11) 完全拡散面内の相互反射による照度分布の研究(I) : 2次元の場合

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タイトル別名
  • 11) STUDIES ON THE ILLUMINATION DISTRIBUTIONS BY THE INTERREFLECTIONS IN PERFECTLY DIFFUSING SURFACES (Part I) : Two-dimentional Cases
  • 完全拡散面内の相互反射による照度分布の研究-1-
  • 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 1

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An approximate numerical solution of integral equations is developed for the illumination distributions by the interreflections in perfectly diffusing surfaces. This report (Part I) is limited to two-dimentional case. This study deals with the integral equation, [table](1) where, E_<r1>(x)=the known illumination by the first reflected light from the internal surface, ρ(ξ)=the known reflectance, e_o'(ξ,x)=the known kernel, and E_r(x)=indirect illumination by interreflections to be determined. Since indirect illumination is usually uniform, E_r(ξ) can be approximated by a function of 2nd degree (parabola) on one side of two-dimentional cross-section, or [table](2) where, E_<i1>, E_<i2> and E_<i3> are respectively unknown indirect illuminations at the one end, the middle point and the another end on the i th side, and h_i is the length of this side. Substituting Eq. (2) into Eq. (1), ρ(ξ)e_o'(ξ,x)ξ^2, ρ(ξ)e_o'(ξ,x)ξ and ρ(ξ)e_o'(ξ,x) are easily integrated analytically or numerically. Then Eq. (1) is approximated to linear simultaneous equation and this solution give indirect illumination distributions in form of parabola. By this method, the indirect illuminations are calculated for very long courts and rooms lighted by day-light. The effects of changing the reflectance of the internal surface are considered, and especially in the very long side-lighted rooms the effects of changing the reflectance of outside ground are discussed. Tne calculated results are compared with several another empirical formulas and errors in this formulas are checked.

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