Since that is the command you are using, assuming the header files are located in that folder, try this:This one
>gcc einterp_mex.c -LC:\Users\atrch\Documents\MATLAB\geos\mvep2\mutils-0.4\mutils\libutils
gcc einterp_mex.c -IC:\Users\atrch\Documents\MATLAB\geos\mvep2\mutils-0.4\mutils\libutils
Also, if you are 100% sure that all those third party headers provided are included with #include "file" and not #include <file>, you can be even more specific and use:
gcc einterp_mex.c -iquoteC:\Users\atrch\Documents\MATLAB\geos\mvep2\mutils-0.4\mutils\libutils
A little correction in case anyone wants to know the actual use , -Ldir is actually used for the subprogram ld for linking, not header includes. I say it because the referenced documents doesn't explicitly say it.gcc -Ldir -- Here dir is the full path where your include files are.