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		CS 99D - Perspective lecture #3, January 18, 2001

				  Marc Levoy
			      Stanford University
				   (c) 2001

		      (with corrections, March 14, 2003)

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	*** History of theories of the geometric aspects of vision ***

(from Lindberg)

Greek theories of light and vision:

460 BC	Democritus
-270 BC	Epicurus
55BC	Lucretius
	Atomists
		o "eidola" - images that stream off object into eye
		o "simulacra" - *material* films, like an animal shedding skins
		o these films are composed of particles (hence atomist)
		o these films shrink as they approach the eye
		o don't address how the eye works

		o difficulty of interpreting meaning of the ancients' writings

-347 BC	Plato
	Extromissionist
		o "visual fire" emanates from the eye and mixes with daylight
		to form a transparent, homogeneous, senory body that extends
		from the eye to the object

			"And the eye obviously has fire within, for when one is
			struck [this fire] flashes out." - Theophrastus, p. 4

		o Greek statues had jewels for eyes
			-> empty eye socket, Gardner, p. 143

384-22B	Aristotle
	Intromissionist
		o the "transparent" medium takes on the color of distant
		objects, as a state, then transmits this through the eye to a
		sensory body inside, as if by touch

129-99	Galen
	Described physiology (wrong)
		o first detailed description of anatomy of eye
		o optic nerve is a hollow tube
		o "optical pneuma" travels through it and out into the air
		o the air becomes percipient just as if it had nerves in it
		o Galen's anatomic errors caused misdiagnosis of apendicitus

-866	al-Kindi's De aspectibus
	Defended extromission
		o transmitted Greek learning to Islam
		o eyes see only what they aim at, so they must send out rays
		o without visual rays, animals could not see at night

-1039	Alhazen's De aspectibus
	Defended intromission
		o Visual rays cannot be corporal or they would interfere with
		one another when they cross in space.
		o If incorporeal, they cannot interact with the object or the
		eye, hence they cannot explain vision.
		o If the air and the eye are transparent, light from objects
		would reach and enter the eye, therefore, visual rays are
		unnecessary to explain vision.
		o If visual rays cannot explain vision, and if they are
		unnecessary to explain vision, then there is no reason to
		suppose they exist.
		o a forerunner of the scientific method!

			"...that which issues from the eye is not sensible but
			conjectural, and nothing ought to be believed except
			for a [sufficient] reason." - Alhazen, p. 65

	Perspectivist ("punctiform") analysis:

		o Each point on the object emits light independently and in all
		directions.  "Simulacra" are not coherent images of the object.
		o re-enabled use of Euclid's geometric theorems of perspective

	First theory of operation of the eye:

		o this light reaches the eye at many points
		o the eye is sensitive across at all these points

		Q. If each point on the eye receives light from many points
		on the object, how are these many inputs distinguished?

		A. Only axial rays are strong enough to be sensed.  Since the
		eye is spherical, this permits a sphere of incoming rays to be
		sensed without confusion.

		o the incoming rays proceed unrefracted through the cornea
		o are refracted on the far side of the lens ("glacial humor")
		o travel parallel through the ocular medium ("vitreous humor")
		o no theory on how this image travels the curved optic nerve

			-> Lindberg, p. 82
			-> Compare to Gray's anatomy, p. 826

	Flaws in this theory:

		o no understanding of image formation
		o rejected possibility that rays crossed to form inverted image

1452-19	Leonardo
	Rejected Alhazen
		o a needle placed in front of the eye does not block vision
		o thus, Alhazen must be wrong, but he proposed no solution
		o proposed many schemes that avoid an inverted image

			-> Lindberg, p. 167

1543	Andreas Vesalius's De humani corporis fabrica
	Redescribed physiology (better)
		o one of the most famous books in 1500's
		o father of scientific illustration
		o corrected Galen's anatomy
		o solid optic nerve
		o suggested retina as "seat of vision"
		o lens still in the wrong place

			-> Lindberg, p. 174

1571-30	Johannes Kepler
	Court mathematician (Prague), astronomer, father of geometric optics
		o Copernicus's heliocentrism -> Tycho Brahe's observations ->
		  Kepler's ellipses -> Newton's gravity
		o Galileo improved telescope, but did not analyze its optics
		  (The Heavenly Messanger, 1610)

	Theory of camera obscura:
		o known to Aristotle, preserved by Arab scholars (Hecht, p.198)
		o refused to accept that paraxial rays had no effect on image
		o camera obscura experiments showed blurring effect of aperture

			-> Lindberg, p. 179

			==> Show camera obscura with varying size apertures

	Theory of image formation:
		o Al Vitellionem paralipomena ("Additions to Witelo") (1604)

		o no formula for refraction, so couldn't reason from geometry
		o a spherical burning glass produces an aberrant image

			-> Lindberg, p. 197

			==> Show image of ceiling lights through burning glass

		o introducing two pinholes allows tracing of individual rays
		o a finite aperture (pupil!) produces a well focused image

			==> place two offset apertures above lens, won't make
			    a ray unless in a dark chamber, so just explain it

			==> Draw ray diagram showing a lens, object, and image

	Theory of retinal image:
		o this produces an inverted image on the retina
		o scrapes off back of an eye and sees this image
		  (done by Christopher Scheiner 5 years earlier, Hecht, p. 177)

			-> Lindberg, p. 201 (Descartes's drawing)

		o Kepler says nothing about how it is uprighted
		o Left this for future perceptual psychologists,
		  a heroic step!

	Principles of geometric optics:
		o Dioptrics (~1610)
		o analyzed lenses, spectacles, inverting and upright telescopes
		o still no formula for refraction, so used approximate index

1621	Snell
		o ratio of sins of angles of incidence and refraction constant

			-> David Park, p. 171

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		       *** Perspective drawing aids ***

Perspective drawing aids:

1525	Durer's compendium of devices

		o not only a famous artist... (optional)
		-> St. Jerome in His Study, Kemp, p. 60
		o ...but also an original mathematician
		-> Method for constructing conic sections, Kemp, p. 56

		o visited Italy to learn perspective
			When he first saw it, trained as he was in the Northern
			European style, it must have seemed "a form of magic, a
			kind of visual alchemy which transformed the base
			materials of art into visionary experience."
				-Kemp, p. 53

		o introduced it to Northern Europe
		o Nuremberg was famous for metalwork and instruments
		o perspective caught on as a way to depict these instruments
		-> Illustration from Tycho Brahe (1573), in Robbins, p. 81

	-> Cole, p. 26-27 (or Kemp, p. 171-2)

		o artist's glass (already done)
		o draftsman's net (grid) -
		  allows drawing on paper instead of glass
		o Jacob de Keyser's gun-style eyepiece -
		  allows viewpoint to be far from glass
		o Durer's ruling pen -
		  combines advantages of two previous devices

Fully mechanical devices: ("perspectographs")

1610	Cignoli's perspective machine
	o draftsman's hand movements mechanically linked to a boresight
	-> Kemp, p. 179

1631	Scheiner's pantograph
	o same, but can also enlarge or reduce
	-> Kemp, p. 181

	o Although used for teaching, and popular as toys during the
	Enlightenment, there is little evidence that these devices were used by
	serious artists.  Cameras, however, were widely used.  -Kemp

Cameras (in the general sense, i.e. imaging devices):

medieval	camera obscura
1500s		introduction of a lens
1685		Zahn's portable Camera Obscura with built-in screen
			-> Kemp, p. 190

		o images light, shadow, and color, as well as geometry
		o very useful for learning to copy nature
		o used by Vermeer (1632-1675)
			-> Gregory's The Artful Eye, pl. 20,21
			-> isometric of his room, p. 363
		o and Canalleto (1697-1768)
			-> sketch of Campo di SS Giovanni e Paolo, Kemp, p. 197
			-> Basin of San Marco (1740), Gardner, p. 900

1806		Wollaston's Camera Lucida
			-> Kemp, p. 200
			o not half-silvered, so had to alternate
			  between real world and paper

			==> Demonstrate using half-silvered mirror

1811		Varley's Graphic Telescope
			-> Kemp, p. 202
			o real world superimposed on paper

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		   *** Perspective after the Renaissance ***

1500's
	o treatises on perspective become more mathematical
		-> Commandino (1558), Kemp, p. 86
	o mathematicians find new applications: (Kemp, p. 92)
		o fortifications - resisting artillery, lines of fire
		o ballistics
		o instrument design

	o Galileo's Starry Messenger (1610)
		o used perspective to deduce astronomical facts

		o copied telescope from Lippershey (Dutch), made better ones
		o some of his are on display in Museum of Science, Florence
		o imprisoned Dutch visitor (not Lippershey?) to avoid scooping
		o shown to nobility of Venice - spot ships from the campanile

		o observations of moon + angle of sun -> perspective ->
		  heights of mountains on the moon
			-> Kemp, p. 93, better is
			-> Harry Robins's The Scientific Image, p. 22
		o painted in watercolor by Galileo himself
		o dangerous image - refuted Ptolemy's crystalline spheres
		o one of the most important books of the 1600's

		o changing speed of motion of sunspots + perspective ->
		  proof they are on sun, not bodies between us and sun (1613)
		o another refutation of Ptolemy
			-> Kemp, p. 94-5
			-> Observed using the method shown in Robbins, p. 82

	o Mannerist:
		o art in crisis - how to surpass the Renaissance masters?
		o imitating the classicals, the "manner" of Michelangelo, etc.
		o bizzare experiments, distortions, caprices
		o in the North, the Reformation discouraged religious paintings

		o deliberately shocking architecture - like post-modernism
			-> Window of Palazzo Zuccari, Gombich SoA, p. 362
			-> Guilio Romano's Palazzo Del Te (1535),
			   Gardner, p. 769
		o distortions
			-> Parmigianino's madonna with the long neck (1540),
			   Gombrich SoA, p. 365 (Uffizi)
		o trompe l'oeil
			-> Mantegna's Salone Delle Prospettive (1518),
			   Cole, p. 30-31
		o anamorphics
			-> Holbein's The Ambassadors (1533),
			   Cole, p. 32-33

1600's
	o the academies of art

	o Baroque:
		o emotion reigns supreme
			-> Bernini's The Ecstasy of St. Teresa (1652),
			   Gombrich SoA, p. 439

		o composition, figures, and color overshadows perspective
			-> Ruben's sketch for Virgin and Child (1628),
			   Gombrich SoA, p. 399

		o trompe l'oeil that breaks out of the frame
			-> Gaulli's Worship of the Holy Name of Jesus (1683),
			   Gombrich SoA, p. 441

	o Rococco:
		o fantasy architecture
			-> Francois de Cuvillies's The Amalienburg (1739),
			   Gardner, p. 889

		o perspective used to create dramatic space
			-> Piranesi's Carceri (1750), Gardner, p. 908
			-> Fragonard's The Swing (1766), Gardner, p. 893
			o low viewpoint, upward view, deep perspective space

Perspective in architecture:
		o replacement for Constantine's basilica
		o Bramante's wedding cake (<1514), only piers were built
		o Michelangelo's colossal order (1547), visible from gardens
		o Michelangelo's dome (1561), copied in many capital bldgs
		o Della Porta's stretched dome (1590), for greater stability
			-> Hibbard's Michelangelo, p. 300
		o Moderno's extended nave and facade (1612)
			-> Gardner, p. 821
		o Bernini's piazza (1656), diverges to heighten look of facade
			-> Gardner, p. 822
		o Bernini's baldacchino (1633)
			-> Gardner, p. 823
		o Bernini's Cathedra Petri (Chair of St. Peter's) (1866)
			-> Gardner, p. 824
1700's
	o professors of perspective

	o Neoclassicism:
		o perspective used to create rational space
			-> David's Oath of the Horatii (1784), Gardner, p. 918
			o eye-level view, level view, calm rational space

	o Industrial revolution:
		o Newcomen - first steam engine (in England) (1712)
		o Boulton and Watt - mass production of steam engines (1779)
		o engineering drawings
			-> Malton's drawings of mechanical devices (1779),
			   Kemp, p. 156

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