Isometric projection

File:Perspective isometrique cube gris 2.svg

An isometric drawing of a cube. Note that the perimeter of the 2D drawing is a perfect regular hexagon, all the black lines are of equal length and all the cube's faces are the same area.

Corresponding camera rotations

Isometric projection is a form of graphical projection — more specifically, an axonometric orthographic 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 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). Isometric projection is one of the projections used in drafting engineering drawings.

Limits of isometric projection

The blue sphere is two levels higher than the red one, but this cannot be seen if one looks only at the left half of the picture. If the pier that the blue sphere is on were extended by one square, it would align perfectly with the square the red sphere is on, creating an optical illusion, making it look like both spheres are on the same level.

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.

"Isometric" projection in video games and pixel art

A television set drawn in near- isometric 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.

Corresponding camera rotations for the form of dimetric perspective commonly found in video games and pixel art

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 "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.

Notable examples of "isometric" computer and video games

Knight Lore was among the first games to use 3/4 perspective.

File:ExampleSimCityCity.PNG

SimCity 2000 is one of many games that use 3/4 perspective.

• Q*bert (1982) : An arcade hit. Truly isometric.
• Zaxxon (1982) : Early arcade space flight fight. Truly isometric.
• 3D 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
• Head over Heels (1987) : The pinnacle of isometric games of the 8-bit home 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) : Action RPG
• SimCity 2000 (1993) : City building simulation game
• Crusader: No Remorse (1995) : Computer action 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
• RollerCoaster Tycoon (1999): Theme park simulation 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

External links

• Explanation of isometric projection from the University of Limerick
• Explanation and tutorial on drawing in Isometric from the University of Hertfordshire
• The Complete Guide to Isometric Pixel Art