Acta Psychologica 54 (1983) 327-340

North-Holland

321

GEOMETRIC TRANSFORMATIONS OF HANDWRITING AS A FUNCTION OF INSTRUCTION AND FEEDBACK *

Herbert L. PICK, Jr.

Uniuersrty of Minnesota, USA

Hans-Leo TEULINGS

Unioersity of Nijmegen, The Netherlands

The present study explores whether the vertical and horizontal components in a well-learned skill

like handwriting can be independently modified. Three experiments are reported. In the first

experiment subjects were able to change voluntarily the horizontal or the vertical orientation of

their writing with only minimal effect on the other component. In the second experiment an

attempt is made to induce subjects to change the slant of their writing spontaneously by providing

real time distorted feedback of either the horizontal or vertical components of their writing or

both. Although little spontaneous adjustment to the distortions was found, when subjects were

instructed to note and to compensate for the distortion independent modifiability of the horizontal

and vertical components was again observed. In the third experiment it was shown that it is

difficult to modify the size of either the vertical or horizontal component without a proportional

modification of the other. The finding that the directions of horizontal and vertical components

can be modified independently but their sizes cannot, is interpreted in terms of different control

modes for direction and size parameters in handwriting.

It is possible to write cursively in any of a large range of body positions without marked variation of orientation or slant of the writing pattern. Although there may be slight perspective distortions of lengths and orientations of letter segments, somehow a writer compensates to a great extent for unusual and even awkward postures of the body. Such ability would suggest that writers could conversely adjust the orienta-

* The research was largely conducted and supported by a grant from ZWO during 1981 while the

first author was a visiting professor at the Katholieke Universiteit, Nijmegen. Preparation of the

manuscript was supported by the Center for Research in Human Learning of the University of

Minnesota and Program Project Grant HD-05027 from the National Institute of Child Health and

Human Development to the Institute of Child Development of the University of Minnesota. The authors are indebted to Claire Holmes and David Rasmussen for help with some of the

experiments. Mailing address: H.L. Pick, Jr., Institute of Child Development, University of Minnesota, 51,

East River Road, Minneapolis, MN 55455, USA.

OOOl-6918/83/$3.00 Q 1983, Elsevier Science Publishers B.V. (North-Holland)

tion, slant, and size of their writing, and perhaps do so independently for different components of their writing. The purpose of the present research is to explore to what extent this prediction is valid.

A number of authors have suggested that handwriting movement can be regarded as the resultant of two more or less orthogonal component movements, such as horizontal and vertical components (e.g., Dooijes 1983; Denier van der Gon and Thuring 196.5; Maarse and Thomassen 1983; Thomassen and Teulings 1983; Hollerbach 1981). Some authors even attribute each component movement to a different set of muscles and limbs. Thus the question of how subjects adjust orientation slant, and size of the components of writing might be approached by investi- gating to what extent it is possible to control independently the vertical and horizontal components of writing.

Orientation, slant, and size may. in principle, be controlled by simply modifying the phase relations between horizontal and vertical compo- nent movements (Hollerbach 1981). On the other hand, some observa- tions suggest that disturbances in one component of a movement may show transfer to another. In general the idea is captured by Bernstein’s (1967) observation that in a skilled act a local perturbation is not corrected at a local level but rather the whole act is modified. For instance, after training simple right-left arm movement while receiving rotated visual feedback subjects showed some spontaneous change in non-trained fore and aft movements (McIntyre and Pick 1974).

Experiment 1

The first experiment was conducted to ascertain whether independent manipulation of the horizontal or vertical components of writing could be attained. If handwriting movements are independently controllable, then it would be expected that Ss could modify one component without affecting the other. If, on the other hand, the move- ments are dependently controlled then it would be expected that Ss would have considerable difficulty in modifying one component without the other.

We seem to be able to write rather well in the absence of any visual feedback if we intend to write in a normal way. The only problems, noted e.g. by Lebrun and Rubio (1972) are repetition errors. In order to investigate to what extent visual feedback constitutes an aid in modifying one’s handwriting by a change of its horizontal and vertical components independently, the writing tasks were first done with feedback of the normal writing trace (trace feedback) via a graphical display and then, after this experience, writing tasks were done with degraded feedback (i.e.. only representing the instantaneous pen position; dot feedback). We expect that this degradation will reduce directional feedback without introducing the above-mentioned repetition errors.

H. L. Pick, H. L. Teulings / Geometric transformations of handwritrng 329

Method

Subjects and procedures Six undergraduate psychology students from the Katholieke Universiteit, Nijmegen,

served as Ss. They were asked to write a nonsense target wordfooch (which contains a

convenient number of vertical, horizontal, and oblique strokes) 10 times in their normal way of writing. Then they wrote the target word 10 times in each of the following six geometric transformations: (a) rotating only the vertical components about 30 degrees clockwise or (b) counterclockwise; (c) rotating only the horizontal components about 30 degrees clockwise or (d) counterclockwise; and (e) rotating both the vertical and the horizontal components about 30 degrees clockwise or (f) counterclockwise (see fig. 1).

The words were written 10 times in each condition on a computer controlled

digitizer pad (Vector General Vectortablet VT-l) with an electronic pen. The pen tip position, expressed in horizontal and vertical coordinate values with a combined accuracy better than 0.2 mm was sampled at a rate of 100 Hz. The S wrote on an ordinary sheet of paper but direct view of the hand was occluded by a shelf extending over the hand. Instead, the writing task could be monitored by a vertical display (Vector General Graphics Display Series 3 Model 2D3 with P4 phosphor) which was placed 125 cm right in front of the S at eye level. The paper and digitizer under it were positioned at right angles with respect to the desk at which the S was sitting.

Each S wrote the target word 10 times normally, and then proceeded to write it 10 times in each of the six transformation conditions. After each 10 trials the S was instructed as to which transformation to produce for the next block of 10 trials. The order of transformation conditions was varied randomly for each S.

VERTICAL

CLOCKWISE

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3 COUNTER-

CLOCKWISE

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COUNTER- v CLOCKWISE

Fig. 1. Example of the various transformations of writing.

After going through the procedure as described the Ss were skilled enough to repeat the whole experiment with the visual feedback no longer retaining the trace of the whole word but rather showing only the current pen position. This was termed the dot feedback in contrast with the previous trace feedback (For two Ss the dot feedback was replaced with no visual feedback at all. i.e., the display was turned off. These results did not differ from the dot feedback and have been combined in analysis.)

Ss were given some preliminary pretraining in the nature of the transformations desired. They were shown samples of the various transformations and asked to practice each kind about 5 times. During this practice they were given feedback as to how they were doing. This feedback focused on the qualitative nature of the transformation and no attempt was made to having the S achieve precisely 30 degrees of change. The .S was also practiced in writing smoothly using the digitizer pen and display. To do this, a buzzer defined time window of 4 set was established. At the beginning this often seemed fast to the Ss but they quickly got used to the task and then the time seemed more than adequate. S’s were also practiced at writing continuously. i.e., not lifting the pen off the paper until the end of the word. The putting of the pen on the paper initiated each trial and Ss were trained to hold their pen on the paper at the end of the word until the buzzer sounded.

Analysis

From the smoothed writing signal (low-pass filtered with transition band 6 to 18 Hz) the absolute (or tangential) velocity as a function of time was determined. When the S writes in a slender, cursive way the absolute velocity pattern will show minima at moments of maximal curvature (cf. Viviani and Terzuolo 1980) at extreme positions where more or less straight successive segments meet. The target word was thus broken up into 16 segments on the basis of these velocity minima. (See fig. 2.) The first and last

Fig. 2. Usual segmentation of the target word Into strokes

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332 H.L. PI&, H.-L. Teulings / Geometrrc trmsformattons of hundwrrting

segments were discarded because of considerable between-subject variability in just how these segments were written.

The slope of a segment was defined by the angle between the horizontal axis and the line connecting the beginning and end point of a segment. The slope of the baseline of the word as a whole was defined by the angle between the horizontal axis and the least squares regression line through the end points of segments 5, 8. 11, 13. and 15 (i.e.. through the bottoms of letters o, o. c. and h).

Results

For each segment and for the base line the modification from normal writing in slope under each instruction condition was plotted against the initial slope under the normal writing instruction. Fig. 3 represents the data of one arbitrary .S since there is no suitable way for combining the data for graphical purposes. The initial slopes repre- sented along the abcissa range from something over - 90 degrees (vertical downward segments) to about + 90 degrees (vertical upward segments). The segments with initial slopes around 0 degrees are horizontal. The data points marked with M‘ on the horizontal axis are the slopes of baseline of the word as a whole. There is great similarity between the modification in slope for the upward and downward vertical segments (those close to + and -90 degrees). This implies that the vertical segments can be combined for statistical analysis. For this purpose the segments were grouped into three categories (plus the overall slope of the word): those with initial slope

Table 1

Amount of change in orientation of letter segments

Transformation Feedback Segment category

Vertical Horizontal Oblique Whole word

Vertical (Clockwise) TWX 34.2 6.3 32.1 3.0 Dot 31.8 6.6 32.0 0.0

(Counter- Trace 18.4 5.1 20.4 - 0.4 clockwise) Dot 20.8 4.0 19.7 2.6

Horizontal (Clockwise) Trace 5.0 22.7 8.2 29.0 Dot 6.9 25.8 9.2 32.0

(Counter- Trace - 8.0 20.6 - 2.2 34.6 clockwise) Dot -6.1 24.2 -4.7 39.7

Rotation (Clockwise) Trace 37.9 37.9 32.3 40.4 Dot 34.3 37.9 35.8 47.6

(Counter- Trace 18.8 32.7 27.X 34.9 clockwise) Dot 24.0 31.8 23.9 46.4

Norr: ‘- ’ indicates unexpected direction

H. L. Pick, H. - L. Teulings / Geomeirrc transformations of handwriting 333

predominantly vertical (segments 2, 3, 5, 6, 8, 9, 13), those with initial slope predomi- nantly horizontal (4, 7, lo), and those with forward upward oblique orientations (12, 14). (Segments 11 and 15 were not included in the statistical analysis because their initial slopes were unique - 11 slants down and backwards and 15 slants down and forward.)

The average changes in slope over all subjects for these categories are presented in table 1. The largest modifications as expected were obtained for those segments which were instructed to be modified. This was verified statistically by means of analysis of variance on medians of 10 repetitions. The factors were subject, feedback (trace versus dot), modification instruction, modification direction (clockwise versus counterclock- wise ), and segment category (horizontal versus vertical versus oblique versus baseline). There is a significant main effect of instruction condition (F(2,14) = 123.6; p < 0.01) due to the generally great change in the rotation condition. More important, however, is a significant interaction between vertical, horizontal, and rotation conditions and the segment categories (F(6,42) = 99.05; p < O.Ol), attributable for the different amounts of change of the lines of differing orientation in correspondence with the instructions. A significant main effect of direction of rotation (F(1,7) = 6.48; p < 0.05) is attributible to a greater (absolute) change in the clockwise direction than in the counterclockwise direction. There was no significant main effect or interaction involving the factor, trace versus dot feedback. As would be expected the changes of the horizontal segments are approximately the same as the changes of the overall horizontal slant of the word. Also as would be expected, the changes of the oblique segments are intermediate between the changes of the horizontal and vertical segments, except, of course, in the case of the rotation condition where all segments were rotated approximately the same amount.

The clear result of the present experiment is that the vertical and horizontal dimensions of writing can be intentionally and independently modified. Although even the horizontal segments in the vertical clockwise instruction condition showed signifi- cant changes in orientation for both the trace and dot feedback conditions (t 2 5.51; p < 0.5) the amount of change was rather small (between 4 and 7 degrees). Further- more, the vertical segments in horizontal counter-clockwise instruction condition even changed in a.direction opposite to that instructed.

It is possible that the two dimensions of handwriting are independently modifiable when that is a specifically instructed task. Perhaps, however, if persons were induced to change the orientation of handwriting without the specific instruction to keep one dimension constant a dependence between the two axes would appear. A second experiment was run with this in mind. The feedback trace was distorted in such a way as hopefully to induce some of the modifications in orientation of writing which had been elicited by instruction in the previous experiment.

Experiment 2

In experiment 2, Ss again wrote the target word fooch as before. Their writing trace appeared on the monitor in real time but distorted by rotating the various components.

334 H. L. Pick. H. -L. Teulinp / Geometric transformations of handwritmg

Method

Subjects Ss were naive undergraduate psychology students. They were selected for being able

to write the target word smoothly and without interruption. Only 12 of the 21 Ss who participated showed few interruptions in writing during the experiment in all feedback conditions. Their data, still forming a complete design, have been analyzed.

Materials and analysis The materials and analysis were the same as in experiment 1. The visual feedback

from Ss’ writing appeared on a monitor as they wrote but the vertical, horizontal, or both components were rotated clockwise 26.6 degrees during distortion conditions.

Procedure and design For four Ss the vertical dimension was rotated clockwise, for four Ss the horizontal

dimension was rotated clockwise and for four Ss the writing as a whole (i.e., both dimensions) was rotated clockwise.

Ss were only practised in writing the target word normally with the pen continu- ously on the paper within the 4 set time window. They did not monitor the display during practice. They were then introduced immediately to the distorted feedback on the monitor without any warning or special instruction and simply asked to continue writingfooch for a total of 20 trials. It was hoped that the distorted appearance of the writing would induce a spontaneous geometric transformation, i.e., a counterclockwise adjustment of either the vertical segments, horizontal segments, or both depending on the distortion. This condition was followed without pause by another block of 20 trials in which the distortion was removed and the feedback was a normally-oriented trace of what they were writing. This block hopefully provided a baseline of performance. Upon completion of this second block with normal feedback, Ss were again presented with the original distorted feedback but this time they were informed that they might have noticed some distortion of their writing at times during the previous trials. They were instructed now specifically to compensate for any distortion of their writing that they noticed. Subsequently, Ss were exposed to each of the other two types of distortion for similar 20-trial blocks, again with instructions to compensate for any distortion they noticed. Thus it was possible to evaluate the spontaneous reaction of four Ss to each of the three types of distortion and the instructed compensation of ail 12 Ss to each of the distortions.

Results

The majority of the Ss did not notice the distortion at all and those that did were not able to indicate the nature of the distortion. Thus it was not surprising that the Ss showed little systematic spontaneous adjustment to the distortion. Their performance was very variable individually and across the four individuals exposed to the same distortion. There were no significant changes of orientation of writing in this condition. Possibly writing with visual guidance from the monitor was so unusual altogether that

H. L. Pick, H. L. Teulings / Geometric transformations of handwriting 335

Table 2

Amount of compensation for distortion (degrees).

Type of distortion

Type of segment

Vertical Horizontal Oblique Whole word

Vertical 3.36 - 2.91 2.51 - 4.25 Horizontal 1.30 4.25 1.02 8.65 Rotation 6.15 5.73 5.85 7.05

distortions of slant and orientation went unnoticed and uncompensated initially. However, when the distortion was removed after trial 20, the change was more frequently noticed.

Performance under the conditions of instructed compensation was somewhat more consistent within Ss exposed to each distortion and a coherent pattern does emerge. Results were analyzed in terms of amount of compensation for each distortion. For any given segment of a letter the slope of that segment was measured under the distorted feedback and again under non-distorted feedback. The difference between these two values is a measure of the amount of change elicited by the distorted feedback. These values averaged across all Ss for vertical, horizontal, and oblique segments (as well as for the overall slope of the word) are presented in table 2. The interaction between type of distortion and type of segment is significant by analysis of variance (F(6,66) = 9.85; p -C 0.01). Inspection of the table reveals that the amount of compensation is greatest for the segments primarily affected by the distortion. Thus, the average compensation for the vertical segments under the vertical distortion (3.36 degrees) is higher than for the horizontal (- 2.91 degrees) or for the overall slope, of the whole word ( -4.25 degrees). The average compensation for the horizontal segments under the horizontal distortion (4.25 degrees) and for the overall slope of the word (8.65 degrees) is higher than for the vertical segments (1.30 degrees). Oblique lines behave somewhat like vertical components. Finally, the average compensation under the rotation distortion is not different for all lines.

These first two experiments support the hypothesis of independent modification of horizontal and vertical components, but is this independence a general aspect of handwriting or specific to its slant or orientation? In order to explore the question of generality, a third experiment was conducted in which Ss were asked to modify the size of the components of their handwriting.

Experiment 3

Method

Subjects

Nine undergraduate and graduate students volunteered to participate in this experi- ment.

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H. L. Pick, H.-L. Teulrngs / Geometrrc transformatmn.s of handwrrmg

, ! -T-

EYES OPEN 1

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LOG INSTRUCTED CHANGE

Fig. 4. Obtained ratio of width to height as a function of the instructed change while the subjects

had their eyes open, (The obtained results for transformations of height only, of width only, and of

both components are indicated by the solid lines. Results to be expected if subjects were able to

vary height only or width only are indicated by the descending and by the ascending dashed line,

respectively.)

8 1

-.3 (.5) CP, i23)

LOG INSTRUCTED CHANGE

Fig. 5. The same as fig. 4 but now the subjects had their eyes closed

H. L. Pick, H. L. Teulings / Geometric transformations of handwrrting 331

Materials The task involved the use of pencil and ordinary unlined writing paper.

Procedure Each S was asked to write the nonsense target word gaggle (which allows the

accurate estimation of vertical extenders, most specifically of the letter g) five times under the following conditions: (a) normally, (b) doubling the overall size, (c) reducing the size by one-half, (d) doubling the width while keeping the height constant, (e) halving the width while keeping the height constant, (f) doubling the height while keeping the width constant, and (g) halving the height while keeping the width constant. They first performed the normal condition and then the other six conditions in a random order. Then, they were skilled enough to allow all conditions to be repeated while the Ss had their eyes closed.

Thus the design consisted of Ss attempting to scale size from half to normal to twice normal with respect to both height and width, height only, and width only. All Ss performed the normal writing first and again in between their attempted scaling of the various components. The order of which the different components were scaled was varied randomly across Ss.

Analysis For analysis, the measure of width was based on the overall length of the word from

the left side of the initial g to the right side of the terminal e. Height was measured by averaging the distance from top to bottom of the three g’s. For each condition of writing (three scale values by these different component variations) a ratio of width to height was calculated.

Results

The logarithms (averaged across Ss) of these ratio values are plotted in fig. 4 for eyes open and fig. 5 for eyes closed as a function of the logarithm of the instructed change. The scaling functions are plotted for the ratios obtained under normal instructions to vary both width and height, width only, and height only.

To the degree that it is possible to perform this task according to instructions, the results should show a horizontal function when both horizontal and vertical compo- nents were to be varied, i.e., double and half the size of writing. That is, the ratio should remain constant. Figs. 4 and 5 indicate this for performance with both eyes open and eyes closed. When one component was to be varied and the other held constant the scaling function should fall along the diagonals indicated in figs. 4 and 5. The greater the departure from these diagonals with slopes of 1, the less it appears that one component is varied without the other. The results plotted in figs. 4 and 5 indicated marked departure from such independent variation. The slopes of these functions with 95% confidence bounds are shown in table 3. From these confidence bounds it is evident that the slopes of the functions, obtained under instructions to change height only or width only, differ significantly from the expected 45 degrees diagonals, which have slopes of - 1 and + 1, respectively. (They also differ from the horizontal, which

338 H. L. Pick, H.-L. Teulings / Geometric transformations of handwritrng

Table 3

Slopes of the regression lines of the logarithm of the obtained width to height ratio on the

logarithm of the instructed ratio with their 95% confidence bounds in parenthesis.

Modify size of Eyes open Eyes closed

Height only

Width and height Width only

-0.43( kO.15) - 0.34( + 0.21)

0.0 ( f 0.08) 0.08( +0.15)

0.49( * 0.13) 0.43( + 0.13)

has a slope 0.) There is no systematic difference between performances with eyes open

and closed. Indeed. these conditions display remarkably similar results.

Discussion

The results of experiment 3 in contrast to those of experiments 1 and 2 indicate a marked dependence between the horizontal and vertical components of writing. Given the different foci of these experiments, the obvious question becomes how is it possible that the horizontal and vertical components of writing can be independently controlled for orientation or slant but not for size? Perhaps the answer lies in how these two parameters are controlled. Observation of the subjects in experiments 1 and 2 suggests that in trying to modify slant of handwrit- ing, the angles of the wrist, elbow, and shoulder joints are often changed and are held in the new orientation for all trials of a given task. A value can be set for the task as a whole and does not have to be controlled after that. For example, when trying to change the slant of the horizontal components of their writing, subjects may change the angles of their elbow and shoulder joints. In order to do this without changing the slant of the vertical components they compensate by adjusting their wrist joint.

Once set up these values can be maintained throughout a particular condition. The proposed mechanism for producing a slant of one component of writing based on changing the posture of the arm as a whole with compensating adjustment of another component, is equiva- lent to what Hollerbach (1981) following Mermelstein (1964), referred to as non-orthogonal axes of writing. When an aspect of writing is adjusted by setting a parameter for the task as a whole it is perhaps best conceived of as what Van Galen (1980) describes as an ambient aspect of writing.

H. L. Pick, H. - L. Teulings / Geometnc transformatrons of hnndwr+ng 339

By contrast, in order to modify independently the size of the hori- zontal and vertical components of writing it would seem to be necessary to initiate vertical changes of direction at different relative horizontal positions during the execution of a letter or letter segment. This modification of the articulatory or program aspect of the letter would be more like what Van Galen has termed the focal aspects of writing. Recent work by Maarse and Thomassen (1983) and Thomassen and Teulings (1983) indicate some of the details of how size transformations are accomplished. Modification of the relative width of the horizontal left to right translation in a writing pattern was mainly realized by the oblique upward segments and to a lesser extent by the vertical down- ward movements. Thus, these components are treated partially indepen- dently. Such a detailed analysis of how transformations are accom- plished is a useful approach to understanding the programming involved in writing. It is useful to know what kinds of transformations can be voluntarily imposed and what kind will occur spontaneously. An at- tempt was made to induce spontaneous transformations in experiment 2 without success. However, presenting the distorted feedback in a different way, for example, after considerable experience with undis- torted feedback, might be successful in inducing significant adjustment. Would the way that adjustment occurs be the same as when produced by instruction? The answer to this question depends partially on how the distortion is perceived. Some distortions and compensations in writing occur normally when one is constrained to write in unusual or even awkward postures. Experience with writing produced in this way with slant variations may be why subjects did not notice (or respond to) the distorted feedback of experiment 2.

The main result of these present experiments is that for some parameters of writing (e.g., slant), the horizontal and vertical compo- nents can be controlled independently. For other components (e.g., size), these two components are more dependent. According to the present interpretation, parameters involving the writing program (which contains focal aspects such as size ratios of the writing) do not allow decomposition, while those parameters involving overall stylistics (or ambient aspects such as slant of the writing) can be decomposed intentionally.

340 H.L. Ptck, N. L. Teulings / Geometric trunsformattons of handwritrng

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