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); |