Duke3D isn't a raycaster; it's a portal-based quad rasterizer. Wall quads are forced vertical, and floor quads are rasterized using a neat trick. The renderer computes successive lines of constant distance along slooped floor surfaces, then draws textures using affine scaling, which is correct along those lines. The portal walls clip the draw of successive sectors, which solves the hidden surface problem.

https://fabiensanglard.net/duke3d/build_engine_internals.php