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    It depends totally on the software that is taking care of rendering or other processing of the "rotated" DEM. If you fiddle with .tfw you do not touch a single pixel in the tiff file, you can even make it read-only. If the result is not good you can make a new permanently rotated image with gdalwarp gdal.org/gdalwarp.html gdalwarp rotated_with_tfw.tif warped physically.tif Test different resampling options but nearest or bilinear should be good for DEM. Read also about the other gdalwarp options. Commented Jan 25, 2015 at 9:45
  • @user30184 Either my math is wrong, or I am missing some fundamental step to properly rotating my data. Any tips you can provide are appreciated. Commented Jan 26, 2015 at 4:52
  • What do you mean with the clipping effect? The top left pixel of the original image is nailed to a fixed coordinate with any rotation angle. The original rectangular image needs a bigger rectangular box to fit in when it is rotated, despite at 90, 180, and 270 degree, and the corner areas are filled with black no-data pixels. Would you rather see the corners filled with white pixels? Commented Jan 26, 2015 at 6:22
  • The clipping effect is the "higher elevation" portions of the terrain becoming all white and apparently losing most of its detail? It is most obvious in the 45 degree rotation shown above. Do you see that occurrence? Commented Jan 26, 2015 at 6:30
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    You have to compare the rendering of the grayscale. QGIS sets limits to 2% and 98% of the min and max values by default. That might get changed when you rotate and introduce NODATA values. You can set the min and max values for rendering manually to compare it better. Commented Jan 26, 2015 at 6:54