| 1 |
{ |
| 2 |
Calculation of relay directions for prismatic glazing |
| 3 |
|
| 4 |
31 July 1991 Greg Ward |
| 5 |
|
| 6 |
Prism is oriented with flat side in xz plane |
| 7 |
and normal in -y direction. The prism is |
| 8 |
extruded along the x axis. |
| 9 |
|
| 10 |
Reflections are not computed. |
| 11 |
|
| 12 |
Parameters: |
| 13 |
A1 - index of refraction |
| 14 |
A2 - thickness of prism triangle |
| 15 |
A3 - height of upper side (segment 1) |
| 16 |
A4 - height of lower side (segment 2) |
| 17 |
|
| 18 |
Computes: |
| 19 |
coef1 - transmission coefficient for upper side |
| 20 |
dx1, dy1, |
| 21 |
dz1 - transmission direction for upper side |
| 22 |
coef2 - transmission coefficient for lower side |
| 23 |
dx2, dy2, |
| 24 |
dz2 - transmission direction for lower side |
| 25 |
} |
| 26 |
{ required formulae } |
| 27 |
tan2sin(a) = sqrt(a*a/(1+a*a)); |
| 28 |
stb(sta,ca,sa) = ca*sta - sa*sqrt(A1*A1-sta*sta); |
| 29 |
cos_p = Sqrt(1-Dx*Dx); |
| 30 |
dtrans(c1,c2) = dtransb(c1, sqrt(1+(c1*c1-1)/A1/A1), |
| 31 |
c2, sqrt(1+(c2*c2-1)/A1/A1)); |
| 32 |
dtransb(c1o,c1i,c2o,c2i) = 8*A1*A1 * |
| 33 |
( c1o*c1i*c2o*c2i/sq((A1*c1o+c1i)*(A1*c2o+c2i)) + |
| 34 |
1/c1o/c1i/c2o/c2i/sq((A1/c1o+1/c1i)*(A1/c2o+1/c2i)) ); |
| 35 |
|
| 36 |
{************************************************ |
| 37 |
Definitions for Segment 1 |
| 38 |
} |
| 39 |
{ slope angle (always positive) } |
| 40 |
sin_a1 = tan2sin(A2/A3/cos_p); |
| 41 |
cos_a1 = Sqrt(1-sin_a1*sin_a1); |
| 42 |
{ computed coefficeint } |
| 43 |
coef1 = A3/(A3+A4) * if(Dy, |
| 44 |
if(1-abs(sin_tB1o), |
| 45 |
dtrans(cos_tA1i, cos_tB1o), |
| 46 |
0), |
| 47 |
if (Dy*cos_a1 + Dz*sin_a1, |
| 48 |
0, |
| 49 |
if (1-abs(sin_tA1o), |
| 50 |
dtrans(cos_tB1i, cos_tA1o), |
| 51 |
0))); |
| 52 |
{ computed direction } |
| 53 |
dx1 = Dx; |
| 54 |
dy1 = if(Dy, |
| 55 |
(cos_a1*cos_tB1o-sin_a1*sin_tB1o)*cos_p, |
| 56 |
-cos_tA1o*cos_p); |
| 57 |
dz1 = if(Dy, |
| 58 |
(sin_a1*cos_tB1o+cos_a1*sin_tB1o)*cos_p, |
| 59 |
-sin_tA1o*cos_p); |
| 60 |
{ incident angle (flat side) } |
| 61 |
sin_tA1i = Dz/cos_p; |
| 62 |
cos_tA1i = Sqrt(1-sin_tA1i*sin_tA1i); |
| 63 |
{ transmitted angle (steep side) } |
| 64 |
sin_tB1o = stb(sin_tA1i, cos_a1, sin_a1); |
| 65 |
cos_tB1o = Sqrt(1-sin_tB1o*sin_tB1o); |
| 66 |
{ incident angle (steep side) } |
| 67 |
sin_tB1i = -Dz/cos_p*cos_a1 - |
| 68 |
Sqrt(1-sq(Dz/cos_p))*sin_a1; |
| 69 |
cos_tB1i = Sqrt(1-sin_tB1i*sin_tB1i); |
| 70 |
{ transmitted angle (flat side) } |
| 71 |
sin_tA1o = stb(sin_tB1i, cos_a1, -sin_a1); |
| 72 |
cos_tA1o = Sqrt(1-sin_tA1o*sin_tA1o); |
| 73 |
|
| 74 |
{************************************************ |
| 75 |
Definitions for Segment 2 |
| 76 |
} |
| 77 |
{ slope angle (always negative) } |
| 78 |
sin_a2 = -tan2sin(A2/A4/cos_p); |
| 79 |
cos_a2 = Sqrt(1-sin_a2*sin_a2); |
| 80 |
{ computed coefficeint } |
| 81 |
coef2 = A4/(A3+A4) * if(Dy, |
| 82 |
if(1-abs(sin_tB2o), |
| 83 |
dtrans(cos_tA2i, cos_tB2o), |
| 84 |
0), |
| 85 |
if (Dy*cos_a2 + Dz*sin_a2, |
| 86 |
0, |
| 87 |
if (1-abs(sin_tA2o), |
| 88 |
dtrans(cos_tB2i, cos_tA2o), |
| 89 |
0))); |
| 90 |
{ computed direction } |
| 91 |
dx2 = Dx; |
| 92 |
dy2 = if(Dy, |
| 93 |
(cos_a2*cos_tB2o-sin_a2*sin_tB2o)*cos_p, |
| 94 |
-cos_tA2o*cos_p); |
| 95 |
dz2 = if(Dy, |
| 96 |
(sin_a2*cos_tB2o+cos_a2*sin_tB2o)*cos_p, |
| 97 |
-sin_tA2o*cos_p); |
| 98 |
{ incident angle (flat side) } |
| 99 |
sin_tA2i = Dz/cos_p; |
| 100 |
cos_tA2i = Sqrt(1-sin_tA2i*sin_tA2i); |
| 101 |
{ transmitted angle (steep side) } |
| 102 |
sin_tB2o = stb(sin_tA2i, cos_a2, sin_a2); |
| 103 |
cos_tB2o = Sqrt(1-sin_tB2o*sin_tB2o); |
| 104 |
{ incident angle (steep side) } |
| 105 |
sin_tB2i = -Dz/cos_p*cos_a2 - |
| 106 |
Sqrt(1-sq(Dz/cos_p))*sin_a2; |
| 107 |
cos_tB2i = Sqrt(1-sin_tB2i*sin_tB2i); |
| 108 |
{ transmitted angle (flat side) } |
| 109 |
sin_tA2o = stb(sin_tB2i, cos_a2, -sin_a2); |
| 110 |
cos_tA2o = Sqrt(1-sin_tA2o*sin_tA2o); |
