In addition to its obvious uses in painting and sculpture, perspective has seen a whole range of technical applications including scenography, marquetry, trompe l’oeil, quadratura, architecture, gardens and the environment. It is also used in a series of alternative methods ranging from inverted perspective and anamorphosis to cylindrical, spherical, conical and various conical methods. In addition it is used in reconstructions of perspective in paintings. For these purposes a series of instruments and machines have been devised. Each of these will be considered in turn.

    Zucker (1925), in his World history of theatre touched upon the use of perspective. Allardyce Nicoll (1927), in her important Development of the theatre, devoted a large section (85-153) to the use of perpective in scenery. Gregor’s (1933), World history of theatre, added some new material. Since then two monumental works have set the standard for studies in the field, namely Kindermann’s (1959), History of European theatre, in ten volumes and the Encyclopaedia of Spectacle (Enciclopedia dello spettacolo), of which the main corpus of nine folio volumes (1954), was followed by a supplement (1954), and an index (1968). Both these works contain rich bibliographies.

Antiquity

    Serious discussion of perspective in Greek theatre came from attempts to reconcile Vitruvius’ claims (see above p. 35*) with the evidence of extant theatres. Haigh (1889, 1907), touched upon this in his Attic theatre when he included a short chapter (170-173) on mechanical arrrangements for scenery as did Pickard-Cambridge (1916, pp. 124-125) in his Theatre of Dionysius at Athens. Bieber (1920), in an important work which catalogued all the known theatres, touched on the problem and in the English version entitled History of the Greek and Roman theatre (1961) also included a chapter on scenery and mechanical devices.

    The absence of direct extant evidence led scholars to look for examples elsewhere that might have been based on the lost originals. The wall paintings at Pompeii became a chief source through a seminal article by von Cube (1906) on "The Roman scenae frons in Pompeian wall paintings of the fourth style". Bieber (1920), broached this problem (76-81) which was developed in the major studies by Curtius (1929) on Pompeian wall paintings and Beyen (1938-1939). Meanwhile, Holl (1906), had related scene paintings to "The development of walls with paintings in the Greek church". Strzygowski (1907), studied the influence of stage architecture on the art of Antioch. Other media were also examined. Strong (1907), broached questions of scene painting and perspective in his Roman sculpture from Augustus to Constantine as did Morey (1924), in his Roman and Christian sculpture. Aurigemma (1923-1924) examined "Mosaics with scenes of an amphitheatre in a Roman villa at Zliten in Tripolitania". Séchan (1926) made Studies on Greek tragedy in relation to ceramics. This led to new attempts at synthesis by Flickinger (1926), in his Greek theater and its drama, and by Bulle (1928). Doxiades (1937,1972), examined these problems of space in Greek theatre in terms of larger questions in his Idea of space in Greek architecture, as did Martiensen (1964). Krause (1985) reviewed these discussions and also included a brief appendix on the graffiti found at the Theatre in Terracina in 1977.

Middle Ages

    Early classics such as Chambers (1905), The medieval stage, merely referred in passing to the role of perspective in this context. Berstl (1919) related concepts of space in philosophy and theology to changes in spatial practice in stage scenery in general without many specific examples. Springer (1924) in Early Christian art and the Middle Ages also broached the theme of perspective. Borcherdt’s (1935) European theatre in the Middle Ages and the Renaissance contrasted the traditions of the German Passion play and the French Mystery play, examining their different approaches to the use of space. Important methodologically was his reliance on paintings for evidence of theatrical practice.

Renaissance Italy

    Modern studies of perspective in the history of Italian theatre began with D’Ancona’s (1872) three volume Sacred representations of the fourteenth, fifteenth and sixteenth centuries, which served as a basis for D’Ancona’s (1891) classic Origins of the Italian theatre. German scholarship introduced a new level of depth to these discussions beginning with an important thesis by Flechsig (1894), on The decoration of modern stages in Italy and a monograph by Hammitzsch (1906), on Modern theatre construction, provided a useful outline. Essential source material was provided by Solerti’s (1905) Music, dance and drama at the Medici court from 1600 to 1637.

    Only gradually was it recognized that the development of theatre decoration and painting were interdependent. Two articles by Fischel were seminal in this context. Fischel (1919-1920) focussed on the theatrical machines attributed to Brunelleschi made for the feast of the Annunciation (25 March 1438) in San Felice in Piazza near the Palazzo Pitti (pl. 57.1), citing both the descriptions of Abraham, the Bishop of Ssusdal and Vasari. Fischel claimed that the configuration of angels used in this Florentine theatre were subsequently adapted by Brunelleschi’s student, Michelozzo, in producing the decorations in the upper section of the Portinari chapel in Sant’Eustorgio in Milan (pl. 57.2). Fischel (1935) in a two part article emphasized the interdependence of "Art and the theatre", noting for instance that Renaissance artists including Jean Fouquet, Hugo van der Goes, Hieronymus Bosch, Brunelleschi, Bramante, Leonardo, Raphael, Rosso, Parmegianino, Buontalenti and Palladio all played a part in the history of the stage, as did later Baroque artists such as Inigo Jones, Bernini, della Bella, Callot, Servandoni, Berain, and eighteenth century individuals such as Tiepolo, Gillot, and Watteau. Fischel cited both cases where stage practice helped in understanding otherwise puzzling aspects of spatial disposition in paintings and specific examples (e.g. Fouquet) of manuscript illustrations which helped to visualize stage practice.

    This interdependence of art and theatre was further explored in two articles by Mariani "The architectonic concept in scenography of the seventeenth and eighteenth century" (1923) and "Perspective as an illusionistic element in the architecture of the Renaissance" (1924) which were preludes to his Italian scenography (1930); in Van Marle’s (1924), groundbreaking work The development of the Italian schools of painting; Scharf’s (1925), dissertation on the history of stage design from the fifteenth to the seventeenth century; an article by Mortimer (1930), on "Architecture in the Italian pictures" and Ricci’s (1930), Italian scenography.

    Schöne (1933), in a seminal dissertation focussed on The development of the perspectival stage from Serlio to Galli-Bibiena according to the perspective treatises. This was the first systematic study of evidence provided by the theoretical literature. An opening chapter examined the early theatrical productions reported by Serlio, Barbaro and Palladio. A second chapter traced the development of a fully three dimensional stage (Reliefbühne) through Danti’s commentary on Vignola, Sirigatti and Accolti; the rise of scientific stage design with Guidobaldo del Monte and Chiaromonti; the transition to depth and altering stages with Sabbatini, Parigi and Furttenbach; and the evolution of wings (Kulissenbühne) through Aleotti, Dubreuil, and Troili, then Pozzo and Ferdinando Galli Bibiena. The practical side of theatre machinery was further explored by Galante-Garrone (1935), in Scenic apparatus of sacred drama in Italy.

    Kernodle (1937), in an important thesis, provided a synthesis of research at the time. He outlined the history of architectural backgrounds in the shaping of space in Greek, Hellenistic and Medieaval examples, noting the convention of exterior settings, tracing the development of both architectural screen and side-house through the middle ages. According to Kernodle there was a basic distinction to be made between a frieze form which dealt with time and a perspective form which dealt with space. The former involved multiple eye-points while the latter involved a single eye-point. A second chapter explored various elements in the development of Italian Renaissance theatre: the shift from a nucleus principle to an enclosing principle; from a frieze form to a single eye-point. He noted the significance of living pictures (tableaux vivants) in triumphal entries and pageants; the role of side house and architectural screens and explored the role of basic elements in the illusionistic perspective scene: floor, wings, heavens, back shutter and vanishing point. A third chapter compared theatre practice in London and Paris in terms of conflicts between mediaeval and modern conventions. Selected passages from perspective treatises were included in an appendix. A revised version appeared as a book, From Art to theatre (1944). That same year in France, Leclerc (1944), published a monograph on Italian origins of modern theatre architecture. Krautheimer (1948), in a famous article argued that the Baltimore and Urbino panels of ideal cities were effectively demonstrations of the tragic and the comic scene.This was challenged by Sanpaolesi (1949) and subsequently taken up anew by Battisti (1960).

    Magagnato’s (1951), article on "The genesis of the Teatro Olimpico" hailed a new attention to the role of individual buildings in this story, an approach which was reflected in Magagnato’s (1954), Italian theatres of the sixteenth century and pursued in an important work by Puppi (1963), on the Olympic theatre at Vicenza.

    Methodologically important, although consciously very speculative at points, was an article by Battisti (1960), on "The visualization of classical scenes in humanistic comedies". He noted that the first tragedy which had these characteristics was Gregorio Correr’s Progne (c.1428-1429), while the first comedy was Leonardo Bruni’s Poliscena (c.1407-1408). He examined Leon Battista Alberti’s Filodosso (composed c.1425, performed 1436-1437), offered a hypothetical reconstruction of its scenery and mentioned Frulovisi’s Corollaria and Claudio Duo (1432), Peregrinatio (1437). This led to a reconsideration of the three panels (Baltimore, Berlin and Urbino) of so called idealized cities which he suggested might more fruitfully be seen as visualizations of ancient cities. Battisti noted that Domenico Veneziano’s Annunciation (Cambridge, Fitzwilliam) could be seen in the context of stage design and offered a classical precedent.

    Eckert (1961), in a dissertation provided a useful survey of the evolution of the perspective scene in Italy. By way of introduction the role of both popular theatre and the revival of classical theatre was noted. His survey of developments in perspective painting and assessment of the significance of the three panels of ideal cities and Bramante’s contribution added little that was new. More useful was his outline of stage practice at Ferrara, Urbino, Rome, Mantua and Florence. Eckert claimed that Serlio brought a synthesis of classical and Renaissance concepts of the theatre and he outlined subsequent developments in mannerist and baroque theatre.

    Beijer (1962), examined historical problems of scenography using scientific methods. A series of four articles by Mancini (1961-1963), outlined the history of Neapolitan stage design. Cruciani Boriosi (1963), in an important article demonstrated links between baroque scenography and garden design. Zorzi (1964), examined Venetian scenography prior to Palladio, drawing on the evidence of both paintings and marquetry as a first step to his subsequent monograph (1977). Lavin (1965), related the Campidoglio to sixteenth century stage design. A significant monograph by Mancini (1966), outlined the history of Italian scenography from the Renaissance to the age of Romanticism.

    Blumenthal (1966-1967), re-examined the literature on Brunelleschi’s stage machinery for the Annunciation and described as a newly identified drawing a folio from the Zibaldone of Buonaccorso Ghiberti (Florence, Biblioteca Nazionale, Ms. BR 228, fol.115) which had been noted in Scaglia’s thesis (1960). Neiendam (1969), examined developments in "Renaissance theatre in Rome" between 1480-1530 to show that there was an emphasis on classical comedies played in the original Latin and that there was reason for accepting Vasari’s claim that Baldassare Peruzzi produced the first trompe l’oeil scene in relief in connection a play on the Capitoline (1513) and with a production of Cardinal Bibbiena’s La Calandria (1514). He also studied the role of humanism in the production of I Suppositi (1519) and La Mandragola (1520)

    A dissertation by Stein (1969), on Italian Renaissance theatre from Brunelleschi to Buontalenti while adding little new material, provided careful chronological lists of events and developments. Marotti (1974), in a significant work on Scenic space analysed the theories of scenography of a number of theorists from the turn of the seventeenth to the end of the eighteenth century: Guidobaldo del Monte (1600), Cigoli (c.1612); Chiaramonti (written c.1614, published 1675), Sabbatini (1638), Troili (1672), Pozzo (1693), Galli Bibiena (1711, 1732), Arnaldi (1762), Vittone (1766), Milizia (1772, 1794), Lamberti (1787) and Riccati (1790). Rutledge (1975), in a speculative dissertation explored the interplay of art and theatre in the late fifteenth and early sixteenth centuries. An appendix contained chronological lists of a number of religious spectacles, pastorals, triumphal entries, classical plays and imitations.

    A fundamental contribution was made by an international conference on Theatre architecture from the Greek era to Palladio, the acts of which were edited by Cevese (1974, published 1976). This began with articles on the theatre at Sabratha and the Greek theatre (Arias), on the architecture of Roman theatre (Frézouls) and on the shift from Carolingian liturgy to liturgical drama. Most of the essays focussed on themes from the time of Brunelleschi to Palladio. These included many leading scholars including Povoledo, Lotz, Chastel, Cruciani, Frommel, and Puppi. Containing 244 illustrations this remains one of the basic reference works.

    An important exhibition focussed on the contributions of Brunelleschi, Vasari, Buontalenti and Parigi to Florentine theatre design. Particularly striking were a series of model reconstructions by Cesare Lisi notably of the device (ingegno) by Brunelleschi for San Felice in Pace (c.1430); for the feast of the Annunciation (14 March 1439) in the church of Santa Annunziata (pl. 57.4); a device for the representation of the Ascension in Santa Maria del Carmine that same year (1439, pl. 57.3); Vasari’s apparatus for the Hall of the Five Hundred in the Palazzo Vecchio (1565) and Buontalenti’s apparatus for the Medici Theatre in the Uffizi (1589). A catalogue edited by Fabbri, E. Zorzi and Tofani (1975), reproduced some of these models and provided a wealth of source material. Another significant exhibition that same year (1975), entitled Illusion and theatrical practice. Proposals for a reading of scenic space from the Florentine intermezzi to the Venetian comic opera, was edited by Mancini, Muraro and E. Povoledo.

    A fable (favola) by Poliziano and an opera by Monteverdi were both entitled Orpheus. Pirrotta (1975), used this as a point of departure for a basic study of the role of music in theatre, devoting a very original chapter on temporal perspective and music. A second part of the book by E. Povoledo re-examined the origins of scenography in Italy from the end of the fifteenth century until the time of the Florentine intermezzi of 1589. These studies prepared the way for Zorzi’s (1977), Theatre and the city, which provided a synthesis of recent research with fundamental new insights. Zorzi focussed on three case studies to trace an evolution from the context of a ducal seat (Ferrara), to a city (Florence) and a republic (Venice ). His work brought into focus a complex interplay between the architectural construction of urban spaces and the representation of spatial settings both in art and the theatre. In an appendix Zorzi examined afresh the portico motive in scenography.

    Zangheri (1976), discussed Ferdinando Tacca’s role in producing the giant automaton of Atlas used in the gardens behind the Pitti palace for the wedding festivities of 1661. Oechslin (1977), examined the interplay of stage design and architecture and its importance for what he termed the theatre of invention, drawing attention to the role of unusual viewpoints in the process. A section of the XXIVth Congress of the International committee of art history devoted to Baroque scenography led to a significant collection of 18 essays edited by Schnapper (1979). Pochat (1980), described a series of "Architectural drawings with scenographic motifs from Northern Italy, 1500-1510" now in the Louvre.

    Following our earlier practice, in the interests of clarity, monographs on individual scenographers such as Juvarra, Galli-Bibiena and Piranesi have been relegated to the Appendices 4 and 5.

Germany

    For Germany a basic study remains Hermann’s (1914) Studies on the history of German theatre of the Middle Ages and the Renaissance. Again, a systematic study is lacking.

England

    Important early studies include Smith (1904), Elizabethan critical essays; Chambers (1923), The Elizabethan stage and Campbell (1923), Scenes and machines on the English stage during the Renaissance. Lawrence (1913), in The Elizabethan playhouse had examined problems such as the "The persistance of Elizabethan conventionalisms" and "Proscenium doors: an Elizabethan heritage." This led to Lawrence’s major work (1927), The physical conditions of the Elizabethan public playhouse, in which he claimed that one needed to rid one’s mind of preconceptions (3): "The Elizabethan theatre had no mysteries to conceal behind an ornate proscenium arch and a front curtain, no capacity to drug the senses by means of illusions of paint and canvas or the jugglery of artificial light". This gave the impression that perspective played no serious role in England. A similar impression is gained if one consults Bentley’s seven volume Jacobean and Caroline stage (1941-1968), the index to which contains two references to perspective (I,52; VI, 293-294).

    A quite different view was given by Welsford (1927), in his The court masque (91): "Some time towards the end of the fifteenth century the picture stage was substituted for the mediaeval system of dispersed decoration and the various houses or mansions were arranged according to the principles of perspective so as to form a single picture". Welsford went on (174) to note that Ben Jonson’s designs for masque settings at Oxford showed the influence of the satirical, tragic and comic scenes in Serlio’s Architecture. Southern (1935), examined The staging of eighteenth century designs for scenery and Bradbrook (1936), analysed Themes and conventions in Elizabethan tragedy.

    Jackson (1962), in a dissertation on The perspective landscape scene in the English theatre, 1660-1682, examined evidence from first editions of plays, contemporary journals and diaries, biographical material and extant paintings of artists who painted theatrical scenery. He noted that in the early years after the Restoration there was a contrast between the architectural quality of continental scenes and a more natural feeling for prospects of the countryside in England, but that after the merger of the two Royal companies in 1682, when the fad for French and Italian opera spread to English theatre, these differences disappeared. Appendices included a study of printed scene directions, theories of scene shifting techniques, catalogues of paintings and a description of Shadwell’s Psyche.

    Orrell (1983), in an important study demonstrated how topographical views of London by Hollar, Visscher, and Norden, could be related to modern maps in order to determine the actual size of the Globe theatre and other buildings in the area.

Baroque

    For the baroque period the standard works remain Tintelnot’s (1939), Baroque theatre and baroque art and Baur Heinhold’s (1966), Baroque theatre, both with rich bibliographies.

3. Marquetry

    From the outset marquetry or intarsia was closely linked with the rise of perspective (cf. Sources, pp. 155-156*), as was noted by Renaissance authors such as Benedetto Dei (c.1470) and Vasari (1558). In Italy it remained of fundamental importance until the early sixteenth century. By the mid sixteenth century it had made a belated appearance in Germany and the Netherlands mainly in secular contexts where it continued a certain importance until the early seventeenth century.

City Building Scholar

Bastie D’Urfé Chapelle Raggio (1972)

Bergamo S.M. Maggiore Angelini (1968)

Bologna San Domenico Alce (1969)

Bologna San Petronio Benati (1984)

Ferrara Cattedrale Venturi (1916)

Genoa San Lorenzo Torriti (1955), Armani (1971)

Gubbio Studiolo Comstock (1941), Remington (1941), Clough (1967)

M.Oliveto M. Abbazia Brizzi (1989)

Reggio Emilia San Prospero Monducci (1965)

Sansepolcro San Francesco Salmi (1972)

Savona Duomo Varaldo (1894), Torriti (1951) (1952), Armani (1971)

Siena Cattedrale Thornton (1974)

Verona S.M. in Organo Rognini (1978)

Fig. 19. List of cities, churches with marquetry work and authors of studies.

    That marquetry had fallen out of fashion by the time when a more critical historiography of art was emerging offers one explanation why there were no major studies on marquetry during the seventeenth, eighteenth or even nineteenth centuries. A second reason relates to general biases within the historiography of art, which favoured attention to so-called high art, notably painting and sculpture, while giving short shrift to the so-called minor or decorative arts. The latter half of the nineteenth century, particularly through the efforts of Semper, Riegl and Ruskin, challenged this tradition and saw the establishment of museums devoted specifically to these decorative arts (Kunstgewerbe, arts décoratifs).

    The scholarly consequences of this shift did not emerge clearly until the twentieth century when specialized studies devoted to lesser known individuals began to appear. With respect to marquetry an article by Schottmüller (1918) on Giuliano da Maiano heralded this new approach. The following year Bonetti (1919) wrote on Paolo del Sacha (1468-1537). For the next decades this approach dominated the field. An anonymous author (1927) wrote on Mattia di Nanni di Stefano detto il Bernacchino. Alce (1949) wrote on Fra Damiano. Thorpe (1951) focussed on a single object: the Plus ultra cabinet (London, Victoria and Albert Museum). Fiocco (1956) wrote on Pietro Antonio degli Abati. Both Quintavalle (1959,1960) and Ciati (1974, 1980) wrote on Lendinara.

    Related to this was another approach which focussed on the evidence provided by a particular church, chapel or monastery (fig. 19). This work, often carried out by local amateurs, admirable both for its detail and its enthusiasm, could not of itself provide more general insights, whether the activities of an artist in Bologna or Urbino represented strictly—an earlier generation might have said merely—local expressions or whether they were recognizably part of larger trends connected with a particular order of the church or other group.

    Serra (1934), was one of the first to consider marquetry as a serious expression of Renaissance art. This approach was taken much further by Chastel whose synthetic studies gave a new sense of how the workshop traditions in Italy represented much more than simple local events. Chastel (1957), specifically addressed the question of the significance of marquetry and explored its uses. Corboz (1964-1965), raised deeper questions in this vein. Kreisel (1968), in his standard work on the history of German furniture illustrated a number of important examples of marquetry in the North. Jockusch (1993), in an important dissertation focussed on architectural motifs in Italian marquetry, focussing on the work of Fra Damiano. While some links with real architecture in the form of town views (e.g. Monte Oliveto near Siena) and of ruins were discovered (e.g. the Colosseum, Rome), Jockusch found that most of the marquetry entailed imaginary buildings and cityscapes.

4. Trompe L’Oeil and Illusion

    The general theme of Art and illusion has provided the title of at least three books in our century: Pap (1914), Johansen (19**), and Gombrich (1960). Trompe l’oeil has entered into discussions of whether or not the eye sees the natural world in the same way that it sees representations of nature in paintings (see above p. 69*). Other discussions involve the psychology of visual illusions (see below p. 135-137**). Several books have provided illustrations of trompe l’oeil images with little or no analysis. Otrange Mastai (197*), remains of interest.

Fig. 20. A classification of trompe l’oeil figures from Kubovy (1986, 68).

    Battersby (1974), offered a rough classification of themes such as curtains and wallpapers, flowers, sculptures, rooms, human figures, niches and cupboards, fireplace screens (devants de cheminée), paper and prints; trophies, birds, musical instruments and painters’ implements. Dars (1979), produced a popular book with 72 trompe l’oeil images. Milman (1982, 1986), produced two books on trompe-loeil painting and trompe l’oeil painted architecture with beautiful colour illustrations and some text.

    Sandström’s (1963), Levels of unreality, was one of the few books to explore the deeper problems of trompe l’oeil. In an opening chapter he examined the role of the narrative tradition in art in "conquering the wall", asking what is a picture and exploring both communication between and content in different spheres of the image. A second chapter focussed on the passage between picture and real space using the Cappella Bufalini (Rome, Santa Maria in Aracoeli) by way of illustration. A third chapter outlined transformations in the concept rooms: differences between an opened and a closed wall, the role of vault decoration and ceiling painting, reflecting on the influence of antiquity. A final chapter used the example of the Sistine Chapel ceiling to explore the structure of objects. As noted earlier (p.66*), Burda (1969) examined types of trompe l’oeil used in the Low Countries. Kubovy (1986), in the context of psychological problems of perspective, offered a more general classification of basic types of visual illusion (fig. 20).

5. Ceiling Painting or Quadratura

    One of the most dramatic applications of perspective has been in the context of fictive ceiling painting and architecture which, since the late seventeenth century has been termed quadratura, presumably in reference to the grid or graticule used both in constructing the quadratura motif and in transferring it to the vault.

    One of the first systematic studies in the field was an important dissertation by Kellermann (1924) on The concept of space in perspectival ceiling painting in Italy. Following a brief survey of previous literature, Kellermann examined the concept of illusionistic painting, tracing its antecedents in Hellenistic and Mediaeval examples. A third chapter was devoted to fifteenth century examples notably Mantegna, Melozzo and Pinturrichio; a fourth chapter focussed on two fifteenth century examples, Leonardo da Vinci’s Sala delle Asse and Michelangelo’s Sistine Chapel. A fifth chapter examined Mannerist examples notably followers of Raphael and imitators of Michelangelo. Chapters followed on early baroque painters including Correggio, Parmigianino, Titian, Tintoretto and Veronese; and on painters from the Academies, the Carracci, Reni, Domenichino and Tassi. An eighth chapter examined ceiling painting of the high baroque, focussing on three different trends: first the quadratura painters per se (the Alberti brothers, Dentone, Colonna, Mitelli, Alboresi, the Roli brothers, Chiavistelli, Franceschini, Stagi and Romei); second a painterly trend (Lanfranco, Cortona, Giordano, Baciccio, and Odazzi), and third, an architectonic-painterly trend (Ansaldo, Benso, Pozzo, the Melani brothers and Fumiani). A ninth chapter examined late baroque ceiling painters (Solimena, Conca, Schor, Coli, Gherardi, Rossi, Piazetta, Amigoni and Tiepolo). A final chapter explored the implications for architecture of these perspectival ceiling paintings. One of Kellermann’s enduring contributions was to focus on the role of brothers (e.g. Alberti, Roli, Melani) and whole families, (e.g. the Carracci, the Colonna) in passing down these techniques from one generation to the next. His thesis included 55 plates.

    An important article by De' Maffei (Italian 1958, English 1965) began with brief discussions of illusionistic perspective, architectural perspective (quadratura) painters and illusionistic painting in religious buildings. She examined the fifteenth century Italian forerunners of illusionism (Masaccio, Niccolo da Tolentino, Piero della Francesca, Mantegna, Melozzo da Forli); considered briefly perspectivists in sixteenth century Rome (Michelangelo, Raphael, Baldassare Peruzzi); illusionistic areial perspective in Emilia (Correggio, Guadenzio Ferrari, Benvenuto Tisi); mannerist perspectivists (Giulio Romano, Girolamo Genga, Bronzino, Vasari). Sections followed on the new theorists (Barbaro, Scamozzi, Vignola); Venetian perspectivists (Palladio, Zelotti and Fasolo--their assistants Antonio Vicentino, Girolamo del Pisano, Alesandro and Giambattista Maganza--, Veronese-- his followers Domenico Riccio, paolo Farinato, Battista Angelo del Moro and Bernardino India--, Lattanzio Gambara...);. Bolognese perspectivists in Rome (Ottavio Mascherino, Tommaso Laureti, Lorenzo Sabatini, Egnazio Danti, Pellegrino Tebaldi, Agostino Tassi); illusionistic figure painting (Carracci brothers, Gaulli, Pozzo) ; the Bolognese school of quadratura painting (Curti, Colonna, Mitelli, Piola, Haffner,de' Ferrari, Giordano, Solimena, Ricci, Fumiani, Piazetta, Crosato, Mingozzi) ; Italian perspectivists active in German Regions (Pozzo, Pellegrini, Amigoni, Appiani, Tiepolo) and German perspectivists (Schor, Waldmann, Asam brothers, , Rottmayr, Gran, Altomonte, Scheffler brothers, Zimmermann, Wink, Holzer, Mgges, Göz, Günther, Zick, Troger...Maulbertsch). Particularly useful was the way in which the author outlined how this Italian approach gradually spread throughout many parts of Europe.

    Unaware of this work, Horstmann (1968), in a dissertation identified eight steps in The development of perspectival ceiling painting, beginning with the first attempts at a view from below prior to the use of a perspectival background (Masaccio, Saint Paul, Santa Maria del Carmine). A second stage involved the construction of a fictive architecture seen from below (Masaccio, Trinity, Santa Maria Novella). A third stage used forehortening of the figure in the case of painted statues (Uccello, John Hawkwood or Giovanni Acuto, first version, Santa Maria Novella). A fourth stage entailed bringing together of individual figures in a view from below within a decorative system, (Uccello, Hour dial and giants or Castagno’s Famous men). A fifth stage introduced many figured narrative scenes seen from below (Donatello’s Handing over of the keys and Miracle of the donkey. A sixth stage adapted methods from relief within the context of painting proper. In a seventh stage there was an increase in the field of depth and perfect foreshortening of figures (Mantegna, Saint Jacob on the way to the courts). Finally an eighth stage introduced an illusionistic extension of the entire space off to the side with the help of perspective from below (Angelo del Maccagnino, Studio of Belfiore). Part two of the thesis surveyed early examples of perspectival ceiling painting, notably, Foppa, Mantegna, Leonardo, Sodoma, Michelangelo, Raphael and Correggio.

    Sjöstrom (1972, English, 1978), returned to this theme in Quadratura. Studies in Italian ceiling painting which was important because it classified these ceilings in terms of nine types (fig. 21, pl. 65-66). While focussed on Italy, Sjöstrom added an excursus on French treatises and cited examples of Domenico Francia in the Royal Castle, Stockholm.

1. Fictive architecture, closed

2. Fictive architecture, open upwards and to the sides

3. Fictive architecture with central opening

4. Fictive architecture with central painting surrounded by niches, reliefs and busts

5. Sieve ceiling (surface bound structure perforated by four openings)

6. Cross between surface bound structure with central fictive cupola and corner openings with barriers

7. Raised fictive ceiling with hovering figure enclosed

8. Raised fictive ceiling with fictive walls angled inwards

9. Fictive barrier

Figure 21. Classification of nine types of ceiling painting by Sjöström (1978).

    Czymmek (1981), in a published dissertation also explored the typology, sources, significance and development of ceiling painting in Italy and Germany until c.1700. Knall-Brskovsky (1984), in a significant dissertation focussed on the use of quadratura in the Austrian baroque.

6. Architecture

    Giedion (1941), in Space, time and architecture, was convinced that a society without a clear perception of its relation to the past would proceed aimlessly and myopically. A knowledge of history was therefore "prerequisite for the appearance of a new and self confident tradition". Giedion’s view of that tradition was sharp and clear cut. He saw Florence as the workshop of the modern spirit. "In the Renaissance the longest step forward was taken during the ten years between 1420 and 1430. Perspective, in his view (31):

came as a complete revolution, involving an extreme and violent break with the medieval conception of space and with the flat, floating arrangements which were its artistic expression.With the invention of perspective the modern notion of individualism found its artistic counterpart. Every element in a perspective representation is related to the unique point of view of the individual spectator.

    Giedion argued that there was no single inventor of perspective, that it was the expression of an epoch, "used at once with complete confidence and sureness", combining both art and science and cited Brunelleschi as an initiator. Masaccio’s Trinity was of particular importance because its longitudinal barrel vault "was to prove the great solution to the vaulting problem that confronted architects of the full Renaissance and baroque periods." He saw the first concrete architectural expressions of this form in the interior of Alberti’s San Andrea at Mantua (1472) and Bramante’s illusionistic choir in Santa Maria presso San Satiro in Milan (1479-1514) and the nave of Saint Peter’s in Rome (1607-1617) as (36) "its culminating point". Giedion claimed that in the Renaissance (42) the exaltation of the individual ego began to supercede the old team spirit of the Middle Ages and paved the way for the absolutism of the seventeenth century". This explanation, which quite overlooked the enormous growth of the guild tradition in the Renaissance, the growth of banks and corporate structures, allowed him to focus on one strand as the only consequence of perspective (43):

The Renaissance was hypnotized by one city type which for a century and a half -from Filarete to Scamozzi- was impressed upon all utopian schemes: this is the star shaped city. From a symmetrical fortified polygon, radial streets lead to a main center. This is the basic diagram. The central area is either left open, as in the completed Palmanova (1593), or contains a central tower- a central observation post- from which the streets are seen in shortened perspective.

    Although he stated explicitly that one should not judge Renaissance town planning simply in terms of ideal cities, Giedion claimed that no artists of the time (55) "left us a plan for a new type of town" and that what was new in their civic design had to be sought in mastery of a town’s constituent elements, e.g. palaces with bold walls, streets which were agglomerations of heterogeneous buildings and open stairways. All this he contrasted to the baroque (54):

Baroque perspective on the other hand, was based on a limitless field of vision. Hence typical towns of the late Baroque period, such as Versailles (second half of the seventeenth century) and Karlsruhe (about a hundred years later) have nothing to do with the star shaped plan. The palace of the ruler stands boldly between town and country, dominating -at least in the optical sense- limitless space.

    In Giedion’s view, perspective continued as a habit for four centuries. Perspective was misused in the nineteenth century, which also saw the rise of a non-Euclidean geometry employing more than three dimensions. This led to a "self conscious enlargement of our ways of perceiving space", which culminated in cubism around 1910 in Paris (436):

Cubism breaks with Renaissance perspective. It views objects relatively: that is from several points of view, no one of which has exclusive authority. And in so dissecting objects it sees them simultaneously from all sides -from above and below, from inside and outside. It goes around and into its objects. Thus to the three dimensions of the Renaissance it adds a fourth one - time....

The advancing and retreating planes of cubism, interpenetrating, hovering, often transparent, without anything to fix them in realistic position, are in fundamental contrast to the lines of perspective, which converge to a single focal point.

    According to Giedion, perspective was entirely abandoned after 1910 (cf. below pp. 156-160**). His work was immensely successful going through at least five editions (and sixteen printings by 1966).

    A considerably more complex approach was outlined in an important dissertation by Lombaerde (1982). Where Giedion was content to identify two stages in perspectival space (Renaissance and Baroque), Lombaerde outlined six stages which he related to corresponding examples of town planning. He argued that the advent of linear perspective in the fifteenth century made possible its application to the physical scale of the town and specifically in terms of public buildings. By way of illustration he used Pienza. Mannerism he claimed changed this approach by putting emphasis on values of significance thus enriching architecture with new values. By way of example he focussed on the town of Montaigue (Belgium). The Cartesian concept of space brought further changes, focussing new attention on the spaces between buildings namely, streets, the square, garden and park as shown by the town of Richelieu.

    The turn of the eighteenth century saw another change whereby space was seen as an assemblage of visible signs. The distinctions between primary and secondary quantities as formulated by Locke and Berkeley meant that links between visible characteristics and those based on sensory perception became a function of learning. According to Lombaerde, Henry Hoare’s garden at Stourhead reflected these trends which were short lived and soon led to two divergent positions: one, based on associationist theories of perception as outlined by Helmholtz in optics and Herman Maertens in town planning; the other, a notion of social utopia as formulated by language analysis which led to drafting becoming an independent system of representation. Lombaerde claimed that the end of the nineteenth century introduced a more aesthetic and psychological approach whereby the panoramic picture and the bird’s eye view became preferential positions of perception which led to garden-districts.

    According to Lombaerde the two diverging tendencies continued in the twentieth century. The perceptual tradition showed less and less interest in distinguishing between idea, perception and interpretation. Keven Lynch’s five organization patterns underlying inhabitants’ understanding of town settings was cited as an example. The second tendency, mainly through drafting, distinguished notions of space from those of the designing process. Influenced by structuralism and semiology this gave rise to three further trends (5): "a semantic spatial interpretation closely linked to various cultures; a more grammatical and syntactic tendency which distinguishes sharply between form and meaning and a more pragmatic approach which stresses the role of the subject in the design making process". Lombaerde concluded with an examination of how proposals concerning various categories (e.g. conception, representation, memory, action, perception etc.) affected both the visual perception theory and the semiology of the built environment.

    Meanwhile, the school of architecture at Cambridge (England) developed an approach which emphasized mapping whereby perspective was reduced to being but one of a series of alternatives as was noted elsewhere (Sources, pp.136-139) in our discussion of the classic work in this context, March and Steadman’s (1971), Geometry of the environment. A similar trend was reflected in the Architecture of form edited by March (1976), which contained fourteen contributions on a quantitative approach to architectural design, three of which dealt with perspectival themes. Derbyshire (74-93), in "Geometric representation of outline design", outlined a shorthand version of representation which recorded a sequence of cross sections and listed objects in terms of their vertices. Hawkes and Stibbs (116-158), described in some detail work being done at Cambridge on "Computer description of built forms" mainly in terms of parallel perspective. Forrest (159-184), discussed "Transformations and matrices in modern descriptive geometry". He noted that "for the purposes of visualisation, graphical information has to be transformed so as to provide a particular view" and suggested that transformations perform three basic functions (160):

i. relating users’ coordinate systems to display, plotter, or computer model coordinate systems;

ii. orientation of the object(s) with respect to the selected coordinate system e.g. by rotation and

translation to obtain a particular view.

iii. various types of projection and distortion such as perspective, isometric projection, stereo etc.

Transformations in the third category are used mainly to aid the visualisation of objects.

There are other visualisation techniques which are worth discussing, such as dynamic

display, selective display, hidden line removal, intensity modulation and shading, which are

not transformations in the conventional sense.

    In this interpretation perspective emerged as a subset of mathematical transformations. A more radical approach was developed by Hillier and Hanson (1984). Architecture, they claimed, was "usually discussed in terms of what buildings look like from the outside. But how buildings and towns work has much more to do with how they create and arrange space". Traditional approaches had tried to link (26):

a material realm of physical space without social content in itself and an abstract realm of social relations and institutions, without a spatial dimension....To remedy this, two problems of description must be solved. Society must be described in terms of its intrinsic spatiality; space must be described in terms of its intrinsic sociality.

    With respect to the history of architecture, Corboz (1978), made an important contribution in his Militant painting and revolutionary architecture, which began by showing that Boullée’s supposedly revolutionary architecture at the time of the French revolution was linked with the paintings of Hubert Robert through the theme of the (perspectival) tunnel. Corboz found that archeological ruins of ancient buildings constituted only one aspect of Robert’s sources. He noted that views described by Robert as being drawn from life (dal vero) were often caprices; that the interplay of real and imaginary was much more complex than usually assumed. He traced these developments to neo-classical theories of architecture of Cordemoy and Laugier, showing how the perspectival tunnel view was applied to vegetative variants of ruins, to canals, to covered arboreal versions. Corboz noted that Robert endowed ruins with a new positive function that emphasized the spectacle of disaster, and even extended to visualizing future ruins.

    Methodologically Corboz insisted on a simple but fundamental idea, that painting was an important source for architects in designing new buildings, a theme which he pursued in his seminal monograph on Canaletto (1985).

7. Gardens and the Environment

    As was noted elsewhere (Sources, pp. 170-182*) comments concerning the use of perspective in gardens can be traced back to the sixteenth century. A passage from Dezallier d’Argenville (1739) suggests that by the early eighteenth century this tradition was being called into question:

Perspectives and grottoes are almost no longer in fashion anymore....As for perspectives they serve to hide gabled walls and walls at the end of a path which one cannot go beyond. They are a fine decoration and very surprising in their illusionistic openings. One paints them in oil or in fresco and covers them above with a little roof.

    As was shown, the latter eighteenth century saw a revival of these fashions which extended the notion of the view as far as the horizon. Meanwhile, thanks to the influence of Chinese ideas, imported to Europe through travellers such as Sir William Chambers, an alternative approach which occluded views gained favour and became increasingly associated with the English taste. The nineteenth century brought a number of new treatises on various aspects of perspective in gardening.

    Even so, serious study of the history of gardens did not begin until the twentieth century. Guiffrey (1913), made a classic study of André Le Nostre, which touched on his use of perspective. However, most of these early studies were primarily collections of illustrations, as was the case with a fundamental survey of Mediaeval gardens by Crips (1924) which has been reprinted (1966). Studies by Gromort (1922), on Gardens of Italy and Tipping (1925), on English gardens pointed the way to more specialized work focussed on a given country. An important book by Shepherd and Jellicoe (1925), on Italian gardens of the Renaissance, subsequently republished (1986), was among the first to include analytical discussion of perspectival gardens.

    Both De Ganay (1949), in his Gardens of France and their decor, and Marie (1949), in his French gardens created in the Renaissance, again broached the problem of perspective in landscape gardening. Rommel (1954), traced the development of the classic French garden in light of new terms in the language, noting that the term perspective came to mean a painting representing gardens and buildings at a distance. Some coffee-table books, such as Great houses of Europe by Sitwell (1961), and Royal gardens by Meyer (1966), have provided useful illustrations (both engravings and photographs) of perspective in gardens. On a more scholarly front, Wimmer (1969), in his History of garden theory provided a useful collection of source material from early treatises. Fleming (1979), in his English gardens provided new examples of perspectival gardens.

    Hazlehurst (1980), in his Gardens of illusion, provided an important biography of André Le Nostre, tracing the influence of Salomon de Caus, Jean François Niceron and Simon Vouet on Le Nostre’s understanding of optics and perspective. A significant contribution of Hazlehurst’s study was to convey a sense of how the effects of foreshortening change as one walks through these gardens of the seventeenth century. As such it remains the best single study in the field. Dennerlein (1981), provided some new material in The art of gardening during the regency and rococo in France, as did MacCubbin and Martin (1984), in a collection of essays on British and American gardens in the eighteenth century, but a systematic study of how perspective transformed European and other gardens has yet to be written.

8. Alternative Methods

    Treatises on other categories of perspective have been considered elsewhere (Sources, pp. 98-110). Some attempts have been made to revise the methods of linear perspective and provide easier methods Here it will be useful to focus on secondary literature concerning inverted perspective, anamorphosis, cylindrical perspective, spherical perspective and variant methods.

Inverted Perspective

    Some Renaissance paintings, such as Dürer’s Adoration of the Trinity (Vienna, Kunsthistorisches Museum, 1511), depict large figures in the upper parts of the picture and small figures in a reduced landscape below. This is exactly the opposite to what the laws of linear perspective predict. Wulff (1907), termed this inverted perspective, related it to a tradition of bird’s eye views, which he claimed originated in old Byzantine art of the fourth century and explained it in terms of Lipps theory of empathy whereby the viewer supposedly imagined themself in the position of the persons represented. Doehlemann (1910), offered another explanation in terms of hierarchic scaling and Hamann (1910), in a review offered further objections.

    Inverted perspective is often found in the context of Russian icons and provoked Florenskij (1920), to write a classic article on the subject in which he argued that this phenomemon could not simply be dismissed as a mistake in linear perspective which he claimed was based on six particular assumptions: 1) that space is Euclidean, i.e. isotropic, homogeneous, and infinite; 2) that in the midst of this infinite space there exists an extraordinary, absolutistic point corresponding to the artist’s eye; 3) that this standpoint is monocular; 4) that the viewer is effectively bound to an absolutistic, immovable throne; 5) that the whole world is treated as unmoving and unalterable and 6) that all psycho-physiological processes of sight are ignored. Linear perspective, he concluded was but one of many alternative methods. Hence far from being a failure to understand the rules, inverted perspective reflected other intentions on the part of artists. Florenskij’s work has only gradually become known in the West through translations into Italian (1983) and German (1989). Meanwhile in Russia one of the members of his group (cf. above p. 54*), Shegin (1970), pursued the question of inverted perspective and became convinced that it was part of a very complex method of representation involving cylindrical and spherical projection planes. Although this study was translated into German (1982), thus far it has had little impact on European and North American scholarship.

    Thouless (1933), speculated that the eidetic aspects of Oriental meditation might help explain the use of divergent perspective in Indian art. Grabar (1945), suggested that Plotinus’ Enneads held the answer: a notion of inspiration whereby the devout person lost themselves in the persons they represented led to the viewpoint becoming that of the represented rather than that of the representer. Stefanini (1956) challenged this and argued that it emerged instead from a mediaeval Christian spiritual tradition which made the individual soul the point of emanation. Thereby the vanishing point was in the projector, i.e. the artist, rather than on the screen. Gioseffi (1957), sought to explain away inverted perspective at San Vitale in Ravenna as compromises between adjacent subsystems of central perspective (pl. 15.2). Zajac (1961), explored the visual properties of parallel receding lines and concluded that: "with normal conditions of observation, the convergence of the parallel lines belonging to objects below the eye level should be increased in the picture, and those placed above the eye diminished, in comparison with the geometrically drawn projection of objectively parallel lines".

    Koyama (1965), focussed on examples in Japanese art and claimed it should be considered in connection a) with special problems of vision, namely, binocular sight, optical illusion, visual constancy, and shifts of viewpoint; and b) with special effects of expression through deliberate distortion, not least to create delicate plastic effects. Brion-Guerry (1966), took up afresh Grabar’s interpretation to sketch the history of art as a pendulum between two extremes: one illusionistic involving linear perspective, the other Plotinian, involving inverted perspective.

    The field of perceptual psychology sparked new interest in the problem. When Gibson (1970), reviewed the symbol-theory of pictorial information (cf. above p. 97*), he argued that "no rule or canon of inverse perspective could possibly be systematic", while suspecting that this technique "was quite unintentional and that the explanation is not simple". In reply, Goodman (1971), insisted that inverted or reverse perspective could be systematically applied and that, when this method was used with a box seen on end, it actually conveyed more information than linear perspective. Couzin (1973), reassessed these opposing views of Gibson and Goodman, claiming that there were systematic ways of depicting spatially limited objects in inverted perspective but not unlimited spaces, whence there were no landscapes using this method. He was convinced however that problems of inverted perspective were superfluous to Gibson’s theory of information, the real dilemmas of which lay in their conflation of questions of fidelity and depiction.

    Almgren (1971), in a carefully documented dissertation examined the phenomenon of inverted perspective in the context of children’s drawings and identified six reasons: through changes in aspect of cubic forms; lack of space; the aim to avoid hidden surfaces; as a result of binocular observation; a quest for symmetrically divisible motifs and as a result of not entirely controlled arm, hand and finger movements.

    Having reviewed earlier interpretations of Wulff and Gioseffi, Arnheim (1972), argued that inverted perspective was best explained as a method of enhancing two basic objectives of picture making, namely visual display and expression. He noted that "the wish to combine frontality with a display of the side-faces favors the use of divergent shapes" in both painting and architecture. In modern art inverted perspective serves "to display relevant aspects of three-dimensional objects in the picture plane"; it fits in with a general trend to reduce or even eliminate the hollow space behind the window of the frame; helps add an aggressive dimension to painting while convergent lines are mainly passive and feminine; and contributes to the total compositional scheme of a painting.

    Zupnick (1976), believed that the philosophical roots for reversed-perspective went back to Euclid’s Optics. Euclid claimed that the eye emitted rays of sight that diverged as they moved from the eye. According to Zupnick artists used this as a basis for "projecting an image on the pictorial surface using their own point of sight...as the point from whence the divergent rays were emitted." Rauschenbach (1980), in a Russian book claimed that inverted perspective reflected principles of visual perception. In a subsequent English article, Rauschenbach (1983), used the phenomenon of size constancy to claim that the eye sees nearby objects in parallel and inverted perspective and related this to Luneburg’s (1947), experiments. According to this account inverted perspective corresponded to how the eye sees.

Anamorphosis

    The phenomenon of anamorphosis, also known as trick perspective or curious perspective, seems first to have caught the attention of authors of literature such as Shakespeare in the early seventeenth century as Gilman (1978) has shown (see below p. 114*). By the late seventeenth century philosophers such as Leibniz (see p. 124*) referred to anamorphosis in their works. Even so it was not until the early twentieth century before scholarly interest in the history of the subject emerged. Böttiger (1910), in his monumental analysis of Gustaf Adolf’s art cabinet (Kunstschrank) in Uppsala noted that the anamorphic images therein were based on Püschel, Maglioli and Merian. Röttinger (1925), identified two anamorphic woodcuts as the work of Erhard Schön, which prompted Weixlgärtner (1926) to explore their context; relating them to the Renaissance tradition of perspectival foreshortening as well as other anamorphic images: Holbein’s Ambassadors and Parmigianino’s Self-portrait.

    Baltrusaitis (1955), made the first serious and only systematic study of anamorphosis, which went through different editions (1969, 1984) and translations (English 1977). He related anamorphosis to the tradition of optical adjustments and scenography; provided a wealth of anamorphic examples, some in paintings or woodcuts, others in treatises. Baltrusaitis traced the spread of these techniques from early German examples in the sixteenth century through the seventeenth century when they became an element in debates first of Dubreuil with Desargues and Bosse; then of Bosse and the Academy and were linked with the Jesuit encyclopaedic tradition (Kircher, Bettini, Schott). Further chapters offered eighteenth and nineteenth century examples; a series involving cylindrical mirrors, plus Chinese adaptations. The 1984 edition added a chapter on twentieth century examples. All this was supported by detailed footnotes and justly remains the standard work on the subject.

    Michel (1961), introduced the surrealist comments of Jean Cocteau concerning a cylindrical anamorphosis of a Crucifixion by Rubens. Without any reference to earlier work, Docci and Janniccari (1963), wrote a brief history which essentially rearranged material analysed earlier by Baltrusaitis. Samuel (1963), doubted that Holbein’s Ambassadors should be seen from the side and suggested instead that it was was intended to be seen from in front using a correcting lens which diminished the size of the image in the longer meridian. Naitza (1970), acknowledged the documentary contribution of Baltrusaitis but claimed that one needed to reconsider the history of anamorphosis. If viewed purely technically, anamorphosis was reduced to a particular case of perspectival virtuosity, as a series of marginal events. In fact, he argued, anamorphosis challenged the legitimacy of traditional perspectival methods. Naitza argued that clear distinctions needed to be made between superficial examples such as Schön’s woodcuts and complex masterpieces such as Holbein’s Ambassadors. To understand seventeenth century examples Naitza suggested that Wölfflin’s concept of open and closed paintings could be extended such that anamorphic experiments were seen as explorations of open space. He noted how science played an essential role in these later works; as did a combination of technique and ideology which led these methods to become part of the Jesuits’ didactic enterprises. Naitza essentially repeated these ideas in a later article (1980).

    Holländer (1972), drew attention to four anamorphic paintings by Niceron (Rome, Palazzo Corsini) not mentioned by Baltrusaitis. A consideration of their artistic and scientific context led to comparisons between Niceron’s treatise and the work of his contemporary Descartes. Leeman, Elffers, Schuyt (1976), produced a popular exhibition (Rotterdam, Brussels, Baden-Baden and Paris) based almost entirely on Baltrusaitis’ work. Reviews by Schwartz (1976), and Marmori (1976), and the accompanying Dutch and French catalogues acknowledged this in passing. An American edition of the catalogue "forgot" to mention Baltrusaitis entirely and was removed from circulation. One of the viewers of the exhibition was inspired to reflect more deeply on the problems involved.

    Margolin (1977), related anamorphosis in art to allegory in literature: both were open to multiple readings. He noted how some of the anamorphic examples were  sexual and scatological; others political, philosophical, mysterious, while some were comical in mood. Margolin suggested that all involved a combination of, rather than an opposition between mathematics and magic, as the sub-title of Baltrusaitis’ book had implied. Masters (1977), a student of Battisti, produced computer programs for basic anamorphic methods. Schickman (1977), drawing on the work of Guillen and others (see p. 114*), interpreted some of Shakespeare’s images in terms of anamorphosis; related these to paintings and speculated on their meaning, concerning which Turner (1977), raised further questions. Lacan (1980), in an interview with Wahl discussed the meaning of Holbein’s Ambassadors in terms of a conflict between eye and gaze: "This picture is simply what any picture is, a trap for the gaze. In any picture, it is precisely in seeking the gaze in each of its points that you will see it disappear". Veltman (1986) noted that anamorphic effects were often produced by the application of linear perspective under special conditions, e.g. when an object is very close to the picture plane. Hence instead of seeing anamorphosis in opposition to perspective one could view both as expressions of a single phenomenon.

Cylindrical Perspective

    Linear perspective entails a basic paradox. Its inverse size-distance law applies only to the distance of objects from the picture plane. Thus a long row of houses because they are all in a plane that is equidistant from the picture plane will all remain the same size on the picture plane, even though those off to the side are increasingly far from the eye. Renaissance artists devised various compromise solutions. For instance, Pacioli (1494), produced a rough formula to calculate the necessary diminution. Leonardo, in his quest to devise a plane which was equidistant from the eye appears to have considered a hemi-cylindrical plane. He drew only a line in the form of a half circle which, if interpreted fully three-dimensionally, would imply a spherical rather than a cylindrical method. Some of his drawings unequivocally show a projection onto a cylindrical ceiling. Pedretti (1963), drew attention to possible links between Leonardo’s work and an instrument for drawing on a cylindrical surface produced by Baldassare Lanci and published by Danti (1583). Maltese (1977-1978, 1980), explored these connections. Veltman (1986, 1986) examined these links in more detail, suggesting that an extant instrument for measuring distance (distanziometro, Florence, Museo di storia della scienza) might be identified as Baldassare Lanci’s instrument to produce cylindrical perspective. Relevant passages from Barbaro (1568) and Danti (1583) were cited, translated and discussed. Such cylindrical planes were frequently considered by seventeenth century authors such as Marolois (1614 etc.), or Bosse (1648). In the nineteenth century authors such as Ware (1882) included a chapter on "Cylindrical, curvilinear or panoramic perspective". This continued in the twentieth century even with authors of standard textbooks such as Abbott (1950,140) who pointed out that:

There is no need to adhere to a plane surface if a curved one will give an advantage. An obvious advantage in compactness results from the use of a cylindrical sheet as a picture plane, when the perspective of an extensive scene or a long range of buildings has to be recorded....The perspective of tall buildings may be recorded on a cylindrical surface having its axis horizontal. A common example of the method is...where an observer views scenes and figures painted upon a cylindrical surface or wall.

    Doesschate (1960), using an example drawn by Dr J. E. Schrek, discussed some of the problems with this method. Historically there has been a certain amount of confusion between cylindrical and spherical methods of perspective, for which there are two clear reasons. One is terminological, when persons speak of curvilinear perspective and do not distinguish clearly between the two. Another is aesthetic. Notwithstanding the well known curvatures of entasis, artists have used curvatures more for long horizontal stretches than for vertical ones. Hence even when they appeal to a spherical method they frequently correct the curved verticals to arrive at a something very close to a cylindrical projection. One could argue of course that the real problem is a conceptual one. For although many persons think of cylindrical and spherical perspective as different methods, they can in fact be seen as the same method of linear perspective applied to different projection planes. This, for instance, is how Bosse (1648), dealt with the problem (Sources, pl. 58). For the purposes of this survey these traditional categories are maintained.

Spherical Perspective

    In Antiquity, Euclid, in his Optics, mentioned apparent curvature of visual space without considering its implications for representation. Renaissance artists such as Leonardo da Vinci, Baldassare Lanci and Daniele Barbaro explored the potentials of cylindrical and spherical projections for both problems of vision and representation, but continued to favour methods of linear perspective. One of the first to challenge this claim was the astronomer Schickhardt (1624) in his Sphere of light:

I say that all, even the straightest lines, as long as they are not directly in front of the eye against the pupil or go through its axis, necessarily appear somewhat curved. No artist believes this, which is why they paint the sides of a building with straight lines although according to the true laws of optics this is not correct.

    Spherical perspective was mentioned by Brook Taylor (1719 etc.), and by Costa (1747). Malton (1779, 95), considered but then dismissed as inpracticable images on the surface of a sphere. Malton may have been a source for Turner who occasionally used curvilinear methods in paintings such as Petworth Park (London, Tate Gallery, 1828), and was specifically cited as a source by Herdman (1853), whose Treatise on the curvilinear perspective of nature appears to have been the first work dedicated specifically to the representation of spherical methods. Herdman, however, applied his principles almost solely to horizontal lines and edges. Vertical architectural lines remained straight. He argued that curvature of verticals (100):

will be found only when lofty elevations are depicted near....In all other instances in which pictures are usually drawn, the vertical attitude is so small as to make any deviation from a straight line either unnecessary or so trifling, as to matter little whether attended to or not.

    As Hansen has noted Herdman’s circular perspective was effectively cylindrical rather than spherical. The great French author on perspective, Jules de la Gournerie (1859), considered circular and hyperbolic surfaces but preferred rectilinear solutions that avoided curvilinear images. Viollet-Le-Duc (1863), also broached the problem: "The eye being a portion of a sphere of which the centre is the visual point, the pinnule, all objects are reproduced on a curved surface", a passage that was later cited by Borissavlievitch (1951).

    Ironically, interest in spherical perspective methods based on analogies with curvature of the retina became more popular in the very generation after the detailed optical experiments of Hering led him to call for a clear distinction between objective retinal space and subjective visual space, and his colleague, Helmholtz insisted that the shape of the retina had no practical effect on the shape of the image (see above p. 90*). In Germany, Scholz (1875), explored these problems in his method of twofold projection which began by projecting an object onto a spherical surface and then projecting the image again by drawing it collinearly. Such problems of perspective were also of particular interest to Guido Hauck, a professor of descriptive geometry in Berlin. One of his earliest articles concerned a general axonometric theory of descriptive geometry (1876). Three years later, Hauck (1879), made a detailed review of modern optics (e.g. Helmholtz, Hering, Wundt, Donders) and developed his own theory of spherical perspective which he believed also accounted for subjective curvatures in Doric architecture (see above p. 37*). He returned to these themes in articles on the relation of mathematics to art (1880), and basic principles of linear perspective (1881, 1882), in which he referred to Scholz (1875). Hauck went on to make contributions to the field of photogrammetry (1873). For over two decades little attention was paid to his work. Then a modernistic art teacher, Stiehler (1906), recommended the use of some of his precepts. He was attacked by a more traditional art teacher, Gehler (1906), in a five part article, who extended his attack to include another teacher (1908), which led to a defence by Grothmann (1909), and led to further comments by both Gehler (1909), and Weinbeer (1910).

    No mention was made of these debates by Deininger (1914), who presented a paper to the Austrian Association of Architects claiming that it was only on a spherical surface that one could represent graphically "perspectival dimensions in their proper relation and their correct size", and described a device he had patented for these purposes. Paulsdorff (1921) reviewed these ideas favourably as if they were fully original.

    In the United States, Ames and Proctor (1921) studied vision in relation to art (see above p. 67*) which led to further studies by Ames, Proctor and Ames (1923), in which the authors reached seven conclusions concerning painting, three of which are relate directly to the theme of spherical perspective (123):

4. A pictorial representation of nature to be technically satisfactory from the artistic point of view should be similar to our subjective impression. It should not attempt to reproduce actuality.

5. Our subjective impressions are, in their general character, similar to the pictures we receive on our retinas while holding one center of focus.

6. A pictorial representation of nature to be technically satisfactory from an artistic point of view should be similar in its general characteristics to the pictures we receive on our retinas while holding one center of focus.

    Later artists in the United States were to pursue this theme, with the exception that they believed they had found objective methods of recording retinal images. This paradox of the objectification of the subjective in the context of alternative methods of perspective has been explored by Veltman (1992). In France, Borissavlievitch (1923, 1925, 1926, 1953) outlined a method of optico-physiological perspective (la perspective optico-physiologique) which he explained: "is not a spherical perspective, and even if it also employs horizontal and vertical circles it is only in considering these as simple perimeters of which the aim is to determine relations between the spatial magnitudes by means of visual angles and not in order to regard the images projected onto these arcs and onto a sphere".

    This was to become a lifetime commitment. Borissavlievitch (1948) wrote a major book on the topic in Serbian, worked for years on a French translation which was not published and instead produced further articles (e.g. 1950, 1955) and another book (1950). He is mentioned here because later critics such as Zanetti (1951) assumed that he had indeed been expounding a method of spherical perspective similar to Hauck.

    Meanwhile in Germany architects were continuing to re-invent the wheel. Birker (1923), an architect in Düsseldorf, secured two patents concerning a simple device for spherical projections. Stark (1928), published his Retinal image. Method for the production of the true visual image following the principle of human vision applied to the drawing construction of perspective, which acknowledged only the influence of the philosopher Francé. In a review of Stark’s book, Opitz (1929), was critical of its practicality but again did not question its originality.

    In an important dissertation, Hegenwald (1931) reviewed a number of these earlier contributions, notably, Scholtz (1875), Hauck (1879, 1880, 1881), Birker (1923) and Stark (1928); noted that the problem of retinal perspective had excited lively debate a half century earlier, had been forgotten and subsequently revived. He cited Hauck’s view that there were conflicts between collinear and conform solutions and that the position one chose along this spectrum determined the kind of perspective one employed. Hauck and his followers who favoured the conform side had chosen spherical perspective. According to Hegenwald, however, it was impossible to record all the optical impressions of a larger object. One needed to choose a particular viewpoint for which collinearity, and consequently linear perspective was best suited. He thus concluded that linear perspective remained the most rational method which had been developed thus far. Hegenwald’s views were accepted in a dissertation by Eith (1936) on the relationship of perspectival representation to mental (Vorstellungsbild) and visual (Sehbild) image.

    In Montreal, Jobin (1932), unaware of these discussions, announced "new theories of artistic perspective and practice" when he wrote Straight line or curved line? a book in which he claimed that the recent development of skyscrapers and airplanes required the application of perspective to vertical as well as horizontal lines, argued that these lines should be curved and maintained that spherical methods of perspective best corresponded to visual experience given the spherical retina (pl. 48.1). In Mexico, Serrano (1934), equally unaware of these discussions, developed his own detailed method of spherical perspective (pl. 50.1). Making no mention of any predecessors, the German engineer Möhrle (1941), produced a retinal perspective sheet applicable to aerial views, interiors, photography and engineering which went through several editions (fourth ed. 1949). Similarly the Italian architect, La Grassa (1947), claimed he had discovered a "new" method for representing the visual field and in the process coined two new terms. One was optical effect (effettottica) for the "new science which reveals the characteristics of points, lines and angles of the elements of bodies of the entire visual space from a given point of view". He also coined the term optical perspective (prospettottica) for the representation in a vertical plane of these characteristics identical to the way that they are seen. While La Grassa’s method was praised by both Giorgi (1947), and Boaga (1948), it was challenged by Zanetti (1951), who related it to earlier methods of both Hauck (1879) and Borissavlievitch (1923, 1926), before claiming that linear perspective in fact remained the most efficient method for reproducing both collinear and conform elements of representation. In Germany, Schumacher (1952), produced another sheet for retinal image perspective very reminiscent of Möhrle’s earlier version, again presented as new without acknowledgement.

    Not everyone worked in such a vacuum. U. Graf (1941), considered five different kinds of perspective: central perspective as in photography, which was linear and four methods with curvilinear elements, namely, stereographic; Hauck’s perspective; azimuthal and a version which was true to spatial angles (Raumwinkeltreue Perspektive). In a doctoral dissertation, Zeise (1947), reconsidered possible links between optical adjustments and Greek architecture, reviewing the work of Hauck and others who claimed that this involved retinal image perspective. Zeise was a student of the ophthalmologist, Jäger at Kiel, who wrote on these questions himself the following year (1948), and was an advisor of a significant dissertation by L. Graf (Münster, 1949) on Perspective as a problem of physiological optics. L. Graf cited optical writers such as Euclid, Leonardo, Helmholtz and Hering; was aware of alternative methods of representation by Hauck, Stark and U. Graf; considered the relative values of both concave and convex spherical projections and recommended his own version of retinal image perspective intended to compensate for shortcomings in linear perspective which had been noted by architects. Von Gerkan (1954, 1959) listed his objections to retinal perspective both in terms of their practical applications in modern architecture (e.g. Stark, Möhrle) and their value in explaining aesthetic principles of Greek architecture as suggested by Jäger and Zeise. Danielowski (1960), an architect at Weimar influenced by both historical studies and the Viennese school of descriptive geometry developed his own solution which cited the earlier work of Hauck and Borissavlievitch.

    In France, the appearance of an important study by Nicod (1962), with an introduction by Bertrand Russell, which claimed to prove that visual space is spherical, served as a point of departure for a brief article by Flocon and Barre (1963) on curvilinear, i.e. spherical perspective. An article by the mathematician Bouligand in conjunction with Flocon and Barre (1964) took these ideas further. The authors claimed that their method of spherical perspective had its roots in Renaissance painting (Fouquet) and cartography (Postel). This served as the basis of a book by Barre and Flocon (1968), for which Bouligand wrote the preface (pl. 47.3-4). Here Fouquet became but one in a list of earlier exponents which included Leonardo da Vinci, Dürer, the author of the Codex Huygens, and practitioners such as Callot, Daguerre, Delaunay and Escher, but left unmentioned the many theoreticians whom we have just considered. A series of seventy eight diagrams illustrated vividly the concepts of spherical perspective and the book gradually became recognized as a basic contribution. Translations into German (1983) and Spanish (1985) followed. Hansen, of hyperbolic perspective fame, produced a translation into English (1987) with a valuable foreword. Meanwhile Docci (1975) had described the principles of this method in an Italian article.

Variant Methods

    There have been a considerable number of variants to these spherical methods. Some have been largely empirical. Dick Termes, for instance, traces his experiments back to 1968 when he was trying to get beyond the limitations of Renaissance perspective:

After looking at one of my drawings of a six point cube I decided it would be interesting to build a bulging out cube to crawl inside of. I was hoping this cube would look much larger than it was as it would have a built in exaggerated perspective in it. One of my fellow students in this class suggested drawing a cube on a ball would give me the same effect as I wanted in this bulging out cube. I sketched the cube on the sphere after I got back to the studio.

    This led to his discovery that the six orientations from the interior of the sphere could be described as six point perspective and thus began a life-long profession of painting on spheres which he called termespheres (pl. 135-138). Termes was initially more interested in practicising his art and only began publishing his ideas much later (e.g. 1982, 1990).

    By contrast, Vero (1970), was concerned with theoretical written statements and the history of the problem as was the artist-philosopher, Robert Hansen (1973), who had studied the writings of Leonardo da Vinci and began his article on hyperbolic linear perspective with a quote from Schickhardt (1624), cited earlier. Hansen claimed that by attending to the appearance of objects we see curves whenever we look at straight lines, curves which appear as hyperbolas rather than arcs. Accordingly he suggested a circular five point hyperbolic natural perspective to record these appearances.

    These descriptions heralded a series of related methods around the world. In Milan, Dan Elias (1973), cited the spherical method of Barre and Flocon as a point of departure for his descriptions of spherical and planispherical perpective, projections less than, equal to and greater than 180 degrees as well as the homosphere. In Rio Di Janiero, the architect Reggini (1974, 1974, 1975), designed a computer programme with curved projection rays which took into account constancy scaling effects such as those studied by Thouless (1931), involving phenomenal regression to a real object. In Madrid, Fuentes Alonso (1975), described his curvilinear method intended to take into account the experience of the eye.

    In London, Adams (1976), examined how images projected onto the four sides of a tetrahedron could be used to approximate the complete sphere of vision. Turner (1976), invented his own version of curved perspective. Shaw (1977), in a fine arts thesis described three variant methods which he coined prisimism, focalism and strokism. Termes (1980), of termesphere fame, patented a total environment photographic mount and photograph to produce a total picture (fig. 19). This involved coordinated images on a tetrahedron, octahedron, dodecahedron and icosahedron and led to new terms such as tetrahome, tetraperspective, and dodecaperspective. Termes explored the idea that different sides of these regular bodies could be used to record different moments in an event such that the resulting sequence of co-ordinated images represented a personal space-time continuum. He also had the idea of combining two or as many as six of these spheres together such that one could look simultaneously at all sequences of a room. Similar goals appear to have guided Casas (1983), who first represented a sphere on a flat surface which he termed flat-sphere perspective and then (1984) combined a series of these flattened spheres in a method he termed polar perspective that also integrated different temporal moments.

    Moose (1986), an architect in Cincinnati, developed his fisheye perspective in response to a practical problem of viewing the interior of a 93 foot high ziggurat-like atrium he was designing. In New York, the artist Clark (1987), organized an important exhibition of such spherical panoramic views which included the work of Lucien Day, Jacqueline Lima (pl.50.2), Richard McKown, and David Hockney. In Paris, Comar and Blotti (1986, 1987), produced a series of variant methods of perspective for a new exhibition at the Museum of Science and Industry at La Villette.

    It is instructive to note that these attempts to record subjective dimensions of visual experience are on the rise although art critics have repeatedly emphasized the logical problems of this approach. For instance, Lalo (1932, 597), pointed out that "the manner of drawing which alters a form or a colour also alters it on the panel and in the same way", a phrase that was cited verbatim by Blanché (1946). Adams (1962, 36) observed: "Yet a retinal image which a spectator would get from looking at such a picture would be doubly curved and so fail to match the image produced by the object." When Friedenwald (1954), suggested that Cezanne’s adjustments were a result of theories of vision to which Luneburg drew attention, Doesschate (1959), challenged this on similar grounds. Heelan (1972), examined Van Gogh’s Bedroom at Arles (Amsterdam) in detail and suggested that it was based on a new kind of perception that re-created the world as non-Euclidean visual space (Blumenberg, Luneburg) with constant Gaussian curvature, not just subjective emotions oriented towards a certain vision of being. By contrast Adams (1975), argued that the curvatures in Cézanne and Mondrian invented new pictorial structures in order to reflect a feature of perception. Gombrich (1975), claimed that (126):

this is a paradox that arises in every case where the artist tries to register his subjective experience regardless of the experience his record will arouse in the beholder. J. J Gibson has referred to the consequences of this aim as the Greco Fallacy, alluding to the naive belief that Greco elongated his figures because his astigmatism distorted them in this way.

9. Reconstructions

    Nielsen (1895, 1898 etc.), appears to have been the first to introduce perspectival reconstruction, in the sense of using perspectival lines superimposed on a drawing (pl. 35.1-2) or photograph of a painting. In the early twentieth century, they became much more significant through the work of Kern (1904, 1912), who, in his debate with Doehlemann (1904-1905, 1906, 1912), claimed that these reconstructions provided an important tool in settling questions of chronology in Netherlandish painting (pl. 36.1-2). Panofsky (1927), in his landmark article used Kern’s reconstructions and made them famous.

    Müller (1911), in a significant dissertation, using as a point of departure, the proportion studies of Hoeber, Berlage, Thiersch, Wölfflin and Dehio, reconstructed the geometrical proportions in early German engravings with architectural motifs,notably the Flagellation of Christ by the Master of Calvary (Meister des Kalvarienberges), the large and the small Madonna of Einsiedeln by Master E.S. (1466) and the altar by the Broederlam Brothers showing the Presentation of Christ (1399, Dijon) which, he claimed (25) entailed a distance point or external eyepoint as he called it. Müller re-examined descriptions of perspective by Alberti and Dürer, suggesting that Dürer's interests in proportion probably linked him with the German tradition of master builders; claiming that, for the artists of the Renaissance, perspective is the harmonic arrangemnt of sizes in space. By implication the seeming discrepancies between German and Italian art, were partly a reflection of different approaches to proportion.

    Beginning in the 1920’s, scholars such as Curtius (1929, pl. 34), Little (1937), Kern (1938), and Beyen (1930), used reconstructions in making claims about whether or not the Ancients were familiar with the principles of linear or curvilinear perspective. Gioseffi (1957), used the reconstruction of perspecctival lines to claim that Giotto knew the principles of linear perspective over a century before Brunelleschi’s demonstration (pl. 7).

    Battisti (197*), used perspectival reconstructions to show that Lombard artists were active in perspective in the second half of the fifteenth century. This theme was developed by Dalai-Emiliani (197*), who analysed the work of Foppa.

    Degl’Innocenti (1975-1976), in a Manual for the perspectival reconstruction of Renaissance paintings with architectural representations, outlined his method which he applied in particular to Ghiberti’s sculptures on the bronze doors of the Baptistery at Florence. Problematic with this approach was a tendency to reconstruct the space as it would have looked if a correct perspective had been used. While very effective this approach was basically ahistorical. Degl’Innocenti (1977), applied this approach to reconstructions of some episodes from the frescoes (c.1460) from Roccabianca depicting the Life of Griselda which formed part of the exhibition at the Castello Sforzesco (Milan, 1977,), on the occasion of the first world conference on perspective. Degl’Innocenti (1980) developed this approach in his beautiful yet misleading reconstructions of Filippo Lippi’s Stories of the Virgin in the Tondo Bartolini (Pitti Palace, Florence, pl. 41-42) and pursued this method in his reconstructions of Leonardo’s paintings for Pedretti’s (1981) work on Leonardo’s architecture.

    Lynch (1982) produced a striking reconstruction of the seemingly irregular polyhedron in Dürer's Melencolia, to show that it was in fact a regular truncated cube. This article helped inspire an imaginative, artistic reconstruction of Melencolia by Hanfeld (1994), which integrated aspects of Rahmann's mpdel of the Potsdamer/Leipziger Platz in Berlin.

    Mazzola, Krömker, Hoffmann (1986), produced a reconstruction of Raphael’s School of Athens, which unleashed considerable controversy because the relatively primitive quality of the computer images was felt to undermine the aesthetic subtleties of the original. That same year, Soddu (1986), in The non-Euclidean image, provided a computer generated reconstruction of Uccello’s Chalice. In the case of Simone Martini’s Child attached by the Wolf (1328), a whole series of alternative re-constructions of the space were provided (64-70). These challenged one to think in new ways about the space involved (pl. 43-44). This principle was repeated in the case of Vincent Van Gogh’s Bedroom (72-79), Paul Klee’s Non-composite in space (80-83) and Balla’s "A moment of mine of 4.4.1928 at 10.02 a.m." (84-87).

    The latter part of the book took objects and displayed these in a series of alternative perspective methods. The first was a mosque in Somalia, beginning with a (88): "verification of the limits of traditional perspective trying to represent in a single perspective drawing, the subject who looks at the space and how it is seen by the subject themself". This was then shown in normal perspective, and then various views entailing curved perspective. The second was a school shown first in a regular perspective, then in a curved perspective from a bird’s eye view, at eye level, and from a position at one or two meters from the entrance, in a total perspective traced on a sphere, on a cylinder, in a version of total perspective for practical use, viewed from a position near the patio and from a position inside. The next series returned to the earlier example a mosque in Somalia which was shown in total perspective on a sphere represented in axonometry, in total perspective of a cylindrical type, with an interior view, a simplified view, an anamorphic view and one in curved perspective. A final series various versions of a restored buiding in Mogadishu.

    Elkins (1994), has provided a useful survey of the history of reconstruction methods.

10. Instruments and Machines

    As noted elsewhere (Sources, pp. 117-122), books of instruments emerged as an independent category in the sixteenth century (e.g. Besson, Ramelli). These typically contained some perspectival drawing instruments as did treatises on perspective, particularly in the German tradition. The first of these with a conscious historical stance was Pfintzing (1598), who noted the names and dates of various sixteenth century Nürnberg inventors. Hartnaccius’ (1683), Mechanical perspective was another treatise in this tradition. Even so it was not until the late nineteenth century that serious lists of available instruments emerged. The most authoritative of these was Dyck’s (1892), classic Catalogue of mathematical and matematico-physical models, apparatus and instruments, the second part of which contained sections on "Geometry. Drawing instruments" (225-243) and "Polyhedra" (246-254). The most popular of these was Ford’s (18**), Mathematical drawing and measuring Instruments. Its seventh edition (1900) contained three chapters of interest for our purposes: namely, "Instruments for reducing, enlarging, and copying drawings of considerable size- the pantagraph,-the eidograph, -cymograph" (128-148); "Instruments intended to facilitate the delineation of natural objects, buildings etc., camera lucida, Amici’s camera, optical compasses, perspective sighting instruments" (149-163); "Ruling edges for producing radial or vanishing lines -the centrolinead, -rolling centrolinead, -notes on perspective excentrolinead".

    Von Rohr (1905), in a fundamental article, examined perspectival images and the mechanical aids used to understand them such as the perspectival window, Cardi’s scenographum catholicum, the camera obscura and camera lucida, Branders’s polymetroscopium, optic machines and show boxes. Part two of his article considered dioramas, cameras, the diaphanoscope, the mono-stereoscope and the Verant. Part three (1905), considered the stereoscope and related instruments such as the alethoscope and graphoscope. After this the first half of the twentieth century saw effectively no further general works in this field, as attention focussed on individual instruments. For instance, Straub’s (1949) History of civil engineering scarcely mentioned the problem.

    The second half of the twentieth century saw a revival of interest beginning with Feldhaus’ (1953), History of technical drawing, which contained a section specifically devoted to "Drawing instruments" (91-111) which was far from comprehensive. This was equally true of Nedoluha (1957-1959, 1960), and Gernsheim and Gernsheim’s (1956), examples of optical aids for artists, Higbee’s (1958) "Development of graphical drawing", Danielowski’s (1962), outline of the art of perspectival drawing, Booker’s (1963) significant History of engineering drawing; Havelka’s (1966), "Outline of the historical development of mechanical perspective constructions", or Veltman’s (1979), survey of some of the chief perspectival instruments used in the Renaissance, his brief outline (1986), of perspectival windows or Sellenriek’s (1987) work on the compass which raised larger questions of representation. A dissertation by Kuns (1980) was exceptional in its attempt to reflect on philosophical aspects of the problem. More recently Turner’s (1987), Early scientific instruments. Europe 1400 to 1800 and Hambly’s (1988), Drawing instruments 1580-1980, have offered a more thorough view of the field. Crary (1990), presented a controversial interpretation of implications for visual theory of early nineteenth century instruments, which is as ahistorical as it is misleading. Meanwhile, there has been considerable attention to the history of individual instruments, notably the camera obscura, camera lucida, camera, magic lantern, perspective box, pantograph, sector, stereoscope and more recently holography, computer and computer graphics, the four C’s, fractals and virtual reality. Each of these will be considered in turn.

Camera Obscura

    While the first allusions to the idea of a camera obscura have been traced back to Aristotle’s Problemata, the first clear descriptions of the camera obscura can be traced back clearly to Alkindi’s Optics in the ninth century. By the eleventh century when Ibn al-Haitham wrote his classic Book of vision (Kitab al-manazir) the camera obscura had acquired a considerable significance and as Saccaro Battisti (1980) has shown these aspects featured in the Italian translation that was used in the west, a theme that has been taken up anew in Salvemini (1990). Through Witelo’s (c.1270), compendium these ideas became more accessible. A Renaissance drawing of a camera obscura by Stefano della Bella has an image of the cathedral of Florence (pl. 9.2). This is all the more interesting because the aperture involved is pyramidally shaped like the aperture that Manetti describes Brunelleschi as having used (pl. 10.1). Leonardo included over 250 references to camera obscuras in his notes as Veltman (1986), showed. Even so these early authors typically reported their methods with little or no historical consciousness. There were some exceptions: Cesariano’s edition of Vitruvius (1521), and a treatise by Ridemannus (1670), which traced its use to Roger Bacon, cited the example of a contemporary instrument maker, Cornelius Drebbel.

    Bayle (1686), reported on examples of optical chambers without attention to their history. The Abbé Nollet (1735), reported on his invention as if it was without precedent. Brander (1767, 1775), at the outset of his books on new camera obscuras explicitly stated that he did not wish to describe various types. Algarotti (1769), reflecting on its uses for painting, mentioned earlier artists such as Spagnoletto, and Leonardo da Vinci. Buesch, in his Encylopaedia of the historical, philosophical and mathematical sciences (1775), and in his Attempt at a mathematics for the use and pleasure of bourgeois life (1802), discussed the camera obscura without reference to its history. Häseler (1779), in a technical study of the camera obscura in connection with magic lanterns and sun microscopes referred only to the theories of Euler.

    As noted earlier (p. 55*), the second half of the eighteenth century saw the rise of writings on the history of mathematics, particularly in Paris. There were similar developments in optics, although here London led the way with Smith (1755), and Priestley (1775), who was translated into German by Klügel (1776), and soon followed by continental treatments of Kästner (1780), and M. J. Brisson’s (1781), Commentated dictionary of physics (Dictionnaire raisonné de physique). These works were cited by Gehler (1798-1799), whose article in the Physical dictionary (Physikalisches Wörterbuch), traced the history of the instrument from Porta and Kepler, through Hertel, Doppelmayr, Cheseldon and Klügel.

    The nineteenth century brought some new contributions such as Wollaston (1812), "On a periscopic camera obscura and microscope", and provided only isolated notes on the history of the instrument. Guyangos (1840, 148), in his History of Muhammadan Dynasties, mentioned Ibn Firnas who reported that he had "a certain figure of heaven...in his house, and where the spectators fancied they saw the clouds, the stars and the lightning and listened to the terrific noise of thunder". W.M.L. (1857-1858), reported on Wooton’s meeting with Kepler during which the camera obscura was used for military purposes. Libri, in his History of mathematical sciences in Italy (1865, note II, 303-314), traced its use to Leonardo da Vinci and focussed on Porta. An important biographical article on the life of William of Saint-Cloud (Guillaume de Saint Cloud) by E. L. (1869), drew attention to his use of a camera obscura during an eclipse of 4 June 1285 (mentioned in Paris, Bibliothèque Nationale, Bib. Imp. n. 7291, Fonds lat. 146v.).

    Meanwhile, other evidence of the camera obscura’s use in fourteenth century astronomical observations came to light through a study of Levi ben Gerson by Boncompagni (1863). Ersch and Gruber’s General encyclopaedia of sciences and arts (1889) included an article on Levi ben Gerson (Zweite section, 43er Theil, 295-300) which drew attention to his astronomical and mathematical work without mention of his use of camera obscuras. Further studies by Steinschneider (1890), Curtze (1898), Eneström (1898), explored this evidence which was continued a decade later by Carlbach (1910), and Sarton (1910). Erdmann (1899), gave the best survey thus far noting that its basic principles could be traced back to Aristotle’s Problemata (XV,6).

    The first two decades of the twentieth century saw an enormous growth in awareness of the early history. Curtze (1901), reviewed what was known, drawing attention to and citing manuscripts of Levi ben Gerson of 1321 and 1342, Cesariano’s (1521), description of Don Papnucio and Porta (1558,1589). General Waterhouse (1901, 1901), provided another important summary of what was known on the subject, adding a note on Boyle’s portable camera obscura (1909), and summarizing the latest findings in his article for the eleventh edition of the Encyclopaedia Britannica (1910-1911). Eder’s (1905), Extensive handbook of photography drew attention to Roger Bacon before discussing Leonardo, Cesariano, Porta etc. but was again essentially a summary of well known facts.

    Developments in Arabic studies changed the picture dramatically. Wiedemann had been active in the field of Arabic optics with an article (1890) on spherical lenses. Wiedemann (1907), drew attention to Al-Kindi’s use of the camera obscura. Wiedemann (1907), turned to Ibn al-Haitham’s use of the camera obscura in his work on the Shape of shadows. This led to a note (1910), and then two important articles on Ibn al-Haitham’s invention of the camera obscura (1910, 1915). These studies were a starting point for Schulz (1914-1915), who explored Ibn al-Haitham’s theory of the camera obscura and Würschmidt (1915), who reviewed the new findings.

    Pauschmann (1922), in a fundamental article reviewed the entire history from Antiquity onwards, with precise references both to sources and to secondary literature and remains the most succinct summary of the evidence. Von Rohr (1925), linked the camera obscura with show boxes. Meanwhile, unaware of these studies, Liesegang (1919), continued to describe Porta as the inventor of the camera obscura. Gliozzi (1932), brought the discussion from Porta back to Leonardo. Court and von Rohr (1935), in a significant article, mentioned camera obscuras in the context of a larger discussion of zograscopes, drawing cameras and show boxes. Schaefer and Naumann (1941), provided a popular historical summary in four pages. Schwarz (1948), gave a similar survey in the context of art and photography.

    Duhem (1958), returned to the use of pinhole images in Roger Bacon and Levi ben Gerson, a theme taken up a decade later in three articles by Lindberg. The "Theory of pinhole images from Antiquity to the thirteenth century" (1968), reviewed the statements of Pseudo-Aristotle, Alkindi, Pseudo-Euclid, Roger Bacon, Witelo and Peckham. Lindberg’s "Theory of pinhole images in the fourteenth century" focussed on Henry of Langenstein and Blasius of Parma. His "Reconsideration of Roger Bacon’s theory of pinhole images" (1970), turned to Bacon’s discussion in his On burning mirrors. A significant dissertation by Straker (1971), explored the function of camera obscuras in Kepler’s optical experiments. Wheelock (1973, published 1977), in his dissertation reconsidered debates concerning Vermeer’s use of a camera obscura, using experiments with an original seventeenth century instrument as the basis for his claims. This was important because hardly anyone writing about the instrument has actually experienced its effects. Wheelock (1977), focussed on "Constantijn Huygens and early attitudes towards the camera obscura". Marek (1971), examined the importance of Kepler’s example in subsequent experiments by Young and Fresnel. A book by Hammond (1981), provided the best general survey of the topic thus far. An unpublished Bibliography of the camera obscura by Fyffe (now London, Science Museum, 1986), was the most comprehensive list to date and gave some indication of the immense literature yet to be examined. Not mentioned by anyone so far was a fascinating demonstration of the dimension of distance (demonstratio dimensionis distantia) in the Textbook (Lehrbuch) by Kepler’s teacher Maestlin (Wolfenbüttel, HAB 48.Noviss.8o, pp. 480-481).

1. Camera obscura Image of the world captured and evanescent

2. Laterna magica Projected phantasy as a real experience

3. Show boxes Trick with magnifying glass and superperspective

4. Photographic camera Time and fixed image of reality

5. Kodak Photography for all everywhere

6. Lumière’s cinématographe Images of the world that move

7. Sunsequent boxes First stage of audiovisual period.

Fig. 22. Seven stages in the development of optical recording devices according to Ganz (1994).

    Ganz (1994), in the World in a Box, claimed that the camera obscura was linked with perspective and that both arose from a new commitment to recording reality. Tracing the whole history of the problem from the camera obscura to the latest developments in audiovision, he suggested that there were seven stages to be identified (fig. 22).

    With respect to historical dates Ganz relied mainly on Hammond (1981) and other standard sources. However, he was aware of little known publications with respect to the laterna magica (37), and as a member of the oldest photographic firm in Zurich had access to a whole range of all but forgotten instruments connected with the early history of moving pictures, all with exotic names, notably: megaletoscopio (71), phenakistiscope (122, 130), praxinoscope (123, 132), mutoscope (124, 134), Wundertrommel (130), Choreutoskop (130), Daumenkino Kinora (132), and Pinacoscop (135). The final section of his book touched on more recent inventions including infra-red photography (1934), Tri-Unials in England, slide projectors, Polyvision with 56 projectors used at the Lausanne world fair (1964), Imax, Omnimax, LCD projectors and virtual reality.

    At least two other instruments were intimately connected in principle to the camera obscura. One was the observation well which has been studied by Sayili (1953). A second was the polar sighting tube discussed by Eisler (19**). Closely related were a series of other instruments: the camera lucida, camera, magic lantern, perspective box and show boxes (q.v.).

Camera Lucida

    The camera lucida is generally attributed to be an invention of Wollaston (1805). It appears to have developed out of the Claude glass, named after Claude Lorraine. Buesch, in his Encylopaedia of the historical, philosophical and mathematical sciences (1775), and again in his Attempt at a mathemetics for the use and pleasure of bourgeois life (1802), discussed a camera clara. In the generation following Wollaston’s paper there were studies by Ronalds (1828), and Chevalier (1833). A book by Hammond and Austin (1987), provides the only serious history of this instrument. It mentions links with other drawing devices such as the camera obscura, the camera; other instruments such as microscopes and telescopes and includes a detailed bibliography.

Camera

    No attempt will be made to review here the enormous literature on photography, almost all of which is in some sense relevant to perspective. By way of introduction the reader is referred to Eder’s classic History of photography (1905, English 1945); Gernsheim and Gernsheim’s (1955), biography of Daguerre, with its history of the diorama and the daguerrotype and Scharf’s (1968), Art and photography. The same Waterhouse who wrote on the history of the camera obscura also produced (1902), "Notes on early tele-dioptric lens-systems and the genesis of telephotography". An important article by Varnedoe (1980), argued against the conventional wisdom that "the fugitive, contingent and fragmentary qualities of impressionist painting were learned from photography".

    In terms of technical principles, A.T. (1862), used perspective in an important article on "Topo-photography or the applications of photography to the making of topographical plans" as did Laussedat in his fundamental studies (1864,1890,1899,1903), themes pursued in the classic work by the Canadian, Deville (1895, 1899), and in a standard text by Deneux (1932), with a bibliography of the principal works on perspective in relation to photography (i.e. métrophotographie, photographie aérienne and sténopé). Streintz (1892) explored the problem of depth perspective and R.B. (1916), the problem of aerial perspective in photography. The same R.B. (1916, 1918), investigated problems of perspectival distortion in photography. F. (1940), considered the question of perspectival distortions produced by tilted cameras and unusual viewpoints. Grabner (1935), claimed that there was no such thing as false perspective in photography. Traenkle (1942), examined the perspectival requirements of devices used to correct distortions. Meinke (1942), in an article on "Secrets of perspective" offered suggestions how to avoid unwanted distortions. Basic in this context was a dissertation by Weibrecht (19**), On the possibility of perspectival requirements in devices that correct distortions, with an important bibliography (149-155). Burkhardt (1958), provided a formula for correcting distorted images. Bartoli (1975), examined the reliability and limits of images in architectural photographs. An anonymous comment (1980), pursued the question of photographic distortion.

    Schiffner (1911), discussed geometrical aspects of photographic perspective. Ponzo (1911), of illusion fame, published an instrument for the plastic vision of photographs. The role of lenses in photographic perspective was examined by Seemann (1912), Beckers (1917), and Klinger (1942). Hansen (1924), and Warstat (1924), discussed the relation of lense size and image frame to perspective. Defossez (1930), discussed differences between photographs and regular objects in terms of perspectival effects. An article by Smith and Gruber (1958), compared apparent depth in photographs viewed from two distances. Smith (1958), explored perception of depth in photographs. A series of articles by Keeling (1973-1975), remains the best technical discussion of perspectival effects in photography.

    In terms of aesthetics, Fechner (1912), explored the significance of perspectival effects in photographs. Schürer (1927), examined photographs of Paris and Prague in order to raise questions of linear and rhythmic perspective. Ziegler (1929), considered perspective and proper viewing of photographs. Sonrel (1937), used photography to demonstrate aspects of Renaissance architectural space in Venice. Reisner (1941), considered photographic space and perspective.

Fig. 23. Dick Termes, patent for a dodecahedral camera with twelve co-ordinated images.

    Philosophical questions on the meaning of photography were raised by Barthes (1961), with no discussion of, but with implications for, perspective. W. Kemp has been one of the only scholars to explore practical and philosophical consequences of the interplay of perspective and photography in his Photo Essays (1978) and The beholder’s share (1983). His three volume anthology of writings on the Theory of photography (1980-1983) provided much valuable material.

Cinema

    Again, no attempt will be made to review here the enormous literature on cinema. Fundamental in this context was Liesegang’s, Dates and sources for the history of projection and cinematography (1926). Basic also was Quigley’s (1969), history. A survey of large screen formats was made by Wysotsky (1971), in Wide screen cinema and stereophonic sound (cf. panoramas and virtual reality, total environments).

    With respect to new optical effects, mention should be made of Casey’s Chemical Man (1962) produced for Abbott Laboratories for exhibition in the Chicago Museum of Industry at the 1964-1965 New York World’s Fair. The film was projected in a circular room with the audience sitting around the circumference of the theatre. At the same world’s fair, KLM sponsored To the Moon and Beyond (1964, later retitled Cosmos), which explored scale in outer and inner space using a spherical screen. Fantastic Voyage (1966) played with concepts of scale by recording the voyage of scientists who entered the human bloodstream in order to repair a heart problem. Projection on a 360 degree circular screen was again demonstrated at the Montreal World’s Fair (1967). At the Japan Expo (1970), the Fuji Pavilion sponsored Tiger Child by Multiscreen (now IMAX) Corporation. These principles were further developed in their Voyage to the Outer Planets (1973) produced for OmniMax theatres.

    George Lucas, through his company Industrial Light and Magic, has been a pioneer in using computers to produce new spatial effects. In Star Wars II (1977), models and computers were first used to create full scale landscapes. The related series from the initial Star Trek, The Motion Picture (1979) to Generations (1994), have pursued this use of models to create a sense of reality, with varying degrees of success. The concept of the holodeck is a particularly felicitous example.

    In The Draughtsman’s contract (1983), Peter Greenaway explored the use of perspectival windows in an historical film. In the Abyss (1989), computers using Alias software were used to create the remarkable transparent form that emerged from the water and acquired the face of a person watching it. In Darkman (1991), computer graphics were used to reconstruct a three dimensional image of a face. In Terminator II (1991), the same basic software was used to create the mechanical terminator which recomposed itself into the shape of a policeman even after being melted down. These ideas were taken further in Memoirs of an invisible man (1992). The thrust of these efforts was to create fictive images that are indistinguishable from the real. In Jurassic Park (1993), for instance, Steven Williams produced computer generated dinosaurs that were as lifelike as physical models which had been carefully filmed. True Lies (1994) took this trend one step further again by inserting into a live action film whole episodes which were computer generated, such as the one involving Arnold Schwarzenegger flying a Harrier jet. The following year two films, Born to be Wild (1995) and Congo (1995), both introduced computer generated gorillas into a seemingly realistic setting.

    The problem of juxtaposition of different scales of reality has been familiar to literary circles since the time of Rabelais' Gargantua and Pantagruel and universally in the English speaking world through Gulliver's Travels by Swift when the protagonist visits Lilliput. More recently this principle of changing scale while retaining other aspects of reality has become a new domain of computer manipulation. For instance, in the Indian in the Cupboard (1995), a toy Indian magically becomes a live Indian only a few inches tall who can be picked up by the young lad who is the protagonist of the film.

    These new technical advances introduce possibilities which are as problematic as they intriguing. One can, for example, replace real with fictive images, which raises questions about whether what we see corresponds to what is actually happened. This theme, implicitly touched upon in Quiz Show (1994), was confronted in In the Line of Fire (1993), where a fictive personage was inserted into actual footage from Bill Clinton's presidential campaign and replaced the original protagonist. Forrest Gump (1994), took this theme further. Here a fictional character played by Tom Hanks was inserted post facto into historical footage such that he appeared to have dealt with presidents of the United States and other important individuals. To an informed viewer today, this has a largely humourous effect. But how would someone a century from now, who did not know all the historical details, and was shown such a sequence out of context, be able to know that this was merely entertaining fiction rather than a true documentary?

    Not surprisingly, the new technologies have introduced a new theme that questions the veracity of images. In Rising Sun (1993), a video, which ought, theoretically to have provided conclusive evidence of what happened on the scene, is revealed, after very careful analysis to have been manipulated. In Judge Dredd (1995), a photo which the protagonist had grown up believing that it represented his family is revealed to be in fact a clever composite of various photographs and therefore not at all what it seemed to be. Similarly, in the same film, a video, which seems to prove conclusively that the protagonist was responsible in the cold blooded murder of a couple, is revelaed to have been the product of brilliant editing using a look-alike.

    Some themes began as analogue problems and are now finding digital parallels. Magnification effects with photographic images, for instance, were the subject of a famous scene in Antonioni's Blowup (1966) and again in Blade Runner (1982). A digital equivalent was shown in Species (1995). Closely related to this are scenes of magnification effects with satellite images in films such as Street Fighter (1995). Here a satellite image of Asia focusses in on Burma and eventually to a building in the ruins of the ancient city of Pagan. Similar scenes occur in Congo (1995). In Under Siege II: Dark Territory (1995), a view of the earth from space focusses on a beach, and finally concentrates on the anatomical features of a person lying on that beach.

    In some cases there has been a fascination with special effects almost as an end in itself. The Star Wars (1977) serties with their extra-ordinary range of realistic, imaginary creatures were a prelude to this approach. F/X - Murder by Illusion (1985) and its sequel F/X2 -the Deadly Art of Illusion (1991) were two excellent examples of this fascination with conscious manipulation of illusory space. The Mask (1994) took this fascination into the playful realm. Lord of Illusions (1995) showed that this theme could equally be adapted to the realm of horror.

    Pixar produced one of the first computer generated three-dimensional forests in the Adventures of André and Wally B (198*) and produced the first fully computerized animations in a series of award winning short films including Luxo Jr (1986); Red’s Dream (1987); Tin Toy (1988) and Knickknack (1989).

    Walt Disney, had traditionally relied on hand drawn animations and emphasized character in individual figures rather than spatial sets. Their Mathematical Applications Group Incorporated (MAGI)-Synthavision and three other special effects groups explored the potentials of computer graphics in Tron (1982). With respect to more traditional animated stories,these techniques were incorporated in The great mouse detective (1986), which involved an impressive sequence within the clockworks of Big Ben. In the Voyage down under (1989), computer graphics were used to create dramatic perspectival views of canyon walls in Australia. In Beauty and the Beast (1990), computer effects were evident throughout the film but most apparent in the ballroom scene which was achieved using a combination of Alias and Renderman software. Aladdin (1993) and the Lion King (1994) considerably expanded the repertoire of computer generated scenes and landscapes. Toy Story (1995), a first example of the combined efforts of Pixar and Disney, moved digital animation to a new plane of realism.

    Lawnmower Man (1992) used computer graphics to produce the first cinematic record of a journey into virtual reality (see below p.), a theme taken up anew in Lawnmower Man II (1995). In Disclosure (1994), this theme of virtual reality was taken up in the form of the so-called corridor, in fact based partly on the interior of Saint Peter's Basilica. More recently, Johnny Mnemonic (1995) and Virtuosity (1995) and Hackers (1995), have offered more elaborate versions of such virtual reality walk-throuhgs and fly-throughs.

A database of films is now available on the Internet (http://www.msstate.edu/M/title-substring).

Dourgnon (1946) made a study of lighting using different perspectives.

Magic lantern

    Another of the instruments closely related to the