1-=."- L». .0. . . “3502337. AET EUNIVERSITY LIBRARIES lllllllllllllllll H N llllllH [ll 3 1293 006114 LIBRARY 3 Michigan State University This is to certify that the thesis entitled THE USE OF DRAWING RULES IN ARTISTS' AND CHILDREN'S ART WORKS presented by WHANG-HEE HONG has been accepted towards fulfillment of the requirements for Master's degree in Art Education ///”/m Z74— Major professor b. Date (V/f//7 / / / 0-7639 MS U is an Affirmative Action/Equal Opportunity Institution PLACE IN RETURN BOX to remove thle checkout from your record. TO AVOID FINES return on or before date due. DATE DUE DATE DUE DATE DUE u“ 1| MSU Is An Affirmmive Action/Equal Opportunity Institution THE USE OF DRAWING RULES IN ARTISTS' AND CHILDREN'S ART WORKS BY Whang-Hee Kong A THESIS Submitted to Michigan State University in partial fulfillment of the requirement for the degree of Master of Arts Department of Art 1989 LOOBSQCU ABSTRACT THE USE OF DRAWING RULES IN ARTISTS' AND CHILDREN'S ART WORKS BY Whang-Hee Hong The purpose of the study is to investigate how drawing rules give us more insight into the nature of representation. The previous literature was reviewed to gather information about the characteristics of drawing rules and children's acquisition of drawing rules. Some selected artists' works since ancient times and children's works, ages 8 to 16, were examined. The leading theory in perceptual psychology says young children draw by knowledge of stereotypes while older children draw by copying the appearance of the scene. However, Willats (1977, 1979, 1981, 1985) argues that children draw the real world not by stereotypes but by drawing rules. Here I compared children's use of drawing rules with that of artists. In conclusion, both children and artists were found to have innate capability to express the real world as well as the conceptual, symbolic and dream-like world freely by using drawing rules. Copyright by WHANG-HEE HONG 19 8 9 ACKNOWLEDGEMENTS I wish to express the most sincere appreciation to Dr. James Victoria, my advisor, who devoted many hours to assisting me in every phase of this study, was always available, and supplied me with the confidence needed to complete this study. My gratitude is extended to Dr. Charles Steele and Dr. Linda Stanford, my committee members, for their suggestion on the writing process. I am grateful to Dr. Elizabeth Saenger for sending me a copy of her thesis along with a letter of encouragement. My thanks are also due to Jerry Catanid and Jane Chang for warm assistance and friendship. Special thanks are due to Professor Irving Taran who supplied me the endless encouragement needed to complete Master's program. I am extremely grateful to my parents and parents-in- law for their patience and financial assistance. Finally, I must express my heartful thanks to my husband, Yong-Sik, for his endless support, patience, and commitment to my education. iv TABLE OF CONTENTS LIST OF FIGURES . . . . . . . . . . Chapter I Introduction . . . . . . . . . . Definition of terms . . . . . Limitation of the study . . . Purpose of the study . . . . Procedure . . . . . . . . . . Chapter II Review of Literature . . . . . . Chapter III General Characteristics of Drawing Rules Understanding of Drawing Systems . Denotation Systems . . . . . . Organization Systems . . . . . The Relationships of Drawing Rules to Language Acquisition, Creativity, Mental Image, Motor Skills and Cognition Chapter IV Drawing Rules in Professional Artists' Works Brief Discussion of the Use of Drawing Rules and Analysis of Selected Art Works from Ancient to Modern Times . Page vii 11 11 27 28 30 37 37 Findings . . Chapter V Drawing Rules in Children's Drawings Acquisition of Drawing Rules . Analysis of Selected Drawings according to the Various Drawing Rules Findings . . Chapter VI Discussion of the Findings Chapter VII Conclusion . . LIST OF REFERENCES vi 65 69 69 78 85 88 9O 93 10. 11. 12. 13. 14. 15. LIST OF FIGURES Orthographic projection (Willats, 1984) . . Horizontal oblique projection (Willats, 1981b, Appendix viii) . . . . . . . . . Horizontal oblique projection (Gioseffi, 1966' pO 190) O O O O O O O O O O O O O Vertical oblique projection (Willats, 1981b, Appendix viii) . . . . . . . . . Vertical oblique projection (Gioseffi, 1966, p. 190) . . . . . . . . . . . . . A cup and saucer in vertical oblique projection (Dubery and Willats, 1983, p. 28). . . . . . . . . . . . . . A cup and saucer in oblique projection (Dubery and Willats, 1983, p. 31) . . . Oblique projection (Willats, 1981b, Appendix x) . . . . . . . . . . . . . . Cavalier oblique projection (Dubery and Willats, 1983, p. 30) . . . . . . . Cabinet oblique projection (Dubery and Willats, 1983, p. 30) . . . . . . Orthogonals diverging projection (Dubery and Willats, 1983, p. 30) . . . . . . Orthogonals converging projection (Dubery and Willats, 1983, p. 30) . . . . . . . Empirical perspective (Bunim, 1940, p. 248) Artificial perspective (Willats, 1981b, Appendix xiii). . . . . . . . . . . The principle axes of a cube . . . . . vii Page 13 14 15 16 17 18 19 20 22 22 22 22 23 24 28 Figure 16. 17. 18. 19. 20. 21. 22.‘ 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. Old stone age cave painting, about 20,000 B.C. (Janson & Janson, 1957, p. 10). . . . . sm wo on a olde sphinx, about 1400 B.C., (Gombrich, 1972' DO 45) O O O O O O O O O O O O O O O O w ' v , about 500 B.C., (Gombrich, 1972, p. 51) . . . . . . . . . . Roman wall painting, 1 B.C., (Janson & Janson, 1957, p. 31). . . . . . . . . . . . e 0 Co m' ‘nus, about 700 A.D (Rice, 1967, p. 100). . . . . , Leonardo Da Vinci, (Berkman, 1949, p. 73). . . . . . . . . . . One-point perspective (Berkman, 1949, p. 88). . Two-point perspective (Berkman, 1949, p. 88). . Two-point perspective . . . . . . . . . . . . Wedding Feast, Peter Brueghel (Berkman, 1949' pO 85) O O O O O O O O O O O O O O O O m , George Seurat, 1885 (Keller, 1980, p. 225). . . . . . . . . . . Eude_in_e_§athtuh. Pierre Bonnard. 1935 (Dubery and Willats, 1983, p. 27) . . . . . , Camille Pissarro, 1880 (Keller, 1980, p. 82). . . . . . . . . - , Camille Pissarro, 1883 (Keller, 1980, p. 83) . . . . . . . . . . . E9n1exerd_ugnmertre_et_§un§ef. Camille Pissarro, 1897 (Keller, 1980, p. 85). . . . . . . . . Negative space and the 'picture box' (Loran, 1963, p. 17). . . . . . . . . . . . Lendeeepe e; Le Roehe-Guyon, Paul Cezanne (Loran, 1963, p. 46). . . . . . . . . . . Photograph of the motif (Loran, 1963, p. 46) viii Page 37 39 4O 42 43 45 46 47 47 48 49 50 51 52 53 54 55 56 IFl—"XAH u. Figure Page 34. fireekfieee, Juan Gris (Dubery and Willats, 1972, p. 93) . . . . . . . . . . . . 58 35. A diagram of fizeekfiee; (Dubery and Willats, 1983’ pO 113) O O O O O O O O O O O O O O O 59 36. Mysgery end Meleneholy e: e Streeg, G. D. Chirico (Janson, 1969, p. 524) . . . . 60 37. a ' e o Kin Khusrau a i , 16th century (Berkman, 1949, p. 31) . . . . . 62 38. Mountain_!illege. Runs-Wang Huang. (Dubery and Willats, 1983, p. 23) . . . . . . 63 39. A part of eehele;;e_;eele, 18th century (Munsterberg, 1968, p. 211) . . . . . . . . . . 64 40. Six transitional stages in children drawings (Victoria, 1982) O O O O O O O O O O O O O O O 70 41. Method 9: Drewigg a 20r§gai§, Albrecht Durer (Dubery and Willats, 1983, p. 68) . . . . . . 71 42. One of the Principles of Artificial Perspective of Alberti (Edgerton, 1975, DO 45)O O O O O O O O O O O O O O O O O O O O 72 43. T junction and Incorrectly used T junction. . . . 75 44. Drawing in orthographic projection (Keiler, 1951, p. 31) . . . . . . . . . . . . 78 45. Drawing in orthographic projection (Mendelowitz, 1963, p. 73). . . . . . . . . . 79 46. Drawing in vertical oblique projection (Viola, 1944, p. 196) . . . . . . . . . . . . 80 47. Drawing in horizontal oblique projection (Lowenfeld, 1955, p. 161) . . . . . . . . . . 81 48. Drawing in oblique projection (Alexander and Carter, 1958, p. 15) . . . . . 82 49. Drawing in empirical perspective. . . . . . . . . 83 50. Drawing in artificial perspective (Cane, 1951, p. 151). . . . . . . . . . . . . 34 ix CHAPTER I INTRODUCTION Man has made drawings since ancient times and children draw from the time they can hold a pencil or crayon. To investigate why people make drawings and what they express in their pictures, there are several theories to consider. For example, man draws either to communicate as a language or to express his view of the real world. In perceptual psychology the leading drawing theories contend that older children draw by copying the appearance of the scene, which is called "visual realism;" and that young children draw from a knowledge of stereotypes, which is called "intellectual realism." There are three views of intellectual realism. The first is that children learn stereotypes from adults' or older children's drawings or from drawing books, or culture, or explicit teaching (Saenger, 1981; Willats, 1977a). The second, in Luquet's view (Willats, 1979, 1987), is that children draw their own stereotypes acquired by chance resemblance to a familiar object, and then children repeat them. The third view is that they draw a form dependent on 'mental image' and then repeat this form (Willats, 1977a, 1979, 1981a&b, 1987). However, Willats (1987) argues that children learn to draw 1 2 the real world not by stereotypes but by the use of drawing rules such as drawing systems, denotation systems, and organization systems. Drawing rules become more complex in children's drawings as children mature. Drawing rules have been used by artists since ancient times. Therefore, it is meaningful to compare how drawing rules are used in children's as well as in artists' drawings. Through this comparison we can gain more understanding of the role of drawing rules. Definition of terms a) Drawing systems determine how spatial relationships in the real scene are transformed to the picture surface (see Chapter III). There are a number of drawing systems such as orthographic projection (Figure I), horizontal oblique projection (Figure 2), vertical oblique projection (Figure 4), oblique projection (Figure 8), empirical (naive) (Figure 13) and artificial perspective (Figure 14). b) Denotation systems determine what the line, line junction and region in the picture indicate (see Chapter V). c) Organization systems determine how shape information is organized either by object-centered, scene-centered or viewer-centered description. In object-centered description the location is defined by the object itself based on the principle axes of the object (Figure 15). In scene-centered description the location is defined by the object itself and its orientation and position are included. In viewer- 3 centered description the location is defined by the viewer's principal line of sight (Figure 14). Limitation of the study In order to know how children and artists use drawing rules in their pictures, a representative sample of drawings and paintings by children and artists are examined. Artists' works from ancient to modern times and children's works, ages 8 to 16, were examined. Purpose of the Study Through this study, I will investigate how drawing rules may give us more insight into the nature of representation. In order to resolve this problem, the following questions need to be answered: What are the characteristics of drawing rules? Do children and artists use drawing rules to solve the same problems? How do children and artists create space? Is there any difference in the use of drawing rules between children and artists? How do artists use more complicated drawing rules? Drawing rules are investigated in drawings or paintings using six projection systems: Orthographic projection, horizontal oblique projection, vertical oblique projection, 4 oblique projection, empirical (naive) and artificial perspective. Procedure First, in order to solve the problems in the study, I will clarify the general characteristics of drawing rules. Second, by examining western and oriental artists' works from ancient times to the present, I will define how drawing systems are used, what drawing systems denote, and what we can perceive from the represented world through the art works. There are three kinds of coordinate systems related to location in the organization systems: object-centered, if the location is defined by objects themselves: scene- centered, if objects include information about their position and orientation within the scene: and, viewer- centered, if location is defined by the viewer. I will, therefore, define which kind of coordinate systems is used in the examined art works. Third, I will study how children acquire drawing rules and discuss some selected drawings by children of ages 8 to 16. Fourth, based on the findings I will discuss similarities and differences between artists' and children's art works using these drawing rules. CHAPTER II REVIEW OF LITERATURE A review of the literature was conducted to investigate the experiments of educators and psychologists concerning how children draw three-dimensional objects. Clark (1896) studied children's attitudes toward perspective problems. He had children, ages of six to sixteen, draw an apple with a hatpin sticking through it horizontally. He divided the children's drawings into three groups. Group 1 children represented the model differently than it appeared. Group 2 children recognized the shape of apple, however, they could not represent it in perspectiVe. Clark said that the drawings in this group result from careless observation or lack of perspective knowledge. Group 3 children attempted to draw the apple as it appeared to them. Clark concludes that children draw what they know about objects, namely, a thought of a model's fact of "form, or taste, or feeling, -- anything but its abstract visual qualities" (p. 287) until they are able to draw a model in perspective. Then, they slowly learn to draw an object from a single point of view. Arnheim (1974) discusses intellectual realism even though he supports the theory of visual realism. According to him, intellectual realism 5 — _ flflli-sh' | 6 occurs when children represent objects as a whole, and their drawings arise from "non-perceptual knowledge"; namely from the mental image. The reason why he supports visual realism is that generalized objects are based on perception. He mentions that children "draw generalities and nonprojective shape precisely because they draw what they see" (pp. 167- 168). Freeman and Janikoun (1972) asked children, ages 5 to 9 , to draw a mug without a handle. The result of this study shows that 5, 6 and 7 year old children drew it with a handle but, children at the age of 8 and 9 drew what they saw. Therefore, they conclude that the younger children draw mental images of objects and that older children draw the appearance of objects. We know that a mug usually has a handle. However, a mental image is different from a stereotype. Phillips, Hobbs and Pratt (1978) experimented with children of ages 6 years and 9 months to 9 years and 11 months. They wanted to know about children's ability to draw three-dimensional objects and two-dimensional patterns under two drawing conditions: when they could see both the model and their own drawings and when they could only see the model. The results show that children's drawings are very different from the appearance of objects. Phillips et al. suggest that children are trying to draw reality (what they know about objects) rather than appearance (what they see from objects) and they can either draw reality or appearance but choose to draw reality. Phillips et al. (1978) argue that intellectual realism uses simpler lines 7 than visually realistic drawings. Intellectual realism explains children's ability to make drawings. This means that they believe that the production of drawings is also controlled by intellectual realism. Through intellectual realism, children slowly learn to draw visually realistic objects. This means that as they get older, they acquire more complex knowledge. Children use intellectual realism‘”' F. until they acquire some form of perspective for drawings. However, intellectual realism never disappears even though they copy the appearance of a scene. Willats study - i- (1977a,b) shows how children's drawings change as they grow up and how they become more realistic. Children of ages of five to seventeen were asked to draw a canonical drawing of a radio and a sauce pan on a table from the same viewpoint. The subjects were arranged into 12 groups. The subject's drawings were classified according to the type of drawing system. They were also given a score for the number of correct representations of overlap. They were divided into 6 classes. Class 1 - no projection system: Class 2 - orthographic projection: Class 3 - vertical and horizontal oblique projection: Class 4 - oblique projection: Class 5 - naive perspective: Class 6 - perspective. The scores for the correct representation of overlap increased continuously. Children's abilities in correct occlusion did not correlate with drawing systems. From his findings, he argues that intellectual realism and visual realism deal mostly with occlusion. However, drawing systems cannot be 8 explained by those theories because orthographic projection and vertical or horizontal oblique projection are different depictions from what children know and see about objects. The theory that children learn to draw by culturally determined stereotypes is not convincing. Each stage is a production of their endeavor to express the real world. The study indicates that drawing systems used by children become more complicated as they mature. In this order, children invent their own rules to show projection in drawings. /”Willats argues that acquisition of drawing systems are similar to the rules of language acquisition. Willats (1979), in his later study, also looked at the different rules used throughout the history of western art. In the medieval period, artists used Vuillard de Honnecourt's instructions based on simple geometrical forms such as curves, triangles and squares. In the early Renaissance, artists were guided by Cennino Cennini's drawing rules which were based on 'secondary geometry' which relates directions of lines in the real scene to those on the picture surface. Later, Brunelleschi and Alberti introduced 'primary geometry' that describes "the way in which rays of light from the object intersect the picture plane on their way to the eye of the spectator" (p. 14). Impressionists and Cubists discarded perspective and adopted vertical and oblique projection in order to emphasize direct sensations. Many Surrealist painters used 'inversions of normal rules.' Therefore, we can see that different drawing 9 systems were used in various historical periods. Jahoda (1981) replicated Willats' experiment (1977a) for adults who had limited schooling or no schooling and for university students to test the hypothesis that "limited experience of formal schooling does not affect drawing style" (p. 134). Jahoda's findings are as follows: There was no difference in drawing systems used by non-schooled subjects and limited schooled subjects. However, university students used more advanced drawing systems. All of the drawing systems were presented in these three classes. Saenger (1981) asked children, aged 5 to 14, to choose.the most realistic pictures in several drawings drawn by different drawing systems and to draw two models: (1) a saucepan and a big box behind a little box: and (2) a chair. Her findings are as follows: 1) children's drawings do not rely on appearance of a model, 2) the same drawing systems are used to depict tables and chairs, 3) most children pick oblique projection as the most realistic and apparent representations, 4) as children get older, they gradually recognize perspective diminution, and 5) some older children use a more complicated drawing system than their representational fpreference. She concludes that drawings are usually I lindependent of our perception and intellectual realism does l l gnot disappear as children grow up but shows itself in more i Lcomplicated drawing systems. Willats (1987) mentions that drawings are not totally independent from what children know about models: namely, by 10 producing drawings children transform their knowledge of objects on the picture surface. Therefore, the problem of drawing is to externalize internal shape descriptions, "and ’fthis can be done by using three kinds of rule systems: denotation, drawing and organization systems" (p. 121). Organization systems state how the coordinate systems such as object-centered and viewer-centered descriptions are related: organization systems are explained by local, modular or absolute descriptions. CHAPTER III GENERAL CHARACTERISTICS OF DRAWING RULES Understanding of Drawing Systems Drawing systems are pictorial devices1 to represent three-dimensional space on a two-dimensional surface (such as paper). Dubery and Willats (1983) define 'drawing . Funn- HA'W". I -‘J.’ '3“ I.“ [1 systems' as the transformation systems which project spatial relationships onto the picture from the real scene. "The drawing system used in a given work can be identified by comparing the relationship of lines representing the edges of objects with the relationship of the actual edges of those objects" (Saenger, 1981, p. 2). We can find evidence of the use of drawing systems from ancient times to the present in various cultures and in children's drawings. According to Saenger (1981), An understanding of such systems would help us in two ways. First, it would suggest both the extent to which we could make inferences about an individual's knowledge and abilities from his drawings and the kinds of inferences we could make. Second, an understanding of drawing systems would tell us a great deal about the nature of one powerful means of representation (pp. 1-2). 1 Beside drawing systems there are several pictorial devices to represent depth, such as, atmospheric perspective, cast shadow, transparency, diminution, and overlapping (Arnheim 1974: Willats 1979). 11 12 There are a number of drawing systems such as orthographic projection, horizontal oblique projection, vertical oblique projection, oblique projection, empirical (naive) perspective and artificial perspective. That will be explained in the next page. In children's drawings,“ X these systems evolve from simple to complex as children (i mature. For example, the simplest one is orthographic T projection and the most complicated one is perspective. Oblique projection lies between these two. In the work of artists, however, there is no explicit order in using - 3 drawing systems. For example, most Renaissance artists use i linear perspective but contemporary artists may use one or. more of these drawing systems in the same work. Willats (1985), defines drawing systems based upon 'primary' geometry and 'secondary' geometry. In primary geometry, the objects are drawn by projection rays which mark line junctions on the picture surface corresponding to the line junctions of the objects in the scene. In secondary geometry, the objects are drawn by lines corresponding to the lengths and directions of edges of the objects in the scene. W In terms of primary geometry (Figure 1), objects are projected by parallel rays which intersect the picture plane at right angles in both the vertical and horizontal directions. In terms of secondary geometry, vertical and horizontal 13 lines in a drawing stand for vertical and horizontal edges in the objects. Projected objects are shown as one face or one side of objects in this drawing system. Therefore, drawings in orthographic projection express only front, top or side faces of objects. The projected scene shows faces as the true size of shapes so that "there is no diminishing projected size with increasing distance" (Hagen, 1985, p. 62). Figure 1 Orthographic projection (Willats, 1984) Since orthographic projection has these merits engineers and architects make extensive use of this drawing system. Lewis (1963) said that this system is one of the naturalistically 14 Figure 2 Horizontal oblique projection (Willats, 1981b, Appendix viii) correct drawing systems. W In terms of primary geometry (Figure 2), objects are projected on the picture plane by oblique rays in the horizontal direction, and right angles in the vertical direction. According to Willats (1981), projected objects are foreshortened relative to the viewer in this drawing system. In terms of secondary geometry, the side face and front face of the object are added together. Orthogonal lines2 of the object are represented by horizontal lines in 2 The lines represent edges of the object receding into distance (Edgerton, 1975). 15 Figure 3 Horizontal oblique projection (Gioseffi, 1966, p. 190) drawing. Even though this drawing system represents orthogonal faces, a drawing in this projection will be rather ambiguous (Willats,1981). Seeing the projected drawing in Figure 3, 16 it is hard to recognize a box by itself. This point of view is the weakest aspect of horizontal oblique projection. This drawing system is used to emphasize the side and front views (Figure 3). In terms of primary geometry (Figure 4) objects are projected to the picture plane by oblique rays in the Figure 4 Vertical oblique projection (Willats, 1981b, Appendix viii) 17 vertical direction. Projected objects in this system are foreshortened relative to the viewer. Figure 5 Vertical oblique projection (Gioseffi, 1966, p. 190) In terms of secondary geometry, the top view of the object is added to the front view. This system also 18 represents orthogonal faces like horizontal oblique projection. However, drawings using this system tend to be ambiguous (Figure 5). This drawing system is suitable where perspective or oblique projection are inappropriate due to distortions (Figure 6). For example, under the use of oblique projection or perspective, 'cylindrical' objects such as cups or bowls are deformed (Figure 7). 4.—-—+ ------------ -————11-———-———— Figure 6 A cup and saucer in vertical oblique projection (Dubery and Willats, 1983, p. 28) 19 0!]. . !' Unlike perspective this system is created "intuitively" rather then "mathematically" (Gioseffi, 1966). In terms of primary geometry (Figure 8), objects are projected by an oblique angle in both the horizontal and vertical directions. ‘—--—-.--—-n--———--— - --- --—- ------------------ ------ -- 7. l? Figure 7 A cup and saucer in oblique projection (Dubery and Willats, 1983, p. 31) In terms of secondary geometry, top and side views of 20 an object are added to the frontal face. In this system, the front face shows true shape, however, the side and top faces are distorted because the edges of the side and top views are attached together by an oblique angle. Dubery and Willats (1983) mention that there is a paradox with oblique projection. In real life, if we see I "I r Figure 8 Oblique projection (Willats, 1981b, Appendix x) the front face as the true size, then we cannot see the side and top views of an object. Furthermore, when we see the front, side and top view of an object, then the front view no longer appears as a true size. However, oblique projection has the true shape of the front view: and also shows the top and side views of an object. In spite of this 21 paradox, this projection makes the clearest representations of the objects themselves, because it shows more invariant in angle, parallelism, shape, and relative size (Hagen, 1985), than the horizontal or vertical oblique projection and perspective are able to show. The advantage of oblique projection is that unlike orthographic, vertical or horizontal oblique projection, it expresses front, top, and side faces of an object. The opposite of the front face of an object is represented as the real size because orthogonal lines are parallel. This system is suitable to express solid objects because represented objects using this drawing system give us "a good impression of solidity" (Freeman,1980, P. 213). As I mentioned before,the disadvantage of this system is that cylindrical objects in this projection appear to be distorted (Figure 7). There is a variety of oblique projections (Dubery and Willats, 1983), such as, cavalier oblique (Figure 9), cabinet oblique (Figure 10), orthogonals diverging(Figure 11), and orthogonals converging (Figure 12). Cavalier oblique projection shows side edges as true lengths, whereas cabinet oblique projection represents sides edges as half their true lengths. Diverging side edges of oblique projection have a function of divergent perspective while converging side edges of it have a function of normal perspective. Therefore, we may define perspective as a kind 22 Figure 9 Figure 10 Cavalier oblique Cabinet oblique (projection projection (Dubery and Willats, 1983, p. 30) l - Figure 11 Figure 12 Orthogonals diverging Orthogonals converging projection projection (Dubery and Willats, 1983, p. 10) 23 Figure 13 Empirical perspective (Bunim, 1940, p. 248) of oblique projection. 'In general , however, oblique projection indicates cavalier or cabinet oblique projection. W There exist two kinds of perspective: 'empirical' and 'artificial' perspective. a) Empirical perspective (naive perspective) This system describes line direction of the real scene 24 Figure 14 Artificial perspective E: The eye point. CV: The central vanishing point Dotted line: The principal line of sight3 (Willats, 1981b, Appendix x) on the picture plane. Unlike artificial perspective, it is not based on mathematics and optics. In this system "the lines representing parallel edges tend to converge toward an 3 It is the shortest distance from the observer to the object in picture plane (Hull, 1943). 25 area rather than to a single point. ... the approximate convergence gives some inkling of depth" (Saenger, 1981, p. 4) (Figure 13). In the early Renaissance, empirical perspective was explained by "Workshop rules" such as "how to paint buildings" (Willats, 1979, p. 13). b) Artificial perspective This system is used for "mechanically correct reproduction" (Arnheim, 1974, p. 283) of the world as we perceive it. In terms of primary geometry (Figure 14), the rays converge to the 'eye point' or 'view point' to make the front face of an object and orthogonal lines of an object converge to the vanishing point on the horizon line: "an imaginary line determined by the eye level of an observer, staring straight ahead and standing on a horizontal plane" (Edgerton, 1975, p. 196). In terms of secondary geometry, the front face of an object is projected as the same shape, as shown in Figure 10, however, the orthogonal lines converge. In linear perspective, as shown in Figure 14, all of the faces are diminished or distorted: nevertheless, this system is "the most realistic way of rendering optical space" (Arnheim, 1974, p. 283). Even though this system reproduces a picture very close to what we see in the world, the picture represented by this system is different from the image projected by the eye or camera lens. Seeing very tall buildings, for example, we recognize that the vertical lines 26 of front faces of buildings converge toward a point somewhere in the sky (Arnheim mentions it as a third vanishing point). In perspective drawings, however, vertical lines of the front face of buildings remain in parallel on the picture plane (Arnheim, 1974). Summer! The characteristics of each drawing system and the representations of these systems are described. Orthographic projection represents true shape as it represents one side of an object. Horizontal and vertical oblique projection represent orthogonal edges, however, the side or top view are represented ambiguously. According to Dubery and Willats (1983), generally, orthogonal lines in oblique projection are made at an angle of 45 degrees on the picture plane. However, "horizontal and vertical oblique projections are simply the special cases of oblique projection in which this angle is either zero or 90 degrees" (p. 29). Projection of converging orthogonals is also one of the varieties of oblique projection. In perspective drawings,‘ orthogonal lines of objects converge to a vanishing point, therefore, perspective may also be a kind of oblique projection. According to the Saenger's findings (1981), children choose those drawings using oblique projection as the nest realistic representation. Hagen (1985) also mentions that the reason why amateurs, adults and children use 27 'orthogonal' (oblique) projection is to show invariant in the angle, parallelism, shape, and relative size. Denotation Systems Drawing systems explain how spatial relationships in the scene are transformed onto the picture surface. However, drawing systems alone cannot explain spatial relationships of the picture that correspond to real objects. Pictorial entities like regions, lines, and line junctions have to denote the entities of real objects such as faces, edges, and corners. Willats (1981a, 1981b, 1985, 1987) describes these characteristics as denotation systems. There are two kinds of dimensional systems contained in denotation systems (Willats 1981a, 1981b). One is "cross dimensional" in which region denotes volume, line denotes surface, and sometimes line junction denotes edge. The drawings based on this system are generally ineffective and ambiguous as representations. The other is an "intra- dimensional" systems in which regions denote faces, lines denote edges and line junctions denote corners. The drawings based on this system are unambiguous as representations. Younger children usually use the cross- dimensional system, while older children use the intra- dimensional system. Denotation systems will be described clearly in Chapter V according to children's developmental stages. 28 Organization Systems When three-dimensional objects are transformed on the surface, shape information will be organized according to local, absolute or modular descriptions (Willats, 1981b). In local descriptions, the object is isolated or remains unaltered when other objects are changed according to position or orientation. Absolute description concerns one single set of axes. This is not economical because ~-----~----- ? r ------......-..-- b Figure 15 The principle axes of a cube specification of every part of the objects has to be changed whenever the drawer moves. If we explain a part of an 29 object with this description, for example, its position has to be described "in terms of seconds, minutes and degrees of latitude and longitude" (Willats, 1987, p. 108). These descriptions are useful for explaining the objects which do not have any obvious principle axes. In modular descriptions, the specification of each smaller shape is concerned with that of a larger one. This means that "if the position or orientation of one of the components is changed ... only the specification of orientation of the principle axis of that component relative to the model axis of the next highest level has to be altered" (Willats, 1981b, p. 159). Therefore, these descriptions are economical, flexible and stable (Willats, 1981b). Organization systems can be explained by two kinds of coordinate systems (Willats, 1981b, 1987). The one is an object-centered description where the location is defined by the object itself based on the principle axes of an object (Figure 15). The other coordinate system is viewer- centered description: the location is defined by the viewer. This description integrates all local viewer-centered description which concerns each part of the scene for expressing the scene as a whole. The viewer-centered coordinate system refers to absolute description. Viewer-centered description cannot explain the orientation of each object because it depends upon the vanishing point. Therefore, this description is used when the distinct views of objects are emphasized. On the other 30 hand, the object-centered description can be used when the canonical form or easily recognizable form of objects are emphasized (Mar and Nishihara, 1978). If object-centered description includes information about the position and orientation of the object within the scene, it is called as scene-centered description (Victoria, 1982). A scene-centered coordinate system refers to modular description. Sometimes local object-centered description is combined with the scene-centered to suggest the orientations of objects within the scene (Willats, 1981b). Local object- centered description occurs when isolated components are described by their own principle axes. The Relationships of Drawing Rules with Language Acquisition, Creativity, Mental Image, Mbtor Skill and Cognition I E i .!. In language acquisition, the popular view was that children acquired language by imitation. Beginning in the 1960's it was argued that children had an innate capacity for language development by nature (Crystal, 1987: McNeill, 1970). There are a number of grammatical relations that already exist when words are combined. "The grammar of a language is a system of rules that determines a certain pairing of sound and meaning" (Chomsky, 1972, p. 125). 31 Children have the innate capacity to use their own styles of grammar. The system of rules used by children is different from those adults use. An example is as follows: Child: Nobody don't like me Mother: No, say "nobody likes me" Child: Nobody don't like me (eight repetitions of this dialogue.) Mother: No, now listen carefully: say "nobody likes me" Child: Oh! Nobody don't likes me (McNeill, 1970, pp. 106-107) Through this example, we recognize that children do not learn language by imitation and their grammatical styles are used in their own way. , When children recognize the order of constituents in their native language, they extend their knowledge far beyond their experience and, in fact, they are aware that a lot of "the data of experience" are ambiguous and insufficient (Chomsky, 1972). Children, therefore, make many mistakes using language rules.' Willats (1977b, 1979) also argues that children learn to draw the real world not by imitation but by the use of drawing rules. Like children who acquire language rules by mistakes, they also learn drawing rules through mistakes. Even though acquisition of drawing rules is similar to that of language rules, there are some differences between the language and drawing rules themselves. The rules of 32 language are established by "convention" while the rules of drawings are based on "optics." Furthermore, language rules consist of "discrete units" while drawing rules are based on "continuous relationships" (Willats, 1981b). Unlike language, pictures cannot explain represented objects literally. Through drawing rules, depicted objects only tell us about what they denote. Creating The term creativity is defined as putting some selected past experiences together into "new ideas," "new patterns" or "new products". Furthermore, creativity makes something unique, original, or different (Smith, 1966). Creativity is nurtured by an open mind to problems. Memorized facts and predetermined concepts cannot,however, develop creativity. Creativity is not a "given talent" and all people have it innately (Smith, 1966). Lowenfeld and Brittain (1982) state "If it were possible for children to develop without any interference from the outside world, no special stimulation for their creative work would be necessary (p. 8)." Even though all children have some creative potential, there is a great difference in degree (Smith, 1966). Children acquire drawing rules not by creative processes but by making mistakes. Creativity, however, depends on drawing rules. Seeing a picture, we can ask three questions - what kinds of drawing systems are used here: what do the line, line junction and region in the 33 picture stand for: and, how is the picture organized by using object-centered, scene-centered or viewer-centered coordinate systems. Willats (1981b) calls these "formal structures". The formal structures carry new ideas in a picture. Mental_lmass According to Piaget, mental images are 'instruments of knowledge' and depend on 'cognitive functions'. They occur from imitation and are composed of internalized reproductions operating without the imaginal objects. In other words, they "act as symbolic instruments of thought, making it possible to reconstruct the past (reproductive image) and to anticipate the future effects of actions and transformations (anticipatory images)" (Pulaski, 1980, pp. 114-115). As I mentioned in the Introduction, one of the traditional theories is that young children draw pictures that are dependent on mental images. There exist, however, differences between the shape of recognized objects and represented objects. Young children, for example, know about objects very well, and they cannot depict them as they are. Studying acquisition of drawing rules, Willats found "With ideal performance, the finished drawing would perfectly reflect the mental image or picture description already available in the child's mind before the drawing 34 process begins" (Willats, 1981b, p. 177). This means that the drawing process is totally different from mental image. Willats states that "the drawing is seen as three- dimensional rather than two-dimensional, and a frame of reference is established for the pictorial image" (Willats, 1981b, p. 181) instead of mental image. That is, children can draw within the spatial system of the pictorial image after the first few marks are drawn. Willats argues that children do not need pre-established mental images to draw. 89:91.88111 Drawing rules such as drawing systems, denotation systems and organization systems are the descriptions due to spatial relationships in the picture. On the other hand, the motor skill used in drawing is a description due to "the controlled spatial and temporal patterning of movements: a skilled response is one which is executed both rapidly and accurately" (Connolly, 1970, p. 10) in the picture. The developmental stages of motor skills are concerned with how children acquire accuracy when trying to draw the shapes of objects. When children draw objects on paper, their motor skill depends on "kinaesthetic sensitivity" which is "necessary to discriminate displacement of the hand from the correct position, and to monitor the direction and extent of the movement in progress (Laszlo and Broderick, 1985, p. 367)." Motor skills contribute to drawing production. If, for 35 example, lines which appear in drawings are clumsy, the drawings do not carry on representational information correctly. The shape of the line has a lot to do with the meaning of a drawing. Therefore, drawing rules as well as motor skills contribute to drawing production. Cognition "Piaget believes the human organism tends to organize reality into coherent and stable patterns at certain points of cognitive development which are structurally different from those at other points and can be analyzed as such" (Hardiman and Zernich, 1980, p. 12). According to Piaget and Inhelder (1967), there are three kinds of conceptual notions of space -- topological, projective and euclidean -- referring to children with ages of 3 to 8. Projective and euclidean space are more complex than topological: however, these are derived from topological space at the same time ("unison") interdependently. Topological space (up to 4 years) expresses intrinsic properties of an object, and does not express the relationship between objects. Projective space (4-7 years) expresses general features of the objects and the objects relationships from the point of view of a viewer. Euclidean space (7-8 years) expresses an object placed 36 in a viewpoint, therefore, the object contains its position and orientation. Piaget's cognitive developmental stages of space in children's drawings are only concerned with organization systems, such as local, absolute and modular descriptions. He does not explain how children develop the notion of denotation and drawing systems. F Projective space explained here as well as euclidean space corresponds to a modular (scene-centered) description because children's drawings represented by projective space do not use one single set of axes. In order to differentiate between projective and euclidean space, some explanations based on drawing and denotation systems are needed. Piaget's theory concerns only children, however, drawing rules concern children and adults. All artists use drawing rules. Therefore, the acquisition of drawing rules to explain cognitive development is more detailed than Piaget's theory. CHAPTER IV DRAWING RULES IN PROFESSIONAL ARTIST'S WORKS Brief Discussion of the Use of Drawing Rules and Analysis of Selected Art Works from Ancient to Modern Times Ancient painting. Ancient painting covers the periods from Palaeolithic art through Roman art. "In general, the trend of the evolution of space as judged from the form of the figures is Figure 16 Old stone age cave painting, about 20,000 B.Cq (Janson & Janson, 1957, p. 10) 37 38 from conceptual to optical representation" (Bunim, 1940, p. 12). Conceptual representation ignores the visual impressions of the object. In Palaeolithic painting, any part of the surface of the wall or the ceiling becomes the picture plane. Objects are represented conceptually, for example, an "animal has a profile body and head and frontal eye and hoofs". The two- dimensional picture plane is emphasized by "giving the impression of a flat two-dimensional form" which combines the profile and frontal views (Ibid. pp. 14-15) (Figure 16). It is drawn by scene-centered description because the direction and position of each animal are depicted. In Egyptian painting, unlike that of the Palaeolithic, the picture plane is a constructed surface. Two-dimensional space is emphasized and all objects and figures are represented conceptually because Egyptian people draw them "for all eternity, the magical substance of men and gods, and their vital activities" (Harris, p. 14). In order to express depth on a flat surface, the picture plane is divided into parts: for example, the lowest part is the foreground (Ibid, 1974). 39 Figure 17 An E tian craftsman at work on a olden s hinx, about 1400 B.C.. (Gombrich, 1972, p. 45) The painting (Figure 17) is represented by orthographic projection because all of objects express frontal features. The craftsmen are represented by a profile view of the head and trunk, and a frontal view of the eye and shoulders.' The objects in the upper sides are isolated in relation to the whole picture, and the objects in the foreground are 40 depicted on a line. These elements, therefore, are transformed by an object—centered description. Mesopotamian and Assyrian painting use a similar method of representation as that used in Egyptian art. However, in Assyrian art, figures are represented by complete profile even though the eye still remains frontal (Bunim, 1940). Figure 18 The warrior's leavetaking, about 500 B.C. (Gombrich, 1972, p. 51) 41 In Greek art, paintings are usually drawn on the surface of the vase. They also do not emerge from the Egyptian methods such as profile figures having frontal eyes. In Figure 18, either side of the figure's body and shield are drawn in exact profile. This means that this figure is a non- conceptual or optical figure. The three - people are drawn in orthographic projection. This picture can be explained by a scene-centered description because each person's position and orientation are depicted within the scene. ' i In the Hellenistic and the Roman period, artists expressed distance by drawing distant things small and near things large. Although they still do not use "the laws of perspective" (Gombrich, 1978), they have a sense of three- dimensional space. "The diminution of the objects in the Roman landscape gives the impression of recession, but the change in scale is not proportionate to the distance from the spectator" (Bunim, 1940, p. 176). The lines of the side view of the objects are converging as receding parallel lines (Figure 13). In Figure 19, the horizontal lines of the side view of buildings incline downward, however, they do not converge at a vanishing point. Buildings are drawn by empirical perspective and can be explained by scene-centered description because each object has its orientation and position within the scene as a whole. 42 III"; rt. 43.9%“va 34.1.59! ZHIJ. I’D»; V Figure 19 , 1 B.C., aintin Roman wall p. 31) 1957, (Janson & Janson, Figure 20 Miniature from the Codex amiatinus, about 700 A.D., (Rice, 1967, p. 100) Medieye; painting Many medieval paintings are expressive of religious concepts which determine the pictorial form. The emphasis on this period is symbolic rather than realistic representation. Therefore, three—dimensional space is not an important problem in this period. 44 In Figure 20, objects are depicted by oblique projection, however, side edges of some objects in this picture are divergent: for example, a chair, a foot stool, and books. It is expressed by a scene-centered description because each object has orientation and position. Even though medieval artists are not interested in depicting the realistic world, objects are drawn three-dimensionally. a R '58 e ’ 'n RenaiSsance artists are interested in artificial perspective in order to represent optical space. The side [d edges of all the objects converge to one point (the vanishing point). Therefore, the positions and orientations of the objects within the scene are ignored. Even though the shape of the objects were learned directly from nature, the forms are organized intellectually by mathematical rule. A composition consisting of artificial perspective is symmetrical (Berkman, 1949). Therefore, space by artificial perspective is monotonous and rigid. "The first known description of artificial perspective is by Alberti, in his Della Pittura Written in 1436" (Dubery and Willats, 1983, p. 56). 45 Figure 21 The Last Suppep, Leonardo Da Vinci (Berkman, 1949, p. 73) In Figure 21, the vanishing point of this picture is located behind the head of Jesus Christ, therefore, all orthogonal lines converge to this point. This vanishing point is placed on the middle of the picture so that the composition is symmetrical. Because this picture consists of one single set of axes, it is explained by viewer- centered description. 46 Frpm 16th eep pzy pp Realism 9 Artists do not use artificial perspective during these periods. In order to express more closely the optical world, they employ two-point perspective. Two-point perspective makes space expandable to directions both left and right, while one-point perspective creates deep space in orthogonal direction. Berkman (1949) explains both r perspective systems with diagrams (Figure 22 and 23). Figure 22 one-point perspective (Berkman, 1949, p. 88) Two-point perspective also uses a horizontal line like one- point perspective, however, it has two vanishing points (Figure 24). It was developed in the 16th century. Figure 25 is made by the use of two-point perspective. Even though, we cannot see two vanishing points in the picture, orthogonal lines are converging to them. Unlike Figure 21 the composition is asymmetrical so that the left side of the space is expressed extensively. 47 Figure 23 Two-point perspective (Berkman, 1949, p. 88) Nb?- Figure 24 Two-point perspective v.p.: Vanishing point H.L.: Horizontal line v4h HJ—. 48 Because this two-point perspective was especially useful for expressing opened space such as "vast stretches of terrain, the beauty of the countryside, nature in all its moods and glory" (Berkman, 1949, p. 97). Figure 25 Wedding Feast, Peter Brueghel (Berkman, 1949, p. 85) Impressionism Impressionists gave up the use of artificial perspective in favor of reliance on "direct sensations" (Willats, 1979), that is, intuition, and visual phenomena Orthographic projection Figure 26 La Promenade au Singe, George Seurat, 1885 (Keller, 1980, p. 225) 50 Vertical oblique projection Figure 27 Nude in a Bathtub, Pierre Bonnard, 1935 (Dubery and Willats, 1983, p. 27) rather than intellectual percepts. All drawing systems (Figures 26, 27, 28, 29, 30) are used to express the shapes of objects excepting artificial perspective in this period. Impressionists transform objects by scene-centered description because the orientation and position of the 51 objects are depicted in the picture. Unlike other impressionists, Cezanne creates three-dimensional space by new methods. In order to make three-dimensional depth, Cezanne uses the picture plane as the front face of the box. Horizontal oblique projection Figure 28 Landscape near Chaponval, Camille Pissarro, 1880 (Keller, 1980, p. 82) 52 Oblique projection Figure 29 Camille Pissarro, 1883 The Pork-Butcher, p. 83) 1980, (Keller, 53 Empirical perspective Figure 30 Boplevard Montmartre at Sunset, Camille Pissarro, 1987 (Keller, 1980, p. 85) Loran (1963) explains it by a diagram (Figure 31). Cezanne rearranges space of the real world to pictorial space plastically. 54 -------------------.’ Figure 31 Negative space and the ‘picture box' (Loran, 1963, p. 17) Comparing the photograph of the motif (Figure 33), Figure 32 explains how Cezanne eliminates perspective. Orthogonal direction of the left side of the photograph is represented as frontal direction in the picture. The edge of the road is represented by horizontal and vertical directions. Rising up the size of the distant hills, a "funnel-like spatial effect" (Loran, 1963) made by 55 artificial perspective is eliminated. Houses are represented by oblique projection. This picture is a scene- centered description because each object has relationship with the picture as a whole. Figure 32 Landscape at La Roche-Guyon, Paul Cezanne (Loran, 1963, p. 46) 56 Figure 33 Photograph of the motif (Loran, 1963, p. 46) Cubism Cubists eliminate the representation based on a particular viewpoint or a particular moment. In order to get some knowledge of the objects, Cubists study each object moving around it without establishing a particular distance. 57 They try to represent objects in themselves instead of representing illusion of the real world. As we see in the Figure 34, Gris expresses parts of the object as a cylinder and as a globe. Gris says that ‘I begin with a cylinder and create an individual of a special type: I make a bottle-- a particular bottle -- out of a cylinder' (Fry, F. 1966, pp. 162: He quotes from D.H. Kahnweiler: Juan Gris, New York 1947, p. 138). This means that the bottle which Gris represented is not a general bottle but a specific bottle which Gris sees. In Figure 34, the table and.other objects are drawn by vertical oblique projection. For example, depicting cups by vertical oblique projection, the intrinsic nature of cups is explained well. A large circle denotes a saucer, a small one denotes the bottom of a cup, a small cylinder in the lower part of a cup denotes as a connective part with the bottom of it. A globe in the upper side of the cup denotes the inside of it (Figure 35). When we see the inside of a cup, in general, we cannot see the bottom of it, and when we see the bottom of the cup then we cannot see the inside of it. A real objects, like the newspaper in the picture, suggest orthographic projection "(a non-spatial system)" (Dubery and Willats, 1972). This picture is made by a mix of two systems, vertical oblique and orthographic projection. It is a scene-centered description because each object has orientation and position in the scene. 58 Figure 34 Breakfast, Juan Gris (Dubery and Willats, 1972, p. 93) Figure 35 A diagram of metres; (Dubery and Willats, 1983, p. 113) 6O Figure 36 Mystery and Melancholy of a Street, Giorgio de Chirico (Janson, 1969, p. 524) 61 Surrealism Creating-a mysterious and dreamlike world, Surrealist painters try "to reveal a world more real than visible reality, in other words, the reality behind appearances" (Haggar, p. 331). They try to seek new meanings from illogical combinations of objects such as an encounter of a sewing machine and an umbrella on an operating table (Ibid., r 1962). In order to eliminate general characteristics of the objects, Surrealist painters put them into incongruous space. In Figure 36, Chirico uses oblique projection and !_ artificial perspective to represent the objects. The two buildings have their own vanishing point, therefore, this picture denotes two different views of infinite space together on one picture plane. By depicting the wagon by oblique projection, one convergence of the right side of the building is restrained. Using mixed systems, Chirico gives us new meanings which we cannot feel in the ordinary world. This picture is explained by local viewer-centered description with local object-centered description because each building has its own vanishing point and the wagon is isolated in the scene. Oriental_art Unlike western art, oriental artists were not interested in artificial perspective. They usually used vertical oblique, horizontal oblique and oblique projection (Willats, 1977b : Dubery and Willats, 1983). 62 Figure 37 Marriage of King Khusrau and Shirin, 16th century (Berkman, 1949, p. 31) In Figure 37, this Persian painting is made by vertical oblique projection. The room which king Khusrau and Shirin 63 are sitting looks like a part of the wall. Actually, Persians "regarded painting primarily as decoration" (Berkman, 1949, p. 33). Therefore, Persian artists were interested in expressing design pattern rather than expressing three dimensional space. This picture is explained by scene-centered description because every object has its orientation and position in the scene. Figure 38 Mountain Village, Kung-wang Huang (Dubery and Willats, 1983, p. 23) 64 In Figure 38, a Chinese painter expressed a landscape by horizontal oblique projection. This picture is compared with a landscape by Pissarro (Figure 28), which is also drawn in horizontal oblique projection. Comparing the two pictures, each artist represents a different feeling. The Chinese painter expresses sublime scenery, on the other hand, Pissarro expresses ordinary scenery which we encounter frequently in the countryside. Therefore, we can see that drawing rules help artists to construct their feelings. This picture also is explained by scene-centered description. Figure 39 A part of Scholar's Table, artist unknown, 18th century (Munsterberg, 1968, p. 211) 65 A still life (Figure 39) drawn by a Korean artist consists of oblique and vertical oblique projection. Expressing rectangular objects (books) by oblique projection, the artist emphasizes the solidity of the books. Depicting the bottles by vertical oblique projection, the artist expresses the intrinsic nature of them. This picture is a scene-centered description because each object has relationship with others within the scene. Findings In the previous section, artists' use of drawing rules throughout history have been examined. Palaeolithic to Greek painters used orthographic projection in order to express flat space which denotes the conceptual world. Hellenistic and Roman painters used empirical perspective in order to express a sense of three-dimensional space which denotes the optical world. Medieval painters used oblique projection in order to express two-dimensional space which denotes the symbolic world. Painters from the Renaissance to Realism used artificial perspective in order to express three-dimensional space which denotes the optical world. Impressionists used all drawing systems excepting artificial perspective to denote the intuitive world which is the sensational moment inspired by the objects. Cezanne and other modern artists used drawing systems to express pictorial space rather than realistic space. The space in some of Cezanne's paintings denotes a firm and solid world. 66 The space in Cubist paintings denotes the living world. The space in.Surrealists' paintings denote an imaginative world. In oriental paintings, Persian artists used vertical oblique projection to express the two-dimensional space which denotes attributes of decoration. The artists in Far East Asia used horizontal and vertical oblique and oblique projection to express three-dimensional space which denotes sublime scenery and intrinsic nature of the objects in the living world. The findings from some selected artists' paintings are as follows: The same drawing systems are used for representing both two and three dimensional space. For example, Medieval artists used oblique projection for representing flat space, on the other hand, Cezanne used it to represent three-dimensional space. The same drawing system is used to represent real objects or the picture itself. For example, Cubists used vertical oblique projection to depict the object itself, however, Persian artists used it to depict objects as a part of the decoration of a wall. The same drawing system is used for representing 67 different feelings of landscapes, for example, the landscape of Pissarro (Figure 28) and that of a Chinese painter (Figure 38). Impressionists demonstrate that all drawing systems can be used for representing three- dimensional space, not only artificial perspective. Emphasized characteristics of drawing systems can create new three-dimensional space. For example, using the characteriStics of oblique projection, Cezanne makes firm and solid space by avoiding the funnel-like spatial effect made by perspective. Drawing systems represent not only the living world but also conceptual, symbolic, and dream- like worlds. The drawing systems as seen through art history, denote some specific world which artists intend to express. For example, Renaissance painters used artificial perspective to denote the optical world. Denotation systems help drawing systems and allow the pictures be understood more clearly, because drawing systems alone cannot explain spatial relationships of the picture that 68 correspond to those of the real objects. For example, the cups in Figure 35 are made by cylinders and globes. Large cylinders denote the main body of the cups and the globes in the upper side of the cups denote the inside of the cups. Historically, most artists transformed objects from objects themselves. Only Renaissance painters transformed them from a fixed point of view of the objects. CHAPTER V DRAWING RULES IN CHILDREN'S DRAWINGS Acquisition of Drawing Rules Willats (1987) mentions that the development of drawing ability in children can be described by the acquisition of three kinds of rule systems such as "drawing systems," "denotation systems," and "organization systems." This chapter will describe how children acquire these drawing rules. Willats (1977a) found that children, age 6 to 17, could use drawing systems -- orthographic projection, vertical and horizontal oblique projection, oblique projection, naive perspective and perspective -- correlating mean age with complexity of the systems used. Children, however, do not acquire these systems with smooth transitions. Whenever children progress from one system to the next, there exists an intermediate stage which is not explained by drawing systems but can be explained by denotation systems. Excluding perspective, there are six transitional stages in children drawings (Willats, 1981a) (Figure 39): Class 1 - pre-single aspect, mean age of 5.1: Class 2 4 single aspect ( orthographic projection ), mean age of 6.6: Class 3 - multiple aspect, mean age of 7.9: Class 4 - 69 70 (Class 1) _ (Class 2) .F____,, ’ J____.l (Class 3) (Class 4) (Class 5) (Class 6) Figure 40 Six Transitional Stages in Children Drawing (Victoria, 1982) 71 horizontal and vertical oblique, mean age of 9.6: Class 5 - near oblique, mean age of 10.5: Class 6 - oblique, mean age: 11.6. Children can learn perspective from the environment or explicit teaching ( Willats, 1981b, 1984: Lowenfeld and Brittain, 1982 ). Willats (1981b) states that in order to draw in perspective, children need to acquire the rule that 'orthogonals converge to a vanishing point' or to use viewer-centered description through direct observation. Figure 41 et 0 awin Portra' , Albrecht Durer (Dubery and Willats, 1983, p. 68) 72 p.----.----o--. O (a) (b) (d) Figure 42 One of the principles of artificial perspective of Alberti. (Edgerton, 1975, p. 45) Making more exact perspective drawings, children have to learn to use some "mechanical device" such as a drawing machine (Figure 41) or to use "a geometric method of construction" (Willats, 1981b) such as one of the principle of linear perspective of Alberti (Figure 424). 4 It explains how to operate distance point to the picture. (a) First of all, he divides the vertical line (as same as the height of a man) into three parts and then divides the horizontal line into several parts of the same length as 73 Willats calls class 2, 4 and 6 main developmental stages and class 1, 3 and 5 intermediate stages. Children acquire these drawing systems with "mistakes" which are the mistakes in the use of drawing rules rather than the mistakes in copying the appearance of the scene (Willats, 1981a, 1981b). Class 1 (pre-single aspect) is based on 'topological' transformation as 'an object as a whole.‘ In this class line denotes surface and region denotes volume. The objects in this stage are explained by local object-centered descriptions because objects are described by their own principle axes. Class 2 (single aspect) can be explained in three ways. First, a square means 'an object as a whole' like in class 1. Second, a square can be regarded as an "isolate face." Region denotes a face. Considering a single face, we can suppose that it can be explained by two kinds of descriptions. One is that we can suppose it is a face of an object-centered description of the object: in this case, the rest of the faces are occluded. The other is that we can suppose it is a true shape of the front face of the object in relation to the viewer's viewpoint. In this case, the part of the vertical line. (b) He calls the highest point in the vertical line as a distance point and from there draw diagonals to the line divisions in the horizontal line. (c) Establishing how far the picture away from the distance point, he inserts a vertical intersection through the diagonals at such a proper distance. (d) The lines pass on to "the vanishing point view" are called "transversals". 74 object's location is "normal to the viewer's line of sight" (p. 178). Third, a square is regarded as an orthographic projection. Region denotes a face, lines denote edges and faces, and junctions denote corners and edges. This projection is explained by scene—centered descriptions, that is, modular description (Willats, 1981b). Through this projection, we can recognize the position and orientation of R the objects described in drawing. Class 3 (multiple aspect) consists of a combination of faces. Regions denote faces and lines can be denoted as the boundaries of regions. Multiple aspect is explained by "a 9: local, two-dimensional, object-centered description" (p. 259) because each face in this class only contributes to make a two-dimensional shape as in pattern. Therefore, the drawings in multiple aspect are insufficient to represent three-dimensional objects (Willats, 1981b). Class 4 (horizontal or vertical oblique) can be described in two ways. One is that two squares may denote faces as in class 3. The other can be regarded as horizontal or vertical oblique projection. In these projections, regions denote faces and some lines denote edges while some lines may denote faces (Willats, 1981b). The drawings depicted by this system represent three- dimensional objects by combining the side and front face of the object or the top and front views of it. This type of drawing is explained by object-centered descriptions. Class 5 (near oblique) consists of a mixture of 75 isometric projection and horizontal oblique projection. The reason that children draw the top face as a diamond shape rather than as a square is that they draw the object in relation to scene- centered descriptions (Willats, 1981b). Using horizontal oblique projection to draw two side faces, children used an incorrect 'T junction' which denotes a vertex incorrectly. The T junction is usually used to represent partial occlusions (Figure 43). :J. 9 ‘1)“. T junction. Incorrect T junction. Figure 43 T junction and Incorrectly used T junction Near oblique drawings present the place where children see an object, such as "above eye level" (Willats, 1981b). The drawing in this class represents that top view of an object as expressed by scene-centered descriptions. On the other hand, the side view of an object is expressed by object- centered descriptions. Therefore, this kind of drawing is incorrect. In this class, regions denote true faces, lines denote edges and junctions denote vertices. Class 6 (oblique) drawings represent unambiguous and 76 coherent corresponding features in the scene. Children, in this class, represent objects better than in any other class of drawings. The drawings of this class are expressed by object-centered descriptions. In detail, they are described by scene-centered descriptions because the orientation of the object is explained. In drawings of the earlier stages denotation systems are "incoherent" and "ambiguous" (Willats, 1981a). In class 6, regions denote faces, lines denote edges and junctions denote vertices. Children arrive at these drawings "after a long and complex learning process" (Willats, 1981a, p. 29). Generally, young children's drawings are usually based on object-centered description: and as they get older, their drawings are based on scene-centered descriptions. Later, their drawings are based on viewer-centered description (Willats, 1981b, 1987). The reason is that scene-centered description is more complicated than object-centered and viewer-centered description is the most complicate one. However, Victoria (1982) found that most children used object-centered descriptions rather than viewer-centered descriptions in an experiment where children, aged 6 to 12 years, were asked to place and draw both familiar and unfamiliar rectangular objects in the most suitable position. When children transit from object-centered to viewer- centered descriptions, they make many mistakes. In order to avoid these errors, children have to learn to place the 77 object in proper positions, and they have to recognize "object- or scene-centered descriptions of the scene, the picture and the pictorial image, and viewer-centered descriptions of the real object and the depicted object" (Willats, 1981b, p.266). Willats (1981b) states that children make use of viewer-centered descriptions after 10 years old, however, even the majority of children aged 12 still use object- centered description. Willats also states that naive perspective (empirical perspective) as well as oblique projection is explained by object-centered description because it implies a direction of view (the convergence of orthogonals) which is different to that employed by linear perspective. Naive perspective is also explained by scene- centered description because orientation of objects are represented. In the drawing process, children acquire denotation systems from cross-dimensional to intra-dimensional. Through this transition they make many mistakes. ~ Children using three kinds of systems - drawing systems, organization systems and denotation systems - make many errors. However, through these errors, they acquire better representations, that is, as they get older, they "wlearn more complicated drawing rules. Using each set of drawing rules, children provide new insights and new knowledge for further action. Thus children learn to draw real objects freely and easily in 78 their own ways. Analysis of Selected Drawings According to the Various Drawing Rules Here, I will examine how children use drawing rules in some selected drawings. Figure 44 Drawing in orthographic projection (Keiler, 1951, p. 31) Figure 44 was drawn by a 9 year old child based on his dish washing experience. This child wanted to explain what kind of work he did, therefore, the child did not necessarily need to depict objects three-dimensionally. 79 Using orthographic projection, he draws them conceptually as the Egyptian painter did. Depicted objects denote the frontal face of objects. Objects are transformed by object- centered description because each object's position and orientation are not depicted. Figure 45 Drawing in orthographic projection (Mendelowitz, 1963, p. 73) Figure 45 was drawn by a 10 year old child. Unlike Figure 44, it is represented optically -- it seems that the child observes the scene apart from proper distance where we can see only the frontal faces of the objects. Even though 80 Figure 45 is depicted in orthographic projection, it is represented more realistically than in Figure 44. We can find this same method of painting in Figure 26. Depicted They are objects denote frontal faces of real objects. transformed by scene-centered description because each object in the scene is not isolated. .1? I’: i- ‘4?’ I 'u. i . .. £1 )-' . - ' . 9“ ‘c . . , “ 0 VI? :- it: 1". \v -- .. . ~ . it.“ = '5. 1 ‘*'- Fm' ..r. - ~4 "’_ -~§ 9: --r - r' 91’: i “‘._‘_ v.“- _- u - 3' “ ‘ 1 . ."N; filial. “' ;‘ ,. s45" . . 59 I : 5:31..- ' . 1 » " 2),-,9, ' sat-3;... ; r - «Hg/Eighfing '- a; ' ‘ .. '-"':-’. ' ‘ r . w I. J ' .; 5 5‘ E. . ... ..b .¥' ‘ I Figure 46 Drawing in vertical oblique projection (Viola, 1944, p. 196) Figure 46 was drawn by an 8 year old child. expresses conceptually and the depiction is by vertical oblique projection. This picture is represented two- dimensionally like a map, however, the child tries to represent two sides of the buildings. denote the frontal and top sides of the real objects. real objects are transformed here by object-centered The child The depicted objects 81 description because each object's orientation and position are ignored. Figure 47 Drawing in horizontal oblique projection (Lowenfeld, 1955, p. 161) Figure 47 was drawn by a child between 12-14 years old. This picture is drawn in horizontal oblique projection. The child does not express distant objects as diminished sizes as Cezanne did. Therefore, distant houses are drawn as large as the houses in the foreground. This child represents three-dimensional space firmly and solidly. Depicted shapes denote frontal and side faces of the real 82 objects. They are transformed by scene-centered description because orientation and position of the objects are represented in this picture. Figure 48 Drawing in oblique projection (Alexander and Carter, 1958, p. 15) Figure 48 was drawn by a fifteen year old child. Depicted by oblique projection, orthogonal lines of objects are represented. Distant objects are drawn smaller than foreground objects so that this picture expresses three dimensional space. However, distant objects are drawn without spatial differences among them, therefore, as 83 Cezanne did, this child avoids making infinite space. The depicted.objects denote frontal and orthogonal faces. This picture is transformed by scene-centered description because the direction and position of objects are depicted. Figure 49 Drawing in empirical perspective Figure 49 was drawn by a twelve-year-old child. Orthogonal lines of the side faces are converging downward, however, they do not converge to a vanishing point. Each object has its own vanishing point. It emphasizes optical space. Depicted shapes denote frontal and orthogonal faces 84 of real objects. Objects are transformed by scene-centered description. \ . ’ ' l ‘ | N. 1 y. ' “‘,b:.hnj“:"‘ ’ I .' Figure 50 Drawing in artificial perspective (Cane, 1951, p. 151) 85 Figure 50 was drawn by a sixteen year old child using artificial perspective. Except for the distant buildings, the orthogonal lines of the objects are converging to a vanishing point. The space made by distant buildings intercepts the funnel-like spatial effect in the foreground. This picture also emphasizes optical space. Depicted objects denote frontal and orthogonal faces of real objects and some of them also denote top faces. The objects are transformed by viewer-centered and scene-centered description. Findings Previously, I examined how children use drawing rules in their drawings. Willats (1981a) gives us the mean age of children's developmental stages. They learn orthographic projection at the mean age of 6.6: horizontal and vertical oblique projection at the mean age of 9.6: oblique projection at the mean age of 11.6. Through examination of selected children's drawings used in this study, the findings are as follows: The child of age 10 still uses orthographic projection. The 8-year-old child uses vertical oblique projection. This child uses it earlier than the mean age. A child, aged between 12-14 years of age, uses horizontal oblique projection even though the child can use oblique projection. 86 A child of age 15 uses oblique projection while another child of age 12 uses empirical perspective. Children represent well what they express depending on the drawing systems used. For example, in Figure 44, we can recognize well the child's experience in dish washing even though the picture is not represented three-dimensionally. In Figure 48, the child expresses firm and solid three- dimensional space very well. If it were represented by empirical or artificial perspective, we could not feel this kind of space because of the characteristics of linear perspective which create a funnel-like spatial effect. The child can represent optical space as in Figure 49 without knowing the laws of artificial perspective. All drawing systems can express three dimensional space depending on the child's ability. Children can express conceptual and map space as artists express conceptual, symbolic and dream world like space depending on the drawing systems 87 used. Usually children transform objects from objects themselves rather than from appearance offered from a fixed point of view. It is shown that children also represent the real world freely depending on drawing rules as artists do. CHAPTER VI DISCUSSION OF THE FINDINGS Examining artists' and children's drawings or paintings, I have found some similarities and differences. The similarities are as follows: Children and artists use drawing rules freely and properly to represent what they want to express about the real world. In order to express three-dimensional space, they depend on artificial perspective, and on all types of drawing systems. Each drawing system does not exist as an intermediate developmental stage to learn artificial perspective. Both artists and children express the real world three- dimensionally and two-dimensionally on a two-dimensional surface. Both know how to get rid of funnel-like spatial effects, depicting distant objects as large as those in the foreground. Both use drawing systems to express the living world as well as the conceptual, symbolic and dream-like world. Artists and children transform real objects primarily using scene-centered rather than object-centered or viewer-centered description. When mixed drawing systems are used in a picture, both children and artists have to know what each drawing system 88 89 denotes in the picture. There are differences between artists' and children's art works. Children make drawings by intuition because they do not plan how to draw them. On the other hand, artists draw with intention. For example, Roman artists tried to express three-dimensional space to denote the optical world using empirical perspective, however, Medieval artists went back to two-dimensional space using oblique projection in order to denote the symbolic world. Another example is that Cezanne makes three-dimensional space plastically using oblique projection to eliminate the effect made by perspective. 1 Children are not affected by culture or tradition, however, artists are affected by them. For example, the Egyptians made drawings to express the eternal and magical world. In children's drawings, the most complicated drawing projection is artificial perspective because when children use this projection they make many more mistakes than when they use others. In artists' works, they create more complicated concepts of space using mixed systems, for example, the paintings of the Cubists and Surrealists. CHAPTER‘VII CONCLUSION Through the review of literature, several theories about how children draw real objects have been enumerated. Two of the theories state that young children draw what they know and older children draw what they see. However, with the introduction of drawing rules by Willats, those theories seem less plausible. I have noted the characteristics of drawing rules such as drawing systems, denotation systems and organization systems in Chapter III. Through these characteristics, we can recognize how the real world is transformed to the picture surface clearly. Each drawing rule serves a different function in the picture. Drawing systems explain how spatial relationships in the real scene are transformed to the picture. Denotation systems explain how pictorial entities denote the entities of real objects. Organization systems explain how shape information is organized onto the picture surface. The way in which children and artists express the real world in their drawings has been clarified. Artists and children represent not only what they know but also what they see depending on certain drawing rules. Evidence clarifies how drawing rules help us to 90 91 recognize the nature of representation in both the drawings of artists and children. Both of them use the same drawing rules to represent the real world. It has been depicted in both two-and three-dimensional space because the real world does not only indicate the optical world. It can be conceptual, symbolic or a dream-like world. Artificial perspective is only one of the devices emphasizing diminishing distance because all drawing systems can represent three-dimensional space. Using mixed drawing systems, artists create more complicated concepts. This study shows that drawing rules are very significant in order to express the nature of space in pictures. f Both children and artists acquire the use of drawing \// rules without explicit teaching. In this study, there are three limitations of the methodology. First, because this study compares drawing rules between artists and children, I omitted the rules found in the transitional stages of children's drawings. Second,I selected only certain drawings and paintings from real artists and children which have demonstrated the drawing rules clearly. Third, the use of drawing rules only within figurative art works were examined. In conclusion, it is important to consider the findings for art education. Children have an innate capability to 92 express the real world by utilizing drawing rules. They can create complex space in their use of drawing rules. For example, in Figure 50, this drawing used artificial perspective in the foreground to express receding distance. However, distant buildings are not diminished among them. Therefore, we can see not only orthogonally deep space but also firm and solid space throughout the picture. Lowenfeld and Brittain (1982) mention that "if it were possible for children to develop without any interference from the outside world, no special stimulation for their creative work would be necessary" (p. 8). They also comment that "whenever we hear children say, 'I can't draw,‘ we can be sure that some kind of interference has occurred in their lives" (p. 8). Lowenfeld and Brittain support the idea that children develop their drawing rules through their own experience. Drawing rules help us to gain insight into what children are expressing, therefore, we can easily understand their relationship to the environment. It is still unsolved how children can be helped when they are discouraged from using drawing rules, as such discouragement may be caused by both external and internal interference. For solving this problem, we need to develop techniques which motivate (or encourage) children to understand the inherent relationships between themselves and the environment. LIST OF REFERENCE LIST OF REFERENCES Alexander, E and Carter, 8. (1958). A;p_fip;_XQppg_£eeple. London: Mills and boon Limited. Arnheim, R. (1974). AIL epd Viepel Repeeppiop : e W Berkeley University of California Press. Berkman, A. (1949). A;§_epd_§peee. New York: Social Sciences Publishers. Bunim, M. S. (1940). S ace ' 'd'ev l ' ' a d the e e s o e 've .. . New York: Columbia University Press. Cane, F. (1951). Th tist i ach s. New York: Pantheon Books. Connolly. 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