Craig posted at Cult of Mac about Tim Langdell’s continuing attempts to sue anyone who uses the word ‘Edge’ (which, last we heard, was an English word) in a videogame context and now, apparently, to prevent anyone making any kind of game involving a sphere.
In passing, Craig mentioned the characteristic use of an axonometric projection in marble-rolling titles, ‘commonly referred to as “isometric” in the games industry’. Which immediately (because I’m a geek, or at least a journalist pretending to be a geek) got me peering at the screenshots working out whether they were in fact axonometric and/or isometric.
As Nikolaus commented, isometric is one type of axonometric projection (he usefully cites Wikipedia’s very good, if not very English, explanation). Unlike a perspective projection – which, by one means or another, makes things look as they would in reality, with more distant objects appearing smaller – an axonometric projection keeps measurements the same all the way along each axis. Isometric takes this one step further and makes the scale of each axis the same, so in a drawing of a cube, for example, the lengths of all the edges are the same on the drawing, as well as in reality; hence ‘iso’, equal.
The angles also match, although they’re plus or minus 30 degrees in the projection. Here’s where the interesting bit comes in the axonometrics of game graphics. When you’re working at low resolution, non-perpendicular lines tend to look ‘jaggy’, because they’re made up of offset pixels that form steps rather than continuous lines. The effect is greatest when there’s no aliasing (interspersing of mid-coloured pixels to smooth edges), as in older games for less graphically capable systems. Where possible, you’ll try to use 45 degree lines, because the stepping is regular, like a staircase. Doubling (or tripling, etc) the length of the steps gives an almost equally neat appearance, but intermediate proportions are rougher:
Because of this, games that present a 3D world but are drawn in 2D often use a bastardised isometric projection using angles of 26.5 degrees* – like the second example above – rather than 30. This is so common that someone must have made up a name for it, but I can’t seem to find one, so I’m going to propose ‘tetarto-orthometric’ (quarter-right-angled). Two of Craig’s examples use this projection, while only one is truly isometric; no coincidence, I think, that this is also the only one based on a 3D engine:
There must be some interesting implications to the non-isometricness of tetarto-orthometric games. Unfortunately, I can’t think of any at the moment. If you’re still reading this, um, sorry.
*This is counter-intuitive: surely it should be 22.5 degrees, half of 45? It does seem logical to expect that rising at half the rate means halving the angle, but the error is quickly seen if you work it through. Your intuitive hypothesis is that if a right-angled triangle has angle A of 22.5 degrees opposite edge a, then doubling the length of a will double A to 45 degrees. OK then, so now let’s double the length of a again; have you just created a triangle containing two 90 degree angles, or is your hypothesis pants? back