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Calculation of relay directions for prismatic glazing |
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31 July 1991 Greg Ward |
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Prism is oriented with flat side in xz plane |
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and normal in -y direction. The prism is |
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extruded along the x axis. |
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Reflections are not computed. |
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Parameters: |
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A1 - index of refraction |
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A2 - thickness of prism triangle |
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A3 - height of upper side (segment 1) |
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A4 - height of lower side (segment 2) |
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Computes: |
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coef1 - transmission coefficient for upper side |
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dx1, dy1, |
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dz1 - transmission direction for upper side |
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coef2 - transmission coefficient for lower side |
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dx2, dy2, |
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dz2 - transmission direction for lower side |
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} |
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{ required formulae } |
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tan2sin(a) = sqrt(a*a/(1+a*a)); |
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stb(sta,ca,sa) = ca*sta - sa*sqrt(A1*A1-sta*sta); |
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cos_p = Sqrt(1-Dx*Dx); |
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dtrans(c1,c2) = dtransb(c1, sqrt(1+(c1*c1-1)/A1/A1), |
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c2, sqrt(1+(c2*c2-1)/A1/A1)); |
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dtransb(c1o,c1i,c2o,c2i) = 8*A1*A1 * |
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( c1o*c1i*c2o*c2i/sq((A1*c1o+c1i)*(A1*c2o+c2i)) + |
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1/c1o/c1i/c2o/c2i/sq((A1/c1o+1/c1i)*(A1/c2o+1/c2i)) ); |
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{************************************************ |
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Definitions for Segment 1 |
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} |
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{ slope angle (always positive) } |
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sin_a1 = tan2sin(A2/A3/cos_p); |
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cos_a1 = Sqrt(1-sin_a1*sin_a1); |
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{ computed coefficeint } |
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coef1 = A3/(A3+A4) * if(Dy, |
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if(1-abs(sin_tB1o), |
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dtrans(cos_tA1i, cos_tB1o), |
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0), |
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if (Dy*cos_a1 + Dz*sin_a1, |
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0, |
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if (1-abs(sin_tA1o), |
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dtrans(cos_tB1i, cos_tA1o), |
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0))); |
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{ computed direction } |
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dx1 = Dx; |
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dy1 = if(Dy, |
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(cos_a1*cos_tB1o-sin_a1*sin_tB1o)*cos_p, |
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-cos_tA1o*cos_p); |
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dz1 = if(Dy, |
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(sin_a1*cos_tB1o+cos_a1*sin_tB1o)*cos_p, |
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-sin_tA1o*cos_p); |
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{ incident angle (flat side) } |
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sin_tA1i = Dz/cos_p; |
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cos_tA1i = Sqrt(1-sin_tA1i*sin_tA1i); |
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{ transmitted angle (steep side) } |
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sin_tB1o = stb(sin_tA1i, cos_a1, sin_a1); |
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cos_tB1o = Sqrt(1-sin_tB1o*sin_tB1o); |
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{ incident angle (steep side) } |
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sin_tB1i = -Dz/cos_p*cos_a1 - |
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Sqrt(1-sq(Dz/cos_p))*sin_a1; |
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cos_tB1i = Sqrt(1-sin_tB1i*sin_tB1i); |
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{ transmitted angle (flat side) } |
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sin_tA1o = stb(sin_tB1i, cos_a1, -sin_a1); |
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cos_tA1o = Sqrt(1-sin_tA1o*sin_tA1o); |
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{************************************************ |
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Definitions for Segment 2 |
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} |
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{ slope angle (always negative) } |
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sin_a2 = -tan2sin(A2/A4/cos_p); |
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cos_a2 = Sqrt(1-sin_a2*sin_a2); |
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{ computed coefficeint } |
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coef2 = A4/(A3+A4) * if(Dy, |
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if(1-abs(sin_tB2o), |
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dtrans(cos_tA2i, cos_tB2o), |
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0), |
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if (Dy*cos_a2 + Dz*sin_a2, |
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0, |
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if (1-abs(sin_tA2o), |
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dtrans(cos_tB2i, cos_tA2o), |
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0))); |
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{ computed direction } |
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dx2 = Dx; |
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dy2 = if(Dy, |
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(cos_a2*cos_tB2o-sin_a2*sin_tB2o)*cos_p, |
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-cos_tA2o*cos_p); |
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dz2 = if(Dy, |
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(sin_a2*cos_tB2o+cos_a2*sin_tB2o)*cos_p, |
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-sin_tA2o*cos_p); |
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{ incident angle (flat side) } |
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sin_tA2i = Dz/cos_p; |
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cos_tA2i = Sqrt(1-sin_tA2i*sin_tA2i); |
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{ transmitted angle (steep side) } |
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sin_tB2o = stb(sin_tA2i, cos_a2, sin_a2); |
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cos_tB2o = Sqrt(1-sin_tB2o*sin_tB2o); |
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{ incident angle (steep side) } |
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sin_tB2i = -Dz/cos_p*cos_a2 - |
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Sqrt(1-sq(Dz/cos_p))*sin_a2; |
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cos_tB2i = Sqrt(1-sin_tB2i*sin_tB2i); |
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{ transmitted angle (flat side) } |
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sin_tA2o = stb(sin_tB2i, cos_a2, -sin_a2); |
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cos_tA2o = Sqrt(1-sin_tA2o*sin_tA2o); |
