Model a Solar Collector 

The Ivanpah solar electric generating system makes use of a circular arrangement of mirrors to redirect the Sun's rays toward a central tower.

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In[1]:=

X makeRectangle[sunDirection_, direction1_, center_, {a_, b_}] := Module[{n = N@Normalize[(Normalize[N@sunDirection] + Normalize[{0, 0, 10.} - center])], dir1, dir2}, dir1 = Normalize[Normalize[direction1] - Normalize[direction1].n n]; dir2 = Cross[dir1, n]; N@{center - a/2 dir1 - b/2 dir2, center + a/2 dir1 - b/2 dir2, center + a/2 dir1 + b/2 dir2, center - a/2 dir1 + b/2 dir2}]; positions = Cases[Flatten[Table[{i, j}, {i, -20, 20, 2}, {j, -20, 20, 2}], 1], {x_, y_} /; Sqrt[x^2 + y^2] <= 20]; date = DateObject[{2014, 7, 1}]; sunrise = Sunrise[date]; sunset = Sunset[date]; timeseries = SunPosition[DateRange[sunrise, sunset, {10, "Minute"}]]; Manipulate[ Module[{sunDir, altitude, azimuth, abstime}, abstime = AbsoluteTime[ DateObject[ DateList[{date["Year"], date["Month"], date["Day"], hour}]]]; {azimuth, altitude} = timeseries[abstime]; sunDir = {Cos[2 Pi - azimuth] Sin[Pi/2 - altitude], Sin[2 Pi - azimuth] Sin[Pi/2 - altitude], Cos[Pi/2 - altitude]}; Graphics3D[{ (* render the Sun *) Yellow, {Lighting -> {{"Ambient", GrayLevel[.3]}, {"Directional", White, ImageScaled[{0, 0, 1}]}}, Sphere[25 sunDir, 2]}, FaceForm[Black, Lighter[Blue, .2]], Specularity[White, 30], Polygon[makeRectangle[ sunDir, {1, 0, 0}, {#[[1]], #[[2]], 1}, {1, 2}] & /@ positions], Red, Cylinder[{{0, 0, 0}, {0, 0, 10}}, 1], Black, Text["E", {0, -22, 0}], Text["S", {-22, 0, 0}], Text["W", {0, 22, 0}], Text["N", {22, 0, 0}]}, PlotRange -> {{-25, 25}, {-25, 25}, {-1, 25}}, SphericalRegion -> True, Axes -> False, Boxed -> True, Lighting -> {{"Ambient", GrayLevel[.7]}, {"Directional", White, 10 Normalize[sunDir]}}]], Row[{Control[{{hour, 12}, {1, 1/60}.# & @@ TimeObject[sunrise], {1, 1/60}.# & @@ TimeObject[sunset] - 1/6., ControlType -> Slider}], Dynamic[DateString[{2014, 7, 1, IntegerPart[hour], 60 FractionalPart[hour]}, {"HourShort", ":", "Minute"}]]}, " "], SaveDefinitions -> True]

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