Leonardo

Leonardo da Vinci's Struggles with Representations of RealityAuthor(s): Nicholas J. Wade, Hiroshi Ono, Linda LillakasSource: Leonardo, Vol. 34, No. 3 (2001), pp. 231-235Published by: The MIT PressStable URL: http://www.jstor.org/stable/1576941 .Accessed: 26/08/2011 04:13

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HISTORICAL PERSPECTIVE

Leonardo da Vinci's Struggles

with Representations of Reality

NicholasJ. Wade, Hiroshi Ono and Linda Lillakas

Virtual reality is concerned with creating an imi- tation of the visual world. The term is an oxymoron consid- ered to be a modern engineering enterprise, made possible by the power of computers. The issues at the center of virtual reality, however, are not new, as they address some ancient questions of visual perception. One of these is the contrast between binocular and monocular vision, which the great sci- entist/engineer/artist Leonardo da Vinci (1452-1519) struggled with in his numerous notebooks. His knowledge of ocular anatomy was wanting but his application of optics to the eye was ahead of his time [1]. Leonardo conducted ex- periments with a camera obscura and drew an analogy be- tween its operation and that of the eye [2]. Moreover, his ob- servational skills were without equal, and his creations of virtual reality on canvas were unsurpassed. Yet, he realized: "A Painting, though conducted with the greatest Art and fin- ished to the last Perfection, both with regard to its Contours, its Lights, its Shadows and its Colours, can never show a Relievo equal to that of Natural Objects, unless these be view'd at a Distance and with a single Eye" [3]. That is, the percep- tion of depth is incomplete in a painting, unlike that for a scene viewed with two eyes.

Leonardo struggled long and hard with the contrast be- tween monocular and binocular vision. He was able to utilize the concept of Alberti's window, which provided a monocular match between a picture and a view of a scene from a single point [4]. But what happens when two viewpoints are adopted? Leonardo examined this many times in the context of a small object lying in front of a background. He returned to the issue repeatedly, as indicated by the many diagrams he made of it. In each instance, vision with two eyes was optically and phenomenally different from that with one (Fig. 1):

Why objects perfectly drawn from nature do not seem to be in the same relief as the natural object. It is impossible for a painting, even though executed with the greatest perfection of outline, shadow, light, and color, to seem in the same relief as the natu- ral model, unless that natural model is looked at from a great distance with one eye. The proof is as follows: Let the eyes, A B, look at the object C, with the convergence of the central lines from the eyes, A C and B C, and those lines converge to the object at the point C, and along the other lines, on the

Nicholas J. Wade (researcher, artist, teacher), Department of Psychology, University of Dundee, Dundee DD1 4HN, Scotland, U.K. E-mail: <n.j.wade@dundee.ac.uk>.

Hiroshi Ono (researcher, teacher), Department 5, ATR Human Information Processing Laboratories, Kyoto, 619-0288,Japan.

Linda Lillakas (researcher), Centre for Vision Research, York University, Toronto, Ontario, M3J 1P3, Canada.

ABSTRACT

Virtual reality systems seek to simulate real scenes so that they will be seen as three-dimen- sional. The issues at the heart of virtual reality are old ones. Leonardo da Vinci struggled with the differences between the per- ception of a scene and a painting of it, which he reduced to the dif- f,ranrore h,'hA,, n hinnr,il:Ir nn,-

sides of the central line, the eyes m.oncur v.Wsion. UHeculd see the space G D behind the ob- monocular vision. He coul

ject; the eye A sees the whole produce on canvas what,

space F D, and the eye B sees the terminology of Ames, was whole space G E. Thus, the two equivalent configuration. T

eyes see the whole space F E be- provided 300 years after hind the object C. The object C remains transparent, according to scope. Modern approache the definition of transparency, by tual reality that can incorpi which nothing is hidden. This moving vewpoints would cannot happen to him who looks cinated Leonardo. with one eye at an object larger than his eye, as it could not hap- pen when the eye looks at objects smaller than the pupil. This is shown in the second diagram. Because of what has been said, we can conclude our investiga- tion, because the painted object covers all the space that is behind it, and it is in no way possible to see any part of the background behind it within the outlines of the object [5].

I 1 ilU

d not n the an 'his was

stereo- s to vir- orate have fas-

The example he used, of viewing a sphere with a diameter less than the distance separating the eyes, reflected one con- dition Euclid analyzed, but Leonardo added the characteris- tic of seeing the whole background [6].

Every time Leonardo returned to the struggle, he came to the same conclusion: that he could not depict correctly on canvas everything he saw with two eyes. He was unable, in the terminology of virtual reality, to simulate what he saw with two eyes. Alberti's procedures (for conveying visual angles to a picture plane) simulate the monocular visual world on a canvas, but not that of the binocular visual world. For ex-

Fig. 1. Leonardo da Vinci's diagrams of viewing a sphere with two eyes or one. The drawing on the left represents binocular observa- tion of a sphere, the diameter of which is smaller than the separa- tion between the eyes. The two drawings on the right, of two monocular views, are not so easy to interpret because Leonardo did not assign any letters to them, nor is the accompanying text as ex- plicit. It is likely that they represent two different stimulus condi- tions, with spheres smaller than the pupil (left monocular diagram) and larger than the eye (right monocular diagram). Leonardo's original sketches have been redrawn from McMahon [27].

LEONARDO, Vol. 34, No. 3, pp. 2231-235, 2001

_ _

? 2001 ISAST

r

m n a )a

b

r f

m Background y x V

Fig. 2. The two monocular conditions in Fig. 1 have been redrawn separately with the eyes of equal size, so that the conse- quences of viewing a sphere smaller and larger than the pupil can be appreciated more readily. If the background is accom- modated in the situation depicted on the left side, the whole background is visible, with the near stimulus appearing blurry. However, part of the background will not be visible in the situation depicted on the right side. The light emitted or reflected from the dark area on the background would not reach the eye, whereas some of the light from the gray areas would. Strictly speaking, the visibility of the background also depends on the distance of the small object from the eye. If the size of the ob- ject is one-half of the pupil opening, the object must be closer than one-half the dis- tance [28].

ample, Leonardo's drawings repro- duced in Fig. 1 represent both binocular

(left) and monocular (right) observa- tion of a small sphere [7]. Leonardo's accompanying text (quoted above) em- phasizes the differences between view- ing a scene and a painting of it in terms of perceived depth and the amount of the background that is visible.

Leonardo's drawings (Fig. 1) display a concern with monocular as well as bin- ocular viewing, but the monocular draw- ings are often omitted from reproduc- tions of his Treatise [8]. This could be because they appear so enigmatic; the representations of the eye in each of the two monocular drawings differ in size, which makes the monocular drawings difficult to interpret. The two monocu- lar views can be understood if it is appre- ciated that (a) they indicate two differ- ent stimulus conditions, and (b) Leonardo represented the eyes (the up- permost circles on the right side of Fig. 1) as different in size. The eye denoted by the upper circle on the left is viewing a small sphere that is placed at the inter- section of the converging lines; the eye

Fig. 3. Leonardo's binocular observation of a sphere, redrawn from Strong [29]. "If the two central lines concur in the object x the subordinate adherent lines s v and r y will see the object t occupy two places on the wall n m, i.e., in v and y. But if such central [lines] terminate in t, then the object x will be seen by the two exterior adherent lines, i.e., r x and s x, because the right eye sees with the right adherent line and the left eye sees with the left adherent line" [30].

represented by the smaller circle on the right is viewing a sphere much larger than the diameter of the pupil. These two monocular conditions have been re- drawn in Fig. 2, with the eyes repre- sented as the same size and the objects as larger and smaller than the pupil.

A drawing similar to the binocular part of Fig. 1 occurs again in Fig. 3 [9]. Leonardo's text again emphasizes the vis- ibility of the background, but it also comes very close to describing the dis- parities of direction attendant upon view- ing a near object. Drawings of retinal dis- parities did not appear in texts on optics until the seventeenth century [10].

Leonardo made another representa- tion of monocular and binocular projec- tions (see Fig. 4), which was reproduced in Richter [11]: A sphere with a diam- eter smaller than the interocular dis- tance will obscure a more distant one when viewed with one eye, but not when two are used:

Why a Painting Can Never Appear De- tached as Natural Objects Do. Painters often fall into despair of imitating na- ture when they see their pictures fail in that relief and vividness which objects have that are seen in a mirror; while they allege that they have colours which for brightness or depth far exceed the strength of light and shade in the reflec- tions in the mirror, thus displaying their own ignorance rather than the real cause, because they do not know it. It is impossible that painted objects should appear in such relief as to resemble those reflected in the mirror, although

Fig. 4. Leonardo's binocular (top) and mo- nocular (bottom) observation of two aligned spheres, redrawn from Richter [31]. A sphere with a diameter smaller than the interocular distance will obscure a more distant one when viewed with one eye.

both are seen on a flat surface, unless they are seen with only one eye; and the reason is that two eyes see one object behind another as a and b see m and n. m cannot occupy [the space of] n be- cause the base of the visual lines is so broad that the second body is seen be- yond the first. But if you will close one eye, as at s the body fwill conceal r, be- cause the line of sight proceeds from a single point and makes its base in the first body, whence the second, of the same size, can never be seen [12].

Essentially the same points were made in Leonardo's drawings shown in Fig. 5, and the reference was made to the inad- equacy of paintings in matching percep- tion with two eyes.

In the remaining three drawings re- produced here (Figs 6-8) Leonardo re- stricted himself to binocular observation of spheres. Figures 6 and 7 are from Richter and Fig. 8 is from Pedretti [13]. In Fig. 6 Leonardo was adopting a proce- dure described by Galen, namely placing a septum (made from four fingers ex- tended along the midline of the head) so that each eye could see beyond it [14]. The region occluded to both eyes is referred to in Fig. 7, and emphasis is again placed on the amount of the dis- tant background that is visible with both eyes. In Fig. 8, Leonardo returns to an aspect of Euclid's analysis in which more than a hemisphere of a small sphere is visible to both eyes; this in turn was re- lated to the apparent size of the sphere.

A similar concern with the interplay between art, optics and binocular vision was evident in the writing of Adelbert Ames II [15]. He was trained as a lawyer but practiced art with the intention of becoming a neo-Impressionist painter.

232 Wade et al., Leonardo da Vinci's Struggles

b a

la

b

d

f

mO 0 Qg h

Fig. 5. Leonardo's binocular (top) and mo- nocular (bottom) observations of a small sphere, redrawn from Richter. "Objects in relief, when seen from a short distance with one eye, look like a perfect picture. If you look with the eyes a, b at the spot c, this point c will appear to be at d, f, and if you look at it with one eye only, g, h will appear to be at m. A picture can never contain in it- self these two aspects" [32].

In the process he came to realize that a thorough understanding of visual optics was a necessary prerequisite, and he later studied physiological optics. Whereas Leonardo was concerned with optical projection, Ames made the equivalence between painting and per- ception in terms of images:

The fundamental idea . . . was that pic- torial art should be similar to our men- tal visual images, and since our mental visual images are probably similar to our retinal pictures, valuable sugges- tions could be obtained from a knowl- edge of the characteristics of our retinal picture. Our mental visual impression, however, is not derived from a single retinal picture but from two, as we nor- mally look with two eyes [16].

He then devised many demonstrations that were based, essentially, on Alberti's window. One of these is now called the Ames room; it consists of a trapezoidal room that is viewed with one eye through a small aperture, so that it is vir- tually rectangular. The room epitomizes the essence of virtual reality by render- ing as equivalent the projections to a single point of a systematically distorted space and a conventionally rectangular room: "Equivalent configurations are de- fined as that family of physical configura- tions for which impingement is invari- ant" [17]. It was a concept that Ames returned to and manipulated with skill: "The definition of equivalent configura- tions implies that identical 'incoming messages' can come from different ex-

m n

Fig. 6. Leonardo's binocular observation of a small sphere, redrawn from Richter [33]. "If you place an opaque object in front of your eye at a distance of four fingers' breadth, if it is smaller than the space be- tween the two eyes it will not interfere with your seeing anything that may be beyond it. No object situated beyond another object seen by the eye can be concealed by this [nearer] object if it is smaller than the space from eye to eye" [34].

ternal physical arrangements. In the ab- sence of other information, . . . equiva- lent configurations will be perceived as identical, no matter how different they be physically" [18]. Thus, despite his ap- peal to visual images, Ames was a twenti- eth-century practitioner of Leonardo's

projective principles. Modern attempts to create "virtual re-

ality" draw upon the principle of equiva- lent configurations [19], and three-di- mensional (3D) visual virtual reality depends on matching two incoming messages, namely, two retinal images. Charles Wheatstone [20], in 1838, with his invention of the stereoscope, was able to match binocular incoming mes- sages and create a virtual reality that can be considered to satisfy Leonardo's de- sire to imitate nature binocularly. Thus, there was a delay of over 300 years from Leonardo's deliberations until the ste- reoscope was invented, by which time Wheatstone was able to enlist photogra- phy to facilitate capturing visual angles.

Neither Leonardo's painted imitation of the world from a single vantage point nor Wheatstone's paired pictures enter- tained the possibility of a moving per- ceiver. Incorporating a moving observer into the scene involved an even longer delay, until 1905, when Heine [21] slaved stimulus movement to body move- ment in studies of depth perception. The head-mounted displays that are used in creating virtual reality today slave

Fig. 7. Leonardo's binocular observation of a small sphere with regard to the amount of background occluded by each eye, redrawn from Richter. "Let the object in relief t be seen by both eyes; if you will look at the ob- ject with the right eye m, keeping the left eye n shut, the object will appear, or fill up the space, at a; and if you shut the right eye and open the left, the object (will occupy the) space b; and if you will open both eyes, the object will no longer appear at a or b, but at e, r, f. Why will not a picture seen by both eyes produce the effect of relief, as [real] relief does when seen by both eyes; and why should a picture seen with one eye give the same effect of relief as real relief would under the same conditions of light and shade?" [35].

Fig. 8. Leonardo's representation of the amount of a small sphere seen by both eyes, redrawn from Pedretti. "If both eyes see a spherical object, the diameter of which is smaller than the distance between the pupils of the eyes, they will see beyond the diameter of that object, and the more so as that object is placed closer to them. And therefore the central visual lines will see the object as being smaller than it really is" [36].

Wade et al., Leonardo da Vinci's Struggles 233

the paired pictures to eye and head movements, so that incoming messages of a more complicated nature can be matched to a mobile observer. Even with this addition, however, the incoming bin- ocular messages of 3D space cannot be matched perfectly from two two-dimen- sional (2D) screens, because the differ- ential defocusing of the retinal image is not yoked to the states of convergence and accommodation of the eyes. Many attempts to increase "virtuality" are pres- ently under way [22]. For example, a vir- tual display screen system that presents hologram-like images [23] allows the matching of convergence and accommo- dation, as does Sony's Visortron, or a de- vice [24] that co-varies the convergence and accommodative requirements. Yet another system [25] attempts to bypass this yoking but incorporates Leonardo's observation and Ames's work on seeing depth from a single picture. This system uses wide-angle lenses with a small depth of field, either to make the incoming message equivalent to that recom- mended by Leonardo (being "view'd at a Distance") or to eliminate the 2D cues that Ames [26] identified when trying to see 3D from 2D pictures.

As a scientist, Leonardo would have been excited by Wheatstone's stereo- scope; as a theorist he would have appre- ciated the subtlety of Ames's concept of equivalent configurations. As an engi- neer he would doubtless have found modern attempts at simulating scenes intriguing. What use would he have made of these modern struggles as an artist? One can only speculate.

Acknowledgments We would like to thank the anonymous reviewers of the original manuscript for the constructive com- ments they made; Richard Held for kindly provid- ing us with a copy of an unpublished manuscript; and York University Faculty of Arts Research Fel- lowship for supporting Hiroshi Ono's work on the manuscript.

References and Notes

1. Leonardo's descriptions of the eye and illustra- tions of its structure can be found in J.P. McMurrich, Leonardo da Vinci the Anatomist (1452- 1519) (Baltimore, MA: Williams & Wilkins, 1930). His deliberations on image formation in the eye and its analogy with the camera obscura have been assessed by K.D. Keele, "Leonardo da Vinci on Vi- sion," Proceedings of the Royal Society of Medicine 48, No. 3, 384-390 (1955).

2. The formation of an image in a camera obscura was described by Ibn al-Haytham (or Alhazen) in the eleventh century (see A.I. Sabra, ed. and trans., The Optics of Ibn Al-Haytham. Books I-Il. On Direct Vi- sion [London: The Warburg Institute, 1989]). Al- though Leonardo did relate the image formation in a camera to that in the eye, there was still uncer- tainty about the nature of light and the structure in the eye that was receptive to it; at that time it was

thought that the lens rather than the retina re- ceived images of objects. It was not until the early seventeenth century, when Kepler outlined the principles of image formation in the eye, that simi- larities between the optics of eyes and cameras could be appreciated (see NJ. Wade, "Light and Sight Since Antiquity," Perception 27, No. 6, 637- 670, 1998). Leonardo's application of optics to art has been commented upon in detail by K.H. Veltman, Studies on Leonardo da Vinci. 1. Linear Per- spective and the Visual Dimensions of Science and Art (Munich: Deutscher Kunstverlag, 1986).

3. The collection of Leonardo's manuscripts, given the title A Treatise of Painting, was first translated into English by an unnamed translator (London: Senex and Taylor, 1721); this quotation appears on p. 178.

4. Alberti's book On Paintingwas published in 1435 and was translated byJ.R. Spencer (L.B. Alberti, On Painting, [New Haven, CT: Yale Univ. Press, 1966]). Alberti described how a painting could be con- structed in perspective by interposing a transparent surface through which the scene was viewed: "When they [painters] fill the circumscribed places with colours, they should only seek to present the forms of things seen on this plane as if it were of transparent glass. Thus the visual pyramid could pass through it, placed at a definite distance with definite lights and a definite position of the centre in space and in a definite place in respect to the observer" (p. 51).

5. Leonardo's quotation is taken from A.P. McMahon's translation of Leonardo's Treatise on Painting (Princeton, NJ: Princeton Univ. Press, 1956) Vol. 2, p. 177.

6. In his Optics, Euclid described the consequences of viewing spheres that were smaller than, the same size as, and larger than the separation between the eyes (see H.E. Burton, "The Optics of Euclid," Jour- nal of the Optical Society of America 35, No. 2, 357- 372, 1945). Euclid's discussion was restricted to the amount of the sphere that was visible in each case, with no reference to what was visible beyond the spheres. When the sphere was smaller than the interocular separation, then more than a hemi- sphere was seen.

7. Leonardo's manuscript sketch was reproduced in McMahon [5] and we have redrawn it and its re- maining figures so that they are comparable.

8. M. Kemp, Leonardo on Painting (New Haven, CT: Yale Univ. Press, 1989) did not reprint the two mo- nocular diagrams.

9. D.S. Strong, Leonardo on the Eye (New York: Gar- land, 1979).

10. Drawings of retinal disparities were published long before their involvement in stereoscopic vi- sion was understood. Detailed diagrams of dispari- ties were produced by Sebastien Le Clerc, an au- thority on perspective, in his Discours Touchant de Point de Veue, dans lequel il es prouve que les chose qu 'on voit distinctement, ne sont veues que d'un oeil (Paris: Jolly, 1679), but he used them as evidence against Descartes's theory of binocular combination; they became a regular feature of texts on optics in the eighteenth century (see NJ. Wade, A Natural His- tory of Vision [Cambridge, MA: MIT Press, 1998]).

11. J.P. Richter, The Literary Works of Leonardo da Vinci (London: Phaidon, 1970). The drawing is on p. 268.

12. Leonardo quoted in Richter [11] pp. 267-268.

13. C. Pedretti, The Literary Works of Leonardo da Vinci (London: Phaidon, 1977).

14. In the second century, Galen, in his On the Useful- ness of the Parts of the Body, M.T. May, trans. (Ithaca, NY: Cornell Univ. Press, 1968), introduced a method of separating the two eyes by means of a septum, and reported that vision of a peripheral target seen by one eye (when both were open) was inferior to that with one eye alone: "If you care to place longitudi- nally on your nose between your eyes a small piece

of wood, your own hand, or anything else that can prevent external objects lying before them from be- ing seen by both eyes, you will see dimly with each eye, but much more clearly if you close one eye, as if the faculty hitherto divided between two were now coming to the other eye" (p. 501).

15. The life of Adelbert Ames II has been chronicled by R.R. Behrens, The Man Who Made Dis- torted Rooms: A Chronology of the Life of Adelbert Ames

Jr. (Univ. of Northern Iowa: published by the au- thor, 1993); and R.R. Behrens, "The Life and Un- usual Ideas of Adelbert Ames Jr.," Leonardo 20, No. 3, 273-279 (1987). An account of his artistic work can be found in R.R. Behrens, "The Artistic and Scientific Collaboration of Blanche Ames Ames and Adelbert Ames II," Leonardo 31, No. 1, 47-54 (1998). Ames subsequently studied physiological optics and developed a range of ingenious devices for producing unexpected perceptual effects. These have been described and illustrated in W.H. Ittelson, The Ames Demonstrations in Perception (Princeton, NJ: Princeton Univ. Press, 1952).

16. In the references to Ames's papers we have used his name as it appears in the publications cited. This quotation is from p. 34 of A. Ames, C.A. Proc- tor, and B.A. Ames, "Vision and the Technique of Art," Proceedings of the American Academy of Arts and Sciences 58, No. 1, 3-47 (1923).

17. W.H. Ittelson, Visual Space Perception (New York: Springer, 1960) p. 50.

18. Ittelson [17] p. 51.

19. H. Rheingold, Virtual Reality (New York: Sum- mit Books, 1991); R. Held, "Perception of Virtual Worlds," unpublished manuscript (1999).

20. Wheatstone invented both mirror and prism stereoscopes in the early 1830s, but he only de- scribed the former in his classic paper: C. Wheat- stone, "Contributions to the Physiology of Vision- Part the First. On Some Remarkable, and Hitherto Unobserved, Phenomena of Binocular Vision," Philosophical Transactions of the Royal Society 128, No. 2, 371-394 (1838). One of the distinctions between Wheatstone's and Leonardo's deliberations related to the object they viewed with two eyes. Leonardo followed Euclid's lead and used a sphere. As Wheat- stone remarked: "Had Leonardo da Vinci taken, instead of a sphere, a less simple figure for the pur- pose of his illustration, a cube for instance, he would not only have observed that the object ob- scured from each eye a different part of the more distant field of view, but the fact would also perhaps have forced itself upon his attention, that this ob- ject itself presented a different appearance to each eye. He failed to do this, and no subsequent writer within my knowledge has supplied the omission" (p. 372). Wheatstone did realize, perhaps better than many have since, that disparity alone would not suffice to yield depth perception. In his second memoir (C. Wheatstone, "Contributions to the Physiology of Vision-Part the Second. On Some Remarkable, and Hitherto Unobserved, Phenom- ena of Binocular Vision," Philosophical Transactions of the Royal Society 142, No. 1, 1-17 [1852]), he de- scribed experiments with a pseudoscope, which re- versed retinal disparities. The resulting projections to the eyes set disparity in conflict with monocular cues, of the type Leonardo discussed, and the mo- nocular cues often dominated.

21. L. Heine, "Uber Wahrnehmung und Vorstel- lung von Entfernungsunterschieden," Archiv fir klinische und experimentelle Ophthalmologie 61 (1905) pp. 484-498.

22. See, for example, S. Yano and I. Yuyama, "Ste- reoscopic HDTV: Experimental System and Psycho- logical Effect," Society of Motion Picture and Television Engineers Journal 100, No. 1, 14-18 (1991); and E. Peli, "Optometric and Perceptual Issues with Head- Mounted Displays," in P. Mouroulis, ed., Visual In- strumentation: Optical Design and Engineering Prin- ciples (New York: McGraw-Hill, 1999) pp. 205-276.

23. See, for example, S.S. Zelitt, 3D imaging system,

234 Wade et al., Leonardo da Vinci's Struggles

United States Patent 5,790,086 (1998); Y. Kajiki, H. Yoshikawa and T. Honda, "Hologram-Like Video Image by 45-Viewes [sic] Stereoscopic Display," SPIE, Vol. 3012 (1997) pp. 154-166.

26. A. Ames, "Depth in Pictorial Art," Art Bulletin, 8, No. 1, 5-24 (1925); and A. Ames II, "The Illusion of Depth from Single Pictures," Journal of the Optical Society of America 10, No. 2, 137-148 (1925).

24. See, for example, S. Onishi, H. Yoshimatsu, A. 27. McMahon [5] Vol. 1, section 487. Kawamura and A. and K. Ashizaki, "An Approach to 28. Another example of this situatior Natural Vision Using a Novel Head-Mounted Dis- in Pedretti [13] p. 193. In the origins play," Society for Information Display 94, Digest 28-31 Fig. 1) Leonardo paid scant attention (1994); R.A. Eagle, E. Paige, L. Sucharov, B.J. sentations of the eyes themselves. Rogers, "Accommodation Cues Reduce Latencies concern was with the contrast betwe for Large-Disparity Detection," Perception 28, and monocular observation of object Supplement (1999) p. 136. projections and the inadequacy of p

more than represent monocular view: 25. M. Siegel, S. Nagata, "Just Enough Reality: Com- fortable 3D Viewing via Microstereopsis," IEEE 29. Strong [9] p. 81. Transactions on Circuits and Systems for Video Technol- ogy 10, No. 3, 387-396 (2000). 30. Leonardo, quoted in Strong [9] p

n is presented il (redrawn in i to the repre- lis overriding een binocular s, their optical ainting to do ing.

pp. 80-81.

31. Richter [11] pp. 267-268.

32. Leonardo, quoted in Richter [11] p. 21.

33. Richter [11] p. 129.

34. Leonardo, quoted in Richter [11] p. 129.

35. Leonardo, quoted in Richter [11] p. 21.

36. Leonardo, quoted in Pedretti [13] p. 193.

Manuscript received 1 June 2000.

Wade et al., Leonardo da Vinci's Struggles 235