null,[m("mo",{"data-mjx-texclass":"OP"},"∫"),m("mrow",{"data-mjx-texclass":"ORD"},[m("mi",{mathvariant:"normal"},"Ω")])]),m("mi",null,"cos"),m("mo",{"data-mjx-texclass":"NONE"},""),m("msub",null,[m("mi",null,"θ"),m("mi",null,"i")]),m("mi",null,"d"),m("msub",null,[m("mi",null,"ω"),m("mi",null,"i")])])])],-1),m("p",null,"计算这个半球积分",-1),m("mjx-container",{class:"MathJax",jax:"CHTML",display:"true",style:{position:"relative"}},[m("mjx-math",{display:"true",style:{"margin-left":"0","margin-right":"0"},class:"MJX-TEX","aria-hidden":"true"},[m("mjx-mstyle",null,[m("mjx-TeXAtom",{texclass:"ORD"},[m("mjx-msub",null,[m("mjx-mo",{class:"mjx-lop"},[m("mjx-c",{class:"mjx-c222B TEX-S2"})]),m("mjx-script",{style:{"vertical-align":"-0.896em","margin-left":"-0.388em"}},[m("mjx-TeXAtom",{size:"s",texclass:"ORD"},[m("mjx-mi",{class:"mjx-n"},[m("mjx-c",{class:"mjx-c3A9"})])])])]),m("mjx-mi",{class:"mjx-n",space:"2"},[m("mjx-c",{class:"mjx-c63"}),m("mjx-c",{class:"mjx-c6F"}),m("mjx-c",{class:"mjx-c73"})]),m("mjx-mo",{class:"mjx-n"},[m("mjx-c",{class:"mjx-c2061"})]),m("mjx-mi",{class:"mjx-i",space:"2"},[m("mjx-c",{class:"mjx-c1D703 TEX-I"})]),m("mjx-mi",{class:"mjx-i"},[m("mjx-c",{class:"mjx-c1D451 TEX-I"})]),m("mjx-mi",{class:"mjx-i"},[m("mjx-c",{class:"mjx-c1D714 TEX-I"})]),m("mjx-mo",{class:"mjx-n",space:"4"},[m("mjx-c",{class:"mjx-c3D"})]),m("mjx-msubsup",{space:"4"},[m("mjx-mo",{class:"mjx-lop"},[m("mjx-c",{class:"mjx-c222B TEX-S2"})]),m("mjx-script",{style:{"vertical-align":"-0.896em","margin-left":"-0.388em"}},[m("mjx-TeXAtom",{size:"s",texclass:"ORD",style:{"margin-left":"0.647em"}},[m("mjx-mi",{class:"mjx-i"},[m("mjx-c",{class:"mjx-c1D70B TEX-I"})])]),m("mjx-spacer",{style:{"margin-top":"1.564em"}}),m("mjx-TeXAtom",{size:"s",texclass:"ORD"},[m("mjx-mo",{class:"mjx-n"},[m("mjx-c",{class:"mjx-c2212"})]),m("mjx-mi",{class:"mjx-i"},[m("mjx-c",{class:"mjx-c1D70B TEX-I"})])])])]),m("mjx-msubsup",{space:"2"},[m("mjx-mo",{class:"mjx-lop"},[m("mjx-c",{class:"mjx-c222B TEX-S2"})]),m("mjx-script",{style:{"vertical-align":"-0.896em","margin-left":"-0.388em"}},[m("mjx-TeXAtom",{size:"s",texclass:"ORD",style:{"margin-left":"0.647em"}},[m("mjx-mi",{class:"mjx-i"},[m("mjx-c",{class:"mjx-c1D70B TEX-I"})]),m("mjx-TeXAtom",{texclass:"ORD"},[m("mjx-mo",{class:"mjx-n"},[m("mjx-c",{class:"mjx-c2F"})])]),m("mjx-mn",{class:"mjx-n"},[m("mjx-c",{class:"mjx-c32"})])]),m("mjx-spacer",{style:{"margin-top":"1.337em"}}),m("mjx-TeXAtom",{size:"s",texclass:"ORD"},[m("mjx-mn",{class:"mjx-n"},[m("mjx-c",{class:"mjx-c30"})])])])])]),m("mjx-mi",{class:"mjx-n",space:"2"},[m("mjx-c",{class:"mjx-c73"}),m("mjx-c",{class:"mjx-c69"}),m("mjx-c",{class:"mjx-c6E"})]),m("mjx-mo",{class:"mjx-n"},[m("mjx-c",{class:"mjx-c2061"})]),m("mjx-mo",{class:"mjx-n"},[m("mjx-c",{class:"mjx-c28"})]),m("mjx-mi",{class:"mjx-i"},[m("mjx-c",{class:"mjx-c1D703 TEX-I"})]),m("mjx-mo",{class:"mjx-n"},[m("mjx-c",{class:"mjx-c29"})]),m("mjx-mi",{class:"mjx-n",space:"2"},[m("mjx-c",{class:"mjx-c63"}),m("mjx-c",{class:"mjx-c6F"}),m("mjx-c",{class:"mjx-c73"})]),m("mjx-mo",{class:"mjx-n"},[m("mjx-c",{class:"mjx-c2061"})]),m("mjx-mo",{class:"mjx-n"},[m("mjx-c",{class:"mjx-c28"})]),m("mjx-mi",{class:"mjx-i"},[m("mjx-c",{class:"mjx-c1D703 TEX-I"})]),m("mjx-mo",{class:"mjx-n"},[m("mjx-c",{class:"mjx-c29"})]),m("mjx-mi",{class:"mjx-i"},[m("mjx-c",{class:"mjx-c1D451 TEX-I"})]),m("mjx-mi",{class:"mjx-i"},[m("mjx-c",{class:"mjx-c1D703 TEX-I"})]),m("mjx-mi",{class:"mjx-i"},[m("mjx-c",{class:"mjx-c1D451 TEX-I"})]),m("mjx-mi",{class:"mjx-i"},[m("mjx-c",{class:"mjx-c1D719 TEX-I"})]),m("mjx-mo",{class:"mjx-n",space:"4"},[m("mjx-c",{class:"mjx-c3D"})]),m("mjx-mi",{class:"mjx-i",space:"4"},[m("mjx-c",{class:"mjx-c1D70B TEX-I"})])])]),m("mjx-assistive-mml",{unselectable:"on",display:"block"},[m("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[m("mstyle",{displaystyle:"true",scriptlevel:"0"},[m("mrow",{"data-mjx-texclass":"ORD"},[m("msub",null,[m("mo",{"data-mjx-texclass":"OP"},"∫"),m("mrow",{"data-mjx-texclass":"ORD"},[m("mi",{mathvariant:"normal"},"Ω")])]),m("mi",null,"cos"),m("mo",{"data-mjx-texclass":"NONE"},""),m("mi",null,"θ"),m("mi",null,"d"),m("mi",null,"ω"),m("mo",null,"="),m("msubsup",null,[m("mo",{"data-mjx-texclass":"OP"},"∫"),m("mrow",{"data-mjx-texclass":"ORD"},[m("mo",null,"−"),m("mi",null,"π")]),m("mrow",{"data-mjx-texclass":"ORD"},[m("mi",null,"π")])]),m("msubsup",null,[m("mo",{"data-mjx-texclass":"OP"},"∫"),m("mrow",{"data-mjx-texclass":"ORD"},[m("mn",null,"0")]),m("mrow",{"data-mjx-texclass":"ORD"},[m("mi",null,"π"),m("mrow",{"data-mjx-texclass":"ORD"},[m("mo",null,"/")]),m("mn",null,"2")])])]),m("mi",null,"sin"),m("mo",{"data-mjx-texclass":"NONE"},""),m("mo",{stretchy:"false"},"("),m("mi",null,"θ"),m("mo",{stretchy:"false"},")"),m("mi",null,"cos"),m("mo",{"data-mjx-texclass":"NONE"},""),m("mo",{stretchy:"false"},"("),m("mi",null,"θ"),m("mo",{stretchy:"false"},")"),m("mi",null,"d"),m("mi",null,"θ"),m("mi",null,"d"),m("mi",null,"ϕ"),m("mo",null,"="),m("mi",null,"π")])])])],-1),m("p",null,"得到",-1),m("mjx-container",{class:"MathJax",jax:"CHTML",display:"true",style:{position:"relative"}},[m("mjx-math",{display:"true",style:{"margin-left":"0","margin-right":"0"},class:"MJX-TEX","aria-hidden":"true"},[m("mjx-msub",null,[m("mjx-mi",{class:"mjx-i"},[m("mjx-c",{class:"mjx-c1D43F TEX-I"})]),m("mjx-script",{style:{"vertical-align":"-0.15em"}},[m("mjx-mi",{class:"mjx-i",size:"s"},[m("mjx-c",{class:"mjx-c1D45C TEX-I"})])])]),m("mjx-mo",{class:"mjx-n",space:"4"},[m("mjx-c",{class:"mjx-c3D"})]),m("mjx-msub",{space:"4"},[m("mjx-mi",{class:"mjx-i"},[m("mjx-c",{class:"mjx-c1D453 TEX-I"})]),m("mjx-script",{style:{"vertical-align":"-0.15em","margin-left":"-0.06em"}},[m("mjx-mi",{class:"mjx-i",size:"s"},[m("mjx-c",{class:"mjx-c1D451 TEX-I"})])])]),m("mjx-msub",null,[m("mjx-mi",{class:"mjx-i"},[m("mjx-c",{class:"mjx-c1D43F TEX-I"})]),m("mjx-script",{style:{"vertical-align":"-0.15em"}},[m("mjx-mi",{class:"mjx-i",size:"s"},[m("mjx-c",{class:"mjx-c1D456 TEX-I"})])])]),m("mjx-mi",{class:"mjx-i"},[m("mjx-c",{class:"mjx-c1D70B TEX-I"})])]),m("mjx-assistive-mml",{unselectable:"on",display:"block"},[m("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[m("msub",null,[m("mi",null,"L"),m("mi",null,"o")]),m("mo",null,"="),m("msub",null,[m("mi",null,"f"),m("mi",null,"d")]),m("msub",null,[m("mi",null,"L"),m("mi",null,"i")]),m("mi",null,"π")])])],-1),m("p",null,[s("考虑一下，如果所有方向都有射向球面的光，而且每个方向的光强度都等于"),m("mjx-container",{class:"MathJax",jax:"CHTML",style:{position:"relative"}},[m("mjx-math",{class:"MJX-TEX","aria-hidden":"true"},[m("mjx-msub",null,[m("mjx-mi",{class:"mjx-i"},[m("mjx-c",{class:"mjx-c1D43F TEX-I"})]),m("mjx-script",{style:{"vertical-align":"-0.15em"}},[m("mjx-mi",{class:"mjx-i",size:"s"},[m("mjx-c",{class:"mjx-c1D456 TEX-I"})])])])]),m("mjx-assistive-mml",{unselectable:"on",display:"inline"},[m("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[m("msub",null,[m("mi",null,"L"),m("mi",null,"i")])])])]),s("，那么小平面受到的入射光照度，应该等于光强度乘以半球面积。")],-1),m("mjx-container",{class:"MathJax",jax:"CHTML",display:"true",style:{position:"relative"}},[m("mjx-math",{display:"true",style:{"margin-left":"0","margin-right":"0"},class:"MJX-TEX","aria-hidden":"true"},[m("mjx-msub",null,[m("mjx-mi",{class:"mjx-i"},[m("mjx-c",{class:"mjx-c1D438 TEX-I"})]),m("mjx-script",{style:{"vertical-align":"-0.15em","margin-left":"-0.026em"}},[m("mjx-mi",{class:"mjx-i",size:"s"},[m("mjx-c",{class:"mjx-c1D456 TEX-I"})])])]),m("mjx-mo",{class:"mjx-n",space:"4"},[m("mjx-c",{class:"mjx-c3D"})]),m("mjx-mn",{class:"mjx-n",space:"4"},[m("mjx-c",{class:"mjx-c32"})]),m("mjx-mi",{class:"mjx-i"},[m("mjx-c",{class:"mjx-c1D70B TEX-I"})]),m("mjx-msub",null,[m("mjx-mi",{class:"mjx-i"},[m("mjx-c",{class:"mjx-c1D43F TEX-I"})]),m("mjx-script",{style:{"vertical-align":"-0.15em"}},[m("mjx-mi",{class:"mjx-i",size:"s"},[m("mjx-c",{class:"mjx-c1D456 TEX-I"})])])])]),m("mjx-assistive-mml",{unselectable:"on",display:"block"},[m("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[m("msub",null,[m("mi",null,"E"),m("mi",null,"i")]),m("mo",null,"="),m("mn",null,"2"),m("mi",null,"π"),m("msub",null,[m("mi",null,"L"),m("mi",null,"i")])])])],-1),m("p",null,[s("根据能量守恒，光出射度"),m("mjx-container",{class:"MathJax",jax:"CHTML",style:{position:"relative"}},[m("mjx-math",{class:"MJX-TEX","aria-hidden":"true"},[m("mjx-msub",null,[m("mjx-mi",{class:"mjx-i"},[m("mjx-c",{class:"mjx-c1D440 TEX-I"})]),m("mjx-script",{style:{"vertical-align":"-0.15em","margin-left":"-0.081em"}},[m("mjx-mi",{class:"mjx-i",size:"s"},[m("mjx-c",{class:"mjx-c1D45C TEX-I"})])])]),m("mjx-mo",{class:"mjx-n",space:"4"},[m("mjx-c",{class:"mjx-c3D"})]),m("mjx-msub",{space:"4"},[m("mjx-mi",{class:"mjx-i"},[m("mjx-c",{class:"mjx-c1D438 TEX-I"})]),m("mjx-script",{style:{"vertical-align":"-0.15em","margin-left":"-0.026em"}},[m("mjx-mi",{class:"mjx-i",size:"s"},[m("mjx-c",{class:"mjx-c1D456 TEX-I"})])])])]),m("mjx-assistive-mml",{unselectable:"on",display:"inline"},[m("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[m("msub",null,[m("mi",null,"M"),m("mi",null,"o")]),m("mo",null,"="),m("msub",null,[m("mi",null,"E"),m("mi",null,"i")])])])])],-1),m("mjx-container",{class:"MathJax",jax:"CHTML",display:"true",style:{position:"relative"}},[m("mjx-math",{display:"true",style:{"margin-left":"0","margin-right":"0"},class:"MJX-TEX","aria-hidden":"true"},[m("mjx-msub",null,[m("mjx-mi",{class:"mjx-i"},[m("mjx-c",{class:"mjx-c1D440 TEX-I"})]),m("mjx-script",{style:{"vertical-align":"-0.15em","margin-left":"-0.081em"}},[m("mjx-mi",{class:"mjx-i",size:"s"},[m("mjx-c",{class:"mjx-c1D45C TEX-I"})])])]),m("mjx-mo",{class:"mjx-n",space:"4"},[m("mjx-c",{class:"mjx-c3D"})]),m("mjx-mn",{class:"mjx-n",space:"4"},[m("mjx-c",{class:"mjx-c32"})]),m("mjx-mi",{class:"mjx-i"},[m("mjx-c",{class:"mjx-c1D70B TEX-I"})]),m("mjx-msub",null,[m("mjx-mi",{class:"mjx-i"},[m("mjx-c",{class:"mjx-c1D43F TEX-I"})]),m("mjx-script",{style:{"vertical-align":"-0.15em"}},[m("mjx-mi",{class:"mjx-i",size:"s"},[m("mjx-c",{class:"mjx-c1D45C TEX-I"})])])]),m("mjx-mo",{class:"mjx-n",space:"4"},[m("mjx-c",{class:"mjx-c3D"})]),m("mjx-mn",{class:"mjx-n",space:"4"},[m("mjx-c",{class:"mjx-c32"})]),m("mjx-msup",null,[m("mjx-mi",{class:"mjx-i"},[m("mjx-c",{class:"mjx-c1D70B TEX-I"})]),m("mjx-script",{style:{"vertical-align":"0.413em"}},[m("mjx-mn",{class:"mjx-n",size:"s"},[m("mjx-c",{class:"mjx-c32"})])])]),m("mjx-msub",null,[m("mjx-mi",{class:"mjx-i"},[m("mjx-c",{class:"mjx-c1D453 TEX-I"})]),m("mjx-script",{style:{"vertical-align":"-0.15em","margin-left":"-0.06em"}},[m("mjx-mi",{class:"mjx-i",size:"s"},[m("mjx-c",{class:"mjx-c1D451 TEX-I"})])])]),m("mjx-msub",null,[m("mjx-mi",{class:"mjx-i"},[m("mjx-c",{class:"mjx-c1D43F TEX-I"})]),m("mjx-script",{style:{"vertical-align":"-0.15em"}},[m("mjx-mi",{class:"mjx-i",size:"s"},[m("mjx-c",{class:"mjx-c1D456 TEX-I"})])])]),m("mjx-mo",{class:"mjx-n",space:"4"},[m("mjx-c",{class:"mjx-c3D"})]),m("mjx-mn",{class:"mjx-n",space:"4"},[m("mjx-c",{class:"mjx-c32"})]),m("mjx-mi",{class:"mjx-i"},[m("mjx-c",{class:"mjx-c1D70B TEX-I"})]),m("mjx-msub",null,[m("mjx-mi",{class:"mjx-i"},[m("mjx-c",{class:"mjx-c1D43F TEX-I"})]),m("mjx-script",{style:{"vertical-align":"-0.15em"}},[m("mjx-mi",{class:"mjx-i",size:"s"},[m("mjx-c",{class:"mjx-c1D456 TEX-I"})])])])]),m("mjx-assistive-mml",{unselectable:"on",display:"block"},[m("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[m("msub",null,[m("mi",null,"M"),m("mi",null,"o")]),m("mo",null,"="),m("mn",null,"2"),m("mi",null,"π"),m("msub",null,[m("mi",null,"L"),m("mi",null,"o")]),m("mo",null,"="),m("mn",null,"2"),m("msup",null,[m("mi",null,"π"),m("mn",null,"2")]),m("msub",null,[m("mi",null,"f"),m("mi",null,"d")]),m("msub",null,[m("mi",null,"L"),m("mi",null,"i")]),m("mo",null,"="),m("mn",null,"2"),m("mi",null,"π"),m("msub",null,[m("mi",null,"L"),m("mi",null,"i")])])])],-1),m("p",null,"可知",-1),m("mjx-container",{class:"MathJax",jax:"CHTML",display:"true",style:{position:"relative"}},[m("mjx-math",{display:"true",style:{"margin-left":"0","margin-right":"0"},class:"MJX-TEX","aria-hidden":"true"},[m("mjx-msub",null,[m("mjx-mi",{class:"mjx-i"},[m("mjx-c",{class:"mjx-c1D453 TEX-I"})]),m("mjx-script",{style:{"vertical-align":"-0.15em","margin-left":"-0.06em"}},[m("mjx-mi",{class:"mjx-i",size:"s"},[m("mjx-c",{class:"mjx-c1D451 TEX-I"})])])]),m("mjx-mo",{class:"mjx-n",space:"4"},[m("mjx-c",{class:"mjx-c3D"})]),m("mjx-mfrac",{space:"4"},[m("mjx-frac",{type:"d"},[m("mjx-num",null,[m("mjx-nstrut",{type:"d"}),m("mjx-mn",{class:"mjx-n"},[m("mjx-c",{class:"mjx-c31"})])]),m("mjx-dbox",null,[m("mjx-dtable",null,[m("mjx-line",{type:"d"}),m("mjx-row",null,[m("mjx-den",null,[m("mjx-dstrut",{type:"d"}),m("mjx-mi",{class:"mjx-i"},[m("mjx-c",{class:"mjx-c1D70B TEX-I"})])])])])])])])]),m("mjx-assistive-mml",{unselectable:"on",display:"block"},[m("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[m("msub",null,[m("mi",null,"f"),m("mi",null,"d")]),m("mo",null,"="),m("mfrac",null,[m("mn",null,"1"),m("mi",null,"π")])])])],-1),m("p",null,"考虑材质的颜色，在这里颜色可定义为对三原色的吸收比例，比如白色(1,1,1)表示不吸收任何光，红色(1,0,0)表示将绿色和蓝色完全吸收掉，所以最终漫反射的BRDF为",-1),m("mjx-container",{class:"MathJax",jax:"CHTML",display:"true",style:{position:"relative"}},[m("mjx-math",{display:"true",style:{"margin-left":"0","margin-right":"0"},class:"MJX-TEX","aria-hidden":"true"},[m("mjx-msub",null,[m("mjx-mi",{class:"mjx-i"},[m("mjx-c",{class:"mjx-c1D453 TEX-I"})]),m("mjx-script",{style:{"vertical-align":"-0.15em","margin-left":"-0.06em"}},[m("mjx-mi",{class:"mjx-i",size:"s"},[m("mjx-c",{class:"mjx-c1D451 TEX-I"})])])]),m("mjx-mo",{class:"mjx-n",space:"4"},[m("mjx-c",{class:"mjx-c3D"})]),m("mjx-mstyle",{space:"4"},[m("mjx-mfrac",null,[m("mjx-frac",{type:"d"},[m("mjx-num",null,[m("mjx-nstrut",{type:"d"}),m("mjx-mi",{class:"mjx-i"},[m("mjx-c",{class:"mjx-c1D450 TEX-I"})])]),m("mjx-dbox",null,[m("mjx-dtable",null,[m("mjx-line",{type:"d"}),m("mjx-row",null,[m("mjx-den",null,[m("mjx-dstrut",{type:"d"}),m("mjx-mi",{class:"mjx-i"},[m("mjx-c",{class:"mjx-c1D70B TEX-I"})])])])])])])])])]),m("mjx-assistive-mml",{unselectable:"on",display:"block"},[m("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[m("msub",null,[m("mi",null,"f"),m("mi",null,"d")]),m("mo",null,"="),m("mstyle",{displaystyle:"true",scriptlevel:"0"},[m("mfrac",null,[m("mi",null,"c"),m("mi",null,"π")])])])])],-1),m("h2",{id:"_4-最终形式",tabindex:"-1"},[m("a",{class:"header-anchor",href:"#_4-最终形式"},[m("span",null,"4.最终形式")])],-1),m("p",null,"Cook-Torrance模型其实就是一种材质的高光模型，公式",-1),m("mjx-container",{class:"MathJax",jax:"CHTML",display:"true",style:{position:"relative"}},[m("mjx-math",{display:"true",style:{"margin-left":"0","margin-right":"0"},class:"MJX-TEX","aria-hidden":"true"},[m("mjx-msub",null,[m("mjx-mi",{class:"mjx-i"},[m("mjx-c",{class:"mjx-c1D453 TEX-I"})]),m("mjx-script",{style:{"vertical-align":"-0.15em","margin-left":"-0.06em"}},[m("mjx-mi",{class:"mjx-i",size:"s"},[m("mjx-c",{class:"mjx-c1D460 TEX-I"})])])]),m("mjx-mo",{class:"mjx-n",space:"4"},[m("mjx-c",{class:"mjx-c3D"})]),m("mjx-mfrac",{space:"4"},[m("mjx-frac",{type:"d"},[m("mjx-num",null,[m("mjx-nstrut",{type:"d"}),m("mjx-mrow",null,[m("mjx-mi",{class:"mjx-i"},[m("mjx-c",{class:"mjx-c1D437 TEX-I"})]),m("mjx-mi",{class:"mjx-i"},[m("mjx-c",{class:"mjx-c1D43A TEX-I"})]),m("mjx-mi",{class:"mjx-i"},[m("mjx-c",{class:"mjx-c1D439 TEX-I"})])])]),m("mjx-dbox",null,[m("mjx-dtable",null,[m("mjx-line",{type:"d"}),m("mjx-row",null,[m("mjx-den",null,[m("mjx-dstrut",{type:"d"}),m("mjx-mrow",null,[m("mjx-mn",{class:"mjx-n"},[m("mjx-c",{class:"mjx-c34"})]),m("mjx-mo",{class:"mjx-n"},[m("mjx-c",{class:"mjx-c28"})]),m("mjx-TeXAtom",{texclass:"ORD"},[m("mjx-mover",null,[m("mjx-over",{style:{"padding-bottom":"0.105em","padding-left":"0.3em","margin-bottom":"-0.516em"}},[m("mjx-mo",{class:"mjx-n",style:{width:"0","margin-left":"-0.25em"}},[m("mjx-c",{class:"mjx-c20D7 TEX-V"})])]),m("mjx-base",null,[m("mjx-mi",{class:"mjx-i"},[m("mjx-c",{class:"mjx-c1D45B TEX-I"})])])])]),m("mjx-mo",{class:"mjx-n",space:"3"},[m("mjx-c",{class:"mjx-c22C5"})]),m("mjx-msub",{space:"3"},[m("mjx-TeXAtom",{texclass:"ORD"},[m("mjx-mover",null,[m("mjx-over",{style:{"padding-bottom":"0.105em","padding-left":"0.311em","margin-bottom":"-0.516em"}},[m("mjx-mo",{class:"mjx-n",style:{width:"0","margin-left":"-0.25em"}},[m("mjx-c",{class:"mjx-c20D7 TEX-V"})])]),m("mjx-base",null,[m("mjx-mi",{class:"mjx-i"},[m("mjx-c",{class:"mjx-c1D714 TEX-I"})])])])]),m("mjx-script",{style:{"vertical-align":"-0.15em"}},[m("mjx-mi",{class:"mjx-i",size:"s"},[m("mjx-c",{class:"mjx-c1D456 TEX-I"})])])]),m("mjx-mo",{class:"mjx-n"},[m("mjx-c",{class:"mjx-c29"})]),m("mjx-mo",{class:"mjx-n"},[m("mjx-c",{class:"mjx-c28"})]),m("mjx-TeXAtom",{texclass:"ORD"},[m("mjx-mover",null,[m("mjx-over",{style:{"padding-bottom":"0.105em","padding-left":"0.3em","margin-bottom":"-0.516em"}},[m("mjx-mo",{class:"mjx-n",style:{width:"0","margin-left":"-0.25em"}},[m("mjx-c",{class:"mjx-c20D7 TEX-V"})])]),m("mjx-base",null,[m("mjx-mi",{class:"mjx-i"},[m("mjx-c",{class:"mjx-c1D45B TEX-I"})])])])]),m("mjx-mo",{class:"mjx-n",space:"3"},[m("mjx-c",{class:"mjx-c22C5"})]),m("mjx-msub",{space:"3"},[m("mjx-TeXAtom",{texclass:"ORD"},[m("mjx-mover",null,[m("mjx-over",{style:{"padding-bottom":"0.105em","padding-left":"0.311em","margin-bottom":"-0.516em"}},[m("mjx-mo",{class:"mjx-n",style:{width:"0","margin-left":"-0.25em"}},[m("mjx-c",{class:"mjx-c20D7 TEX-V"})])]),m("mjx-base",null,[m("mjx-mi",{class:"mjx-i"},[m("mjx-c",{class:"mjx-c1D714 TEX-I"})])])])]),m("mjx-script",{style:{"vertical-align":"-0.15em"}},[m("mjx-mi",{class:"mjx-i",size:"s"},[m("mjx-c",{class:"mjx-c1D45C TEX-I"})])])]),m("mjx-mo",{class:"mjx-n"},[m("mjx-c",{class:"mjx-c29"})])])])])])])])])]),m("mjx-assistive-mml",{unselectable:"on",display:"block"},[m("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[m("msub",null,[m("mi",null,"f"),m("mi",null,"s")]),m("mo",null,"="),m("mfrac",null,[m("mrow",null,[m("mi",null,"D"),m("mi",null,"G"),m("mi",null,"F")]),m("mrow",null,[m("mn",null,"4"),m("mo",{stretchy:"false"},"("),m("mrow",{"data-mjx-texclass":"ORD"},[m("mover",null,[m("mi",null,"n"),m("mo",{stretchy:"false"},"→")])]),m("mo",null,"⋅"),m("msub",null,[m("mrow",{"data-mjx-texclass":"ORD"},[m("mover",null,[m("mi",null,"ω"),m("mo",{stretchy:"false"},"→")])]),m("mi",null,"i")]),m("mo",{stretchy:"false"},")"),m("mo",{stretchy:"false"},"("),m("mrow",{"data-mjx-texclass":"ORD"},[m("mover",null,[m("mi",null,"n"),m("mo",{stretchy:"false"},"→")])]),m("mo",null,"⋅"),m("msub",null,[m("mrow",{"data-mjx-texclass":"ORD"},[m("mover",null,[m("mi",null,"ω"),m("mo",{stretchy:"false"},"→")])]),m("mi",null,"o")]),m("mo",{stretchy:"false"},")")])])])])],-1),m("p",null,[s("中的"),m("mjx-container",{class:"MathJax",jax:"CHTML",style:{position:"relative"}},[m("mjx-math",{class:"MJX-TEX","aria-hidden":"true"},[m("mjx-mi",{class:"mjx-i"},[m("mjx-c",{class:"mjx-c1D439 TEX-I"})])]),m("mjx-assistive-mml",{unselectable:"on",display:"inline"},[m("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[m("mi",null,"F")])])]),s("就是高光反射的分量比例"),m("mjx-container",{class:"MathJax",jax:"CHTML",style:{position:"relative"}},[m("mjx-math",{class:"MJX-TEX","aria-hidden":"true"},[m("mjx-msub",null,[m("mjx-mi",{class:"mjx-i"},[m("mjx-c",{class:"mjx-c1D458 TEX-I"})]),m("mjx-script",{style:{"vertical-align":"-0.15em"}},[m("mjx-mi",{class:"mjx-i",size:"s"},[m("mjx-c",{class:"mjx-c1D460 TEX-I"})])])])]),m("mjx-assistive-mml",{unselectable:"on",display:"inline"},[m("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[m("msub",null,[m("mi",null,"k"),m("mi",null,"s")])])])]),s("，所以结合在一起，得到最终的渲染方程为")],-1),m("mjx-container",{class:"MathJax",jax:"CHTML",display:"true",style:{position:"relative"}},[m("mjx-math",{display:"true",style:{"margin-left":"0","margin-right":"0"},class:"MJX-TEX","aria-hidden":"true"},[m("mjx-msub",null,[m("mjx-mi",{class:"mjx-i"},[m("mjx-c",{class:"mjx-c1D43F TEX-I"})]),m("mjx-script",{style:{"vertical-align":"-0.15em"}},[m("mjx-mi",{class:"mjx-i",size:"s"},[m("mjx-c",{class:"mjx-c1D45C TEX-I"})])])]),m("mjx-mo",{class:"mjx-n"},[m("mjx-c",{class:"mjx-c28"})]),m("mjx-TeXAtom",{texclass:"ORD"},[m("mjx-mover",null,[m("mjx-over",{style:{"padding-bottom":"0.105em","padding-left":"0.524em","margin-bottom":"-0.516em"}},[m("mjx-mo",{class:"mjx-n",style:{width:"0","margin-left":"-0.25em"}},[m("mjx-c",{class:"mjx-c20D7 TEX-V"})])]),m("mjx-base",null,[m("mjx-msub",null,[m("mjx-mi",{class:"mjx-i"},[m("mjx-c",{class:"mjx-c1D714 TEX-I"})]),m("mjx-script",{style:{"vertical-align":"-0.15em"}},[m("mjx-mi",{class:"mjx-i",size:"s"},[m("mjx-c",{class:"mjx-c1D45C TEX-I"})])])])])])]),m("mjx-mo",{class:"mjx-n"},[m("mjx-c",{class:"mjx-c29"})]),m("mjx-mo",{class:"mjx-n",space:"4"},[m("mjx-c",{class:"mjx-c3D"})]),m("mjx-msub",{space:"4"},[m("mjx-mi",{class:"mjx-i"},[m("mjx-c",{class:"mjx-c1D43F TEX-I"})]),m("mjx-script",{style:{"vertical-align":"-0.15em"}},[m("mjx-TeXAtom",{size:"s",texclass:"ORD"},[m("mjx-mi",{class:"mjx-i"},[m("mjx-c",{class:"mjx-c1D452 TEX-I"})])])])]),m("mjx-mo",{class:"mjx-n"},[m("mjx-c",{class:"mjx-c28"})]),m("mjx-TeXAtom",{texclass:"ORD"},[m("mjx-mover",null,[m("mjx-over",{style:{"padding-bottom":"0.105em","padding-left":"0.524em","margin-bottom":"-0.516em"}},[m("mjx-mo",{class:"mjx-n",style:{width:"0","margin-left":"-0.25em"}},[m("mjx-c",{class:"mjx-c20D7 TEX-V"})])]),m("mjx-base",null,[m("mjx-msub",null,[m("mjx-mi",{class:"mjx-i"},[m("mjx-c",{class:"mjx-c1D714 TEX-I"})]),m("mjx-script",{style:{"vertical-align":"-0.15em"}},[m("mjx-mi",{class:"mjx-i",size:"s"},[m("mjx-c",{class:"mjx-c1D45C TEX-I"})])])])])])]),m("mjx-mo",{class:"mjx-n"},[m("mjx-c",{class:"mjx-c29"})]),m("mjx-mo",{class:"mjx-n",space:"3"},[m("mjx-c",{class:"mjx-c2B"})]),m("mjx-msub",{space:"3"},[m("mjx-mo",{class:"mjx-lop"},[m("mjx-c",{class:"mjx-c222B TEX-S2"})]),m("mjx-script",{style:{"vertical-align":"-0.896em","margin-left":"-0.388em"}},[m("mjx-TeXAtom",{size:"s",texclass:"ORD"},[m("mjx-mi",{class:"mjx-n"},[m("mjx-c",{class:"mjx-c3A9"})])])])]),m("mjx-mrow",{space:"2"},[m("mjx-mo",{class:"mjx-s3"},[m("mjx-c",{class:"mjx-c28 TEX-S3"})]),m("mjx-msub",null,[m("mjx-mi",{class:"mjx-i"},[m("mjx-c",{class:"mjx-c1D458 TEX-I"})]),m("mjx-script",{style:{"vertical-align":"-0.15em"}},[m("mjx-mi",{class:"mjx-i",size:"s"},[m("mjx-c",{class:"mjx-c1D451 TEX-I"})])])]),m("mjx-mstyle",null,[m("mjx-mfrac",null,[m("mjx-frac",{type:"d"},[m("mjx-num",null,[m("mjx-nstrut",{type:"d"}),m("mjx-mi",{class:"mjx-i"},[m("mjx-c",{class:"mjx-c1D450 TEX-I"})])]),m("mjx-dbox",null,[m("mjx-dtable",null,[m("mjx-line",{type:"d"}),m("mjx-row",null,[m("mjx-den",null,[m("mjx-dstrut",{type:"d"}),m("mjx-mi",{class:"mjx-i"},[m("mjx-c",{class:"mjx-c1D70B TEX-I"})])])])])])])])]),m("mjx-mo",{class:"mjx-n",space:"3"},[m("mjx-c",{class:"mjx-c2B"})]),m("mjx-mstyle",{space:"3"},[m("mjx-mfrac",null,[m("mjx-frac",{type:"d"},[m("mjx-num",null,[m("mjx-nstrut",{type:"d"}),m("mjx-mrow",null,[m("mjx-mi",{class:"mjx-i"},[m("mjx-c",{class:"mjx-c1D437 TEX-I"})]),m("mjx-mi",{class:"mjx-i"},[m("mjx-c",{class:"mjx-c1D43A TEX-I"})]),m("mjx-mi",{class:"mjx-i"},[m("mjx-c",{class:"mjx-c1D439 TEX-I"})])])]),m("mjx-dbox",null,[m("mjx-dtable",null,[m("mjx-line",{type:"d"}),m("mjx-row",null,[m("mjx-den",null,[m("mjx-dstrut",{type:"d"}),m("mjx-mrow",null,[m("mjx-mn",{class:"mjx-n"},[m("mjx-c",{class:"mjx-c34"})]),m("mjx-mo",{class:"mjx-n"},[m("mjx-c",{class:"mjx-c28"})]),m("mjx-msub",null,[m("mjx-TeXAtom",{texclass:"ORD"},[m("mjx-mover",null,[m("mjx-over",{style:{"padding-bottom":"0.105em","padding-left":"0.311em","margin-bottom":"-0.516em"}},[m("mjx-mo",{class:"mjx-n",style:{width:"0","margin-left":"-0.25em"}},[m("mjx-c",{class:"mjx-c20D7 TEX-V"})])]),m("mjx-base",null,[m("mjx-mi",{class:"mjx-i"},[m("mjx-c",{class:"mjx-c1D714 TEX-I"})])])])]),m("mjx-script",{style:{"vertical-align":"-0.15em"}},[m("mjx-mi",{class:"mjx-i",size:"s"},[m("mjx-c",{class:"mjx-c1D45C TEX-I"})])])]),m("mjx-TeXAtom",{texclass:"ORD"},[m("mjx-mover",null,[m("mjx-over",{style:{"padding-bottom":"0.105em","padding-left":"0.3em","margin-bottom":"-0.516em"}},[m("mjx-mo",{class:"mjx-n",style:{width:"0","margin-left":"-0.25em"}},[m("mjx-c",{class:"mjx-c20D7 TEX-V"})])]),m("mjx-base",null,[m("mjx-mi",{class:"mjx-i"},[m("mjx-c",{class:"mjx-c1D45B TEX-I"})])])])]),m("mjx-mo",{class:"mjx-n"},[m("mjx-c",{class:"mjx-c29"})]),m("mjx-mo",{class:"mjx-n"},[m("mjx-c",{class:"mjx-c28"})]),m("mjx-msub",null,[m("mjx-TeXAtom",{texclass:"ORD"},[m("mjx-mover",null,[m("mjx-over",{style:{"padding-bottom":"0.105em","padding-left":"0.311em","margin-bottom":"-0.516em"}},[m("mjx-mo",{class:"mjx-n",style:{width:"0","margin-left":"-0.25em"}},[m("mjx-c",{class:"mjx-c20D7 TEX-V"})])]),m("mjx-base",null,[m("mjx-mi",{class:"mjx-i"},[m("mjx-c",{class:"mjx-c1D714 TEX-I"})])])])]),m("mjx-script",{style:{"vertical-align":"-0.15em"}},[m("mjx-mi",{class:"mjx-i",size:"s"},[m("mjx-c",{class:"mjx-c1D456 TEX-I"})])])]),m("mjx-TeXAtom",{texclass:"ORD"},[m("mjx-mover",null,[m("mjx-over",{style:{"padding-bottom":"0.105em","padding-left":"0.3em","margin-bottom":"-0.516em"}},[m("mjx-mo",{class:"mjx-n",style:{width:"0","margin-left":"-0.25em"}},[m("mjx-c",{class:"mjx-c20D7 TEX-V"})])]),m("mjx-base",null,[m("mjx-mi",{class:"mjx-i"},[m("mjx-c",{class:"mjx-c1D45B TEX-I"})])])])]),m("mjx-mo",{class:"mjx-n"},[m("mjx-c",{class:"mjx-c29"})])])])])])])])])]),m("mjx-mo",{class:"mjx-s3"},[m("mjx-c",{class:"mjx-c29 TEX-S3"})])]),m("mjx-msub",null,[m("mjx-mi",{class:"mjx-i"},[m("mjx-c",{class:"mjx-c1D43F TEX-I"})]),m("mjx-script",{style:{"vertical-align":"-0.15em"}},[m("mjx-mi",{class:"mjx-i",size:"s"},[m("mjx-c",{class:"mjx-c1D456 TEX-I"})])])]),m("mjx-mo",{class:"mjx-n"},[m("mjx-c",{class:"mjx-c28"})]),m("mjx-TeXAtom",{texclass:"ORD"},[m("mjx-mover",null,[m("mjx-over",{style:{"padding-bottom":"0.105em","padding-left":"0.474em","margin-bottom":"-0.516em"}},[m("mjx-mo",{class:"mjx-n",style:{width:"0","margin-left":"-0.25em"}},[m("mjx-c",{class:"mjx-c20D7 TEX-V"})])]),m("mjx-base",null,[m("mjx-msub",null,[m("mjx-mi",{class:"mjx-i"},[m("mjx-c",{class:"mjx-c1D714 TEX-I"})]),m("mjx-script",{style:{"vertical-align":"-0.15em"}},[m("mjx-mi",{class:"mjx-i",size:"s"},[m("mjx-c",{class:"mjx-c1D456 TEX-I"})])])])])])]),m("mjx-mo",{class:"mjx-n"},[m("mjx-c",{class:"mjx-c29"})]),m("mjx-mo",{class:"mjx-n"},[m("mjx-c",{class:"mjx-c28"})]),m("mjx-msub",null,[m("mjx-TeXAtom",{texclass:"ORD"},[m("mjx-mover",null,[m("mjx-over",{style:{"padding-bottom":"0.105em","padding-left":"0.311em","margin-bottom":"-0.516em"}},[m("mjx-mo",{class:"mjx-n",style:{width:"0","margin-left":"-0.25em"}},[m("mjx-c",{class:"mjx-c20D7 TEX-V"})])]),m("mjx-base",null,[m("mjx-mi",{class:"mjx-i"},[m("mjx-c",{class:"mjx-c1D714 TEX-I"})])])])]),m("mjx-script",{style:{"vertical-align":"-0.15em"}},[m("mjx-mi",{class:"mjx-i",size:"s"},[m("mjx-c",{class:"mjx-c1D456 TEX-I"})])])]),m("mjx-TeXAtom",{texclass:"ORD"},[m("mjx-mover",null,[m("mjx-over",{style:{"padding-bottom":"0.105em","padding-left":"0.3em","margin-bottom":"-0.516em"}},[m("mjx-mo",{class:"mjx-n",style:{width:"0","margin-left":"-0.25em"}},[m("mjx-c",{class:"mjx-c20D7 TEX-V"})])]),m("mjx-base",null,[m("mjx-mi",{class:"mjx-i"},[m("mjx-c",{class:"mjx-c1D45B TEX-I"})])])])]),m("mjx-mo",{class:"mjx-n"},[m("mjx-c",{class:"mjx-c29"})]),m("mjx-mi",{class:"mjx-i"},[m("mjx-c",{class:"mjx-c1D451 TEX-I"})]),m("mjx-msub",null,[m("mjx-mi",{class:"mjx-i"},[m("mjx-c",{class:"mjx-c1D714 TEX-I"})]),m("mjx-script",{style:{"vertical-align":"-0.15em"}},[m("mjx-mi",{class:"mjx-i",size:"s"},[m("mjx-c",{class:"mjx-c1D456 TEX-I"})])])])]),m("mjx-assistive-mml",{unselectable:"on",display:"block"},[m("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[m("msub",null,[m("mi",null,"L"),m("mi",null,"o")]),m("mo",{stretchy:"false"},"("),m("mrow",{"data-mjx-texclass":"ORD"},[m("mover",null,[m("msub",null,[m("mi",null,"ω"),m("mi",null,"o")]),m("mo",{stretchy:"false"},"→")])]),m("mo",{stretchy:"false"},")"),m("mo",null,"="),m("msub",null,[m("mi",null,"L"),m("mrow",{"data-mjx-texclass":"ORD"},[m("mi",null,"e")])]),m("mo",{stretchy:"false"},"("),m("mrow",{"data-mjx-texclass":"ORD"},[m("mover",null,[m("msub",null,[m("mi",null,"ω"),m("mi",null,"o")]),m("mo",{stretchy:"false"},"→")])]),m("mo",{stretchy:"false"},")"),m("mo",null,"+"),m("msub",null,[m("mo",{"data-mjx-texclass":"OP"},"∫"),m("mrow",{"data-mjx-texclass":"ORD"},[m("mi",{mathvariant:"normal"},"Ω")])]),m("mrow",{"data-mjx-texclass":"INNER"},[m("mo",{"data-mjx-texclass":"OPEN"},"("),m("msub",null,[m("mi",null,"k"),m("mi",null,"d")]),m("mstyle",{displaystyle:"true",scriptlevel:"0"},[m("mfrac",null,[m("mi",null,"c"),m("mi",null,"π")])]),m("mo",null,"+"),m("mstyle",{displaystyle:"true",scriptlevel:"0"},[m("mfrac",null,[m("mrow",null,[m("mi",null,"D"),m("mi",null,"G"),m("mi",null,"F")]),m("mrow",null,[m("mn",null,"4"),m("mo",{stretchy:"false"},"("),m("msub",null,[m("mrow",{"data-mjx-texclass":"ORD"},[m("mover",null,[m("mi",null,"ω"),m("mo",{stretchy:"false"},"→")])]),m("mi",null,"o")]),m("mrow",{"data-mjx-texclass":"ORD"},[m("mover",null,[m("mi",null,"n"),m("mo",{stretchy:"false"},"→")])]),m("mo",{stretchy:"false"},")"),m("mo",{stretchy:"false"},"("),m("msub",null,[m("mrow",{"data-mjx-texclass":"ORD"},[m("mover",null,[m("mi",null,"ω"),m("mo",{stretchy:"false"},"→")])]),m("mi",null,"i")]),m("mrow",{"data-mjx-texclass":"ORD"},[m("mover",null,[m("mi",null,"n"),m("mo",{stretchy:"false"},"→")])]),m("mo",{stretchy:"false"},")")])])]),m("mo",{"data-mjx-texclass":"CLOSE"},")")]),m("msub",null,[m("mi",null,"L"),m("mi",null,"i")]),m("mo",{stretchy:"false"},"("),m("mrow",{"data-mjx-texclass":"ORD"},[m("mover",null,[m("msub",null,[m("mi",null,"ω"),m("mi",null,"i")]),m("mo",{stretchy:"false"},"→")])]),m("mo",{stretchy:"false"},")"),m("mo",{stretchy:"false"},"("),m("msub",null,[m("mrow",{"data-mjx-texclass":"ORD"},[m("mover",null,[m("mi",null,"ω"),m("mo",{stretchy:"false"},"→")])]),m("mi",null,"i")]),m("mrow",{"data-mjx-texclass":"ORD"},[m("mover",null,[m("mi",null,"n"),m("mo",{stretchy:"false"},"→")])]),m("mo",{stretchy:"false"},")"),m("mi",null,"d"),m("msub",null,[m("mi",null,"ω"),m("mi",null,"i")])])])],-1),m("p",null,"其中",-1),m("mjx-container",{class:"MathJax",jax:"CHTML",display:"true",style:{position:"relative"}},[m("mjx-math",{display:"true",style:{"margin-left":"0","margin-right":"0"},class:"MJX-TEX","aria-hidden":"true"},[m("mjx-msub",null,[m("mjx-mi",{class:"mjx-i"},[m("mjx-c",{class:"mjx-c1D458 TEX-I"})]),m("mjx-script",{style:{"vertical-align":"-0.15em"}},[m("mjx-mi",{class:"mjx-i",size:"s"},[m("mjx-c",{class:"mjx-c1D451 TEX-I"})])])]),m("mjx-mo",{class:"mjx-n",space:"4"},[m("mjx-c",{class:"mjx-c3D"})]),m("mjx-mo",{class:"mjx-n",space:"4"},[m("mjx-c",{class:"mjx-c28"})]),m("mjx-mn",{class:"mjx-n"},[m("mjx-c",{class:"mjx-c31"})]),m("mjx-mo",{class:"mjx-n",space:"3"},[m("mjx-c",{class:"mjx-c2212"})]),m("mjx-mi",{class:"mjx-i",space:"3"},[m("mjx-c",{class:"mjx-c1D439 TEX-I"})]),m("mjx-mo",{class:"mjx-n"},[m("mjx-c",{class:"mjx-c29"})]),m("mjx-mo",{class:"mjx-n"},[m("mjx-c",{class:"mjx-c28"})]),m("mjx-mn",{class:"mjx-n"},[m("mjx-c",{class:"mjx-c31"})]),m("mjx-mo",{class:"mjx-n",space:"3"},[m("mjx-c",{class:"mjx-c2212"})]),m("mjx-mi",{class:"mjx-i",space:"3"},[m("mjx-c",{class:"mjx-c1D440 TEX-I"})]),m("mjx-mo",{class:"mjx-n"},[m("mjx-c",{class:"mjx-c29"})])]),m("mjx-assistive-mml",{unselectable:"on",display:"block"},[m("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[m("msub",null,[m("mi",null,"k"),m("mi",null,"d")]),m("mo",null,"="),m("mo",{stretchy:"false"},"("),m("mn",null,"1"),m("mo",null,"−"),m("mi",null,"F"),m("mo",{stretchy:"false"},")"),m("mo",{stretchy:"false"},"("),m("mn",null,"1"),m("mo",null,"−"),m("mi",null,"M"),m("mo",{stretchy:"false"},")")])])],-1)]))}const u=x(i,[["render",t],["__file","render_function_1.html.vue"]]),r=JSON.parse('{"path":"/note/graphics/illumination_model/render_function/render_function_1.html","title":"渲染方程（一）","lang":"zh-CN","frontmatter":{},"headers":[{"level":2,"title":"1. 定义","slug":"_1-定义","link":"#_1-定义","children":[{"level":3,"title":"1.1 反射方程","slug":"_1-1-反射方程","link":"#_1-1-反射方程","children":[]},{"level":3,"title":"1.2 渲染方程","slug":"_1-2-渲染方程","link":"#_1-2-渲染方程","children":[]}]},{"level":2,"title":"2. 反射方程分解","slug":"_2-反射方程分解","link":"#_2-反射方程分解","children":[]},{"level":2,"title":"3. Lambert漫反射模型","slug":"_3-lambert漫反射模型","link":"#_3-lambert漫反射模型","children":[]},{"level":2,"title":"4.最终形式","slug":"_4-最终形式","link":"#_4-最终形式","children":[]}],"git":{"updatedTime":1740235322000,"contributors":[{"name":"thejinchao","username":"thejinchao","email":"thejinchao@gmail.com","commits":1,"url":"https://github.com/thejinchao"}]},"filePathRelative":"note/graphics/illumination_model/render_function/render_function_1.md"}');export{u as comp,r as data};
|