A short list of game engines
The dimensionality of a game gives rise to how players interact with your world. Originally games had 2D graphics, utilizing classic cartoon animation techniques in real time. In the background of 2D games static pictures are layered on top of each other to build a scene, while in the foreground tiled images and 2D animations called Sprites are drawn each frame to create the moving parts of the game. Because animation is limited to sliding the sprite across the screen the player’s experience is limited to moving across that 2D plane. That being said changing the perspective of the player gives rise to many different experiences.
Modern computer graphics place Models made up of triangles into 3D worlds. While this makes it possible to build things like First and Third Person shooters many 3D games still use the Top Down, Side Scroller, or Isometric projection to create the stylistic feel of their games.
When designing your game it’s important to think about how dimensionality affects the kinds of art assets that go into your world as well as how that affects your player’s experience.
Video game programs are all simulations: programs which change their state over time given inputs from a user or AI. The complexity of these simulations ranges from simple, like an interactive story waiting for a user to click, to 2D physical effects, like the ball bouncing off the paddle in Pong, to full 3d physical simulations, like when you flip the tank over in Halo. Some simulations are only possible in Dd or in 3D engines, while some experiences are shared between the two. This has implications for your game: an experience like Street Fighter or Halo might only make sense in their respective engines. However A Link to the Past (SNES) and A Link Between Worlds (3DS) have the same physical feel, but their artistic style give way to two different games.
For games that take place on the 2d Plane, deciding a 2d or 3d engine can dictate the artistic style of your game
The picture that the player ends up seeing in your game is dictated by the Player Camera. In 2d graphics, the camera is just the visible portion of the screen, with images either being on screen or off. This gives rise to the three perspectives: you’re either looking straight on at a scene, top down, or at a fixed angle.
In 3D graphics we display content on the screen by figuratively positioning a pinhole camera in a scene.
For each pixel on your monitor, a “Ray” of light is cast from the pixel, through the pinhole, and into the scene.
In this scene the trees are made of a background image. The floor is made of tiles, and Lakitu and Mario are animated sprites.
A Link To the past is made up entirely of background tiles, interactive tiles like the tombstones/brush, and foreground sprites like Link and that asshole walking around
Isometric games are effectively top down 2D games where the game is drawn at a diagonal angle to grant perspective on content that would be missed from side scrollers / top down games
Full 3D graphical experiences are governed by the Camera, the player’s perspective.
Quake 1 was the first (probably) fully 3D video game. The player’s controls are attached directly to the Camera, and a physics simulation dictates how the player moves (sliding across the floor, stuck to the ground by gravity)
In third person games the Camera follows the player character though the world. In Super Mario they had Lakitu follow Mario around to really drive that point home
Many 3D games fix their camera in place to recreate a 2D game effect in 3D. This Likitung Sushi game from Pokemon stadium gives the impression that you are playing an Isometric 2D game, but they are eating 3d sushi with their 3d bodies.