11 完全拡散面内の相互反射による照度分布の研究(II) : 3次元の場合

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  • 11) STUDIES ON THE ILLUMINATION DISTRIBUTIONS BY THE INTERREFLECTIONS IN PERFECLY DIFFUSING SURFACES (PART II) THREE-DIMENSIONAL CASES
  • 完全拡散面内の相互反射による照度分布の研究-2-
  • カンゼン カクサンメン ナイ ノ ソウゴ ハンシャ ニ ヨル ショウド ブンプ ノ ケンキュウ 2

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This report is the apporoximate numerical solution of integral equation of the interreflections in perfectly diffusing surfaces for three-dimentional cases. As part I (Two-dimensional Cases), this study deals with the integral equation in which unknown fuction is the indirect illumination, or [numerical formula] (1) where, E_γ(x)= indirect illumination by interreflections to be determined, E_<γ1>(x)=the known illumination by the first reflecred light from the internal surface, ρ(x')=the known reflectance, e_o(x',x)=the known kernel, S=the area of internal surface. On each rectangular surface which forms a rectangular light-well or room, the indirect illumination is approximated by the next function. E_γ(x,y)=(Ay^2+By+C)x^2+(Dy^2+Ey+F)x+Gy^2+Hy+I (2) wher, A, B, C, ……are respectively given by the unknown nine indirect illumination values on this surface. In this reprt, the nine position of this unknown values are the four corner points, the four middle points of each side, and the center point on this rectangular surface. Substituting Eq. (2) into Eq. (1), we get equations contained the next integral terms, [numerical formula] (3) where, e_o(x',y'; x,y)=the known kernel, ρ=the known refrectance. a and h=the each side length of the rectangular surface. Since the analytical integral of this term (3) is difficult, it is integrated analytically to the one direction only, and numerically to the other. Then Eq. (1) is apporoximated to linear simultaneous equations and these solutions give inbirect illumination distributions. By this method, the indirect illuminations are calculated for the rectangular light-wells and the square rooms, lighted from one side window by daylight. The effects of changing the refflectance of the internal surface are considered, and especially in the square side-lighted rooms the effects of changing the reflectance of outside ground are discussed. The calculated results are compared with the several another empirical formulas and errors in these formulas are checked.

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