Composition: how to make a day and night world map?

Question

Given the following world images:

day   = Import["http://eoimages.gsfc.nasa.gov/images/imagerecords/55000/55167/earth_lights_lrg.jpg"]
night = Import["http://eoimages.gsfc.nasa.gov/images/imagerecords/57000/57752/land_shallow_topo_2048.tif"]

how would you use Mathematica to create an accurate “day and night map” (examples here and there) of the Earth for a given date and time?

Answer 1

Let me first name your maps correctly (you switched night and day maps):

night= Import["http://eoimages.gsfc.nasa.gov/images/imagerecords/55000/55167/earth_lights_lrg.jpg"];
day= Import["http://eoimages.gsfc.nasa.gov/images/imagerecords/57000/57752/land_shallow_topo_2048.tif"];

The images have different sizes:

ImageDimensions[day]

(*
==> {2048, 1024}
*)

ImageDimensions[night]

(*
==> {2400, 1200}
*)

so, I rescale the night image. Artefacts (if any) will probably be less visible there.

night = ImageResize[night, ImageDimensions[day]];

Now, for the calculation of the mask we don't need to use external sources. AstronomicalData will do:

mask =
 Rasterize[
  RegionPlot[
   AstronomicalData["Sun", {"Altitude", {2012, 6, 21}, {lat, long}}] <
     0, {long, -180, 180}, {lat, -90, 90}, Frame -> None, 
   PlotRange -> Full, PlotStyle -> Black, PlotRangePadding -> 0, 
   AspectRatio -> (#2/#1 & @@ ImageDimensions[day])],
  ImageSize -> ImageDimensions[day]
  ]

Then, stealing the ImageCompose idea from Yu-Sung:

pl=ImageCompose[night, SetAlphaChannel[day, mask]]

Borrowing and adapting some code from the Texture doc page:

Show[
 Graphics3D[{White, Tube[{{0, 0, -1.4}, {0, 0, 1.4}}, .04]}],
 SphericalPlot3D[1 , {u, 0, Pi}, {v, 0, 2 Pi}, Mesh -> None, 
  TextureCoordinateFunction -> ({#5, 1 - #4} &), 
  PlotStyle -> Texture[Show[pl, ImageSize -> 1000]], 
  Lighting -> "Neutral", Axes -> False, RotationAction -> "Clip"], 
 Lighting -> "Neutral", Boxed -> False, 
 Method -> {"ShrinkWrap" -> True}
]

Answer 2

Yes, the basic idea is here: Demonstration: Day and Night World Clock

Now, to use the images, create an alpha channel using the computed the day-night curve--called "terminator" curve (rasterize it in grayscale), and compose two images using ImageCompose with the generated alpha channels (SetAlphaChannel to the second image).

Try the following code:

a = Image[ConstantArray[{255, 0, 0}, {200, 300}]];
b = Image[ConstantArray[{0, 255, 0}, {200, 300}]];

(* This is just a made-up mask. Don't mind Plot[] part *)
mask = Rasterize[
  Plot[Sin[x], {x, -Pi/2, 3 Pi/2}, PlotRangePadding->0,
    Filling->-1, FillingStyle->Black, Frame->False, 
    Axes->False, ImageSize->{300, 200}, AspectRatio->2/3],
  "Image", ColorSpace->"GrayScale"];

ImageCompose[a, SetAlphaChannel[b, mask]]

You should get an image with green and red mixed as below. Now you can replace a and b with your day and night textures.

I have to tell you that although the code there computes pretty close approximation of the actual terminator curve, it is not exact. To compute it accurately (or based on actual data), see: NOAA: Day Night Terminator

The following code and output is for the actual images (again the mask is fake):

day = ImageResize[day, {2048, 1024}]; (* Match the dimensions *)

mask = Rasterize[
   Plot[Sin[x], {x, -Pi/2, 3 Pi/2}, PlotRangePadding -> 0, 
    Filling -> -1, FillingStyle -> Black, Frame -> False, 
    Axes -> False, ImageSize -> {2048, 1024}, 
    AspectRatio -> 1024/2048], "Image", ColorSpace -> "GrayScale"];

ImageCompose[night, SetAlphaChannel[day, mask]]