Cubiculum (bedroom) from the Villa of P. Fannius Synistor at Boscoreale MET DP170950.jpg|Fresco from the
Villa of Publius Fannius Synistor in
Boscoreale near
Pompeii, 1st ct. BC Song Dynasty Hydraulic Mill for Grain.JPG|A
Song dynasty watercolor painting of a mill in an
oblique projection, 12th century Ambrogio_Lorenzetti_Annunciation.jpg|The floor tiles in
Lorenzetti's
Annunciation (1344) strongly anticipate modern perspective
Early history The earliest art paintings and drawings typically sized many objects and characters hierarchically according to their spiritual or thematic importance, not their distance from the viewer, and did not use foreshortening. The most important figures are often shown as the highest in a
composition, also from
hieratic motives, leading to the so-called "vertical perspective", common in the
art of Ancient Egypt, where a group of "nearer" figures are shown below the larger figure or figures; simple overlapping was also employed to relate distance. Additionally, oblique foreshortening of round elements like shields and wheels is evident in
Ancient Greek red-figure pottery. Systematic attempts to evolve a system of perspective are usually considered to have begun around the fifth century BC in the
art of ancient Greece, as part of a developing interest in
illusionism allied to theatrical scenery. This was detailed within
Aristotle's
Poetics as
skenographia: using flat panels on a stage to give the illusion of depth. The philosophers
Anaxagoras and
Democritus worked out geometric theories of perspective for use with
skenographia.
Alcibiades had paintings in his house designed using
skenographia, so this art was not confined merely to the stage.
Euclid in his
Optics () argues correctly that the perceived size of an object is not related to its distance from the eye by a simple proportion. In the first-century BC
frescoes of the
Villa of P. Fannius Synistor, multiple
vanishing points are used in a systematic but not fully consistent manner. Oblique projection is also seen in Japanese art, such as in the
Ukiyo-e paintings of
Torii Kiyonaga (1752–1815). It has been claimed that comprehensive systems of perspective were evolved in antiquity, but most scholars do not accept this. Hardly any of the many works where such a system would have been used have survived. A passage in
Philostratus suggests that classical artists and theorists thought in terms of "circles" at equal distance from the viewer, like a classical semi-circular theatre seen from the stage. The roof beams in rooms in the
Vatican Virgil, from about 400 AD, are shown converging, more or less, on a common vanishing point, but this is not systematically related to the rest of the composition. Medieval artists in Europe, like those in the Islamic world and China, were aware of the general principle of varying the relative size of elements according to distance, but even more than classical art were perfectly ready to override it for other reasons. Buildings were often shown obliquely according to a particular convention. The use and sophistication of attempts to convey distance increased steadily during the period, but without a basis in a systematic theory.
Byzantine art was also aware of these principles, but also used the
reverse perspective convention for the setting of principal figures.
Ambrogio Lorenzetti painted a floor with convergent lines in his
Presentation at the Temple (1342), though the rest of the painting lacks perspective elements.
Renaissance 's
St. Peter Healing a Cripple and the Raising of Tabitha (), the earliest extant artwork known to use a consistent
vanishing point. It is generally accepted that
Filippo Brunelleschi conducted
a series of experiments between 1415 and 1420, which included making drawings of various
Florentine buildings in correct perspective. According to
Vasari and
Antonio Manetti, in about 1420, Brunelleschi demonstrated his discovery of perspective by having people look through a hole on his painting from the backside. Through it, they would see a building such as the
Florence Baptistery for which the painting was made. When Brunelleschi lifted a mirror between the building and the painting, the mirror reflected the painting to an observer looking through the hole, so that the observer can compare how similar the building and the painting of it are. (The
vanishing point is centered from the perspective of an experiment participant.) Brunelleschi applied this new system of perspective to his paintings around 1425. This scenario is indicative, but faces several problems that are still debated. First of all, nothing can be said for certain about the correctness of his perspective construction of the Baptistery of San Giovanni because Brunelleschi's panel is lost. Second, no other perspective painting or drawing by Brunelleschi is known. (In fact, Brunelleschi was not known to have painted at all.) Third, in the account written by Antonio Manetti in his
Vita di Ser Brunellesco at the end of the 15th century on Brunelleschi's panel, there is not a single occurrence of the word "experiment". Fourth, the conditions listed by Manetti are contradictory with each other. For example, the description of the eyepiece sets a visual field of 15°, much narrower than the visual field resulting from the urban landscape described. 's use of upward foreshortening in his frescoes, Basilica dei Santi Apostoli, Rome, Soon after Brunelleschi's demonstrations, nearly every interested artist in Florence and in Italy used geometrical perspective in their paintings and sculpture, notably
Donatello,
Masaccio,
Lorenzo Ghiberti,
Masolino da Panicale,
Paolo Uccello, Masaccio (d. 1428) achieved an illusionistic effect by placing the vanishing point at the viewer's eye level in his
Holy Trinity (), and in
The Tribute Money, it is placed behind the face of Jesus. In the late 15th century,
Melozzo da Forlì first applied the technique of foreshortening (in Rome,
Loreto,
Forlì and others). This overall story is based on qualitative judgments, and would need to be faced against the material evaluations that have been conducted on Renaissance perspective paintings. Apart from the paintings of
Piero della Francesca, which are a model of the genre, the majority of 15th century works show serious errors in their geometric construction. This is true of Masaccio's
Trinity fresco and of many works, including those by renowned artists like Leonardo da Vinci. As shown by the quick proliferation of accurate perspective paintings in Florence, Brunelleschi likely understood (with help from his friend the mathematician
Toscanelli), but did not publish the mathematics behind perspective. Decades later, his friend
Leon Battista Alberti wrote '''' (), a treatise on proper methods of showing distance in painting. Alberti's primary breakthrough was not to show the mathematics in terms of conical projections, as it actually appears to the eye. Instead, he formulated the theory based on planar projections, or how the rays of light, passing from the viewer's eye to the landscape, would strike the picture plane (the painting). He was then able to calculate the apparent height of a distant object using two similar triangles. The mathematics behind similar triangles is relatively simple, having been long ago formulated by Euclid. Alberti was also trained in the science of optics through the school of Padua and under the influence of
Biagio Pelacani da Parma who studied
Alhazen's
Book of Optics. This book, translated around 1200 into Latin, had laid the mathematical foundation for perspective in Europe. 's use of perspective in
Delivery of the Keys (1482), a fresco at the
Sistine Chapel Piero della Francesca elaborated on
De pictura in his
De Prospectiva pingendi in the 1470s, making many references to Euclid. Alberti had limited himself to figures on the ground plane and giving an overall basis for perspective. Della Francesca fleshed it out, explicitly covering solids in any area of the picture plane. Della Francesca also started the now common practice of using illustrated figures to explain the mathematical concepts, making his treatise easier to understand than Alberti's. Della Francesca was also the first to accurately draw the
Platonic solids as they would appear in perspective.
Luca Pacioli's 1509
Divina proportione (
Divine Proportion), illustrated by
Leonardo da Vinci, summarizes the use of perspective in painting, including much of Della Francesca's treatise. Leonardo applied one-point perspective as well as
shallow focus to some of his works. Two-point perspective was demonstrated as early as 1525 by
Albrecht Dürer, who studied perspective by reading Piero and Pacioli's works, in his
Unterweisung der Messung ("Instruction of the Measurement"). ==Limitations==