Thats a pretty cool tutorial, nicly layed out. However there is a better way than that of making a raycaster that removes the distortion. It involves making a camera of sort, but I didnt understand it.
I have had my thinking cap on about the textures, and in the process come across probably a nicer way of rendering the world so that its not this blocky world that everyone referances to.
Before making this I never realised that all raycasters are effectively doing is making the pixel into a rectangle, and renering that. What I was thinking was what if you take the points at the center of that square and connect them up, that would remove the blocky look, and allow for sloped edges at 45 deg angles, unlike now where you get a jagged edge.
Originally I was thinking of using lines to reprisent the world, but thanks to metabballs it seemed clear that you could make the lines up from the pixels them selfs.
This way will lend it self to a texure mapper really well, and provide the coords for mapping the texture.
I will post more soon. Heres a pic to show what I mean: -