Isometric graphics in video games and pixel art

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In video games and pixel art, "isometric" refers to some form of axonometric projection (commonly, the form of dimetric projection with a 2:1 pixel ratio) where the viewpoint is angled to reveal other facets of the game environment than are typically visible from a purely top-down perspective or side view, thereby producing a three-dimensional effect. In almost all cases, however, the term "isometric" is misapplied; in true isometric projection, the representations of the x, y and z axes are strictly oriented 120° to each other, whereas in other projections the angles vary. The terms "3/4 perspective", "2.5D" and "pseudo-3D" are also frequently applied, though these terms can possess slightly different meanings in different contexts.

Once common, isometric projection became less so with the advent of more powerful 3D graphics systems, and as games began to focus more on the action and on individual characters.^[1] However, isometric projection has seen somewhat of a resurgence in recent years, especially on Kickstarter.^[1][2]

Overview

True isometric drawing of a cube. Note the 120° angles separating the x, y and z axes, as well as the equal lengths of each of the cube's edges.

Common form of dimetric projection used in video games and pixel art. The angle 26.565° forms a 2:1 pixel ratio, and is equal to arctan 0.5.

Advantages

In the fields of computer and video games and pixel art, the technique has become popular because of the ease with which 2D sprite- and tile-based graphics can be made to represent a 3D gaming environment. Because parallelly projected objects do not change size as they move about the game field, there is no need for the computer to scale sprites or do the complex calculations necessary to simulate visual perspective. This allowed older 8-bit and 16-bit game systems (and, more recently, handheld and mobile systems) to portray large 3D areas easily. And, while the depth confusion problems of parallel projection can sometimes be a problem, good game design can alleviate this.

There are also gameplay advantages to using an isometric or pseudo-isometric perspective in video games. For instance, compared to a purely top-down game, they add a third dimension, opening up new avenues for aiming and platforming.^[1] Secondly, compared to a first- or third-person game, they allow you to more easily field and control a larger number of additional units, such as a full party of characters in a role-playing game.^[1] Further, they may alleviate situations where a player may become distracted from a game's core mechanics by having to constantly manage an unwieldy 3D camera.^[1] I.e. the player can focus on playing the game itself, and not on moving and rotating the camera.^[1]

Lastly, there is an artistic advantage. Though not limited strictly to isometric video games, pre-rendered 2D graphics can possess a higher fidelity and use more advanced techniques than may be possible on commonly available computer hardware, even with 3D hardware acceleration enabled.^[3] Similarly to modern CGI used in motion pictures, graphics can be rendered once on a powerful super computer or render farm, and then displayed on less powerful consumer hardware, such as tablet computers and Web browsers. This means that static pre-rendered isometric graphics often look better compared to their real-time rendered counterparts, and may age better over time compared to their peers.^[2] However, this advantage may be less pronounced now than it was in the past.

One disadvantage of pre-rendered graphics is that, as display resolutions continue to increase, the static 2D images need to ideally be re-rendered to keep pace, or otherwise suffer from pixelation. This is not always possible, however; as was the case in 2012, when BioWare's Baldur's Gate (1998) was remade into Baldur's Gate: Enhanced Edition by the studio Beamdog. The new developer opted for simple 2D graphics scaling, or "zooming", without re-rendering the game's sprites, as they were lacking the game's original creative art assets. (The original data was lost in a flood.^[4]) Changing the resolution of a real-time rendered game is trivial, in comparison.

Differences with "true" isometric projection

Corresponding 3D camera rotation angles for true isometric projection (at left) and the form of dimetric perspective commonly found in video games and pixel art (at right).^[5] The angle 35.264° is equal to arctan(sin(45°)).

The projection commonly used in videogames deviates slightly from "true" isometric due to the limitations of raster graphics. Lines in the x and y directions 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 axis 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.) Therefore, 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 to each other (116.565°, 116.565°, 126.870°).

History of isometric video games

While the history of computer games saw some true 3D games as soon as the early 1970s, the first video games to use the distinct visual style of isometric projection in the meaning described above were arcade games in the early 1980s.

1980s

Zaxxon from 1982 was the first game to use an isometric view.

The use of isometric graphics in video games began with the appearance of Sega's Zaxxon,^[6][7] released as an arcade game in January 1982.^[8] It is an isometric shooter where the player flies a space plane through scrolling levels. It is also one of the first video games to display shadows.^[6]

Another early isometric game is Q*bert,^[9] which Warren Davis and Jeff Lee began programming in April 1982 and released in October/November 1982.^[10] Q*bert shows a static pyramid in an isometric perspective, with the player controlling a character which can jump around on the pyramid.^[6]

The following year in March 1983, the isometric platformer arcade game Congo Bongo was released, running on the same hardware as Zaxxon.^[11] It allows the player character to move around in bigger isometric levels, including true three-dimensional climbing and falling. The same is possible in the arcade title Marble Madness, released in 1984.

2D (at left) and 3D (at right) coordinates of a typical dimetric video game sprite.

At this time, isometric games were no longer exclusive to the arcade market and also entered home computers with the release of Blue Max for the Atari 8-bit family and Ant Attack for the ZX Spectrum in 1983. In Ant Attack, the player could move forward in any direction of the scrolling game, offering complete free movement rather than fixed to one axis as with Zaxxon. The views could also be changed around a 90 degrees axis.^[12] The ZX Crash magazine consequently awarded it 100% in the graphics category for this new technique, known as "Soft Solid 3-D".^[13]

A year later the ZX Spectrum saw the release of Knight Lore, which is generally regarded as a revolutionary title^[14] that defined the subsequent genre of isometric adventure games.^[15] Following Knight Lore, many isometric titles were seen on home computers – to an extent that it once was regarded as being the second most cloned piece of software after WordStar, according to researcher Jan Krikke.^[16] Other examples out of those were Highway Encounter (1985), Batman (1986), Head Over Heels (1987)^[17] and La Abadía del Crimen (1987). Isometric perspective was not limited to arcade/adventure games, though; for example, the 1989 strategy game Populous used isometric perspective.

1990s

A television set drawn in near-isometric 2:1 pixel art. (Enlarged to show the pixel structure.)^[18]

POV-Ray render mimicking Fallout's trimetric projection and hexagonal grid.

Throughout the 1990s some very successful games like SimCity 2000 (1994), Civilization II (1996), X-COM (1994), and Diablo (1996) used a fixed isometric perspective. But with the advent of 3D acceleration on personal computers and gaming consoles, games previously using a 2D perspective generally started turning to true 3D (e.g. perspective projection) instead. This can be seen in the successors to the above games: For instance SimCity (2013), Civilization VI (2016), XCOM: Enemy Unknown (2012) and Diablo III (2012) all use full 3D; and while Diablo II (2000) used a fixed perspective like its predecessor, it optionally allowed for perspective scaling of the sprites in the distance to lend it a "pseudo-3D" appearance.^[19]

Also during the 1990s, isometric graphics began being used for Japanese role-playing video games (JRPGs) on console systems, particularly tactical role-playing games, many of which still use isometric graphics today. Examples include Front Mission (1995), Tactics Ogre (1995) and Final Fantasy Tactics (1997)—the latter of which used 3D graphics to create an environment where the player could freely rotate the camera. Other titles such as Vandal Hearts (1996) and Breath of Fire III (1997) carefully emulated an isometric view, but actually used perspective projection.

Infinity Engine

Black Isle Studios and Interplay Entertainment helped popularize the use of isometric projection in role-playing games in the late 1990s and early 2000s, alongside BioWare, a famous studio whose early games Interplay published. These studios utilized the Infinity Engine game engine in several of their titles, which was created by BioWare for Baldur's Gate (1998). This engine gained significant traction among players, and many developers since then have tried to emulate and improve upon it in various ways.^[1] The Infinity Engine itself has also been revamped and modernized recently in preparation for Beamdog's Baldur's Gate: Enhanced Edition (2012), as well as for remakes of other classic Infinity Engine titles. Two other titles by Black Isle Studios, Fallout (1997) and Fallout 2 (1998), used trimetric projection.

Kickstarter

Isometric projection has seen continued relevance in the new millennium with the release of several newly-crowdfunded role-playing games on Kickstarter.^[1] These include the Shadowrun Returns series (2013-2015) by Harebrained Schemes; the Pillars of Eternity series (2015-2017) and Tyranny (2016) by Obsidian Entertainment; and Torment: Tides of Numenera (2017) by inXile Entertainment. Both Obsidian Entertainment and inXile Entertainment have employed, or were founded by, former members of Black Isle Studios and Interplay Entertainment; and Obsidian Entertainment in particular wanted to "bring back the look and feel of the Infinity Engine games like Baldur's Gate, Icewind Dale, and Planescape: Torment" with Pillars of Eternity.^[1] Lastly, several pseudo-isometric RPGs, such as Divinity: Original Sin (2014), Wasteland 2 (2014) and Dead State (2014), have also been crowdfunded using Kickstarter in recent years. These titles differ from the above games, however, in that they use perspective projection instead of parallel projection.

Rather than being based purely on nostalgia, the revival of isometric projection is based on its real, tangible benefits as well.^[1]

Similar projections

The term "isometric perspective" is often misapplied to any game with an—usually fixed—angled, overhead view that appears at first to be "isometric". These include games that utilize trimetric projection, such as Fallout (1997)^[20] and Fallout 2 (1998), as well as SimCity 4 (2003);^[21] games that utilize oblique projection, such as The Legend of Zelda: A Link to the Past (1991),^[22] Divine Divinity (2002)^[23] and Ultima Online (1997);^[24] and games that utilize a combination of perspective projection and a bird's eye view, such as Silent Storm (2003),^[25] Torchlight (2009)^[26] and Divinity: Original Sin (2014).^[27] There are also titles that utilize polygonal 3D graphics, but still render their graphics to the screen using parallel projection. These include Syndicate Wars (1996), Dungeon Keeper (1997) and Depths of Peril (2007). Finally, there are a number of games that use a mix of pre-rendered and real-time rendered isometric graphics, including The Temple of Elemental Evil (2003) and Torment: Tides of Numenera (2017), which use pre-rendered 2D backgrounds and real-time rendered 3D character models; and Final Fantasy Tactics (1997) and Disgaea: Hour of Darkness (2003), which use real-time rendered 3D backgrounds and pre-drawn 2D character sprites.

Mapping screen to world coordinates

Finding world coordinates

Comparison of several types of graphical projection. The presence of one or more 90° angles is often a good indication that the perspective used is oblique projection.

One of the most common problems with programming games that use isometric (or more likely dimetric) projections is the ability to map between events that happen on the 2d plane of the screen and the actual location in the isometric space, called world space. A common example is picking the tile that lies right under the cursor when a user clicks. One such method is using the same rotation matrices that originally produced the isometric view in reverse to turn a point in screen coordinates into a point that would lie on the game board surface before it was rotated. Then, the world x and y values can be calculated by dividing by the tile width and height.

Another way that is less computationally intensive and can have good results if our method is called on every frame, rests on the assumption that a square board was rotated by 45 degrees and then squashed to be half its original height. A virtual grid is overlaid on the projection as shown on the diagram, with axes virtual-x and virtual-y. Clicking any tile on the central axis of the board where (x, y) = (tileMapWidth / 2, y), will produce the same tile value for both world-x and world-y which in this example is 3 (0 indexed). Selecting the tile that lies one position on the right on the virtual grid, actually moves one tile less on the world-y and one tile more on the world-x. This is the formula that calculates world-x by taking the virtual-y and adding the virtual-x from the center of the board. Likewise world-y is calculated by taking virtual-y and subtracting virtual-x. These calculations measure from the central axis, as shown, so the results must be translated by half the board. For example, in the C programming language:

float virtualTileX = screenx / virtualTileWidth;
float virtualTileY = screeny / virtualTileHeight;

// some display systems have their origin at the bottom left while the tile map at the top left, so we need to reverse y
float inverseTileY = numberOfTilesInY - virtualTileY;

float isoTileX = inverseTileY + (virtualTileX - numberOfTilesInX / 2);
float isoTileY = inverseTileY - (virtualTileY - numberOfTilesInY / 2);

This method might seem counter intuitive at first since the coordinates of a virtual grid are taken, rather than the original isometric world, and there is no one-to-one correspondence between virtual tiles and isometric tiles. A tile on the grid will contain more than one isometric tile, and depending on where it is clicked it should map to different coordinates. The key in this method is that the virtual coordinates are floating point numbers rather than integers. A virtual-x and y value can be (3.5, 3.5) which means the center of the third tile. In the diagram on the left, this falls in the 3rd tile on the y in detail. When the virtual-x and y must add up to 4, the world x will also be 4.

Gallery

• 
  LinCity-NG (2005), a tile-based city-building game
• 
  Ravenwood Fair (2010), a business simulation game
• 
  Goodgame Empire (2011)
• 
  FreeCol (2003) is a 4X strategy game
• 
  The MMORPG, Daimonin, in its fourth beta
• 
  Vulture's Eye, a roguelike
• 
  OpenTTD (2004) is a business simulation game
• 
  A party of adventurers in the role-playing game, Tales of Trolls & Treasures
• 
  Freeciv (1996) is a 4X strategy game
• FreedroidRPG is a point-and-click action RPG

See also

• Clipping
• Filmation engine
• Category:Video games with isometric graphics: listing of isometric video games
• Category:Video games with oblique graphics: listing of oblique video games
• Commons:Category:Isometric video game screenshots: gallery of isometric video game screenshots

References

External links

• The classic 8-bit isometric games that tried to break the mould at Eurogamer.com
• The Best-Looking Isometric Games at Kotaku.com
• The Best Isometric Video Games at Kotaku.com