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Foldout includes foreshortening in drawings by a blind man

John M. Kennedy e Sherief Hammad
p. 31-45

Abstract

In a case-history, Ben, a university-graduate blind adult, is shown to draw a cube as if it were folded out, but with slim rectangles for the sides around a central square. This form is drawn by sighted 8-year-olds. It might involve foreshortening and parallel projection, despite the presence of more sides than would be present in parallel projection in a single direction. Also, Ben drew a glass’s brim as both a straight line and as an ellipse, a form common in drawings by sighted 8-year-olds that may include the circular brim foreshortened to an ellipse in a ¾ view. In several drawings made later in the testing session Ben only showed aspects of the depicted object facing one direction. In elevation and plan drawings, he showed aspects facing to the side of the object or above the object. Also, Ben’s use of foreshortening advanced in sophistication in the testing session. We hypothesize that the blind and the sighted are on the same drawing developmental trajectory.

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Testo integrale

1Here, in a case-history, we show foreshortening is used in drawings by a blind adult, Ben, who drew a cube as if folded-out but with slim sides. His foreshortening advances in sophistication during a single testing session. We speculate that drawing development in the blind and the sighted may progress similarly.

  • 1 Lopes 2006; Hopkins 2008.
  • 2 Axel and Levent 2003; Eriksson 1998.
  • 3 Kennedy 2003; Kennedy and Juricevic 2003.
  • 4 Kennedy and Juricevic 2008a, b.
  • 5 Caron-Pargue 1985; willats 2005.

2Although the proper interpretation of perspective, projection and foreshortening in drawings by blind people is still debated1, there are now many studies on their pictorial abilities2. Blind subjects who have experience in drawing are rare3 and many blind adults asked to draw for the first time begin like sighted preschoolers. It is clearly important for theory of drawing development in the sighted and the blind to find and assess blind people drawing slightly more advanced drawings. Of particular concern for the present case-study are foldout drawings. These drawings by Ben and sighted children may be evidence the blind and the sighted use the same systems, including foreshortening, in early phases in their development of drawing4. Indeed, Ben not only drew a foldout cube, in drawing a glass he drew the brim twice, a format related to his foldoutplus-foreshortening cube drawing that is also devised by sighted children5. To support our claim about foreshortening in the foldout cube and glass, we show Ben drew cubes and glasses using plans, elevations and ¾ views, single vantage points and appropriate amounts of foreshortening.

  • 6 Eriksson 1998.

3In contrast to the present proposal, it might be argued that the blind have no reason to use foreshortening. That they use foldout may be less controversial6. The basis of this opposing view is the claim that touch does not encounter foreshortening. Whether objects are close to our body or at arm’s reach their proportions remain the same to touch, and not foreshortened. Parallels are parallels, in touch, and do not shrink in one dimension (foreshorten) or converge (in linear perspective) as they do for the eye. If so, only in vision would doors foreshorten as they open, and only in a picture for the sighted should the top and bottom of the door be shown by converging lines. Parallel railroad tracks that recede to the horizon in 3d are shown by converging lines in 2d photos, but the parallel sides of a ruler remain parallel in touch no matter what its orientation, and its width, length and depth dimensions remain unchanged.

  • 7 Hatwell 2003; Heller, et al. 2006, 2009; Kennedy 2009.
  • 8 Kennedy and Juricevic 2006.

4An argument for foreshortening’s relevance to touch can be made as follows: in touch, we use a vantage point from which we can reach out. Thereby we obtain information about directions from a vantage point7. Hence, touch facilitates pointing to distant objects and it can support the awareness that railroad tracks converge as the tracks becomes more distant8. Likewise, if we reach for the handle or the hinges of the door, the angle between the two at our vantage point may be wide if the door is closed, and narrow if it is open. This is foreshortening in the azimuth or horizontal dimension.

  • 9 Golomb 2002, p.11; 2004, p. 103.

5Even if foreshortening and perspective convergence are part of the everyday awareness of direction for the sighted and the blind, drawing development achieves many skills with perspective relatively late if at all. Use of linearperspective’s converging lines to show depth usually emerges only in early adolescence9. However, foreshortening is present in parallel projection as well as in linear perspective. In parallel projection, a square can be drawn foreshortened as a slim rectangle, and a circle as an ellipse. In this scheme a door could be drawn as a slimmer and slimmer rectangle as it swung open because parallel projection foreshortens in one dimension, leaving parallels in the referent scene depicted by parallels on the picture surface.

  • 10 Willats 2005.
  • 11 Caron-Pargue 1985.
  • 12 Nicholls and Kennedy 1992.
  • 13 Caron-Pargue 1979.

6Consider where foreshortening in one dimension might arise in drawing development. Toddlers scribble before drawing curves and straight lines, and then drawings by novices simply copy shapes of parts of target objects with no foreshortening. (The sighted use visible lines to make their drawings and the blind use raised lines. Raised-line drawing kits use a plastic sheet instead of paper. The sheet rests on a rubber-covered board and a ball-point pen writing on the plastic sheet makes a tangible raised line.) Like sighted preschoolers beginning to draw, blind adults who are inexperienced in drawing, once encouraged to try, represent cubes as rough squares and spheres as rough circles. After copying a single aspect of an object as a true form, a curious phenomenon often arises in drawing development. Many sighted children draw the object as if folded-out and the result resembles the work of cubists. That is, many aspects are drawn, shown attached to one another. Cubes are pictured as several squares attached to each other10. In foldout style, cylindrical objects such as glasses are drawn with rectangles for the elevation of the glass and, simultaneously, rounded forms for a plan view of the brim11 akin to cubism’s profile and front views together. Nicholls and Kennedy12 found foldout drawings frequent in drawings of cubes by 8-year-old sighted children, and Caron-Pargue13 found cylinders often drawn as cubist foldouts by 8-year-old sighted children.

  • 14 Nicholls and Kennedy 1992.
  • 15 Nicholls and Kennedy 1993.

7Foldout drawings that use squares for the sides of cubes and circles for the brims of glasses offer true forms with no foreshortening. However, what if a central square is flanked by slim rectangles? Nicholls and Kennedy14 found the mean age of children drawing in this fashion to be 8. Further, foreshortened obliques are taken by adults to show cubes15, so foreshortening looks right to adults, and therefore probably also to the 8-year-old children. Hence slim rectangles could reveal foreshortening is present for individual facets in foldout forms that, on the face of it, violate perspective principles about the number of faces that should be shown, and do not use convergence to show receding sides.

8Granted the 4 slim rectangles flanking the square are inconsistent with parallel projection since a cube only shows 2 or 3 faces in a given direction, if this foldout form includes foreshortening and parallel projection, over the course of a series of tasks in which the direction of the cube from the observer matters, the use of foreshortening and projection might become consistent. That is, without correction from another person, Ben might come to draw cubes and glasses placed in different locations with respect to his vantage point not only foreshortened but also with the number of faces consistent with a single direction of observation. The number of faces should decrease from 5 to 2 or 3. Two faces could indicate a cube sitting to one side of the observer, and three faces suit a cube moved to the side and down. Also, he might draw a glass initially in foldout style, but if the glass’s orientation matters, he might modify his foreshortening to suit.

9To test our conjectures about foreshortening accompanying foldouts, and increasing consistency over a series of tasks to do with a vantage point, consider Ben’s response to drawing tasks involving cubes and glasses. Filler tasks (crossed pencils, person standing) were included to help maintain motivation. We report here the tests of foreshortening.

Method

Subject

10Ben (aged 28) was blind from birth. He had light sensitivity at birth, and could see colours and some shapes but he never had enough vision to read large print. He lost all sight before 4 years of age. He has successfully completed university level education in Australia, with a Monash university Ba in linguistics and languages (German and Russian). He is an accomplished musician and music teacher. He can read Braille at a basic level, and he uses some Braille contractions for languages, music, chemistry and electronics. He has modest drawing experience. He used a raised-line drawing kit as a child for writing and printing letters, for drawing and for being given pictures of animals. He used a raised-line drawing kit in mathematics for figures such as graphs, and in geometry. He reports he had no drawing classes (the standard experience for blind people we have tested in several countries). Ben’s roommate at university reports he did not see Ben draw during the years they studied together.

Procedure

11Ben was given a series of drawing tasks and was asked to use a raised-line drawing kit (purchased from the Swedish organization for the Blind). Ben was given a few moments practice with the kit and then the drawing tasks.

12In order, the drawing tasks including filler tasks were (1) two pencils one crossing the other, (2) a cube, (3) a glass, (4) a person standing, (5) a cube in front of Ben’s head, this cube moved to the right, this cube moved to the right and down below head level, and a cube balanced on a vertex with a vertex towards Ben, (6) two parallel rows of glasses on a table with three glasses per row, one row on his left and the other on his right, stretching away from Ben, (7) a cube near Ben on the table paired with three glasses, one beside the cube, one in the middle of the table and one on the far side of the table, (8) a scene with three cubes, one in front of Ben on the table, one to Ben’s right and one further to his right, (9) a glass on the table and directly below Ben’s head, and a glass further away on the table, and a glass still further away, (10) a glass tilted back and a glass lying down with its base towards Ben. The pencils, cubes and glasses were shown to Ben as the tasks were given.

13The duration of the testing session was about two hours, including short breaks.

Results

14Scans of drawings are given here in chronological order, with comments from Ben and brief interpretations.

15The first drawings (not shown) in the session were practice in making lines with the drawing kit. In his drawing of one pencil lying on top of another (also not shown since it does not pertain to foreshortening), to show which pencil was on top he added an extra line to the interior to the drawing of one pencil, describing this as “shading-in” the top pencil.

Figure 1. Drawing of a cube in foldout style.

16Figure 1 is Ben’s drawing of a cube. Slim rectangles flank a central square (proportions about 1:3). The mean age of children drawing in this fashion was 8 in Nicholls and Kennedy (1992). Ben said the cube is «flayed, like a two-dimensional thing». He said it shows «a cube viewed from the top». He commented that the sides «would appear foreshortened… in some way attenuated». The forms all use roughly parallel sides, suggesting parallel projection, but parallel projection used consistently would show only 1 or 2 side faces. The foreshortening is horizontal (left and right sides shortened in the x dimension of the page) and vertical (top and bottom sides foreshortened in the y dimension).

  • 16 Caron-Pargue 1985.

17Figure 2 shows a glass in two ways in one drawing. The glass is shown from the side with straight lines for the base and rim of the glass (an elevation in parallel projection). The rim is also depicted by an ellipse. Circles become ellipses if foreshortened in parallel projection in a ¾ view (that is, from above the front of the glass, midway between a plan and an elevation). Drawings of glasses which combine two aspects such as elevations and ¾ views are common in drawings from sighted children aged 816. Ben commented: «If something’s got a round top, if you’re seeing it from the side, you’re not going to see it all». This comment applies well to the straight line for the rim, not so much to the ellipse. All of the round top is projected foreshortened vertically as an ellipse.

18After drawing the glass, Ben was asked to draw a person. He drew a stick figure (not shown) with a rounded head, arms akimbo, legs spread and feet pointing left and right.

Figure 3. A cube in front of Ben and a cube moved to the right and down.

  • 17 Nicholls and Kennedy 1992.

19For the cube in front of him, Ben drew two shaded-in faces (Figure 3 left), the front shown by a freehand-square quadrilateral and the top shown by a slim rectangle, suggesting foreshortening vertically in parallel perspective. Showing only two faces suits a ¾ view, with a vantage point above the front of the cube. For the cube moved to the side and down, Ben drew three forms (Figure 3 right), as a foldout, with the side of the cube shown by a freehand-square form and the front by a slim rectangle as if foreshortened horizontally. The top was shown by a slim form (rectangular but for the top lines), reduced in both horizontal and vertical extents. He drew this cube as if the side and top were folded-out, a variant on Figure 1 in which only 3 faces are shown to suit a vantage point above and to the left of the cube. He noted he was drawing what was «prominent to the eye» and just as he shaded in the top of two crossed pencils, Ben shaded-in the rectangular forms, saying: «My math books used shading. Later the single curve would be drawn». The foldout form of Figure 1 may be surpassed developmentally by Figure 3 since the left and right forms only show faces that could confront a single vantage point17, unlike the 5 quadrilaterals in Figure 1.

20Of interest, the Figure 3 drawing on the right includes foreshortening of the cube’s front face, shown by the lower-right quadrilateral. It is slim horizontally, while the side face is projected as a freehand square i.e. not foreshortened, in keeping with a side face projecting a wider and wider angle as the cube moves to Ben’s right. If it is a projection, the drawing uses two picture planes. The picture surface may be parallel to the front face of the cube on the left in Figure 3. On this picture surface the front face of a cube placed to the right would have projected as a square, not foreshortened horizontally. To show the front face foreshortened, the picture surface has to be rotated. Hence, the front-face drawing on the right suggests parallel projection onto a picture surface orthogonal to the line joining the observer to this cube. In sum, Figure 3 may be a mixture of foldout, foreshortening, projections and different picture planes, rather than projection onto a constant picture surface.

21Ben was asked to draw a cube balanced on a vertex, with a vertex towards him. He said: «I don’t really know how to start».

22Ben drew 6 glasses in two parallel rows as 6 freehand circles, with no u shape for the sides of the glass, as if the glasses were drawn in plan view, i.e. from above. He described his drawing as «area layout». The lower forms show nearer glasses. Since its forms were similar to the upper forms in Figure 4, the 6-glasses drawing is omitted here.

23Figure 4 is a drawing of a cube on the near side of the table and a glass beside the cube (lower forms), halfway across the table (middle form), and on the far side of the table (upper form).

Figure 4. A cube and three glasses.

  • 18 Juricevic, Kennedy and abramov 2009.

24Ben commented that the shading applied to the form showing the top of the cube represented the dominant face, but the foreshortening of the front face (drawn as a slim rectangle) would be «enough to say that it is not the dominant face». The near glass (lower form) is drawn with a complete ellipse for the brim, a horizontal line across the glass to show he imagined liquid in the glass, and half of an ellipse for the base. The ellipses suggest a cup in ¾ view, though the horizontal line for the liquid level is an elevation. Being circles, the middle and top drawings may be plans, i.e. from above. The switch from ¾ view to plan could be due to a near glass being reached by a hand approaching from front-and-above, and far glasses often being approached from directly above to avoid collision with near, intervening obstacles. The plan drawings are fully shaded, likely again indicating all their brims are equally prominent and therefore not foreshortened. as in his 6-glasses drawing, the 2d dimension from the bottom to the top of the page in Figure 4 stands for the z or depth dimension in 3d. For an object standing on a ground surface in 3d, the elevation of the base of the object is perfectly correlated with its depth18.

Figure 5. Two cubes: one to the right, and one further to the right

25Ben was asked to draw three cubes on the table in front of him. Ben drew the cube in front of him with a form similar to Figure 3, right, so it can be omitted in Figure 5.

26Ben shaded the freehand square depicting the front face of the cube moved slightly to the right, which he deemed the more “prominent” face (Figure 5 left). He foreshortened the side face horizontally, leaving it unshaded. The cube moved further to the right he drew with a freehand square for the side face, shaded, and the front face was also depicted by a freehand square left partly unshaded (Figure 5 right). His drawings indicate that as a cube moves appreciably to the side its erstwhile side face can project unforeshortened. He uses shading to show the erstwhile front face is less “prominent” but he does not foreshorten the face (a change from Figure 3, right, that is noteworthy but of uncertain significance).

Figure 6. Glass sitting on the table, directly below Ben.

27Ben was asked to draw three glasses, one directly below him, one in the middle of the table and one further away. The two further away are repeats of Figure 4’s further glasses, and he drew them as what he said were meant to be circles (plans, in our terms). To depict a glass directly below him, Ben drew an arc at the bottom of the picture, concave towards the bottom (Figure 6). He said “For the one directly below me. I’ll just draw an arc as [an] acknowledgment that it is there.” His vantage point influenced the location of the drawing (bottom of the picture signifying near) and the amount of the object drawn, as if only a fraction would be apparent. Perhaps we might reach for a glass that is very close to us with our hand approaching it from its rear, just as we might reach towards the front of a slightly further glass, and further glasses in a row might be approached from above. For sure, Ben depicts rear, front and top features of a glass selectively, revealing influences from an observer’s vantage point.

Figure 7. Glass in front of Ben, glass tilted back at 45 degrees with its base towards Ben, and glass lying on the table with its base towards Ben.

28Ben drew a glass standing on the table as a u shape with a flat base and oblique lines for the glass’s sides (Figure 7 left). The glass tilted back at 45 degrees was depicted by a shallow u with short oblique lines for the glass’s sides, with the base shown not only by a straight line but also by half an ellipse above the straight line (Figure 7 middle), showing the base foreshortened. The glass lying on the table was drawn as a circle for the base (not foreshortened, suiting the vantage point) with a highly foreshortened side of the class shown by a curve concave downwards (Figure 7 right). The side is shaded, and two flanking lines are highly foreshortened.

29Ben commented he was considering the “direction” of the glass and added «I think I can figure out how to draw it not from the top». About the curve in the drawing of the tilted glass he said «the front edge is an arc» as he touched this part of the glass. For the lying-down glass with very short flanking lines he said «I’m going to draw a truncated cone. I’ll give that a little bit of shade. The sides of the glass taper off». He foreshortens the sides more extensively to show the glass increasing its tilt from his vantage point, and decreases the foreshortening to show the base tilted to face the vantage point correspondingly.

Discussion

30Ben begins with foldout geometry. Slim rectangles in Figure 1 suggest foreshortening but showing 4 sides is not consistent with projection of a cube in one direction. Likewise, a glass is initially shown in Figure 2 with an ellipse for a brim suggesting foreshortening due to a ¾ view, but simultaneously the brim is shown as a straight line, as in an elevation. His later drawings reflect the number of aspects of a cube facing in a single direction (Figure 3 left, Figure 4 bottom left, and Figure 5 left and right) and apply foreshortening to faces that would not be facing the vantage point directly. Most especially, in the last drawing (Figure 7 right) he only depicts aspects of the glass facing in one direction and in Figure 7 middle and right he shortens the flanks more as tilt increases.

  • 19 Willats 2005.

31Ben depicts parallels in the object by parallels on the picture surface, foreshortening horizontally or vertically. He foreshortens in both directions in Figure 3, depicting the top of the cube by a small freehand square. (The top is pointed, probably accidentally since he did not comment on it.) He makes no explicit use of oblique dimensions of the page, which 11-year-old sighted children use to show the z dimension19. Rather, his obliques depict oblique sides of a glass (and, in his terms, are “truncated” to show the sides receding). Likely, failure to use oblique dimensions to show depth blocks him from drawing a cube balanced on a point with a vertex towards him, in which three faces simultaneously recede while oriented at 45 degrees to the horizontal. Oblique lines depicting their 45 degree orientation could simultaneously show depth. But he uses horizontals and verticals for depth, and obliques only for slant.

  • 20 Kennedy 2003.
  • 21 Kennedy and Juricevic 2008a.
  • 22 Willats 2005.

32Gaia, a blind 12 year old girl, who commonly used parallel projection in her drawings, started with a y shape to show the cube’s vertex pointing towards her, and began using obliques to show depth but she could not complete the drawing20. A blind woman who also draws parallels as parallels resorted to what resembles inverse perspective in like tasks to show depth21. These and Ben’s drawings fit with the claim that in drawing development horizontal and verticals on the picture surface show depth prior to the use of obliques22.

33Ben makes explicit reference to foreshortening and occasionally implies vantage points and projection. He never mentioned projection explicitly, so for some figures he might be using the rule «to show depth compress horizontals and verticals» which makes no reference to projection outside of the picture surface. However, in explaining Figures 1 and 2, he noted what one might see from the top or side of an object, which entails a vantage point, and in reference to Figures 3, 4 and 5 he considered what would be prominent or dominant in vision. In planning to draw Figure 7, he explicitly mentioned direction, adding «not from the top». Also, ¾ views (Figure 2, Figure 4 bottom right and Figure 7 middle) require projection to a vantage point outside of the picture surface. Further, restricting the drawing to aspects of objects that face in a single direction (Figure 3 left, Figure 4 left bottom, Figure 5 left and right, and Figure 7 left and right) suggests projection. In sum, though Ben does not state that he is using projection, his comments and drawings entail it. Since he represents parallels in the object by parallels on the picture surface, most likely he uses parallel projection.

  • 23 Kennedy 1993.
  • 24 Kennedy 2003.
  • 25 Kennedy and Juricevic 2008b.
  • 26 Kennedy and Juricevic 2006.

34Ben’s final drawings are surely more sophisticated than his initial drawing. Figure 5 restricts the number of faces to those that face a vantage point, and applies foreshortening only to one face (Figure 5 left), not to either face of an object placed to one side. Both Figure 1 and 7 use foreshortening but Figure 7 uses it in a graded fashion adroitly to both the sides and to the base, in a complementary fashion, the base expanding while the sides shrink. The changes could be due to Ben advancing along what is normally a developmental progression in sighted children. A novice at drawing advanced from scribbles to foldout in one testing session23. Gaia (aged 12) changed from foldout to inverse perspective in one drawing session24. Tt, a blind woman with some drawing experience, advanced from one- to two-point perspective in one drawing session25. E.a., a blind man highly practiced in drawing, advanced from one-point perspective to two- and three-point perspective in one drawing session26. The direction of the changes supports the speculation that a drawing-development sequence is shared by the blind and the sighted. Alternatively, advances in sophistication in drawings in one testing session could be due to the problems being tackled later being different than those earlier. Ben initially was asked to draw a cube and a glass, but in later drawings he was asked to draw objects in a particular location with respect to the vantage point. Practice, duration and type of problem are confounded. Studies with groups of blind informants and different orders of tasks could disentangle the confounds that limit case-histories such as the present one. Ben’s use of foreshortening is clear, but reasons for changes in his use are not.

35In sum, foreshortening may come along in drawing development shortly after the use of foldout. A blind adult used a foldout system at the start of a series of drawing tasks, and included foreshortening. He used foreshortening in ¾ views and drawings of tilted objects. In later drawings he restricted the drawing to showing aspects facing in one direction, and graded the foreshortening to suit the directions. His initial use of foldout and the increasing sophistication of the foreshortening during a testing session support the conjecture that drawing development is similar in the blind and the sighted.

Acknowledgements

36Help in the preparation of this report was provided by Hsin-yi Chao, Marta Wnuczko, Justin Denoraine, Kim Yee, Barry Richardson, Dianne Wuillemin, George Vandoorn and Mark Symmons.

Alessandro Pignocchi, Barges à queue noire, crayon et aquarelle.

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Bibliografia

Axel, e.S. and Levent, N.S. (eds.)

2003, Art beyond sight: A resource guide to art creativity, and visual impairment, New York, AFB Press

Caron-Pargue, J.

1985, Le dessin du cube chez l’enfant. Bern, Peter Lang Eriksson, Y.

1998, Tactile pictures: Pictorial representations for the blind 1784-1940, Göteborg, Gothenburg University Press

Golomb, C.

2002, Child art in context: A cultural and comparative perspective, Washington DC American Psychological Association

20042, The child’s creation of a pictorial world, Mahwah, Lawrence Erlbaum

Hatwell, Y.

2003, Manual exploratory procedures in children and adults, in Y. Hatwell, A. Streri, and E. Gentaz (eds.), Touching for knowing, Philadelphia, Benjamins: 67-82

Heller, M.A. et al.

2009, The influence of viewpoint and object detail in blind people when matching pictures to complex objects, “Perception”, 38: 1234-1250

Heller, M.A. et al.

2006, Viewpoint and orientation influence picture recognition in the blind, “Perception”, 35: 1397-1420

Hopkins, R.

2008, Reasons for looking: Lopes on the value of pictures, “Philosophy and Phenomenological Research”, 77: 556-569

Juricevic, I., Kennedy, J.M. and Abramov, I.

2009, Foreshortened tiles in paths converging on an observer viewing a picture: Elevation and visual angle ratio determine perceived size, Aattention, Perception & Psychophysics”, 71: 217-224

Kennedy, J.M.,

2003, Drawings from Gaia, a blind girl, “Perception”, 32: 321-340

2009, Outline, mental states and drawings by a blind woman, “Perception”, 38: 1481-1496

Kennedy, J.M. and Juricevic, I.

2003, Haptics and projection: Drawings by Tracy, a blind adult, “Perception”, 32: 1059-1071

2006 Blind man draws using diminution in three dimensions, “Psychonomic Bulletin and Review”, 13, 3: 506-509

2008a, Drawings by a blind woman: Copies of shapes or linear and inverse perspective?, “Journal of the Institute for critical Theory”, 12/13, 33-38, Zurich, Hochschule for Kunst

2008b, Drawings from a blind adult: Orthogonals, parallels and convergence in two directions without T-junctions, in a. Vintner and c. Lange-Kuettner (eds.), Drawing and the Non-Verbal Mind. A Life-Span Perspective. Cambridge University Press: 317-335

Lopes, D. McI.

2006, Sight and sensibility: Evaluating pictures. Oxford, Clarendon Press

Nicholls, A. and Kennedy, J.M.

1992, Drawing development: from similarity of features to direction, “Child development”, 60: 227-241

1993, Foreshortening and the perception of parallel projections, “Perception & Psychophysics”, 54: 665-674

Willats J.

2005, Making sense of children’s drawings. Mahwah, Erlbaum Press

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Note

1 Lopes 2006; Hopkins 2008.

2 Axel and Levent 2003; Eriksson 1998.

3 Kennedy 2003; Kennedy and Juricevic 2003.

4 Kennedy and Juricevic 2008a, b.

5 Caron-Pargue 1985; willats 2005.

6 Eriksson 1998.

7 Hatwell 2003; Heller, et al. 2006, 2009; Kennedy 2009.

8 Kennedy and Juricevic 2006.

9 Golomb 2002, p.11; 2004, p. 103.

10 Willats 2005.

11 Caron-Pargue 1985.

12 Nicholls and Kennedy 1992.

13 Caron-Pargue 1979.

14 Nicholls and Kennedy 1992.

15 Nicholls and Kennedy 1993.

16 Caron-Pargue 1985.

17 Nicholls and Kennedy 1992.

18 Juricevic, Kennedy and abramov 2009.

19 Willats 2005.

20 Kennedy 2003.

21 Kennedy and Juricevic 2008a.

22 Willats 2005.

23 Kennedy 1993.

24 Kennedy 2003.

25 Kennedy and Juricevic 2008b.

26 Kennedy and Juricevic 2006.

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Indice delle illustrazioni

Legenda Figure 1. Drawing of a cube in foldout style.
URL http://estetica.revues.org/docannexe/image/1964/img-1.jpg
File image/jpeg, 1,1M
Legenda Figure 2. A glass.
URL http://estetica.revues.org/docannexe/image/1964/img-2.jpg
File image/jpeg, 1,2M
Legenda Figure 3. A cube in front of Ben and a cube moved to the right and down.
URL http://estetica.revues.org/docannexe/image/1964/img-3.jpg
File image/jpeg, 1,1M
Legenda Figure 4. A cube and three glasses.
URL http://estetica.revues.org/docannexe/image/1964/img-4.jpg
File image/jpeg, 1,3M
Legenda Figure 5. Two cubes: one to the right, and one further to the right
URL http://estetica.revues.org/docannexe/image/1964/img-5.jpg
File image/jpeg, 524k
Legenda Figure 6. Glass sitting on the table, directly below Ben.
URL http://estetica.revues.org/docannexe/image/1964/img-6.jpg
File image/jpeg, 428k
Legenda Figure 7. Glass in front of Ben, glass tilted back at 45 degrees with its base towards Ben, and glass lying on the table with its base towards Ben.
URL http://estetica.revues.org/docannexe/image/1964/img-7.jpg
File image/jpeg, 364k
Legenda Alessandro Pignocchi, Barges à queue noire, crayon et aquarelle.
URL http://estetica.revues.org/docannexe/image/1964/img-8.jpg
File image/jpeg, 753k
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Per citare questo articolo

Notizia bibliografica

John M. Kennedy e Sherief Hammad, « Foldout includes foreshortening in drawings by a blind man », Rivista di estetica, 47 | 2011, 31-45.

Notizia bibliografica digitale

John M. Kennedy e Sherief Hammad, « Foldout includes foreshortening in drawings by a blind man », Rivista di estetica [Online], 47 | 2011, online dal 30 novembre 2015, consultato il 22 novembre 2017. URL : http://estetica.revues.org/1964 ; DOI : 10.4000/estetica.1964

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