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.

Isometric projection is a form of graphical projection — more specifically, an axonometric 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. Rio de Janeiro birds-eye view. ... A worms-eye view is a view of an object from below, as though the observer were a worm. ... Grand Theft Auto Top-down perspective, also sometimes referred to as birds-eye view or helicopter view, is a view used in computer and video games that shows the player and the area around him or her from above. ... The Mercator projection shows courses of constant bearing as straight lines. ... Image File history File links No higher resolution available. ... Image File history File links No higher resolution available. ... Graphical projection in the visual sciences is an imaging procedure the protocols of which preclude the necessity of mathematical calculation. ... Example of a dimetric axonometric drawing from a US Patent (1874). ... Stereo card image modified for crossed eye viewing. ... A coordinate axis is one of a set of vectors that defines a coordinate system. ... Technical drawing, also known as drafting, is the practice of creating accurate representations of objects for technical, architectural and engineering needs. ... An engineering drawing is a type of drawing that is technical in nature, used to fully and clearly define requirements for engineered items, and is usually created in accordance with standardized conventions for layout, nomenclature, interpretation, appearance (such as typefaces and line styles), size, etc. ...

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 or farther to or from the viewer.

Visualization

An isometric projection of a Bayer filter on a CCD

Corresponding camera rotations

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). Image File history File links Bayer_pattern_on_sensor. ... Image File history File links Bayer_pattern_on_sensor. ... The Bayer arrangement of color filters on the pixel array of an image sensor Front page of Dr. Bryce Bayers 1976 patent on the Bayer pattern filter mosaic, showing his terminology of luminance-sensitive and chrominance-sensitive elements A Bayer filter mosaic is a color filter array (CFA) for... A specially developed CCD used for ultraviolet imaging in a wire bonded package. ... Image File history File links No higher resolution available. ... Image File history File links No higher resolution available. ... A coordinate axis is one of a set of vectors that defines a coordinate system. ...

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). A scale is either a device used for measurement of weights, or a series of ratios against which different measurements can be compared. ...

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. Image File history File links IsometricFlaw_2. ... Image File history File links IsometricFlaw_2. ... In computer graphics, a sprite (also known by other names; see Synonyms below) is a two-dimensional image or animation that is integrated into a larger scene. ... “Computer and video games” redirects here. ... Perspective projection is a type of drawing that graphically approximates on a planar (two-dimensional) surface (e. ... 3D computer graphics are different from 2D computer graphics in that a three-dimensional representation of geometric data is stored in the computer for the purposes of performing calculations and rendering 2D images. ... Maurits Cornelis Escher (June 17, 1898 – March 27, 1972), usually referred to as M. C. Escher, was a Dutch graphic artist known for his often mathematically inspired woodcuts, lithographs and mezzotints which feature impossible constructions, explorations of infinity, architecture, and tessellations. ... Waterfall is a lithograph print by the Dutch artist M.C. Escher which was first printed in October, 1961. ...

"Isometric" projection in video games and pixel art

A television set drawn in near- isometric pixel art. Note the 2:1 pixel pattern ratio in this zoomed-in image.

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. Image File history File links No higher resolution available. ... Image File history File links No higher resolution available. ... This monster (The Gunk) is an example of pixel art drawn using Microsoft Paint. ... “Computer and video games” redirects here. ... This monster (The Gunk) is an example of pixel art drawn using Microsoft Paint. ... 2D computer graphics is the computer-based generation of digital images—mostly from two-dimensional models (such as 2D geometric models, text, and digital images) and by techniques specific to them. ... A tile-based game is a game that uses tiles as one of the fundamental elements of play. ... 3D computer graphics are different from 2D computer graphics in that a three-dimensional representation of geometric data is stored in the computer for the purposes of performing calculations and rendering 2D images. ... Perspective when used in the context of vision and visual perception refers to the way in which objects appear to the eye based on their spatial attributes or dimension and the position of the eye relative to the objects. ... In the history of video games, the 8-bit era was the third generation of video game consoles, but the first after the video game crash of 1983 and considered by some to be the first modern era of console gaming. ... In the history of video games, the 16-bit era was the fourth generation of video game consoles. ... A handheld game console is a lightweight, portable electronic machine for playing video games. ...

Blurring of the definition

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" or "genuine" 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. Image File history File links Wikipedia_dimetric_cube_3. ... Image File history File links Wikipedia_dimetric_cube_3. ... Suppose the smiley face in the top left corner is an RGB bitmap image. ... In digital signal processing, anti-aliasing is the technique of minimizing the distortion artifacts known as aliasing when representing a high-resolution signal at a lower resolution. ... This example shows an image with a portion greatly enlarged, in which the individual pixels are rendered as little squares and can easily be seen. ... Example of a dimetric axonometric drawing from a US Patent (1874) Dimetric projection is a form of axonometric projection, in which its direction of viewing is such that two of the three axes of space appear equally foreshortened, of which the attendant scale and angles of presentation are determined according... An example of the 3/4 game perspective, taken from the Zelda game The Minish Cap. ...

More blurring

Increasingly, the term is being applied to games that don't use any form of axonometric projection. Games that use oblique projection, such as Ultima VI, as well as games that use perspective projection, such as Age of Decadence^[1], are sometimes referred to as being isometric, or "pseudo-isometric", due to visual similarities or similarities in how the game allows a greater field of view over a large playing field. In the latter case, "bird's-eye view" might be more appropriate. This article needs to be cleaned up to conform to a higher standard of quality. ... Ultima VI: The False Prophet, released in 1990, is the sixth part in the computer role-playing game series of Ultima. ... Perspective projection is a type of drawing that graphically approximates on a planar (two-dimensional) surface (e. ... Age of Decadence is an old school isometric 3D turn-based computer role-playing game by Iron Tower Studios. ... Rio de Janeiro birds-eye view. ...

Notable examples of "isometric" computer and video games

A game which uses "isometric" graphics (Lincity).

• Q*bert (1982) : An arcade hit.
• Zaxxon (1982) : Early arcade space flight fight.
• 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) : Popular action-adventure game from the end of the 8-bit computer era.
• La Abadía del Crimen (The Abbey of Crime) (1988).
• Populous (1989) : God simulator.
• Snake Rattle 'n' Roll (1990) : An action/platformer game.
• Cadaver (1990) : Adventure/role-playing game.
• A-Train (1992) : Simulation/Buisness
• Landstalker (1992) : Platformer/role-playing game.
• SimCity 2000 (1993) : City building simulation game.
• Little Big Adventure (1994) : an action-adventure game
• Civilization II (1996) : Turn-based strategy game.
• Super Mario RPG (1996) : A role-playing game.
• Age of Empires (1997) : History-based RTS game.
• Final Fantasy Tactics (1997) : A strategic role-playing 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.
• The Sims (2000) : A simulation of people controlled by the player.

Image File history File links No higher resolution available. ... Image File history File links No higher resolution available. ... Lincity is a Sim game which puts the player in control of managing every aspect of a citys socio-economy. ... For the Futurama character, see Cubert Farnsworth. ... Zaxxon is a 1982 arcade game developed by Ikegami Tsushinki and released by Sega. ... 3D Ant Attack is a ZX Spectrum computer game by Sandy White. ... Congo Bongo (J: Tip Top )) is an arcade game developed by Ikegami Tsushinki and released by Sega in 1983. ... Knight Lore is a computer game developed and released by Ultimate Play The Game in 1984. ... Marble Madness is an arcade game by Atari Games released in 1984. ... Spindizzy is a computer game released in 1986 for the Commodore 64 computer. ... For the rock group Cocteau Twins album, see Head over Heels Head Over Heels is a arcade adventure, first released in 1987 for Z80-microprocessor-based home computers (ZX Spectrum, Amstrad CPC, MSX) by Jon Ritman (game design and programming) and Bernie Drummond (graphics). ... La Abadía del Crimen (The Abbey of Crime) is a computer video game programmed in 1988 by Paco Menéndez based in the novel The Name of the Rose written by Umberto Eco. ... Rattle in Level 1 Snake Rattle n Roll is a 1991 video game designed by Rare Ltd. ... Platform games, or platformers, are a very popular genre of video games that originated in the early 1980s. ... Screenshot out of episode The last supper Cadaver is an isometric adventure game by the Bitmap Brothers, originally released on the Amiga by Image Works in 1990. ... A Train or the variant A-Train may mean: A-Train, a computer game developed by Artdink in 1992 the A-C (New York City Subway service), made famous by the jazz song Take the A Train the Green Line A Branch in Boston, Massachusetts a set of five environmental... Landstalker: The Treasures of King Nole is a Sega Mega Drive game somewhat similar to The Legend of Zelda: A Link to the Past game that was available on the competing SNES at the time. ... SimCity 2000 (SC2K) is a simulation/city building computer game and the second installment in the SimCity series. ... This article is about the general term. ... Little Big Adventure (LBA) is a computer game developed by Adeline first released at the end of 1994. ... Sid Meiers Civilization II, a. ... A turn-based game, also known as turn-based strategy (TBS), is a game where the game flow is partitioned into well-defined and visible parts, called turns or rounds. ... Super Mario RPG: Legend of the Seven Stars (スーパーマリオRPG) was the last Mario game made and released for the Super Famicom/Super Nintendo Entertainment System, and was the last Square-produced game for a Nintendo video game console until 2003, with the debut of Final Fantasy: Crystal Chronicles for the... Age of Empires, abbreviated to AoE or AOE, is a history-based real-time strategy computer game released in 1997. ... For the similar computer game genre, see Real-time tactics. ... Final Fantasy Tactics ) is a tactical role-playing game developed and published by Square (now Square Enix) for the Sony PlayStation video game console. ... A tactical role-playing game (usually simply called tactical RPG, sometimes referred to as strategy role-playing game or SRPG) is a type of computer role-playing game (CRPG) in which the focus of the gameplay is on making tactical decisions in battles. ... Baldurs Gate is a computer role-playing game in a high fantasy setting, developed by BioWare and released in 1998 by Interplay Entertainment. ... It has been suggested that Forgotten Realms Campaign Setting be merged into this article or section. ... “D&D” redirects here. ... “Starcraft” redirects here. ... For games with Sim in the title, see List of Sim games. ...

References

See also

• Filmation engine

Filmation in Knight Lore Filmation II in Nightshade Filmation is the trademark name of the isometric graphics engine employed in a series of games developed by Ultimate Play The Game during the 1980s, primarily on the 8-bit ZX Spectrum platform (although also on the BBC Micro, Amstrad CPC, and...

External links

• Explanation and tutorial on drawing in "isometric" perspective from the University of Hertfordshire
• Comprehensive document to derive the basic formulae for isometric projections (ASP)