Anamorphosis is a distorted projection or perspective requiring the viewer to occupy a specific vantage point, use special devices or both to view a recognizable image. Some of the media it is used in are painting, photography, sculpture and installation, toys, and film special effects. The word "anamorphosis" is derived from the Greek prefix ana‑, meaning "back" or "again", and the word morphe, meaning "shape" or "form". 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.
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.
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. The deformed image is created by using the laws of the angles of the incidence of reflection. This reduces the length of the flat drawing's curves when the image is viewed in a curved mirror, so that the distortions resolve into a recognizable picture. Unlike perspective anamorphosis, catoptric images can be viewed from many angles. The technique was originally developed in China during the Ming Dynasty. The first European manual on mirror anamorphosis was published around 1630 by the mathematician Vaulezard.
With Channel anamorphosis or tabula scalata two different images are on different sides of a corrugated carrier. A straight frontal view shows an unclear mix of the images, while each image can be viewed correctly from a certain angle.
The prehistoric cave paintings at Lascaux may make use of anamorphic technique, because the oblique angles of the cave would otherwise result in distorted figures from a viewer's perspective. The ancient historians Pliny and Tzetzes both record a sculpture competition between Alcamenes and Phidias to create an image of Minerva. Alcamenes' sculpture was beautiful, while Phidias' had grotesque proportions. Yet once both had been mounted on pillars, the decelerated perspective made Phidias' Minerva beautiful and Alcamenes' ugly.
During the Renaissance, artists' experimentation with optics and perspective led to more advanced development of anamorphic imagery. At this time, religious thought and science were equally important to the technique's growth in Europe.  The earliest known example, known as Leonardo's Eye, was executed by Leonardo da Vinci and is included in the Codex Atlanticus (1483-1518). He later completed several large-scale anamorphic commissions for the King of France. Giacomo Barozzi da Vignola credited Tommaso Laureti as the originator of a perspectival anamorphic technique in one of the earliest written descriptions in The Two Rules of Practical Perspective, compiled between 1530 and 1540 but not published until 1583. Without access to Vignola's work, many other descriptions and examples were created before 1583.
The Ambassadors (c. 1533) by Hans Holbein the Younger is well known for the prominent oblique anamorphic transformation in the painting. 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. The painting is regarded as a vanitas - a meditation on the transience of life - with the skull a symbolic memento mori. The altered perspective required to see the image reflects the contemporary practice of painting skulls on the reverse of otherwise tranquil paintings. Four centuries later, the painting inspired the psychoanalyst Jaques Lacan to note in 'Of the Gaze as Objet Petit a' (1973) that the use of anamorphism, particularly in this painting, is one of the few methods for making viewers aware of their gaze.
By the 17th century, a revival of fantastical anamorphic imagery occurred. Magical and religious connotations were largely abandoned, and the images were understood as a scientific curiosity. Two major works on perspective were published: Perspective (1612) by Salomon de Caus, and Curious Perspective (1638) by Jean-Francois Niceron. Each contained extensive scientific and practical information on anamorphic imagery. In Niceron's work, three types of large-scale anamorphism are explained: 'optical' (looking horizontally); 'anoptric' (looking upwards); and 'catoptric' (looking down i.e. from a mezzanine). A conical perspective is also described. Towards the end of the century, Charles Ozanam's Mathematical Recreations widely popularized the techniques for the creation of anamorphic images.
Between 1669 and 1685, both perspective and mirror anamorphosis were introduced in China by the Jesuits to the Emperor K'ang-hi and monks at the Peking Mission. However, Chinese production of anamorphic images were already occurring on a large scale during the late Ming Dynasty. The images were mostly created freehand, unlike the grid system used in the west. As Chinese anamorphoses primarily focused on erotic themes, Jesuit influence is unlikely. It is considered likely that Chinese catoptric techniques, which are technically unrelated to geometric anamorphosis, influenced European mirror anamorphosis, and not the other way around.
Baroque trompe l'oeil murals often used anamorphism to combine actual architectural elements with illusory painted elements to create a seamless effect when viewed from a specific location. 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.
Anamorphosis could be used to conceal images for privacy or personal safety, and many secret portraits were created of deposed royalty. A well-known anamorphic portrait of the English King Edward VI was completed a year before his death in 1546, only visible when viewed through a hole in the frame. It was later hung at Whitehall Palace, and may have influenced Shakespeare during the writing of Richard II. Many anamorphic portraits of King Charles I were created and shared following his 1649 execution. A secret mirror anamorphosis portrait of Bonnie Prince Charlie 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.
By the 19th century, a revival of interest in anamorphism for architectural illusion occurred, as well as a fashion for classical themes. Reprints of Renaissance-era engravings became popular, as did political, obscene and popular subjects. Edgar Allen Poe's famous poem Ligeia describes a room filled with "simple monstrosities" that resolve in to "an endless succession of ... ghastly forms" as the narrator walks through the room. This mass popularization was to later have effect on the Surrealists.
By the twentieth century, some artists wanted to renew the technique of anamorphosis for aesthetic and conceptual effect. During the First World War Arthur Mole, an American commercial photographer, used anamorphic techniques to create patriotic images from massive assembled groups of soldiers and reservists. When seen from a tower at their base, the gathered people resolved into recognizable pictures.
Marcel Duchamp was interested in anamorphosis. His last work Given: 1. The Waterfall, 2. The Illuminating Gas (1946-66) used mild anamorphosis to force viewers into the position of peep-hole voyeurs in order to see a nude, anonymous human body.
Surrealist artist Salvador Dalí used extreme foreshortening and anamorphism in his paintings and works. A glass floor installed in a room next to his studio enabled radical perspective studies from above and below. The Dalí Theatre and Museum 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.:156:28 Interestingly, Lacan also compared Holbein's 16th century painting to Dali's imagery, rather than the other way around.
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.
The Ames room was invented by American scientist Adelbert Ames, Jr. in 1946. When viewed through a peephole, the room appears to have normal perspective. However, all other viewpoints reveal that the room is constructed of irregular trapezoids. Similar effects had been achieved during the Renaissance through the use of "accelerated perspective" in stage design. These included productions by Scamozzi (1588-9), Furtenbach (1625), Sabbattini (1637) and Troili (1672).
One of the most interesting effects of an Ames room is that the distorted perspective can make people and objects look much bigger or smaller than they really are. For this reason, Ames rooms are widely used in cinema for practical special effects. A well-known example is the homes in the Shire from the Lord of the Rings and The Hobbit films. Through the use of forced perspective, the character of Gandalf appeared much larger than the characters of Frodo and Bilbo, without the use of digital effects.
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.
Road surface marking warning text is predistorted for oblique viewing by motorists
Anamorphic writing on riot helmets. Despite being written on a curved sloping surface the onlooker sees it horizontally and undistorted.
While not as widespread in contemporary art, anamorphosis as a technique has been used by contemporary artists in painting, photography, printmaking, sculpture, film and video, digital art and games, holography,street art and installation. The latter two art forms are largely practised in public areas such as parks, city centres and transit stations.
In 1975 a major exhibition was held focusing exclusively on anamorphic imagery: Anamorphoses: Games of Perception and Illusion in Art. The artist Jan Beutener created The Room, a major new installation specifically for the exhibit.
Since the mid-20th century, many artists have made use of anamorphosis in public artworks. American Land art pioneer Michael Heizer's Complex One (1972-1974), a massive earth and concrete structure in the Nevada desert, creates a rectangular frame for a mastaba when viewed from a specific location. Inspired by Luxor and other ancient monumental sites, it is part of the larger work City, an enormous sculpture running a mile and a half long. The entire work will not be completed until 2020.
Shigeo Fukuda, a Japanese artist and designer globally renowned for his satirical posters on anti-war and environmental advocacy, created posters and sculptures making use of both types of anamorphosis in the 1970s and 1980s. He also wrote multiple books on the topic of optical illusions.
Felici Varini's 2014 work Three Ellipses for Three Locks in Hasselt, Belgium is an image of three loops that are made up of segments painted on to over 100 buildings. It is only visible from a specific vantage point over the city.
Marcus Raetz's Kopf is a large scale public installation that reveals the form of a person's head in profile when viewed from a specific vantage-point. It was installed in a public park in Basel, Switzerland.
While anamorphic images were not his exclusive area of focus, the American artist Jonathan Borofsky created installations in the 1980s using anamorphic techniques, exhibiting at institutions such as the Museum of Modern Art.
The Swedish artist Hans Hamngren produced and exhibited many examples of mirror anamorphosis in the 1960s and 1970s.
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. This involved the incorporation of land art into his work, where areas dug out of the Earth formed squares from specific perspectives.
Anamorphic effects are popular in street art, sometimes called "Slant Art" when accomplished on sidewalks. 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 2016, the street artist JR completed a massive temporary anamorphic illusion over the Louvre's pyramid, making the modern structure disappear and the original building appear as though it was still in the 17th century.
Anamorphic frog sculpture by Jonty Hurwitz
Vera Bugatti: cylindrical mirror anamorphosis with portrait
Three views of a conical anamorphosis by Dimitri Parant
Jean-Max Albert, Reflet anamorphose, Bronze, Parc de la Villette (1985)
Since the 18th century, anamorphosis has been a widespread art form in popular culture. It has been used for children's toys, album art, advertising, videogames and movies, among other things.