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{
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Compute distribution on ceiling or wall of cove lighting
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system employing linear fixtures.
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10Feb91 Greg Ward
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This is the closed-form solution to the integral of
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illumination from a one-dimensional extended source.
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Solution assumes that both fixture endpoints are in front
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of surface element -- negative values may result if this
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assumption is wrong!
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Multiply cove_mult by radiant flux per unit source length
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times cove surface reflectance. To account for interreflection
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with room surfaces, multiply this value by 1/(1-RcRr), where
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Rc is the average ceiling reflectance and Rr is the average
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reflectance of the floor and walls (biased towards the floor).
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A1-A6 - Begin and end point coord's of first fixture
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A7-A12, A13-A18, ... - Coord's for second, third, ... fixtures
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}
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cove_mult = cove_sum(arg(0)/6, 1);
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cove_sum(n, i0) = if(n-.5,
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cove_coef(
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(arg(i0)-Px)*Nx
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+(arg(i0+1)-Py)*Ny
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+(arg(i0+2)-Pz)*Nz,
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(arg(i0+3)-arg(i0))*Nx
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+(arg(i0+4)-arg(i0+1))*Ny
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+(arg(i0+5)-arg(i0+2))*Nz,
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sq(arg(i0)-Px)
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+sq(arg(i0+1)-Py)
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+sq(arg(i0+2)-Pz),
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(Px-arg(i0))*(arg(i0+3)-arg(i0))
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+(Py-arg(i0+1))*(arg(i0+4)-arg(i0+1))
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+(Pz-arg(i0+2))*(arg(i0+5)-arg(i0+2)),
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sq(arg(i0+3)-arg(i0))
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+sq(arg(i0+4)-arg(i0+1))
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+sq(arg(i0+5)-arg(i0+2)))
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+ cove_sum(n-1, i0+6),
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0);
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cove_coef(a, b, g, h, k) = 1/Sqrt(g*k-h*h)/(2*PI*PI*PI)
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*( (a*k+b*h)/Sqrt(g*k-h*h)
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*(atan((k-h)/Sqrt(g*k-h*h))+atan(h/Sqrt(g*k-h*h)))
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+ (a*k+b*h-a*h-b*g)/(k-2*h+g)
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+ (a*h+b*g)/g );
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