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 This "Taxonomy of Virtual Spaces" (Rowe, unpublished) is a tool for recognizing and clearly defining the aesthetic styles of digital games that I call spatial paradigms.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?
One might think that many of the terms used in the creation of graphic spaces would be well-defined and agreed upon. In truth, there are a number of terms that are used in different ways and may have conflicting definitions in computer graphics, engineering, and architecture. Because of this game developers, journalists, academics, and critics may end up picking and choosing the meanings behind these words from different sources.
One particularly troublesome word is axonometric.
Axonometry defined
An axonometric (taken from the Ancient Greek roots axon (axis) + metron (measure)) drawing is one in which a rendered object can be measured across all three axes (x axis, y axis, and z axis). The object's axes are not parallel and not orthogonal to the projection plane, allowing three faces of the object to be seen in the image.
"An axonometric projection usually represents an object so that three adjacent faces are visible, in order to get a three-dimensional representation in one view." from "Planar Geometric Projections and Viewing Transformations" by Ingrid Carlbom and Joseph Paciorek, Computing Surveys, vol. 10, no. 4 (1978) pg. 473
"Axonometric projection is a method of parallel projection in which the axes of the object represented are not parallel to the projective plane in order to represent all three points of views (x, y and z)." from "A New Angle on Parallel Languages" by Audrey Larochelle, GAME: The Italian Journal of Game Studies, vol. 1, no. 2 (2013) pg. 35
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| Axonometric projection of an object from 3-D space to 2-D screen, from Engineering Drawing for Manufacture by Brian Griffiths (2002), pg. 26 |
An axonometric drawing is a type of parallel projection in which a 3-D object is transformed into a 2-D image on the projection plane (a.k.a. screen or picture plane or projective plane). This is an affine (from Latin affinis "connected with") transformation, meaning that the angles on the object may differ, but straight lines remain straight and parallel lines remain parallel. Being a parallel projection (or a paraline drawing), lines do not converge and objects do not reduce in size with distance from the projection plane (as seen in perspectival projections (a.k.a. linear projections).
"... allow angles to differ, so long as all straight lines remain straight and all parallels remain parallel. Such transformations are known as 'affine.'" from Drawing Distinctions by Patrick Maynard (2005) pg. 24
"[An] important property of axonometry is its fixed relation between sizes of objects in world space and those on projected space, independent of the positions of the objects in projected space. In linear perspective, objects become smaller when they move farther away; not so in axonometric perspective. This means that you can measure the size of an object of a axonometric drawing and know how big the real object is (you need to know the scale of the drawing and the properties of the projection, but nothing else), something that cannot be done with linear perspective. This leads to the name of the projection: the word 'axonometry' means 'measurable from the axes.'" from "Axonometric Projections - A Technical Overview" by Thiadmer Riemersma (2009)
Testing the Definition
So far, so good. The above defining qualities are valid for any use of the word "axonometric" with regard to rendering an object to a 2-D surface. Well, almost any use, that is:
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| "3/4 view" here classified as "axonometric," even though it only shows two faces of an object, from "Game Developer's Guide to Graphic Projections, Part 1" by Matej Jan (2017) |
Other than that previous exception, axonometric always means a parallel projection in which all three main faces of an object can be seen in one image.
Now, how axonometric renderings developed through history?
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