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How can I generate a DEM of an area given the vertex list of the polygon that includes it?

What I want to achieve is similar to the output of gdalwarp, eg:

gdalwarp -t_srs EPSG:4326 -te x_min y_min x_max y_max output_srtm.tif -te_srs EPSG:4326 output.tif

but not of a rectangle like this case but of a polygonal area, everything that is outside the polygon should be generate as nodata value.

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