Inverse Sideways Perspective on a Road: A Drawing by a Blind Adult

Abstract

An unusual drawing of a road has two lines converging sideways, from right to left. The left side of the picture is explicitly described as the location of the observer. Also, the fronts of the cars on the road face left, with the largest car on the right. This sideways perspective is novel. In linear perspective, roads running parallel with the picture surface should be drawn with parallel lines. Lines for roads running orthogonal to the picture surface should converge with elevation. The rule for roads is if converging, then upward, and if sideways, then not converging. The sketch is by a blind woman with modest experience in drawing, including perspective. It suggests an intermediate stage of drawing development, with inconsistent use of the observer’s vantage point, in keeping with theories of perspective drawing by the blind and sighted of Willats, Kennedy and others.

Keywords

blind development drawing sideways inverse perspective

Linear perspective is thought to have been formalized as a method for constructing pictures in Italy in the early decades of the XV century (Howard & Allison, 2011; Kubovy, 1986), following demonstrations by the Florentine architect Filippo Brunelleschi. An important technique during the Renaissance, it was used by artists to depict three dimensions -- 3D. Dubbed perspectiva artificialis, it inspires a convincing impression of pictorial depth and creates illusions (Mastandrea et al., 2014). Linear perspective was celebrated and codified in treatises by Leon Battista Alberti in De Pictura and by Piero della Francesca in De perspectiva pingendi and adopted rapidly by major artists such as Masaccio and Leonardo (Bussagli, 2005). Kubovy (1986, p. 28–30) describes Alberti’s use of a vanishing point in constructing a perspective picture of a piazza of square tiles, and Alberti’s method for checking the result using diagonals of the tiles (Kubovy, 1986, p.29, Figure 1–12).

Linear perspective is in accord with optics, the laws of light coming to a single vantage point (Falco, 2016; Pierantoni, 1981; Pirenne, 1970). In that respect, it is more than an arbitrary convention (Feeney, 2019; Gombrich, 1960; Laursen, 2017). Also, “perspective is the science of directions and angles, and is available to touch” (Heller & Gentaz, 2014, p. 137). Put simply, pictures in linear perspective show the directions to items in a scene from a vantage point. They display what is to the left and right of the vantage point, and what is up or down—higher in elevation with respect to the vantage point. The directions make sense to haptics—the sense of touch involved with actions (Wnuczko & Kennedy, 2014). In a study on mental images, Arditi et al. (1988) suggested congenitally blind observers do not image objects at different distances depending on their size. However, blind and sighted observers reach out to find what is to their left or right, and, seated at a long table, they would reach low in elevation to pick up a nearby spoon, and higher to pick up the salt further down the table. On the ground, distance and angles are closely related. By isosceles triangles, a distance along the ground equal to our height is 45° in elevation. Hence, it is understandable that drawings by early and late blind people often have some perspective features (Eriksson, 1998; Hatwell et al., 2003; Hayhoe, 2017; Heller & Gentaz, 2014; Kennedy, 2019; Vinter et al., 2018), but to date there has been no report of a novice’s sketch from the blind or the sighted in inverse sideways perspective.

In Figure 1, a photograph of a path in linear perspective, contours converge with height up the page (elevation) due to foreshortening. The contours are obliques –/ \. The space between the contours (azimuth) diminishes with elevation. Figure 2 shows a path running parallel to the picture surface, by means of horizontal contours. In Figure 3, obliques show receding edges. Willats (1997, 2002) described the features on the picture surface (elevations, horizontals, obliques, and converging contours) as “picture primitives” and features in the depicted world (such as roadsides) as “scene primitives.”

Figure 1.

Path: Convergence With Elevation.

Figure 2.

Path: Horizontal Contours Show the Sides Running Parallel to the Picture Surface.

Figure 3.

Receding Edges of the Cube on the Right Are Shown by Three Obliques.

Prior to Brunelleschi, pictures of tables and buildings, like most pictures throughout the history of art (with significant exceptions in Roman art), were quite inconsistent with linear perspective, and of interest, surfaces such as cubetops and tabletops were often drawn in inverse perspective (Howard & Allison, 2011, p. 1019, their Figure 2a–e) as if getting larger with distance (Figure 4). Multiple sides of objects were shown as if they were “folded-out” (Arnheim, 1969, 1972; Kennedy, 1993). Contours on the picture surface depicting parallels diverged with elevation –\/– as objects receded in the scene. (In inverse perspective—aka reverse perspective—the contours in Figure 1 showing the road would be diverging with height on the picture surface.) Often, in such pictures, scene primitives that should be hidden were depicted by picture primitives. The Byzantine Abraham lunette mosaic, San Vitale, Ravenna, includes inverse perspective (Derȩgowski et al., 1994), and saintly figures on the far side of a table have feet occluding a low crossbar on the near side of the table (Landerer, 2000). (As was standard in Byzantine and early Renaissance art, bars parallel to the picture surface are shown by parallels on the picture surface.) Many features of the pre-Brunelleschi pictures are found in drawings “simple and primitive in appearance” by inexperienced artists (Golomb, 2002, p. 128). Writing about variations on perspective in drawings by the blind, Feeney (2019, p. 259) argued: “[that] the principles of pictorial representation are broadly perceptual rather than being confined to vision is positive in a lot of ways that are not at all difficult to discern.”

Figure 4.

Cube in Inverse Perspective, Sides “Folded Out” (After Arnheim, 1969, Figure 147b).

Learning to draw in linear perspective is not an easy task. Novices use many provisional schemes that are permutations of general principles, such as elevations (Figure 1), horizontals (Figure 2) and obliques (Figure 3), occlusion, and selection of the vantage point. Specific permutations may be dropped after brief use, with development or practice (Kennedy, 1993; Landerer, 2000; Mitchelmore, 1985; Nicholls, 1995; Willats, 1997; Wilson & Wilson, 1984; Winner, 1982), and convergence, foreshortening and the selection of features with respect to the vantage point may be inconsistent (Kennedy & Juricevic, 2003, 2006; Vinter et al., 2018). Generally, no one draws in linear perspective applied to all three dimensions of space without formal training. Willats (1985, p. 79) wrote “even by the age of 16 or 17 only a minority of children [use] anything approaching true perspective.” Testing 10-year-olds, Chen (1985) found fewer than 50% used foreshortening correctly in copying line drawings of a cube in linear perspective. Testing 14- and 15-year-olds drawing a cube freehand, Nicholls and Kennedy (1992) found about 70% used parallel projection. A further 9% drew cubes that did not fit parallel or linear perspective, for example, sides of the cube were drawn as triangles.

We present here a rare case in point. The sketch uses an original permutation of diminution (for cars), occlusion (for wheels), horizontal convergence (for a road), and the observer’s vantage point (stated explicitly).

Drawn by a blind adult, the sketch depicts cars on a road. We ask here whether it is in inverse perspective, but sideways, tapering right-to-left. This scheme for a road was not entertained in art commentary or drawing-development theory (Arnheim, 1969, 1972; Freeman, 1994; Golomb, 2002; Landerer, 2000; Willats, 1997). In keeping with what accompanies inverse perspective pre-Brunelleschi, Figure 5 picture primitives show occluded scene primitives (notably, wheels).

Figure 5.

M’s Drawing of a Street With Four Cars and, on Top, an Unfinished Car Drawing (the First Item M Drew). The cars were drawn in order from right to left. Finally, M drew the converging lines showing the road.

Method

Apparatus

The original of Figure 5 is a raised-line drawing (size in the original 13 × 30 cm), made using a raised-line drawing kit from Cambratech, Milan, that comprises a polyester film sheet (size 25 × 35 cm) lying on a drawing board with a rubberized surface. Lines drawn on the film with a ballpoint pen become raised and tactile, easily traced by a finger.

Participant and Procedure

The person who made the drawing is a blind woman, M (aged 37 years), tested in Lombardy, Italy, in Italian. She was born prematurely (7 months) and placed in an incubator. As a child, she had severe low vision: The left eye had visually acuity of 20/400. (Note that 20/200 is “legally blind.”) Her right eye was totally blind. At the age of 20 years, the retina of her left eye detached. Presently, she is only light sensitive.

M completed high school in business management and worked in business. She had some experience drawing. Prior to the retinal detachment, at school, she used video magnifiers and a magnifying glass to read and draw. Two decades ago, her mother enrolled her in a 1-year private class—after school—on painting and drawing. She was taught to draw vases with flowers, tables, and landscapes in perspective (email from M, November 21, 2019). In this class, she used a pencil and paper to make her drawings. In our experience, foldout, divergent and sideways perspective are not taught in drawing classes (Laursen, 2017), and sighted and blind children and adults invent many schemes for themselves (Kennedy, 1993, 2003).

M was asked to make a series of drawings, in a session that lasted almost 30 minutes. This is her first experience making raised-line drawings, she said. The series began with a frontal face and a profile face. Then, she was asked to draw a street with cars, in perspective. (“Maria potresti disegnarmi una strada in prospettiva con le macchine per favore?”). The result was Figure 5. M granted permission to publish the figure.

Results

Figure 5 is the case in point. Is it in inverse sideways perspective?

The first car that M drew is at the top of Figure 5. An outline drawing, lines depict edges of surfaces (Kennedy, 2019; Thompson et al., 2003). In the sketch, the front of the car is on the left. “I made the windshield wipers,” M said. It follows from the use of the wipers on the left that the occluded back of the car is on the right, without wipers. She also said she had drawn the roof of the car.

The lower part of Figure 5 shows a street with four cars. They face left, that is the fronts of the cars are on the left side of the drawing. The front edges of the cars (where the front bumpers would be) are shown by oblique lines in the case of three of the cars in the road, and the first car that M drew. A curved line is used in the second car from the right.

Three of the car drawings have four wheels. The second from the right has three wheels.

The car drawing on the right is the largest and the car on the left is a third smaller. The diminution of the cars is not fully consistent because the second car from the right is the same size as the one on the left. M described the second car as a specific make (a “Smart car”), which may have interrupted the regular diminution of the other cars.

The last lines that M drew were the lines for the sides of the street. Enclosing the cars, the two lines converge to the left. M declared that the observer is on the left side of the picture. (In her colloquial Italian, “La strada di allarga perché io la vedo in prospettiva da di qua. Perché bisognerebbe guardarlo da di qui e poi quando lo vedi in prospettiva, lo vedi sempre da di qui” [sinistra]). She tapped the picture on the left side. She added that in perspective, one cannot see all of the car, and that the different sizes of her car drawings were due to perspective.

Discussion

Consider the car-drawings first, and then the road. We interpret features that are likely deliberate, and note others in passing. We suggest M offers an intermediate stage in drawing development, meaning some features in Figure 5 are early in drawing development (foldout in style), some later (and consistent with a vantage point). We suggest influences from personal experience and hearsay and argue that the final combination is novel.

M did not finish the first car drawing (the one on the top), Figure 6. She said she was dissatisfied: “I didn’t like it. I am making another one.”

Figure 6.

Car in Foldout, Unfinished.

If it is indeed a foldout drawing, the roof and attached sides in the scene are shown by attached shapes on the picture surface and an occluded scene primitive—in this case the rear of the car—is shown. The drawing is not restricted to facets that are in front of the observer’s vantage point.

The front and the rear are shown by oblique lines, one by a backward-leaning oblique –\, and the other by the opposite –/. This suggests M is considering the implications of vantage points. However, as in Figure 3, the\oblique implies a vantage point to the left of the car and the/suggests one to the right.

Her next drawing (the car on the right) shows the roof, front, and sides of the car but not the back. This suggests the use of a single vantage point, from a three quarter or bird’s-eye location. She said, “Since it’s in perspective, you can’t see the whole car.” However, she drew all four wheels. That is, a picture primitive shows an occluded scene primitive, a fourth wheel. Hence, the drawing is a mixture of vantage point and foldout schemes.

Her next drawing (second from the right, her Smart car) shows only three wheels. Portraying only three wheels is consistent with the use of a vantage point, since the front wheels and the near-side rear wheel are exposed to an observer’s vantage point. However, in her next two drawings (third and fourth from the right), she included all four wheels—foldout drawings again.

Does M advance in sophistication between her very first drawing of a car and the next, which is within the lines for the street? With opposite obliques, the first shows sides facing two vantage points, as if the car was folded out. If one vantage point were used that would be ahead developmentally—one side would be the rear, self-occluded by the car. She judges the drawing unsatisfactory. The second sketch omits the back of the car. The lower line of the chassis terminates by the right most wheel. This suggests a single vantage point. Also, if Occam’s razor is the judge, using fewer principles and omitting more of the car is an advance in sophistication. However, she includes four wheels, which suggests the use of a vantage point is inconsistent.

In the last two cars, M drew four wheels again. In each car with four, the placement of one differs informatively from the other three. Three are at corners of the car. This is a feature of the scene primitive. The fourth sits along the base line of the car sketch, just in from the rear wheel and under the upper rear corner of the sketch of the car. Possibly, odd-man-out placement of a wheel would cause novice artists, developing beyond the use of foldout, to rethink the need to draw four and omission with its information for occlusion and a coherent fit with a single vantage point would follow.

The pair of cars in the middle have fewer details than the two that flank them, which might be because of different car models or because they are understood to be “more of the same,” an “etcetera” principle (Kennedy, 1974).

The combination of foldout and vantage point schemes in drawing the cars suggests an intermediate stage in drawing development. Nicholls and Kennedy (1992) found foldout was most evident in primary-school children (a fifth of their sighted 8-year-olds used foldout). Vantage point drawings become steadily more common with age (46% of 11-year-olds in Nicholls & Kennedy, 1992). With age, children shift from showing shapes of objects to showing the directions to parts facing the vantage point. The same may be true for blind novices drawing at their own devising.

M described the scene as drawn as if she was on the left side of the scene, tapping the left side of the picture, close to its edge. The verbal report makes the vantage point clear. Also, M’s cars face left. Furthermore, M drew the fronts of the cars as backward-leaning obliques – \. As Figure 3 shows, if the vantage point is on the left side of the picture, this is how orthogonals to the picture surface project (Kubovy, 1986, Figure 7–8, p. 113; Pirenne, 1970, Figure 9.11b, p. 127). (Figure 3 shows that obliques further from the vantage point lean more, but of the cars within the roadsides the leftmost has the oblique leaning most. Obliques are used for other parts of M’s cars but inconsistently, some parallel, some not.)

M’s largest drawing of the four roadway cars is on the right. She said her sizing of the cars was deliberate. The largest car being furthest from the vantage point suggests inverse perspective. Of note, the body of the second car from the left is a rectangle. (The other car shapes are diverse.) True form for the side of a car (which is achieved early in development), obliques for front edges (later), and change of size with distance (still later) suggest an unsettled intermediate stage in drawing development yet again.

With distance from M’s vantage point on the left, the two lines for the road diverge, accommodating the largest car drawing. This is inverse perspective, by definition, but sideways. In linear perspective, roads running away from the vantage point are drawn converging with elevation (Figure 1). The rule for roads is if converging, then upward, and if the road runs sideways, then not converging (Figure 2). However, M said, “The street gets larger because I see it in perspective from this side [left].” M takes it that “perspective” involves distance and convergence but reverses the direction of convergence. She makes no mention of elevation. The result is an original scheme.

Many blind people indicate that hearsay descriptions of perspective, distance, and size-change are puzzling (Arditi et al., 1988; Wnuczko, 2019). They are in good company. In our experience, sighted people are confused about the same things. (People hear “objects change size with distance.” They should be hearing “the angles they subtend change with distance.”) Also, Heller et al. (1996) found that early-blind adults did not use foreshortening in drawing a rectangular board at a slant. Late blind participants did. Furthermore, university students produce drawings that do not conform to linear perspective’s convergence (Howard & Allison, 2011). Indeed, we have observed that engineering students experienced with CAD programs (computer aided design) cannot draw in linear perspective freehand. M likely had features of perspective mentioned to her in her drawing class. It included a scene, notably. This was two decades ago, and now she is given a novel task and produces an original combination of features to do with observing from a vantage point.

Walls and tabletops are often drawn in divergent perspective by novices. The same was true in pre-Brunelleschi Italian art. What is novel here concerns a road. A horizontal scene primitive running parallel to the picture surface should be shown by a horizontal picture primitive. Figure 5’s inverse sideways perspective is original.

In linear perspective, convergence upward works for roads, convergence downward shows a track on a ceiling, and convergence sideways depicts a wall. Each convergence option is reversed in meaning in inverse perspective, yielding six options. Drawing development could proceed by trying options before settling on one.

In drawing development, to show depth, artists pick from four picture-primitives—horizontals, verticals, obliques, and convergence/divergence. Typically, depth via horizontal alignment comes early in development, then vertical alignment, obliques later, convergence, or divergence even later (Golomb, 2002; Mitchelmore, 1985; Willats, 1997). Idiosyncratic combinations of the primitives may be adopted on occasion. If juggled with slight regard for scene directions, the results would include divergent sideways perspective. With practice, influences from directions from a vantage point would be expected to lead the idiosyncrasy to an approximation to linear perspective.

One reason why novices only approximate linear perspective is a complication in diminution with distance. Think of rails and ties of railways. The rails are drawn as /\ shapes because of diminution in their azimuth angle with distance. This follows a linear function. The space between ties also subtends an angle, in elevation. This elevation angle also diminishes with distance but at a quadratic rate (Juricevic & Kennedy, 2006; Wnuczko et al., 2016). The linear/quadratic relation between azimuth and elevation angles is not understood by the vast majority drawing freehand.

For good reasons, M is not alone in struggling to draw a 3D scene freehand. She has selected a unique set from an array of options. Presumably M offers a “creative synthesis” (Eardley & Pring, 2004). In development, schemes that capture more directions to scene primitives may last longer (Kennedy, 1993; Willats, 1997). Novel uses of perspective such as Figure 5’s may be fleeting.

We should mention that inverse perspective is often called reverse perspective in technical literature on scene analysis, for example, in automated-driving research. To our knowledge, reverse sideways perspective is not discussed.

In sum, M’s lines depict a road running sideways, the observer at a narrow end of the lines, facing oncoming cars. This inverse sideways use of perspective by a blind woman is unusual. It suggests modest experience in drawing in perspective. It is a novel combination of options entertained by the sighted and the blind which, we suggest, relate to the experience of directions from a vantage point.

Footnotes

Acknowledgements

For helpful comments, the authors thank D. Bernhardt-Walther, P. Cavanagh, P. Coppin, R. Klein, J. Lloyd, C. Maurer, D. Maurer, M. Niemeier, K. Singh, M. Wnuczko, and N. Yaari.

Declaration of Conflicting Interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

ORCID iD

John M. Kennedy

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