Ray Casting the Wall Columns

Wolfenstein 3D’s famous view is produced by a grid-based ray-casting renderer, not by a general 3D polygon engine. WL_DRAW.C contains the game-specific drawing path, while WL_MAIN.C and related initialization code prepare tables and display state needed by that path.

For each screen column, the renderer derives a view direction and advances through the tile grid until it encounters a wall. The traversal alternates between crossings of vertical and horizontal grid boundaries, a digital differential analysis whose next crossing is determined by the current ray position and direction. Once the hit is known, the perpendicular distance determines the projected wall height, and the corresponding texture column is scaled into the framebuffer.

$$ h_{\mathrm{screen}}\proptorac{1}{d_{\perp}}. $$

The use of perpendicular distance is essential because raw distance along an oblique ray would produce fisheye distortion. Wolfenstein’s renderer is specialized: its grid-aligned walls and restricted world representation make the algorithm practical, while its column-oriented output matches the VGA framebuffer and the performance expectations of the time.