Anamorphosis is a distorted projection or perspective requiring the viewer to use special devices or occupy a specific vantage point (or both) to reconstitute the image. An optical anamorphism is the visualization of a mathematical operation called an affine transformation. The process of extreme anamorphosis has been used by artists to disguise caricatures, erotic and scatological scenes, and other furtive images from a casual viewer, while revealing an undistorted image to the knowledgeable spectator.

Anamorphosis is a reversible deformation of an image using an optical system – for example a curved mirror – or a mathematical transformation. Anamorphosis is also known as the distortion of the image of a film or television program using an optical or electronic system in order to adapt it to a computer or television screen (anamorphic wide format, format 4/3 or 16/9). The word derives from the Greek ἀναμορφόω, anamorphoein, “transform”.

Some artists created by this process deformed works that recompose from a pre-established point of view. Historically, anamorphosis is one of the applications of Piero della Francesca’s work († 1492) on perspective. Indeed, it is the rationalization of the vision that has led to systematize the projection techniques, whose anamorphoses are one of the results. Albrecht Dürer’s “art of secret perspective” has many applications in architecture and trompe-l’oeil as well as in utilitarian uses. His first theorist was Jean-Louis Vaulezard (seventeenth century). The last surviving wall anamorphosis in France (8 meters long) is in the Jesuit chapel of the Sacré-Coeur high school in Aix-en-Provence.

There are two main types of anamorphosis: perspective (oblique) and mirror (catoptric). More-complex anamorphoses can be devised using distorted lenses, mirrors, or other optical transformations.

Examples of perspectival anamorphosis date to the early Renaissance (fifteenth century). Examples of mirror anamorphosis were first seen in the late Renaissance (sixteenth century).

With mirror anamorphosis, a conical or cylindrical mirror is placed on the drawing or painting to transform a flat distorted image into an apparently undistorted picture that can be viewed from many angles. The deformed image is painted on a plane surface surrounding the mirror. By looking into the mirror, a viewer can see the image undeformed.

Anamorphoses are used in statistical mapping to show the importance of a given phenomenon: this type of map is commonly called a cartogram. The map no longer represents the geographical reality, but the reality of the phenomenon. For example, one commune will be enlarged compared to the others if it contains more unemployed than the average of the others.

Anamorphosis maps are also used to perceive the effects of transport networks, for example the rail transport network in France. Because the means of transport distort the space: geographically, Marseille is farther from Paris than Périgueux, but since one can go faster to Marseille by the fast TGV line, this last city will be placed on the map closer to Paris. Thus, space can be differently perceived if we consider human mobility.

Finally, anamorphosis can be used to highlight some important details. For example, for city maps or road maps, roads (streets, roads, highways) are represented larger than they would be at scale, while their length is scaled.

Leonardo’s Eye (Leonardo da Vinci, c. 1485) is the earliest known definitive example of perspective anamorphosis in modern times. The prehistoric cave paintings at Lascaux may also use this technique, because the oblique angles of the cave would otherwise result in distorted figures from a viewer’s perspective.

Hans Holbein the Younger is well known for incorporating an oblique anamorphic transformation into his painting The Ambassadors. In this artwork, a distorted shape lies diagonally across the bottom of the frame. Viewing this from an acute angle transforms it into the plastic image of a human skull, a symbolic memento mori. During the seventeenth century, Baroque trompe l’oeil murals often used anamorphism to combine actual architectural elements with illusory painted elements. When a visitor views the art work from a specific location, the architecture blends with the decorative painting. The dome and vault of the Church of St. Ignazio in Rome, painted by Andrea Pozzo, represented the pinnacle of illusion. Due to neighboring monks complaining about blocked light, Pozzo was commissioned to paint the ceiling to look like the inside of a dome, instead of building a real dome. As the ceiling is flat, there is only one spot where the illusion is perfect and a dome looks undistorted.

Mirror anamorphosis emerged early in the 17th century in Italy and China. It remains uncertain whether Jesuit missionaries imported or exported the technique.

Anamorphosis could be used to conceal images for privacy or personal safety. A secret portrait of Bonnie Prince Charlie (now held at the West Highland Museum, Scotland) is painted in a distorted manner on a tray and can only be recognized when a polished cylinder is placed in the correct position. To possess such an image would have been seen as treason in the aftermath of the 1746 Battle of Culloden.

In the eighteenth and nineteenth centuries, anamorphic images had come to be used more as children’s games than fine art. In the twentieth century, some artists wanted to renew the technique of anamorphosis. Marcel Duchamp was interested in anamorphosis, and some of his installations are “visual paraphrases” of anamorphoses (see The Bride Stripped Bare by Her Bachelors, Even / The Large Glass). Jan Dibbets conceptual works, the so-called “perspective corrections” are examples of “linear” anamorphoses. In the late twentieth century, mirror anamorphosis was revived as children’s toys and games.

Surrealist artist Salvador Dalí used extreme foreshortening and anamorphism in his paintings and works, and had a glass floor installed in a room next to his studio to enable radical perspective studies from above and below. His Dalí Theatre and Museum in Figueres, Spain features a 3-dimensional anamorphic living-room installation with custom furniture that looks like the face of Mae West when seen from a certain viewpoint.

Anamorphosis improves the readability of messages or symbols seen from a distance. In this case, the optical distortion experienced by the pattern represented because of the acute angle under which it is seen by the viewer is detrimental to his understanding. This disadvantage can be circumvented thanks to the anamorphosis which makes it possible to restore satisfactory optical proportions for the good perception of the message.

Since the 1990s, advertisers have exploited the playground of some sports as advertising space. The process appeared in the United States in the context of sports using synthetic surfaces (eg American football) or parquet (eg basketball). This practice was transposed in Europe on sports using turf, especially rugby, but the shooting angle of the cameras broadcasting the matches on television distorted the logotypes and made them appear very elongated. Anamorphoses have therefore been applied to the visuals of the advertisers so as to appear on the screen in a manner consistent with the original appearance of the logo.

Beginning in 1967, Dutch artist Jan Dibbets based an entire series of photographic work titled Perspective Corrections on the distortion of reality through perspective anamorphosis. The Swedish artist Hans Hamngren produced and exhibited many examples of mirror anamorphosis in the 1960s and 1970s. Shigeo Fukuda, a Japanese artist, designed both types of anamorphosis in the 1970s and 1980s. Patrick Hughes, Fujio Watanabe, William Kentridge, István Orosz, Felice Varini, Matthew Ngui, Kelly Houle, Nigel Williams, and Judy Grace are artists creating anamorphic images.

Un carré pour un square is an anamorphosis made by the French artist Jean-Max Albert in 1988. From the specific vantage point, the perspective of a square is seen, inscribed in Place Fréhel, Paris, France. The design is formed by a set of lines of narrow plates of Carrara marble imbricated in the walls of the surrounding buildings and in the vestiges of a former construction site. A low wall and a pillar in masonry were created to shape the other side of the design. In another example by the same artist, the specific vantage point is indicated by one of the Observation Sculptures set in Paris, Parc de la Villette. In this work, the anamorphosis appears as a reflection of a bronze construction This reflection discreetly shows the inclusion of a circle in a square in a triangle, in reference to the concept plan of the park by the architect Bernard Tschumi.Notably, Reflet Anamorphose allows, from the specific vantage point, to observe simultaneously the design and its anamorphosis.

From 2006, artist Jonty Hurwitz pioneered the area of anamorphic sculpture using mathematical techniques and 3D printing. His work rose to fame in early 2013 when it was blogged by art critic Christopher Jobson on his Webby Award-winning site Colossal, receiving 30 million views online. The Savoy Hotel engaged Hurwitz as artist in residence to produce an anamorphic work for their River Room, for a restaurant called Kaspars.

The Dutch artist Leon Keer made an optical illusion painting with a life-size mirror cylinder during the 3-D street painting event FringeMK, in 2010.

Another form of anamorphic art is often called “Slant Art”. Examples are the sidewalk chalk drawings of Kurt Wenner and Julian Beever, where the chalked image, the pavement, and the architectural surroundings all become part of an illusion. Art of this style can be produced by taking a photograph of an object or setting at a sharp oblique angle, then putting a grid over the photograph. Another elongated grid is placed on the sidewalk based on a specific perspective, and visual elements of one are transcribed into the other, one grid square at a time.

In November, 2011, an article published on the website of the Smithsonian magazine questioned if an anamorphic garden work by French artist François Abélanet featured in front of Paris city hall, the Hôtel de Ville entitled, “Qui croire?” (“Who to believe?”) was really the “World’s Greatest New Artwork?”, citing an online video of it.

Road signage painted directly on the ground also uses this method so that road users have a non-distorted view of an image or text when they are at a distance. In many countries, an anamorphosis is used to indicate a bike path, a bicycle painted on the ground and seems stretched in height when viewed from above.

Some packages are printed flexographically (a sort of ink pad, which allows printing in many colors and large dimensions, up to 1.3 m × 2 m, including thin films such as plastic bags9). The drawing on the matrix must be stretched in the direction of scrolling, so anamorphic.

Likewise, printing on a cylindrical support, of bobbin type, or of more complex shape, requires having an anamorphic pattern on the matrix10. A number of packages are deformed polymer sheets (thermoforming, blowing), for example to give trays.

In the twentieth century, artists began to play with perspective by drawing “impossible objects”. These objects included stairs that always ascend, or cubes where the back meets the front. Such works were popularized by the artist M. C. Escher and the mathematician Roger Penrose. Although referred to as “impossible objects”, such objects as the Necker Cube and the Penrose triangle can be sculpted in 3-D by using anamorphic illusion. When viewed at a certain angle, such sculptures appear as the so-called impossible objects.

Cinemascope, Panavision, Technirama, and other widescreen formats use anamorphosis to project a wider image from a narrower film frame. The IMAX company uses even more extreme anamorphic transformations to project moving images from a flat film frame onto the inside of a hemispheric dome, in its “Omnimax” or “IMAX Dome” process.

The technique of anamorphic projection can be seen quite commonly on text written at a very flat angle on roadways, such as “Bus Lane” or “Children Crossing”, to make it easily read by drivers who otherwise would have difficulty reading obliquely as the vehicle approaches the text; when the vehicle is nearly above the text, its true abnormally elongated shape can be seen. Similarly, in many sporting stadiums, especially in Rugby football in Australia, it is used to promote company brands which are painted onto the playing surface; from the television camera angle, the writing appear as signs standing vertically within the field of play.

Much writing on shop windows is in principle anamorphic, as it was written mirror-reversed on the inside of the window glass.

Since 1993, Myrna Hoffman’s company, OOZ & OZ, has been producing mirror anamorphosis art kits and activities for children, such as the “Morph-O-Scopes” kit. Hoffman’s kits have earned more than two dozen national toy awards.

Rick Wakeman’s 1976 album No Earthly Connection featured front and back cover photographs that are mirror anamorphoses. The original vinyl release included a mirrored Mylar sheet which could be curled into a cylinder for viewing the images.

In the 2007 detective film Anamorph, the plot line revolves around the solution of gruesome anamorphically distorted images.

Some 0.5 liter Sprite bottles in Europe were imprinted with what appeared to be an extra “bar code”. When the bottle was tilted towards the mouth while drinking, the bar code resolved into writing, due to the oblique perspective.

The 2009 video game Batman: Arkham Asylum has a series of riddles posed by the classic Batman antagonist The Riddler, the solution of which is based on perspective anamorphosis.

In 2013, Honda released a commercial which incorporated a series of illusions based on anamorphosis.