Expression 11: left parenthesis, "X" Subscript, "s" , Baseline left parenthesis, cos left parenthesis, phi Subscript, "i" , Baseline , right parenthesis sin left parenthesis, theta Subscript, "i" , Baseline , right parenthesis , sin left parenthesis, phi Subscript, "i" , Baseline , right parenthesis sin left parenthesis, theta Subscript, "i" , Baseline , right parenthesis , cos left parenthesis, theta Subscript, "i" , Baseline , right parenthesis , right parenthesis , "Y" Subscript, "s" , Baseline left parenthesis, cos left parenthesis, phi Subscript, "i" , Baseline , right parenthesis sin left parenthesis, theta Subscript, "i" , Baseline , right parenthesis , sin left parenthesis, phi Subscript, "i" , Baseline , right parenthesis sin left parenthesis, theta Subscript, "i" , Baseline , right parenthesis , cos left parenthesis, theta Subscript, "i" , Baseline , right parenthesis , right parenthesis , right parenthesis "t"Xscosϕisinθi,sinϕisinθi,cosθi,Yscosϕisinθi,sinϕisinθi,cosθit
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domain t Minimum:
less than or equal to "t" less than or equal to≤t≤
11
domain t Maximum:
11
BRDF
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Expression 13: "s" equals 0.5 6s=0.56
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piπ
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Expression 14: "A" equals 1 minus StartFraction, "s" squared Over 2 left parenthesis, "s" squared plus 0.3 3 , right parenthesis , EndFractionA=1−s22s2+0.33
equals=
0.7 5 6 3 7 0 4 1 6 4 0 80.756370416408
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Expression 15: "B" equals StartFraction, 0.4 5 "s" squared Over "s" squared plus 0.0 9 , EndFractionB=0.45s2s2+0.09
equals=
0.3 4 9 6 5 3 1 2 1 9 0 30.349653121903
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Expression 16: "F" Subscript, "r" , Baseline left parenthesis, phi Subscript, "o" , Baseline , theta Subscript, "o" , Baseline , right parenthesis equals StartFraction, 1 Over pi , EndFraction left parenthesis, "A" plus "B" max left parenthesis, 0 , cos left parenthesis, phi Subscript, "i" , Baseline minus phi Subscript, "o" , Baseline , right parenthesis , right parenthesis sin left parenthesis, max left parenthesis, theta Subscript, "i" , Baseline , theta Subscript, "o" , Baseline , right parenthesis , right parenthesis tan left parenthesis, min left parenthesis, theta Subscript, "i" , Baseline , theta Subscript, "o" , Baseline , right parenthesis , right parenthesis , right parenthesisFrϕo,θo=1πA+Bmax0,cosϕi−ϕosinmaxθi,θotanminθi,θo
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Expression 17: Start integral from 0 to 2 pi , end integral, Start integral from 0 to StartFraction, pi Over 2 , EndFraction , end integral, "F" Subscript, "r" , Baseline left parenthesis, "u" , "v" , right parenthesis cosine left parenthesis, "v" , right parenthesis times sine left parenthesis, "v" , right parenthesis "d" "v" "d" "u"∫2π0∫π20Fru,vcosv·sinvdvdu