The Science of Art: Perspective in Painting Quiz

Answer: Pompeii

Characterized by a high level of technical accomplishment, the Second Style of Roman wall painting flourished in the 1st century BC. Though it spread quickly from Italy to other parts of the Roman sphere of influence, it is mostly identified with the stunning frescoes found in Pompeii and other towns buried by the eruption of Mount Vesuvius in 79 AD. The frescoes in the photo come from the Villa of Publius Fannius Synistor in Boscoreale, where they decorated the walls of the "cubiculum" (bedroom). The frescoes were detached from the walls in 1903, and the room was reconstructed in the Metropolitan Museum of Art (New York), where they are part of the Roman Gallery.

The Second Style was also known as architectural, as the depiction of architectural elements with illusionistic effects that expanded space was its key element. Though not based on the accurate mathematical calculations that became the norm in the Renaissance, linear perspective was used to create depth in a way that revealed an intuitive grasp of the concept of vanishing point - the point where the lines parallel to the viewer's line of sight converge on the picture plane. In the right-hand section of the Boscoreale frescoes, these lines converge in the middle of the painting, at the base of the round temple. Colour was also employed with a high degree of skill to create volume and distance.

This sophisticated knowledge of the basics of perspective was lost for most of the Middle Ages, but was reintroduced in the early 14th century by Giotto and other influential Italian painters of that time.

Answer: the floor tiles

Like other 14th-century Sienese painters, Ambrogio Lorenzetti often used gold leaf backgrounds in his religious works, which emphasized the mystical, otherworldly nature of the scenes and the elegance of the figures - as well as evoking a feeling of flatness rather than depth. However, having studied the art of classical antiquity, Lorenzetti also experimented with the creation of three-dimensional spaces - an innovative pursuit that can be clearly observed in his later works, which depart from the Byzantine influences of his early output.

Housed in Siena's Pinacoteca Nazionale, the "Annunciation" is Lorenzetti's final work, painted in 1344 - just four years before the artist (along with his brother and fellow painter Piero) succumbed to the Black Death. The painting contains one the earliest uses of one-point perspective in the late Middle Ages, achieved through floor tiles that gradually decrease in size as they incline upwards. The vanishing point lies in some point of the slender column that supports the arches, neatly bisecting the scene. The figures of the Virgin and the angel appear solid and monumental rather than flattened on the background as in the Byzantine tradition. The Virgin's throne, though not completely realistic, is also rendered as a three-dimensional space.

Answer: Filippo Brunelleschi

Painted about one year before the artist's untimely death in 1428, Masaccio's "Holy Trinity" fresco puts Filippo Brunelleschi's studies of linear perspective (the first to be precisely described in writing) into practice: it is believed that the great architect may have assisted the young painter in his work. The fresco, located in the right aisle of the Dominican church of Santa Maria Novella in Florence, creates the illusion of a three-dimensional chapel so convincingly that Giorgio Vasari, the famed biographer of the Florentine Renaissance, observed that the wall seemed to have holes in it. The central depiction of the Trinity, framed by a brightly-coloured arch, is flanked by two symmetrically-arranged sets of roughly life-sized figures - the Virgin Mary and Saint John at the foot of the cross, and the two donors kneeling outside the arch. The lower section depicts a skeleton in a tomb - a reminder of the fate that awaits every human being - also rendered with amazing sculptural precision.

Along with the rigorous architectural construction of the piece - whose theological meaning is also quite complex - Brunelleschi's influence is evidenced by the meticulously rendered, coffered barrel vault (reminiscent of the portico of Brunelleschi's own Pazzi Chapel in the Basilica of Santa Croce, also in Florence), which seems to recede into the wall if observed from below. The vanishing point is situated at the centre of the bottom step, roughly at the viewer's eye level.

Bramante was born 16 years after Masaccio's death, while Palladio was born in the early years of the 16th century. Bernini was active during the 17th century. None of these great architects were from Florence.

Answer: fisheye

The painters of the Northern Renaissance, in particular those from the Low Countries (Flanders and present-day Netherlands), are famous for their stunningly accurate representations of spatial relations and three-dimensional objects. Flemish painter Jan van Eyck, a contemporary of Italian Early Renaissance artists such as Masaccio, Donatello and Brunelleschi, was in many ways a trailblazer, moving away from the International Gothic style to develop a more naturalistic approach - including an empirical but highly convincing use of perspective.

Van Eyck's best-known work, the "Arnolfini Portrait" (1432, now at the National Gallery in London), was innovative in subject matter as well as in its painstakingly detailed depiction of the titular couple and their surroundings. The long, narrow space of the room neatly encloses the two elegant figures like a box. Centred between them, on the back wall, an elaborately framed, convex mirror draws the viewer's eye, reflecting two more figures (one of which may be the artist himself) framed by a doorway that faces the couple. The mirror is an early example of curvilinear, or five-point, perspective - also known as fisheye by analogy to a fisheye lens. In this kind of perspective, four vanishing points are placed at the four cardinal points around a circle, with the fifth located in the centre: the straight lines projected on this surface are perceived as curved.

The three animal-related wrong answers are all words that can be found in the English dictionary, but bear no relation to art or the use of perspective.

Answer: anamorphosis

German-born Hans Holbein the Younger painted "The Ambassadors" (now held by the National Gallery in London) in 1533, when he was working in England under the patronage of Anne Boleyn, Henry VIII's second wife. Some art historians believe that the ill-starred queen may have commissioned the painting as a gift to one of the two subjects, French ambassador Jean de Ditteville. Along with the portraits of the sitters - one richly dressed, the other (Georges de Selve, Bishop of Lavaur) in ecclesiastical robes - the work contains a highly detailed still life consisting of scientific objects, plus two books and a lute with a broken string, arranged on two tables. Various elements, such as the folds in the curtains and the Oriental carpet that covers the upper table, create a sense of depth. The objects are also rendered in lifelike three-dimensionality - in particular, the carefully foreshortened lute.

However, the component that has mostly contributed to the painting's fame is what appears to be a greyish slash floating on the meticulously depicted mosaic floor - an object that, if viewed from a particular angle, is revealed to be a human skull. The inclusion of skulls or skeletons in Renaissance and Baroque art is usually meant as a "memento mori" - a stark reminder of humankind's mortality. The skull is one of the best-known examples of anamorphosis, a distorted projection that requires the viewer to stand at a specific vantage point: in this case, at the side of the painting rather than in front of it. An ancient technique perfected in the Renaissance, anamorphosis was often used to disguise potentially controversial images. An anamorphic image is created by placing a grid on a drawing of the undistorted image to find the key points of the design - which is then transferred onto a distorted grid.

The word anamorphosis is also used in biology to denote a gradual change of form in the evolution of a group of animals or plants. The three incorrect choices bear no relation to the world of art.

Answer: the open doorway

Widely regarded as Diego Velázquez's masterpiece, "Las Meninas" ("The Maids of Honour", housed in Madrid's Prado Museum) was painted in 1656, when the artist was working as a high-ranking court official for King Philip IV. His library in the royal palace included key treatises on perspective, geometry, optics and human proportion that helped him develop his considerable professional skills. He also owned ten mirrors, which he very likely used as compositional aids, and other technical equipment.

"Las Meninas" is at the same time a portrait, an interior scene and a virtuosic exercise in the use of perspective and effects of shadow and light. The setting - Velázquez's own studio - is rendered through a series of rectangular shapes that form a framework for the figures in the foreground and background. While the attendants seem to be largely interacting with each other, the artist - standing in front of a large canvas - looks directly out of the painting in the direction of the viewer. The mirror on the back wall reflects the figures of the king and queen, whose portrait Velázquez is painting: the little princess looks at her parents, who are standing in the same position as the viewer.

The vanishing point is located in the open doorway at the back, where the lines projecting from the bases and tops of the paintings on the side walls, as well as those from the four corners of the canvas and other elements in the picture, converge. There the figure of a man stands, holding a curtain open and revealing an empty space that seems to lure the viewer's eye into its depths.

Answer: camera obscura

Also known as "Woman Standing at the Virginal", "The Music Lesson" was painted by Johannes Vermeer between 1662 and 1665. Originally held in the artist's own home, it is now housed in Buckingham Palace, where it is part of the Royal Collection. The work depicts a young woman playing the virginal while her teacher (a man) stands next to her, apparently singing along with the music. The scene is contained in a room whose details are rendered with almost photographic precision - which has led experts to believe that the artist used a device called a camera obscura ("dark chamber") to create his astonishingly accurate depictions of interiors. A camera obscura originally consisted of a dark room or closet with a pinhole on the top or one one side: light from an external source passed through the hole, striking a surface where an inverted view of the outside scene was projected. In the 18th century, the device became a portable box, which in the 19th century developed into the photographic camera.

Vermeer is likely to have achieved his stunning depictions of interior spaces by adopting a combination of techniques rather than through a single, rigorously systematic approach. Though no drawings by him survive, his skill as a draughtsman must have been exceptional. In "The Music Lesson", the orthogonal lines from the windows and the tiled floor converge on the figure of the girl, who stands at the heart of the painting.

A magic lantern ("lanterna magica" in Latin) is an early type of image projector.

Answer: trompe l'oeil

Already widely employed in Roman mural painting, trompe l'oeil means "deceive the eye". Andrea Pozzo's most famous work, the ceiling fresco of the Jesuit church of Saint Ignatius of Loyola in Rome, is regarded as one of the definitive masterpieces of this ancient technique. At the turn of the 18th century Pozzo (a Jesuit lay brother) earned international renown for his daring experiments in using perspective techniques such as quadratura, in which architectural illusion creates the effect of opening up walls. In the Renaissance, influential artists such as Andrea Mantegna and Melozzo da Forlì had successfully employed "sotto in su" (seen from below) perspective, which relied on foreshortened figures and an architectural vanishing point to create the illusion of space on a painted ceiling. Quadratura, on the other hand, was developed in the Baroque era, blending principles from architecture, painting and sculpture to produce even more striking illusionistic effects.

Pozzo designed the expansive scene on the nave ceiling of the Jesuit church to be seen from a single correct viewing point, indicated by a metal disc embedded in the floor: from there, the eye is attracted towards the figure of Jesus Christ, the picture's vanishing point. If viewed from the wrong angle, the grandiose architectural construction begins to fall apart, and the figures topple from their perches. A mirror has now been placed in that point to allow visitors to view the fresco more closely. The artist devised an elaborate contraption - a network of strings - to project his drawing of the false architecture onto the ceiling.

All three wrong choices are French terms widely used in reference to painting: en plein air refers to painting outdoors rather than in a studio, gouache is a kind of water-based paint, and grisaille is a technique that uses only shades of gray.

Answer: Caspar David Friedrich

Caspar David Friedrich's "The Sea of Ice" can be read in many different ways, as the artist's rendition of volume and depth is tightly meshed with the painting's appeal to the viewer's emotions. Probably inspired by William Edward Parry's expedition in search of the Northwest Passage (1819-1820), the work is a stark depiction of the unequal struggle between nature (represented by the towering mass of ice) and humankind (represented by the barely-visible shipwreck next to the ice tower). The remarkable difference in size between these two elements of the painting conveys a pessimistic message about the uselessness of human attempts to conquer nature.

"The Sea of Ice" (part of the collection of the Kunsthalle in Hamburg, Germany) is often praised for Friedrich's use of atmospheric (also known as aerial) perspective in the depiction of this intensely dramatic scene. Unlike linear perspective, atmospheric perspective relies on colour and shading rather than accurate mathematical calculations. While the jagged shards of ice in the foreground are depicted with a three-dimensional quality that looks almost tactile, the illusion of depth of the titular sea of ice receding in the distance is achieved through increasingly cooler, less saturated shades of blue. Several other ice towers loom in the background like ghostly shapes, barely outlined in pale blue-grey until they seem to merge with the sky.

Widely employed in Chinese landscape painting, atmospheric perspective was introduced in Western art by Leonardo da Vinci, and can be observed in famous works such as "Mona Lisa" and the two "Virgin of the Rocks".

Answer: Japan

With the opening of Japan to foreign trade in 1854, Western artists became acquainted with the archipelago's rich and varied artistic heritage. In French, the word "Japonisme" was coined to describe the popularity and influence of Japanese art and culture on Western art in the late 19th century. One of the artists who found Japanese art an unending source of inspiration was Anglo-American painter James McNeill Whistler, who began collecting ukiyo-e woodblock prints in the 1860s. These stunning works of art by masters such as Hokusai and Hiroshige were characterized by bold, original colour schemes and compositional structures that were quite different from Western modes.

Painted in 1872, Whistler's "Nocturne in Blue and Gold" (held by London's Tate Britain) was inspired by one of the prints from Hiroshige's famed "One Hundred Views of Edo"(1856-1859), titled "Bamboo Yards, Kyobashi Bridge". Hiroshige was known for asymmetrical compositions that featured cut-off objects or architectural elements in the foreground to create a sense of depth. In Whistler's painting, only a part of Old Battersea Bridge is shown: the exaggerated vertical pier breaks up the space in simple portions, while the small boat next to it counterbalances the pier's bulk and leads the viewer's eye towards the hazy, boundless expanse of water and sky on the right.

The cultural exchange between Japan and the West went both ways: Hiroshige, who is regarded as the last of the great ukiyo-e artists, studied Western perspective techniques and incorporated them into his work.