[SDL] Building Linux SDL game for Windows

[David Bruce]

Sorry about the general nature of this question - I haven't gotten very far 
with Google.  I have been working on Bill Kendrick's game "Tux, of Math 
Command" aka "Tuxmath" and I want to make a Windows build.  I have install 
Cygwin and have tried to get the SDL libs set up but I have not gotten 
SDL_image to build under Cygwin - the errors say that headers are missing for 
jpeg and maybe some other image formats - I would provide more details but I 
am posting from my home (Linux) machine.  I am pretty sure that the code of 
Tuxmath itself contains little if anything that is platform-specific, but I 
need a functioning SDL Windows build environment.

Is Cygwin + SDL the right way to go to make a Windows package, and can anyone 
point me to a way to get SDL_image installed under Cygwin?  Alternatively, I 
would be happy to cross-compile for Windows using my Debian system, but I 
have found even less info through Google on how to do that.
-- 
David Bruce