SOME COMPUTATION FORMULAE OF SOLID ANGLES SUBTENDED BY GEOMETRICALLY SIMPLE FORMS : An applicative study on equi-solid angle-representation II

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  • 幾何学的に簡単な形態の立体角の計算 : 等立体角写像の応用研究 その2
  • 等立体角写像の応用研究-2-幾何学的に簡単な形態の立体角の計算
  • トウ リッタイカク シャゾウ ノ オウヨウ ケンキュウ 2 キカガクテキ ニ

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The authors of this paper have got some computation formulae of the mesure for solid angle ω, subtended by geometrically simple forms-right-angled triangles and rectangle-in normalized positions as given in Fig. 3. First they reached the formula for the trapezoidal form as given in Fig. 1 after succesive substitutions and integrations. The final expression of the formula is given as equation (10) and the expressions of x_1/√<1-ξ^2> and x_2/√<1-ξ^2> written above equation (10). Solid angles subtended by right-angles triangles and rectangle are derived respectively from the expression above mentioned, as special cases where L_1=0, L_2=L (Right-angled triangle, Fig. 3 (1)) L_1=L, L_2=0 (Right-angled triangle, Fig. 3 (2)) L_1=L_2=L (Rectangle, Fig. 3 (3)). The expressions of the formulae are given as the expression (14), (15) and (20) respectively in this paper. The authors have worked out computing charts for the formulae got above. They are given in this paper as Fig. 4, Fig. 5 and Fig. 15 respectively. The applications of them to more generalized positions are also discussed. The authors have developed the expression of integrated mesure of ω for rectangles in an normalized rectangular domain to get the mesure of ω over the domain and discussed also the applications of them to more generalized cases. Fig. 4, Fig. 5 and Fig. 15 are given in equi-solid angle-representation as Fig. 12, Fig. 13 and Fig. 17 respectively.

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