/usr/share/radiance/prism.cal is in radiance-materials 4R1+20120125-1.1.
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Calculation of relay directions for prismatic glazing
31 July 1991 Greg Ward
Prism is oriented with flat side in xz plane
and normal in -y direction. The prism is
extruded along the x axis.
Reflections are not computed.
Parameters:
A1 - index of refraction
A2 - thickness of prism triangle
A3 - height of upper side (segment 1)
A4 - height of lower side (segment 2)
Computes:
coef1 - transmission coefficient for upper side
dx1, dy1,
dz1 - transmission direction for upper side
coef2 - transmission coefficient for lower side
dx2, dy2,
dz2 - transmission direction for lower side
}
{ required formulae }
tan2sin(a) = sqrt(a*a/(1+a*a));
stb(sta,ca,sa) = ca*sta - sa*sqrt(A1*A1-sta*sta);
cos_p = Sqrt(1-Dx*Dx);
dtrans(c1,c2) = dtransb(c1, sqrt(1+(c1*c1-1)/A1/A1),
c2, sqrt(1+(c2*c2-1)/A1/A1));
dtransb(c1o,c1i,c2o,c2i) = 8*A1*A1 *
( c1o*c1i*c2o*c2i/sq((A1*c1o+c1i)*(A1*c2o+c2i)) +
1/c1o/c1i/c2o/c2i/sq((A1/c1o+1/c1i)*(A1/c2o+1/c2i)) );
{************************************************
Definitions for Segment 1
}
{ slope angle (always positive) }
sin_a1 = tan2sin(A2/A3/cos_p);
cos_a1 = Sqrt(1-sin_a1*sin_a1);
{ computed coefficeint }
coef1 = A3/(A3+A4) * if(Dy,
if(1-abs(sin_tB1o),
dtrans(cos_tA1i, cos_tB1o),
0),
if (Dy*cos_a1 + Dz*sin_a1,
0,
if (1-abs(sin_tA1o),
dtrans(cos_tB1i, cos_tA1o),
0)));
{ computed direction }
dx1 = Dx;
dy1 = if(Dy,
(cos_a1*cos_tB1o-sin_a1*sin_tB1o)*cos_p,
-cos_tA1o*cos_p);
dz1 = if(Dy,
(sin_a1*cos_tB1o+cos_a1*sin_tB1o)*cos_p,
-sin_tA1o*cos_p);
{ incident angle (flat side) }
sin_tA1i = Dz/cos_p;
cos_tA1i = Sqrt(1-sin_tA1i*sin_tA1i);
{ transmitted angle (steep side) }
sin_tB1o = stb(sin_tA1i, cos_a1, sin_a1);
cos_tB1o = Sqrt(1-sin_tB1o*sin_tB1o);
{ incident angle (steep side) }
sin_tB1i = -Dz/cos_p*cos_a1 -
Sqrt(1-sq(Dz/cos_p))*sin_a1;
cos_tB1i = Sqrt(1-sin_tB1i*sin_tB1i);
{ transmitted angle (flat side) }
sin_tA1o = stb(sin_tB1i, cos_a1, -sin_a1);
cos_tA1o = Sqrt(1-sin_tA1o*sin_tA1o);
{************************************************
Definitions for Segment 2
}
{ slope angle (always negative) }
sin_a2 = -tan2sin(A2/A4/cos_p);
cos_a2 = Sqrt(1-sin_a2*sin_a2);
{ computed coefficeint }
coef2 = A4/(A3+A4) * if(Dy,
if(1-abs(sin_tB2o),
dtrans(cos_tA2i, cos_tB2o),
0),
if (Dy*cos_a2 + Dz*sin_a2,
0,
if (1-abs(sin_tA2o),
dtrans(cos_tB2i, cos_tA2o),
0)));
{ computed direction }
dx2 = Dx;
dy2 = if(Dy,
(cos_a2*cos_tB2o-sin_a2*sin_tB2o)*cos_p,
-cos_tA2o*cos_p);
dz2 = if(Dy,
(sin_a2*cos_tB2o+cos_a2*sin_tB2o)*cos_p,
-sin_tA2o*cos_p);
{ incident angle (flat side) }
sin_tA2i = Dz/cos_p;
cos_tA2i = Sqrt(1-sin_tA2i*sin_tA2i);
{ transmitted angle (steep side) }
sin_tB2o = stb(sin_tA2i, cos_a2, sin_a2);
cos_tB2o = Sqrt(1-sin_tB2o*sin_tB2o);
{ incident angle (steep side) }
sin_tB2i = -Dz/cos_p*cos_a2 -
Sqrt(1-sq(Dz/cos_p))*sin_a2;
cos_tB2i = Sqrt(1-sin_tB2i*sin_tB2i);
{ transmitted angle (flat side) }
sin_tA2o = stb(sin_tB2i, cos_a2, -sin_a2);
cos_tA2o = Sqrt(1-sin_tA2o*sin_tA2o);
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