DOOM (the classic version) was 2.5D, not 3D. I don't think you're going to be able to pull off a high enough polygon count for a FPS type game in full 3D--but you could easily make a space flight sim (like XWing or XWing vs Tie Fighter)
yes i didnt use the zbuffer or any occlusion removal algorithms....my algorithm calculates the centroid distance from camera focus to the centroid of each face and determines the draw order...so there might be some errors
Just a thought here--but I think there may be a quick fix to this problem. Instead of computing the distance from the centroid to the focus, compute the distance from the centroid to the plane representing the screen.