Isometric projection
Isometric projection is a form of graphical projection—more specifically, an axonometric projection. It is a method for the visual representation of three-dimensional objects in two dimensions in which the angles between the projection of the x, y, and z axes are all the same, or 120°. For objects with surfaces that are substantially perpendicular to and/or parallel with one another, it corresponds to rotation of the object by +/- 45° about the vertical axis, followed by rotation of approximately +/- 35.264° [= arcsin(tan(30°))] about the horizontal axis starting from an orthographic projection relative to an object's face (a perpendicular view to a face of an object).
Isometric projection can be visualized by considering the view of a cubical room from an upper corner, looking towards the opposite lower corner. The x-axis is diagonally down and right, the y-axis is diagonally down and left, and the z-axis is straight up. Depth is also shown by height on the image. Lines drawn along the axes are at 120° to one another. The term isometric comes from the Greek for "equal measure.", which reflects that the scale along each axis of the projection is the same (this is not true of some other forms of graphical projection). Isometric projection is one of the projections used in drafting engineering drawings.
Limits of isometric projection
A problem with isometric projection is that because the lines representing each dimension are parallel on the page, objects do not appear larger or smaller as they extend closer to the viewer. While advantageous for architectural drawings and sprite based video games, this can easily result in situations where depth and altitude are impossible to gauge, as is shown in the illustration to the right. Most contemporary video games have avoided this situation by dropping isometric perspective in favor for 3D rendering with vanishing points. Some of the famous "impossible architecture" works of M.C. Escher exploit this isometric limitation. Waterfall (1961), is a good example, in which the building is isometric, but the faded background is not.
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Isometric projection in video games and pixel art
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In the fields of computer and video games and pixel art, isometric projection has been popular because of the ease in which 2D sprites and tile-based graphics can be made to represent a 3D gaming environment. Because objects don't change size as they move about the game field, there is no need for the computer to scale sprites or calculate the effects of perspective. This allows older 8-bit and 16-bit game systems, (and more recent handhelds) to portray large 3D areas easily. While the depth confusion problems illustrated above can sometimes be a problem, good game design can alleviate this. With the advent of more powerful graphics systems, isometric projection is becoming less common.
The projection used in videogames usually deviates slightly from true isometric due to the limitations of raster graphics. Lines in the x and y axes would not follow a neat pixel pattern when drawn in the required 30° to the horizontal. While modern computers could eliminate this problem with anti-aliasing, earlier computer graphics did not support enough colors or CPU power to do this. So instead, a 2:1 pixel pattern ratio would be used to draw the x and y axes lines, resulting in these axes following a 26.565° (arctan 0.5) angle to the horizontal. Further deviations from true isometric could result from game systems that did not use square pixels. It should therefore be noted that this variation of isometric projection is more accurately described as a form of dimetric projection, since only two of the three angles between the axes are equal (116.565°, 116.565°, 126.87°). Many in video game and pixel art communities, however, continue to refer to this projection as "isometric perspective"; the term "3/4 perspective" is also commonly used.
Notable examples of "isometric" computer and video games
- Q*bert (1982) : An arcade hit
- Zaxxon (1982) : Early arcade space flight fight
- 3D Ant Attack (1983) : home computer game and one of the first games to use isometric graphics
- Congo Bongo (1983) : Arcade game
- Knight Lore (1984) : One of the first games to use 3/4 perspective
- Marble Madness (1984) : Arcade game
- Spindizzy (1986) : Exploration-based puzzle and maze game for 8-bit computers
- Head over Heels (1987) : The pinnacle of isometric games of the 8-bit home computer era
- Populous (1989) : God simulator
- Snake Rattle 'n' Roll (1990) : An action/platformer game
- SimCity 2000 (1993) : City building simulation game
- Transport Tycoon Deluxe (1995) : Transport company simulator/strategy game
- Civilization II (1996) : Turn-based strategy game
- Diablo (1996) : Dungeon-romping RPG game
- Super Mario RPG (1996) : A role-playing game
- Age of Empires (1997) : History-based RTS game
- Breath of Fire III (1997) : A role-playing game
- Final Fantasy Tactics (1997) : A strategic role-playing game
- Ultima Online (1997) : Massively multiplayer online fantasy combat game
- Baldur's Gate (1998) : Computer role-playing game in the Forgotten Realms D&D campaign setting
- Habbo Hotel (2000) : A massively multiplayer online game run by Sulake Corporation
- The Sims (2000) : A simulation of people controlled by the player
- Virtual Magic Kingdom (2005) : A massively multiplayer online game run by The Walt Disney Company