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http://mathematica.stackexchange.com/questions/13361/mollweide-maps-in-mathematica




cart[{lambda_, phi_}] := With[{theta = fc[phi]}, {2 /Pi*lambda Cos[theta], Sin[theta]}]
fc[phi_] := Block[{theta}, If[Abs[phi] == Pi/2, phi, theta /. 
 FindRoot[2 theta + Sin[2 theta] == Pi Sin[phi], {theta, phi}]]];






grid = With[{delta = Pi/18/2},
            Table[{lambda, phi}, {phi, -Pi/2, Pi/2, delta}, {lambda, -Pi, Pi, delta}]];
gr1 = Graphics[{AbsoluteThickness[0.05], Line /@ grid, Line /@ Transpose[grid]},
               AspectRatio -> 1/2];
gr0 = Flatten[{gr1[[1, 2]][[Range[9]*4 - 1]],gr1[[1, 3]][[Range[18]*4 - 3]]}] // 
Graphics[{AbsoluteThickness[0.2], #}] &;
gr2 = Table[{Hue[t/Pi], Point[{ t , t/2}]}, {t, -Pi, Pi, 1/100}] // 
Flatten // Graphics;
gr = Show[{gr1, gr0, gr2}, Axes -> True]






gr /. Line[pts_] :> Line[cart /@ pts] /. Point[pts_] :> Point[cart[ pts]]