Fitts' law describes constraints on the speed of a pointing movement in terms of two parameters, as incorporated into an index of difficulty (ID): the amplitude of ...
PROCEEDINGS of the HUMAN FACTORS AND ERGONOMICS SOCIETY 49th ANNUAL MEETING—2005
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TASK AND EFFECTOR CONSTRAINTS ON THE KINEMATICS OF POINTING MOVEMENTS Michael Bohan, Daniel McConnell, Shelby Thompson and Alex Chaparro Department of Psychology Wichita State University Wichita, KS Recent work has emphasized the distinction between task and effector constraints underlying performance in Fitts’ type discrete pointing tasks. We explored the relative contributions of these constraints in a cursor-pointing task by manipulating the controldisplay scale, thereby dissociating movement scale at the level of the hand from movement scale at the level of the cursor. Using linear regressions to predict movement time, we found that effector constraints best predict the primary transport phase of the movement, bringing the hand near the target. Visual task constraints underlie the secondary target acquisition phase of the movement. We present a reformulation of Fitts’ (1954) index of difficulty, capturing the relative contributions of effector and visual task constraints. INTRODUCTION The advent of the graphical user interface, and the development of the mouse as an input device mediating human-computer interaction, has led to the development of a body of research devoted to understanding mousing and cursorpointing behavior in terms of efficiency. In particular, Fitts’ law (Fitts, 1954) has been used to describe mousing behavior, and has successfully been applied to the evaluation of different input devices (Card, English & Burr, 1978). In recent years, characteristics of the mouse and/or the on-screen display of cursor movements have been examined as a means of improving the efficiency of mousing behavior, and potentially “beating” Fitts’ law (see Balakrishnan, 2004, for a review). Fitts’ law describes constraints on the speed of a pointing movement in terms of two parameters, as incorporated into an index of difficulty (ID): the amplitude of the movement, and the width of the target. Movement time (MT) scales proportionately to movement amplitude, and inversely with target width. These constraints can thus be minimized in human-computer interaction
by reducing the amplitude of pointing movements, or increasing the size of the targets. An important question regarding the amelioration of these constraints deals with the source of the constraint. Do they reflect constraints on the visual perception of cursor movement? Do they reflect constraints on the kinesthetic resolution of the movement? Do they reflect motoric (inertial or biomechanical) constraints on producing the movement? These questions have been addressed in recent work by Bootsma and colleagues (Bootsma, Fernandez & Mottet, 2004; Fernandez & Bootsma, 2004). By manipulating the control-display ratio (the ratio between movements of the effector, described as distance traveled by the hand/mouse in the physical workspace, relative to movements of the cursor, described as on-screen distance traveled in units of pixels), they successfully dissociated human-computer interaction into movements in effector space and movements in task space (the cursor movement on screen). They found that constraints in task space accounted for variations in movement velocity and acceleration, indicating the importance of visual factors underlying pointing performance. This would imply that cursor-
PROCEEDINGS of the HUMAN FACTORS AND ERGONOMICS SOCIETY 49th ANNUAL MEETING—2005
pointing behavior could be improved by facilitating the visual aspects of the task, including increasing the size of on screen targets (e.g. icons). Conversely, Blanch, Guiard and Beaudouin-Lafon (2004) found that cursor-pointing movements could be improved by facilitating the motoric aspects of the task. In their study, they used a control-display ratio that shortened the distance traveled by the effector by decreasing the ratio during approach to the target, and increasing it once the cursor was inside the target. This allows the hand to make a smaller movement when moving the cursor a large distance across the screen, and then make larger movements, relative to the displayed cursor motion, when acquiring the target. The results of these studies fail to paint a conclusive picture of which factors underlie performance in a Fitts-type pointing task. It is important to note that both sets of studies employed a non-linear control-display gain, such that cursor accelerations scaled as a function of effector velocity (Fernandez & Bootsma, 2004) or as a function of cursor position relative to the intended target (Blanch, et al., 2004). In the current study, we provide a more detailed manipulation of the control-display ratio, using only linear mappings between effector and task spaces, with the goal of understanding which of these two descriptions account for kinematic features of the movement. METHOD Participants Ten adults participated in the study. All were right handed and had normal or corrected-tonormal vision. Apparatus Participants were seated approximately 60 cm from a 19-inch computer monitor, with a resolution of 1400x1050 (100 DPI) and a refresh rate of 75 Hz. Participants pointed to circular targets appearing on screen, using a mouse (Logitech
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MX300 Optical Mouse, 800 DPI) to move the cursor to the target. The two-dimensional position data from the mouse, sampled at 125 Hz, were transformed before displaying the resultant cursor motion on screen. This manipulation resulted in a scaling of the actual movement of the hand/mouse relative to the visual appearance of the motion of the cursor. Procedure Participants pointed to circular targets of four different widths (1.5, 3, 6 and 12 mm), executing movements of four different amplitudes (18.75, 37.5, 75 and 150 mm), resulting in seven different indices of difficulty, ranging from 1.64 to 7.64 in increments of one. Seven different controldisplay gain settings (1:.125, 1:.25, 1:.5, 1:1, 1:2, 1:4, and 1:8) were applied to create unique combinations of amplitudes and widths. It is important to note that in scale settings other than 1:1, the visual task parameters (amplitude of cursor motion and on-screen target size) differed from the movement parameters (amplitude of hand/mouse movement and target width as an effective final constraint on the hand). These manipulations will then allow us to assess whether movement amplitude (AM), movement width (WM), visually displayed amplitude (AV) or visually displayed target width (WV) underlie the constraints manifested in the relationship known as Fitts’ law. Movement kinematics were examined to assess the relative effects of visual and effector constraints. The tangential velocity curves for each trial were smoothed using a weighted average technique. We determined the beginning of a trial by finding the earliest point that exceeded 8% of the peak velocity for that trial. The end of the trial was determined in a similar fashion: data at the end was discarded so long as it was less than 2% of the global peak. Movement time was then derived. Sub-movements were defined as regions of the velocity curve that fulfilled several criteria: (a) local peak velocity must be at least 15% of the global
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PROCEEDINGS of the HUMAN FACTORS AND ERGONOMICS SOCIETY 49th ANNUAL MEETING—2005
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peak; (b) local minimum velocities surrounding the local peak must be at least 15% of the global peak and at most 50% of the local peak; (c) a local minimum is said to occur not only when the velocity profile turns back upward, but when it levels out to a near-horizontal slope (that slope being 0.5% of the global peak, per sample). Movement time was then divided into primary MT (duration of the primary sub-movement) and secondary MT (duration of the remainder of the trial).
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Figure 1. Movement amplitude regressed against the duration of the primary sub-movement. 1
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We analyzed MT across all values of gain in terms of Fitts’ law, and found a relatively poor fit compared to previously reported performance in discrete reaching tasks (e.g. Fitts & Peterson, 1964). The best fitting line was of the form y = 0.14 + .22 ID, (r2 = .48). However, this analysis alone does not allow for an appreciation of the separate contributions of visual and motoric constraints since the ratios log2 AM / WM and log2 AV / WV were identical for all conditions. This is because the gain manipulation affected movement amplitude and target width by the same scale factor, in both visual and effector space. However, only the ratios remain constant across gain settings, not the individual movement parameters. This allowed us to determine whether MT was constrained in visual or effector space, by separately analyzing performance as a function of movement amplitude (AM), display amplitude (AV), movement width (WM), and display width (WV). We first analyzed the effect of these individual parameters of the primary (PT) and secondary (ST) sub-movements. Simple linear regressions determined that the single best predictor of PT, as illustrated in Figure 1, was the variable AM (r2 = .88), as compared to AV (r2 = .001), WM (r2 = .51), and WV (r2 = .30). For ST, the single best predictor as illustrated in Figure 2, was WV (r2 = .27), as compared to WM (r2 = .04), AM (r2 = .03), and AV (r2 = .001).
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Figure 2. Visually displayed target width regressed against the duration of the secondary sub-movement.
The implication of these individual regressions is that the duration of the primary submovement is constrained in proportion to the distance traveled in effector space, while the duration of the secondary sub-movement is constrained inversely by the visually displayed target width. This implies that these two factors can be combined into a single ratio that captures the overall constraint on MT. This ratio (AM / WV ) represents a new index of difficulty, which can be
PROCEEDINGS of the HUMAN FACTORS AND ERGONOMICS SOCIETY 49th ANNUAL MEETING—2005
used to predict MT. We performed a simple linear regression on MT using this new formulation of ID, revealing a prediction of MT, y = 0.43 + .14 ID (r2 = .82), as shown in Figure 3, which improved upon the prediction of the original ID. We take this result to mean that MT is constrained by both effector and visual task parameters, in particular the movement amplitude and the visually specified target width. 1.6
phases of the pointing movement. The visual and motoric systems each have upper (bandwidth) limits, so that Fitts’ law is a manifestation of these limits as reflected in an index of difficulty, ID = log2 AM / WV. REFERENCES Balakrishnan, R. (2004). “Beating” Fitts’ law: virtual enhancements for pointing facilitation. International Journal of Human-Computer Studies, 61, 857-874. Blanch, R., Guiard, Y. & Beaudouin-Lafon, M. (2004). Semantic pointing: Improving target acquisition with control-display ratio adaptation. In Proc. CHI 2004, 6(1), 519-526.
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Bootsma, R.J., Fernandez, L. & Mottet, D. (2004). Behind Fitts’ law: kinematic patterns in goal-directed movements. International Journal of HumanComputer Studies, 61, 811-821.
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Card, S., English, W. & Burr, B.J. (1978). Evaluation of mouse, rate-controlled isometric joystick, step keys, and text keys for text selection on a CRT. Ergonomics, 21, 601-613.
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Figure 3. The reformulated Index of Difficulty (bits) regressed against movement time (sec).
DISCUSSION Our results show that both visual and effector constraints underlie Fitts’ law. As a pointing movement unfolds, the primary submovement serves the purpose of getting the hand into the vicinity of the target. This is primarily a physical task constrained by the inertial properties of the effector, and thus the duration of the primary sub-movement scales with the distance to be covered. Once the effector is close to the target, visual feedback becomes more important, and the duration of the final phase of the movement scales inversely with target size; as the target gets smaller, the movement becomes more difficult and its duration increases. We conclude that Fitts’ law reflects both visual information processing and motor control, and that each constrains performance in different
Fernandez, L. & Bootsma, R.J. (2004). Effects of biomechanical and task constraints on the organization of movement in precision aiming. Experimental Brain Research, 159, 458-466. Fitts, P.M. (1954). The information capacity of the human motor system in controlling the amplitude of movement. Journal of Experimental Psychology, 47, 381-391. Fitts, P.M. & Peterson, J.R. (1964). Information capacity of discrete motor responses. Journal of Experimental Psychology, 67, 103-112.
