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Lambert模型认为，材质的漫反射是均匀发射到所有方向的，所以")),Q("mjx-container",b,[(t(),a("svg",v,T[25]||(T[25]=[m('',1)]))),T[26]||(T[26]=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("msub",null,[Q("mi",null,"f"),Q("mi",null,"d")])])],-1))]),T[35]||(T[35]=l("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")),Q("mjx-container",y,[(t(),a("svg",j,T[27]||(T[27]=[m('',1)]))),T[28]||(T[28]=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("msub",null,[Q("mi",null,"k"),Q("mi",null,"d")]),Q("mo",null,"="),Q("mn",null,"1"),Q("mo",null,","),Q("msub",null,[Q("mi",null,"k"),Q("mi",null,"s")]),Q("mo",null,"="),Q("mn",null,"0")])],-1))]),T[36]||(T[36]=l(",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")),Q("mjx-container",O,[(t(),a("svg",R,T[29]||(T[29]=[m('',1)]))),T[30]||(T[30]=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("msub",null,[Q("mi",null,"f"),Q("mi",null,"d")])])],-1))]),T[37]||(T[37]=l("和")),Q("mjx-container",C,[(t(),a("svg",k,T[31]||(T[31]=[m('',1)]))),T[32]||(T[32]=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("msub",null,[Q("mi",null,"L"),Q("mi",null,"i")])])],-1))]),T[38]||(T[38]=l("都是常数，可以提到积分外面。反射方程变成"))]),Q("mjx-container",A,[(t(),a("svg",B,T[39]||(T[39]=[m('',1)]))),T[40]||(T[40]=Q("mjx-assistive-mml",{unselectable:"on",display:"block"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[Q("msub",null,[Q("mi",null,"L"),Q("mi",null,"o")]),Q("mo",null,"="),Q("msub",null,[Q("mi",null,"f"),Q("mi",null,"d")]),Q("msub",null,[Q("mi",null,"L"),Q("mi",null,"i")]),Q("msub",null,[Q("mo",{"data-mjx-texclass":"OP"},"∫"),Q("mrow",{"data-mjx-texclass":"ORD"},[Q("mi",{mathvariant:"normal"},"Ω")])]),Q("mi",null,"cos"),Q("mo",{"data-mjx-texclass":"NONE"},""),Q("msub",null,[Q("mi",null,"θ"),Q("mi",null,"i")]),Q("mi",null,"d"),Q("msub",null,[Q("mi",null,"ω"),Q("mi",null,"i")])])],-1))]),T[81]||(T[81]=Q("p",null,"计算这个半球积分",-1)),Q("mjx-container",X,[(t(),a("svg",F,T[41]||(T[41]=[m('',1)]))),T[42]||(T[42]=Q("mjx-assistive-mml",{unselectable:"on",display:"block"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[Q("mstyle",{displaystyle:"true",scriptlevel:"0"},[Q("mrow",{"data-mjx-texclass":"ORD"},[Q("msub",null,[Q("mo",{"data-mjx-texclass":"OP"},"∫"),Q("mrow",{"data-mjx-texclass":"ORD"},[Q("mi",{mathvariant:"normal"},"Ω")])]),Q("mi",null,"cos"),Q("mo",{"data-mjx-texclass":"NONE"},""),Q("mi",null,"θ"),Q("mi",null,"d"),Q("mi",null,"ω"),Q("mo",null,"="),Q("msubsup",null,[Q("mo",{"data-mjx-texclass":"OP"},"∫"),Q("mrow",{"data-mjx-texclass":"ORD"},[Q("mo",null,"−"),Q("mi",null,"π")]),Q("mrow",{"data-mjx-texclass":"ORD"},[Q("mi",null,"π")])]),Q("msubsup",null,[Q("mo",{"data-mjx-texclass":"OP"},"∫"),Q("mrow",{"data-mjx-texclass":"ORD"},[Q("mn",null,"0")]),Q("mrow",{"data-mjx-texclass":"ORD"},[Q("mi",null,"π"),Q("mrow",{"data-mjx-texclass":"ORD"},[Q("mo",null,"/")]),Q("mn",null,"2")])])]),Q("mi",null,"sin"),Q("mo",{"data-mjx-texclass":"NONE"},""),Q("mo",{stretchy:"false"},"("),Q("mi",null,"θ"),Q("mo",{stretchy:"false"},")"),Q("mi",null,"cos"),Q("mo",{"data-mjx-texclass":"NONE"},""),Q("mo",{stretchy:"false"},"("),Q("mi",null,"θ"),Q("mo",{stretchy:"false"},")"),Q("mi",null,"d"),Q("mi",null,"θ"),Q("mi",null,"d"),Q("mi",null,"ϕ"),Q("mo",null,"="),Q("mi",null,"π")])])],-1))]),T[82]||(T[82]=Q("p",null,"得到",-1)),Q("mjx-container",S,[(t(),a("svg",G,T[43]||(T[43]=[m('',1)]))),T[44]||(T[44]=Q("mjx-assistive-mml",{unselectable:"on",display:"block"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[Q("msub",null,[Q("mi",null,"L"),Q("mi",null,"o")]),Q("mo",null,"="),Q("msub",null,[Q("mi",null,"f"),Q("mi",null,"d")]),Q("msub",null,[Q("mi",null,"L"),Q("mi",null,"i")]),Q("mi",null,"π")])],-1))]),Q("p",null,[T[47]||(T[47]=l("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")),Q("mjx-container",J,[(t(),a("svg",N,T[45]||(T[45]=[m('',1)]))),T[46]||(T[46]=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("msub",null,[Q("mi",null,"L"),Q("mi",null,"i")])])],-1))]),T[48]||(T[48]=l("，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。"))]),Q("mjx-container",E,[(t(),a("svg",P,T[49]||(T[49]=[m('',1)]))),T[50]||(T[50]=Q("mjx-assistive-mml",{unselectable:"on",display:"block"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},[Q("msub",null,[Q("mi",null,"E"),Q("mi",null,"i")]),Q("mo",null,"="),Q("mn",null,"2"),Q("mi",null,"π"),Q("msub",null,[Q("mi",null,"L"),Q("mi",null,"i")])])],-1))]),Q("p",null,[T[53]||(T[53]=l("根据能量守恒，光出射度")),Q("mjx-container",q,[(t(),a("svg",z,T[51]||(T[51]=[m('',1)]))),T[52]||(T[52]=Q("mjx-assistive-mml",{unselectable:"on",display:"inline"},[Q("math",{xmlns:"http://www.w3.org/1998/Math/MathML"},[Q("msub",null,[Q("mi",null,"M"),Q("mi",null,"o")]),Q("mo",null,"="),Q("msub",null,[Q("mi",null,"E"),Q("mi",nul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