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I have downloaded a certain tile from https://www.eorc.jaxa.jp/ALOS/en/aw3d30/data/index.htm, and after the requisite logistics (unzipping, putting all *.AVE_DSM.tif files into a single folder), I built a virtual dataset with gdalbuildvrt *.tif asia.vrt. Now gdalinfo asia.vrt gives this:

Size is 108000, 90000
Coordinate System is:
GEOGCS["WGS 84",
    DATUM["WGS_1984",
        SPHEROID["WGS 84",6378137,298.257223563,
            AUTHORITY["EPSG","7030"]],
        AUTHORITY["EPSG","6326"]],
    PRIMEM["Greenwich",0],
    UNIT["degree",0.0174532925199433],
    AUTHORITY["EPSG","4326"]]
Origin = (89.999999999999957,50.000000000000028)
Pixel Size = (0.000277777777778,-0.000277777777778)
Corner Coordinates:
Upper Left  (  90.0000000,  50.0000000) ( 90d 0' 0.00"E, 50d 0' 0.00"N)
Lower Left  (  90.0000000,  25.0000000) ( 90d 0' 0.00"E, 25d 0' 0.00"N)
Upper Right ( 120.0000000,  50.0000000) (120d 0' 0.00"E, 50d 0' 0.00"N)
Lower Right ( 120.0000000,  25.0000000) (120d 0' 0.00"E, 25d 0' 0.00"N)
Center      ( 105.0000000,  37.5000000) (105d 0' 0.00"E, 37d30' 0.00"N)
Band 1 Block=128x128 Type=Int16, ColorInterp=Gray

I can query the data as follows: gdallocationinfo -geoloc asia.vrt 110.00 30.00, meaning "Find the elevation of the point at 110 degrees East and 30 degrees North", and get a proper

Report:
  Location: (72000P,72000L)
  Band 1:
    <LocationInfo><File>N029E110_AVE_DSM.tif</File></LocationInfo>
    Value: 894

Now I would like to project the entire region I've got here to a rectangle P = [a,b]x[c,d], so that I can query not with lat/lon pairs but rather with a point from P. Naturally, I need the distance between the two points be somewhat reflective of their "original" distance. I do not care much about the specific values of a,b,c,d, and anyway I think they depend on the units option we would supply to gdalwarp. Now my question is, what is the exact gdalwarp-command I need to issue to accomplish this? I know it has to do with proj-string, but I am lost to its multitude of parameters.

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    Look at -te and -te_srs. Those will let you specify the target extents of your rectangle in whatever spatial reference you want – mikewatt Apr 3 at 23:32
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It appears that the answer to my question is about this: gdalwarp -t_srs '+proj=eqc +lat_0=37.5 +lon_0=105.0 +units=m' *.tif result.tif

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