"The two previous 3D games Hovertank and Catacombs 3D were done in an object space rendering where it drew limited polygons. They were one-dimensional in terms that they were just line segments that were restricted on axises. We had something that resembled a polygon rasterizer and a polygon clipper and those were both done in four to six weeks a piece. I had really quite a bit of difficulty with it. Going back in time twenty years, there weren't all of the references in existence, books and tutorials on this subject. I was having a hard time getting some of that stuff to be as robust and reliable as it needed to be. You could get a few freak out cases in Catacombs 3D and one of my real goals was to simplify it enough that it would be really rock and solid."
--John Carmack, "Wolfenstein 3D - Director's Commentary"
Rasterisation (or rasterization) is the task of taking an image described in a vector graphics format (shapes) and converting it into a raster image ( A series of pixels, dots or lines that when they come together on a display, they recreate the image). The rasterised image may then be displayed on a computer display, video display or printer, or stored in a bitmap file format. Rasterisation may refer to either the conversion of models into raster files, or the conversion of 2D rendering primitives such as polygons or line segments into a rasterized format. The latter is used to convert the polygonal vector world created for Catacomb 3D and present it as a pixel display that matched with the raster sprites used for game objects.
This approach was later replaced by raycasting in the engine's successor, first used in Wolfenstein 3D (1992). Compared with other rendering techniques such as ray tracing, rasterisation is extremely fast. However, rasterization is simply the process of computing the mapping from scene geometry to pixels and does not prescribe a particular way to compute the color of those pixels. Shading, including programmable shading, may be based on physical light transport, or artistic intent.
"Catacombs 3D was the very first commercial game that we did that had 3D aspects to it. That was limited in that the entire map was made out of nothing but tile blocks. You could put textures on the blocks.There were limits like, there were no doors. You just had blocks that would disappear. It had scaled, bit-mapped creatures. So that was the first 3D-action shooter. The next step was Wolfenstein 3D, which was still a block-based map, but it had a few minor, new features in there. We had doors that slid side-to-side and push- walls and a few interactive features; but the characters and items were still basically the same. The internal rendering was very different from Catacombs 3D. Catacombs used basically a line- rasterization approach, while Wolfenstein used a much more robust ray-casting approach. But the end result was that they rendered the same pictures."
--John Carmack, The Making of Doom III