2.5D Ray-casting
2.5D raycasting is a unique form of 3D rendering. Instead of projecting polygons or casting rays for every pixel of the screen, in raycasting, we cast a single ray for every column of the screen.
This leads to significant performance improvements over raytracing, but it also places restrictions on the camera and world design. In a raycasting engine, cameras can only look left and right (although pitch can be faked by panning), and generally surfaces must be exactly vertical or horizontal (but as we’ll learn, there are clever tricks to get around this too.)
So why would someone want to create a raycasting engine? There are a few motivations. Firstly, raycasting is fast—a bare-bones, cuboid grid, shading-free raycasting engine can run at 15–30 fps in 480x360 in vanilla Scratch. Secondly, raycasting is simple—both conceptually and programmatically. This is why simple sprite-based raycasting is a popular project for 3D beginners, and plenty of tutorials for that can be found on YouTube, the Scratch Wiki, and on Scratch itself.
But although I’ll start with a simple conceptual model, I want to show you how raycasting can be pushed to its limits to create visually stunning, complex worlds with polygonal walls and ceilings, advanced lighting, and even terrain. Not many raycasting engines have done these things before—so buckle up for the ride!
“Raycasting?”
What do I mean by “raycasting” exactly? It’s just as the name implies—we’re casting rays in a virtual 3D world, then drawing the results on the screen.
Let’s start with a simple example. Let’s say we have a simple rectangular map, with outer walls, and a pillar in the center, like this:
████████████████
██ ██
██ ██
██ ██ ██
██ ██
██ @ ██
██ ██
████████████████
The camera is represented by the @ symbol here. Intuitively, we know that the camera can only see things which it can hit using rays. A person can only see something if there’s an uninterrupted line from their eye to the object. We also know that things appear smaller the further away they are. Can we use these facts to our advantage?
If we know the height of an object, and how far away it is, we can calculate its apparent height using this calculation: height / distance.