Studies and research on perspective in "spherical visions" have an implicit influence on the development of panoramic photography due to the fact that the classical perspective is incapable of representing a view with an angle of view greater than 90-100 degrees.
Immersive photography is instead the "spherical" reproduction of a scene, 360 °, and inevitably has to do with the projection of the sphere on the plane.
I try to retrace here what in art history, as in cartography, has had to do with a concept of curvilinear perspective, therefore not with the rectilinear perspective, but with the description of the "real" consequent to the idea of "widening" of the visual field.
How to reproduce a spherical surface on the plane was a research carried out first by cartographers.
As early as the 6th century BC Greek philosophers such as Pythagoras, Plato, Aristotle, sensed that the earth was a sphere; Eratosthenes in 200 BC around, he estimated the circumference, but traces of actual studies on how to represent it on the plane, we have with Hipparchus of Nicaea, to whom is attributed the subdivision of the ecliptic (and of the circles in general) in 360 degrees, with Ptolemy, who describes the earth known through conical projections and with Marino di Tire to whom the invention of the equirectangular (equidistant) projection of the sphere around the second century AD is attributed
Farnese atlas, II century AD
Equirectangular projection with Tissot indicators that serve to highlight deformations at the poles
Johannes Schnitzer, illustration for Eucumene of Ptolemy, 1482
Further studies on the projection of the sphere are made with Gerardus Mercator in the 16th century, and then with Johann Heinrich Lambert in the 18th century, a pioneer of non-Euclidean geometry.
Planisphere of Gerardo Mercator, 1567
Jean Cossin Dieppe's planisphere of 1570. Sinusoidal projection
In the history of art there is no evidence of a "spherical vision" until the fifteenth century, and in general the knowledge and practice of perspective that Leon Battista Alberti and Brunelleschi were defining was more important: the classical perspective, the way optimo, the rectilinear view.
The first representations of a view with a curvilinear perspective, even if it does not show an extremely "wide" angle of view, are found in some paintings by Jean Fouquet from 1450.
It is not yet known which technique Fouquet used to obtain his perspectives.
However, it is likely that he used a convex mirror. Van Eyck (see below) twenty years earlier had inserted a convex mirror into the Arnolfini painting.
Jean Fouquet, Entrée de l'empereur Charles IV à Saint-Denis
1455-1460
Fausto Baiocco, Perspective elaboration of the painting by Jean Fouquet
Jean Fouquet, La charité de saint Martin 1455-1460
Jean Fouquet, L'empereur Charles IV et les dignitaires de Paris 1455-1460
Leonardo observes (1) that the curvilinear perspective, reporting the distortions in width and height, is more consistent with the effects of vision. More precisely Leonardo makes a "distinction between the artificial perspective, which consists in the projection of the forms by the painter on a plane and the synthetic or natural perspective, which concerns the perception of the dimensions of real objects in nature". (2)
Around 1560, the architect Baldassarre Lanci invented a topographic survey device called the Prospectographer, which replaced the "flat intersection wall of the visual cone" with a "circular wall equidistant to the eye": more precisely, a cylindrical wall tangent to a sphere of where the eye (materialized in the pin of the nib) occupies the center.
The machine basically transforms a rectilinear perspective into a curvilinear perspective.
There is no news of artistic applications of this machine, but it is still a testimony to the fact that from the end of the 1500s the curvilinear perspective can be reproduced with an "exact" mechanism.
Baldassarre Lanci's Prospectographer (first half of the 16th century) - Laboratory of Mathematical Machines, University of Modena and Reggio Emilia
Still in curvilinear perspective appears this small painting (15x31 cm approx.) by Carel Fabritius which, according to some scholars of the National Gallery in London, may have been part (as background) of a Perspective Box (see: (vedi: Origins of virtual reality)
Carel Fabritius, View of Delft - 1652
Few painters apply the curvilinear perspective, one of them is Turner.
Although not clearly delineated, the impression is curvilinear.
JMW Turner, Petworth Park - 1828-1830
More precise is instead that of John Vanderlyn
John Vanderlyn, Panoramic View of the Palace and Gardens of Versailles - 1818
From the early fifteenth century they find themselves represented in the painting of convex mirrors that reflect the scene in front: they are first representations (more intuitive than according to a precise rule) of "spherical" vision.
From Van Eyck to Robert Campin, Petrus Christus and Quentin Metsys, there are several painters who use to insert a convex mirror in their paintings, and probably, due to the spread of these mirrors in the fifteenth century, given by the evolution of the technique in their manufacture . Caravaggio in Marta and Maria Maddalena and Giovanni Bellini in Allegory of Prudence or Vanity also include the convex mirror in their paintings.
Van Eyck, Portrait of the Arnolfini couple - 1434
Robert Campin, Saint John the Baptist and the Franciscan master Enrique de Werl - 1438
Petrus Christus, Sant'Eligio nella bottega di un orafo - 1449
Quentin Metsys, Le Prêteur et sa femme - 1514
Later, we find in Botticelli's circle a hint to the curvilinear perspective (it can be seen in the size of the Madonna's hand), but in Parmigianino's self-portrait the effect is well delineated, and includes the consistent deformation of the background environment.
Botticelli, Madonna del Magnificat - 1483
Parmigianino, Self-portrait within a convex mirror - 1524
Other examples of curvilinear perspective of the early twentieth century, still mediated by the mink in the convex mirror, are found with George Lambert, Harold Gresley, Otto Dix, William Orpen, Mark Gertler etc.
George Lambert, The Convex Mirror - c.1916
Otto Dix, Dr Mayer-Hermann - 1926
Incredibly, the 360-degree view is initially expressed with a zenithal vision even before being represented with vanishing points on the horizon like the classic panorama. Today this type of perspective is called nowadays "Little Planet".
Cortés letters published in Nuremberg in 1524.
illustration from the book Montezuma by C.A.Burland (Einaudi 1976)
Hans Sebald Beham, engraving - Vienna during the Turkish siege - 1529
For the volume Voyage dans les Alpes, the naturalist and mountaineer Horace-Benedict de Saussure depicts the panorama of the Alps with a zenithal vision. The "Little Planet" mink was used in the nineteenth century, when the Panorama was established, for the information brochures that were given at the entrance to the rotunda.
Horace-Benedict de Saussure: Vûe circulaire des Montagnes qu'on découvre du sommet du Glacier de Buet. From the book "Voyage dans les Alpes", Vol. 1, plate 8 - 1776
Orientation brochure for the Panorama of London painted by R.Barker and exhibited at the rotunda in Leicester Square, 1792. Bilingual.
Brochure for Malta Panorama, at the Leicester Square rotunda, by H.A.Barker, 1810
Brochure for the Panorama von Palermo, by K. F. Schinkel, 1808.
Note that the projection is oriented towards the zenith.
Still in an illustrative-artistic spirit, in the mid-nineteenth century exquisite engravings with a top view are produced, sometimes called "Bird eye view". With a term derived from photographic optics for their type of perspective deformation, they could be called "fish-eye views".
Anonimus, View of London and surrounding Country Taken From the Top of St Paul's Cathedral - c. 1845
John Bachmann, Bird view of New York and environs - 1859
With M.C. Escher in the twentieth century, one has total mastery of the curvilinear perspective.
Escher was the inspiration for André Barre and Albert Flocon's text, La perspective curviligne of 1968, the first exhaustive treatise on curvilinear perspective.
M.C. Escher, Balcony - 1945
M.C. Escher, Tethrahedral planet -1954
Among contemporary artists, the American Dick Termes is recognized as a master in the art of perspective with 6 vanishing points. His works are called "Termesphers".
In the rules of the spherical perspective the number of vanishing points determines the possibility of the spherical representation.
Dick Termes, New Perspective Systems - 1998
Dick Termes, St.Mark (sfera fotografata da tre lati)
Pictorial examples of "spherical vision" are also found in the decoration of ceramics, as in this example of Castelli ceramics from around 1950.
Lid of ceramic vase from the Rosa Arbace di Castelli company, 1950s. On the side, the cylindrical projection obtained on the computer.
Analog photography presents a non-rectilinear perspective both with rotating or oscillating lens cameras, and with the advent of fish-eye wide-angle lenses, while digital photography, with software for image processing. Ford Oxaal is among the first to apply perspective transformation algorithms in digital photography.
Philippe Halsman, Salvador Dali at a book signing, taken with a fisheye lens - 1963.
Ford Oxaal, Pictosphere - 1994
NOTES 1) Leonardo da Vinci's treatise on painting, sculpture and architecture has been lost, but is remembered by Cellini who came into possession of it.
See also: Elkins, James, "Did Leonardo Develop a Theory of Curvilinear Perspective?", in Journal of the Warburg and Courtauld Institutes, LI, 1988, pp. 190-196. 2) Vanna Bagarolo, Vladimiro Valerio - Jacopo de' Barbari Una nuova ipotesi indiziaria sulla genesi prospettica della veduta Venetie MD -2006. The term "synthetic perspective" is defined by J.White in Birth and rebirth of the pictorial space - 1957
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