Isometric projection
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Isometric projection is a form of graphical projection — more specifically, an axonometric orthographic projection. It is a method of visually representing three-dimensional objects in two dimensions, in which the three axes of space appear equally foreshortened, of which the displayed angles among them and also the scale of foreshortening are universally known, and each angle between two of the three axes is 120°. Isometric projection is one of the projections used in drafting engineering drawings.
In creating a final, isometric instrument drawing, in most cases a full-size scale, i.e., without using a foreshortening factor, is employed to good effect because the resultant distortion is difficult to perceive. 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.
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[edit] Visualization
Isometric projection dictates the direction of viewing in that 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 or camera by approximately +/- 35.264° [= arcsin(tan(30°))] about the horizontal axis, followed by rotation of +/- 45° about the vertical 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", reflecting that the scale along each axis of the projection is the same (this is not true of some other forms of graphical projection).
[edit] 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 projection in favor of perspective 3D rendering utilizing 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.
[edit] "Isometric" projection in video games and pixel art
In the fields of computer and video games and pixel art, axonometric projection has been popular because of the ease with 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 do the calculations necessary to simulate visual perspective. This allowed older 8-bit and 16-bit game systems (and, more recently, handheld systems) 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, axonometric 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 if drawn in the required 30° to the horizontal. While modern computers can eliminate this problem using anti-aliasing, earlier computer graphics did not support enough colors or possess enough CPU power to accomplish 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. (Game systems that do not use square pixels could, however, yield different angles, including true isometric.) It should therefore be noted that this form of projection is more accurately described as a variation 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 mistakenly refer to this projection—as well as other forms of axonometric projection—as "isometric perspective"; the term "3/4 perspective" is also commonly used.
For the form of dimetric perspective commonly found in video games and pixel art, it corresponds to rotation of the object or camera by +/- 30° about the horizontal axis, followed by rotation by +/- 45° about the vertical axis.
[edit] Notable examples of "isometric" computer and video games
- Q*bert (1982) : An arcade hit. Truly isometric.
- Zaxxon (1982) : Early arcade space flight fight. Truly isometric.
- Ant Attack (1983) : Home computer game.
- Congo Bongo (1983) : Arcade game.
- Knight Lore (1984) : Action-adventure computer game.
- Marble Madness (1984) : Arcade game.
- Spindizzy (1986) : Exploration-based puzzle and maze game for 8-bit computers.
- Amaurote (1987) : 8-bit arcade game using 3/4 perspective.
- Head over Heels (1987) : Popular action-adventure game from the end of the 8-bit computer era.
- Populous (1989) : God simulator.
- Solstice: The Quest for the Staff of Demnos (1990) : Puzzle game.
- Snake Rattle 'n' Roll (1990) : An action/platformer game.
- Landstalker (1992) : Platformer/role-playing game.
- SimCity 2000 (1993) : City building simulation game.
- Transport Tycoon Deluxe (1995) : Transport company simulator/strategy game.
- Civilization II (1996) : Turn-based strategy game.
- Super Mario RPG (1996) : A role-playing game.
- Age of Empires (1997) : History-based RTS game.
- Fallout (1997) : A post nuclear sci-fi role playing game by Interplay. Technically trimetric.
- Final Fantasy Tactics (1997) : A strategic role-playing game.
- Ultima Online (1997) : Massively multiplayer online fantasy combat game.
- Commandos (1998) : A stealth-oriented real-time tactics game.
- Baldur's Gate (1998) : Computer role-playing game in the Forgotten Realms D&D campaign setting.
- StarCraft (1998) : Science-fiction real-time strategy game.
- 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.
[edit] Computer desktops and GUIs
It is possible to use isometric projection when drawing icons for computer desktop or graphical user interface of computer program.
