Planar Geometric Projections

Taxonomy of Virtual Spaces

Part of my research is in defining a framework and vocabulary for analyzing and describing the concept of spatiality in digital media (especially in digital game environments). This "Taxonomy of Virtual Spaces" (Rowe, unpublished) is one of the tools for recognizing and clearly defining the aesthetic styles of digital games that I call spatial paradigms. How are these virtual spaces of the game world projected as 2-D images onto the display screen?

"Projection" is used here in the sense of a virtual 3-D object or scene that is projected (transformed) into a 2-D image on a screen. This may be accomplished by a computer rendering 3-D object data into a 2-D graphics matrix or a human artist drawing a 2-D game image (such as a sprite or a tile) using techniques that may give an object visual depth cues (such as axonometric or oblique drawing methods).

This system was initially based on the pioneering work by Dominic Arsenault, Audrey Larochelle, and other researchers at the University of Montreal that led to their "Game FAVR" system of analyzing digital game graphics ("The Game FAVR: A Framework for the Analysis of Visual Representation in Video Games" by Dominic Arsenault, Pierre-Marc Côté, and Audrey Larochelle (2015) Loading…Journal of the Canadian Game Studies Association, vol.9, no.14). I briefly wrote about Game FAVR on this blog before. It is a system that takes the inherently hybrid nature of all video game imagery into account, but it is specifically a means of analyzing the construction of graphic images, not game spatiality.

Game FAVR divides a video game image into three conceptual "image planes:" the characters and interactive elements (agents), the environment, and the background/foreground elements. Each of these different frames may be (and often are) rendered to the screen in different methods. I adapted the Game FAVR system to analyzing projected spatiality (since game space is presented graphically) and refined the categories of graphic techniques (planar geometric projections) used in games.

My latest update to my "family tree" of rendering methods is as follows:

Planar Geometric Projections from "A Taxonomy of Virtual Spaces" by Tony A. Rowe (unpublished)

This chart is only a current revision and is not meant to be exhaustive. It does not include curvilinear perspective, cartoon structures), divergent perspective ("reverse perspective"), or stereographic projection (usually used in cartography). I may expand the chart with these other methods, if needed. This may be more categories than I need for my study, but I would rather start with more details than I need and trim back later (for example, the vertical/horizontal oblique and vertical/horizontal orthogonal projections are almost identical).

The terms above are not universally agreed upon in the English-speaking world. I listed alternate or more specific terms (in gray italics) under each category, as appropriate. Different words may have different meanings to different disciplines and in different contexts. Game developers and journalists are also known for adapting and using terminology in an ad-hoc manner. There are many different graphic methods or camera angles that may all be described as "isometric," "3/4 view," "2.5-D," or "top-down" by different people. From my own studio work, I thought that "hit spang" (the visual effect of a projectile colliding with an object) was a standard visual effect term. Not so, it seems to have been a term that was adapted by my team and carried forward on later projects.

Take the term "axonometric," for example. I recently went through the work of defining what axonometric means, writing an overview of the history of axonometric drawing, and finally determined there are multiple ways of understanding the geometry behind a projection, or drawing, of an object. In the end, I adapted the "primary geometry" method of classifying graphic projections, as that is the standard method used in computer graphics for decades. However, I have noted a "secondary geometry" relationship between the three axonometric and some oblique projections in my chart, above (see the dashed line box). These are all methods of "pictorial" drawing (to use a term from engineering) and may otherwise be defined as "axonometric."

In addition to the projection methods, the three conceptual image planes (agents, environment, background/foreground) are classified by projection angle (the "camera angle" on the object). There are also examples of image planes that are "rendered" by other methods, such as symbols or text description.

The projection methods are just one factor of my taxonomy method. A game's spaces are further classified by its frame mobility (how the "camera" moves across the environment), the topology of the game world, the dimensionality of navigable game space, and other details like gravity.

A game's spatiality goes hand-in-hand with a game player's affordances to navigate that space to create what I call a spatial paradigm.