Undergraduate

On this page, you will find resources related to the study of perspective at the undergraduate level.

We are developing a comprehensive series of courses on technical perspective for undergraduates, but these may take some time to put together. Until we have those courses available in full, here we show an outline of two undergraduate courses on ‘The History of Perspective’; namely: ‘Perspective from Antiquity to the 19th Century’ and ‘Perspective in the Twentieth Century’.

Both of these courses were presented at the University of Toronto by Professor Kim Veltman in the early 1990s, and they are based on second or third-year degree course(s) in the History of Science. Enjoy!

Undergraduate Perspective Course: Perspective from Antiquity to the 19th Century

Perspective has been described (Edgerton 1975) as the most important discovery of the West. In the fifteenth and sixteenth centuries it involved many of the key individuals in Renaissance art and architecture, notably Brunelleschi, Alberti, and Piero della Francesca. The projection methods of perspective were linked with astronomy (astrolabes and sundials), cartography, stonecutting, and surveying. Leonardo da Vinci linked perspective with physics and made it one of the cornerstones in his new approach to science through his pyramidal law, a principle that also inspired the first universal analogue reckoning instruments: the sector and proportional compass.

Since the seventeenth century, the development of perspective has entailed some of the leading mathematicians: Desargues, Pascal, Euler, Monge, Poncelet. In its metaphorical sense, perspective has been explored by philosophers such as Leibniz and Nietzsche; played a fundamental role in the work of Schutz, one of the founding fathers of modern sociology, and has affected profoundly most disciplines, including anthropology, ethnography, psychology and theology.

This course sets out to reconsider the history of perspective. It examines optical adjustments methods among the Egyptians and the Greeks; debates concerning ancient perspective, mediaeval contributions and focusses on the period 1300-1600. Developments in Italy, Burgundy, Germany and France are explored.

A survey is made of major themes: instruments, shadow projection, regular and semi-regular solids, intarsia, interiors, quadratura, trompe l’oeil, anamorphosis, stage scenery, columns, ideal architecture, ruins and gardens. Links with mathematical themes such as planisphere projection, conic sections, sundials, and stonecutting are addressed. Developments from the seventeenth to the nineteenth century are considered. The significance of perspective is assessed in terms of science, art, the environment and the imagination, in order to draw attention to a paradox: How was it that a method of representation that imposed scientific rules became a new key to artistic freedom and creativity?

Basic readings will include:

[1] Sir Ernst Gombrich, Art and Illusion, Princeton: Princeton University Press, 1960.

[2] John White, The Birth and Rebirth of Pictorial Space, London: Faber, 1967

[3] Lewis B. Andrews, A Space of Time: Continuous Narrative and Linear Perspective in Quattrocento Tuscan Art, PhD, Columbia University, 1988.

[4] Martin Kemp, The Science of Art. Optical Themes in Western Art from Brunelleschi to Seurat, New Haven: Yale University Press, 1990 and 1992.

[5] Kim H. Veltman, Sources of Perspective (Encyclopaedia of Perspective: 1). 

PERSPECTIVE FROM ANTIQUITY TO THE NINETEENTH CENTURY

LECTURES

Lecture 1. Optical Adjustments in Antiquity

Lecture 2. Basic Shapes in the Late Middle Ages

Lecture 3. Surveying, Instruments and Geometry

Lecture 4. Proportional Compass

Lecture 5. Transformational Geometry and Science

Lecture 6. Towns, Topography and Geography

Lecture 7. Narrative (Italy)

Lecture 8. Roomscapes and Landscapes (Netherlands)

Lecture 9. Sacred and Secular Spaces (Germany)

Lecture 10. Geometry and Architecture (France)

Lecture 11. Shadow Projection 

Lecture 12. Regular Solids

Lecture 13. Semi-Regular Solids

Lecture 14. Intarsia

Lecture 15. Interiors

Lecture 16. Quadratura

Lecture 17. Anamorphosis

Lecture 18. Stage Scenery

Lecture 19. Columns

Lecture 20. Roman Ruins

Lecture 21. Ruins and Capriccios

Lecture 22. Ideal and Real Buildings

Lecture 23. Fountains, Gardens, and Landscapes

Lecture 24. Stonecutting and Descriptive Geometry

Lecture 25. Architecture and Urbanism

Lecture 26. Optics and Psychology (1850-1900)

READINGS

Lecture 1: Optical Adjustments in Antiquity

Heinrich Sch„fer, Principles of Egyptian Art, ed. E. Brunner-Traut, Oxford: Clarendon Press, 1974, pp. 159-198.

A. M. G. Little, Roman Perspective Painting and the Ancient Stage, New York: Moretus Press, 1971.

Lecture 2. Basic Shapes in the late Middle Ages

John North, “The Astrolabe”, Scientific American, New York, Vol. 230., Nr.1, January 1974, pp.96-101.

Miriam Schild Bunim, Space in Medieval Painting and the Forerunners of Perspective, New York: AMS Press Inc. (1940), 1970, pp. 175-192.

John White, The Birth and Rebirth of Pictorial Space, London: Faber, 1967, pp. 135-198.

Lecture 3. Surveying, Instruments and Geometry.

B.A. R. Carter, “Perspective”, Oxford Companion to Art, ed. Harold Osborne, Oxford: Clarendon Press, 1970, pp. 840-861.

Kim. H. Veltman, Military Surveying and Topography: the Practical Dimension of Renaissance Linear perspective, Lisbon: Junta de Investigacoes Cientificas do Ultramar, 1979, pp. 338-368.

Lecture 4. Proportional Compass

Galileo Galilei, Operations of the Geometric and Military Compass, trans. Stillman Drake, Washington:Smithsonian Institution, 1978.

Lecture 5. Transformational Geometry and Science

J. McCabe, Leonardo da Vinci’s De Ludo Geometrico, PhD University of California at Los Angeles, 1972.

Lecture 6. Towns, Topography and Geography

Lewis B. Andrews, A Space of Time: Continuous Narrative and Linear Perspective in Quattrocento Tuscan Art, PhD, Columbia University, 1988.

Marilyn Aronberg Lavin, The Place of Narrative: Mural Decoration in Italian Churches, 431-1600, Chicago: University of Chicago Press, 1990.

Lecture 7. Narrative (Italy)

Erwin Panofsky, La perspective comme forme symbolique, Paris: Les ditions de Minuit, 1975, 99. 37-93.

Leon Battista Alberti, On Painting, ed. John Spencer, New Haven: Yale University Press, 1056, pp. 43-49, 68-73.

Lecture 8. Roomscapes and Landscapes (Burgundy and the Netherlands)

James Mitchell Collier, Linear perspective in Flemish Painting and the Art of Petrus Christus and Dirk Bouts, PhD Dissertation, University of Michigan, 1975, pp.105-184.

Lecture 9. Sacred and Secular Spaces (Germany)

J. G. Links, Townscape Painting and Drawing, New York: Harper And Row, 1972.

Lecture 10. Geometry and Architecture (France)

Liliane Brion-Guerry, Jean P‚lerin, Viator. Sa place dans l’histoire de la perspective, Paris: Soci‚t‚ d’Edition les Belles Lettres, 1962, pp. 116-150.

William M. Ivins, On the Rationalization of Sight, New York: Da Capo Press, 1973. 

Lecture 11. Shadow Projection

Thomas Da Costa Kauffman

Lecture 12. Regular Solids

H.M. Cundy, and A. P. Rollett, Mathematical Models, Oxford: Clarendon Press, 1951.

Lecture 13. Semi-Regular Solids

Kim H. Veltman, A Brief History of the Not so Regular Solids, New York: Timken, 1991.

Lecture 14. Intarsia

Andr‚  Chastel, “Cit‚s id‚ales”, L’Oeil, Paris, n. 36, 1957, pp. 32-39.

Cecil H. Clough,”Federigo da Montefeltro’s Private Study”, Apollo, London, vol. 81, October 1967, pp. 278-287.

Lecture 15. Interiors

L. Sandstr”m, Levels of Unreality, Uppsala: Almqvist and Wiksell, 1963, (Figura. Uppsala Studies in the History of Art, New Series, 4).

Lecture 16. Quadratura

Ingrid Sj”str”m, Quadratura. Studies in Italian Ceiling Painting, Stockholm: Almqvist and Wiksell, 1978, pp. 11-48. (Acta universitatis Stockholmiensis).

Lecture 17. Anamorphosis

Jurgis Baltrusaitis, , Anamorphoses, Paris: O. Perrin, 1969.

Lecture 18. Stage Scenery

G. Kernodle, Perspective and the Renaissance Stage, PhD, Yale University, 1937.

Eckert, W., The Renaissance Stage in Italy: A Study of the Evolution of the Perspective Scene, PhD, State University of Iowa, 1961.

Lecture 19.Columns

John Onians.

Lecture 20. Ruins

TBD

Lecture 21. Ruins and Capriccios

TBD

Lecture 22. Ideal and Real Buildings

TBD

Lecture 23. Fountains, Gardens, and Landscapes

F. Hamilton Hazlehurst, Gardens of Illusion, The Genius of Andr‚ Le Nostre, Nashville: Vanderbilt University Press, 1980.

Lecture 24. Stonecutting and Descriptive Geometry

TBD

Lecture 25. Architecture and Urbanism

Marianne Marcussen, “L’‚volution de la perspective lin‚aire au XIXe siŠcle en France”, Hafnia. Copenhagen Papers in the History of Art, Copenhagen, No. 7, 1980, pp.51-73.

Lecture 26. Optics and Psychology (Nineteenth Century)

Hermann von Helmholtz, Treatise on Physiological Optics, trans. James P. C. Southall, New York: Dover, 1962, vol. 3. pp. 179-185.

Maurice Pirenne, Optics, Painting and Photography, Cambridge: Cambridge University Press, 1970, pp. 145-150.

Undergraduate Perspective Course: Perspective in the Twentieth Century

Perspective in the twentieth century has evoked fundamentally different interpretations. On the one hand, developments in abstract art led scholars such as Novotny (1939) to claim that perspective died with Cezanne. On the other hand, more books have been published on perspective in this century than in any previous century. In art, perspective has remained important for surrealists, super-realists and hyper-realists. In architecture and technical drawing, perspective has become increasingly important.

The rise of computers has greatly enhanced this interest in systematic treatment of space and has led to the four C’s: computer aided design (CAD); computer aided engineering (CAE); computer aided manufacture (CAM) and computer integrated manufacture (CIM). This course explores these developments, and raises questions about their consequences.

It begins with changes in classification, examples in art, particularly spherical and alternative methods. This leads to the importance of illusions, the blind, spatial development and parallel perspective in connection with psychology. The impact of architecture and technical drawing is examined. Particular attention is given to the significance of new technologies: photography, cinema, video, computer graphics, robotics, fractals, holography, stereoscopy, space masks and virtual reality.

No technical knowledge is assumed. The concern is philosophical: what are the consequences of these new methods of spatial representation for our approaches to the world, for concepts of knowledge, for the problem of knowing ourselves?

Basic readings will include:

[1] Maurice Pirenne, Optics, Painting and Photography, Cambridge: Cambridge University Press, 1970.

[2] Lenny Lipton, Foundations of the Stereoscopic Cinema. A study in Depth, New York: Van Nostrand Reinhold Company, 1982.

[3] Nadia Magnenat Thalmann, Daniel Thalmann, Image Synthesis. Theory and Practice, Tokyo: Springer Verlag, 1987.

[4] Richard Mark Friedhoff, Mark Benzon, The Second Computer Revolution. Vizualization, New York: Harry Abrams, 1989.

PERSPECTIVE IN THE TWENTIETH CENTURY

LECTURES

Lecture 1. Classification

Lecture 2. Art

Lecture 3. Spherical Methods

Lecture 4. Alternative Methods

Lecture 5. Illusions*

Lecture 6. Blind*

Lecture 7. Development*

Lecture 8. Architecture

Lecture 9. Technical Drawing

Lecture 10. Parallel Perspective and Psychology*

Lecture 11. Photography

Lecture 12. Aerial Photography

Lecture 13. Cinema

Lecture 14. Video

Lecture 15. Computer Graphics 1960-1979

Lecture 16. Computer Graphics 1980-1989

Lecture 17. Computer Graphics 1990-

Lecture 18. Robotics

Lecture 19. Coordinate Conversion

Lecture 20. Transformation

Lecture 21. Fractals

Lecture 22. Holography

Lecture 23. Stereography

Lecture 24. Space Masks

Lecture 25. Virtual Reality

Lecture 26. Time.

READINGS

Lecture 1. Classification

Kim H. Veltman, “Classification” in Ibid., The Sources of Perspective, New York: Caratzas, 1991. pp. 112-139.

Lecture 2. Art

H. H. Arnason, A History of Modern Art, London: Thames and Hudson, 1969.

Lecture 3. Spherical Methods

Andr‚ Barre et Albert Flocon, La perspective curviligne. De l’espace visuel … l’image construite, Paris: Flammarion, 1968. Cf. English Translation: Curvilinear Perspective, trans. Robert Hansen, Berkeley: University of California Press, 1988.

Lecture 4. Alternative Methods

Robert Hansen, “Hyperbolic Perspective”,

Lecture 5. Illusions*

M. Luckiesh, Visual Illusions, New York: D. Van Nostrand, 1922; New York: Dover, 1965; J.O. Robinson, The Psychology of Visual Illusions, London: Hutchinson and Co., 1972. .

Lecture 6. Blind*

John M. Kennedy, Paul Gabias, Andrea Nicholls, “Tactile Pictures”: Touch Perception, ed. M. Heller and W. Schiff, Hillsdale: L. Erlbaum, 1991.

Lecture 7. Development*

Suzi Gablik, Progress in Art, London: Thames and Hudson, 1976; Sidney J. Blatt, Continuity and Development in Art. The Development of Modes of Representation, Hillsdale: Lawrence Erlbaum, 1984.

Lecture 8. Architecture

Lionel March, Philip Steadman, The Geometry of Environment, London: R.I. B.A., 1971.

Lecture 9. Technical Drawing

Peter Jeffrey Booker, A History of Engineering Drawing, London: Chatto and Windus, 1963.

Lecture 10. Parallel Perspective and Psychology*

Lecture 11. Photography

Keeling.

Lecture 12. Aerial Photography

TBD

Lecture 13. Cinema

TBD

Lecture 14. Video

TBD

Lecture 15. Computer Graphics 1960-1979

William M. Newman, Robert F. Sproull, Principles of Interactive Computer Graphics, Tokyo: McGraw Hill Kogakusha Ltd., 1973. 

Lecture 16. Computer Graphics 1980-1989

Nadia Magnenat Thalmann, Daniel Thalmann, Image Synthesis. Theory and Practice, Tokyo: Springer Verlag, 1987.

Richard Mark Friedhoff, Mark Benzon, The Second Computer Revolution. Vizualization, New York: Harry Abrams, 1989.

Lecture 17. Computer Graphics

TBD

Lecture 18. Robotics

TBD

Lecture 19. Coordinate Conversion

Tralaine Conversion

Lecture 20. Transformation

TBD

Lecture 21. Fractals

Benoit Mandelbrot, The Fractal Geometry of Nature, New York: W. H. Freeman and Co.

Lecture 22. Holography

Yu. N. Denisyuk, Fundamentals of Holography, Moscow: MIR Publishers, 1984.

Lecture 23. Stereography

Lenny Lipton, Foundations of the Stereoscopic Cinema. A study in Depth, New York: Van Nostrand Reinhold Company, 1982.

Lecture 24. Space Masks

TBD

Lecture 25. Virtual Reality

TBD

Lecture 26. Time.

TBD