Beyond Fitt’s Law : Model for Trajectory-Based HCI Tasks

1. Beyond Fitt’s Law : Model for Trajectory-Based HCI Tasks Johnny Accot & ShuminZhai 고려대학교 정보경영공학부 사용자인터페이스 연구실

2. Contents • Introduction • Experiment 1 : Goal Passing • Experiment 2 : Increasing Constraints • Experiment 3 : Narrowing Tunnel • Experiment 4 : Spiral Tunnel • Discussion • Design Implications • Conclusion

3. Introduction (1/2) • Few theoretical, quantitative tools are available in UI R&D • A rare exception to this is Fitt’s Law • The time T needed to point to a target of width W and at distance A is logarithmically related to the inverse of the spatial relative error A/W, that is: • What Fitts’ laws revealed is • Intuitive tradeoff in human performance : Speed/accuracy trade off • in three experimental tasks (bar strip tapping, disk transfer, nail insertion) • addresses only one type of movement : pointing / target selection • So, Fitts’ law paradigm is not sufficient • To model for today’s input device : trajectory-based tasks • drawing, writing and steering in 3D space Target width : W, Distance : A, a & b : Constant

4. Introduction (2/2) • Experimental paradigm • Is focused on Steering between boundaries • Apparatus • 19 inch monitor (1280 × 1024 pixels) and equipped with 18 × 25 inch tablet ; 1cm = 20 pixels • Subject held and moved a stylus on the surface of the tablet, producing drawings on the computer monitor Target width : tunnel width Amplitude : tunnel length

5. Experiment 1 : Goal Passing (1/2) • Task • Subjects were asked to pass Goal 1 and then Goal 2 as quickly as possible • Procedure and design • a fully-crossed, within-subjects factorial design with repeated • 10 subjects • Independent variables • Amplitude : A = 256, 512, 1024 pixels (12.8, 25.6, 51.2 cm) • Path width : W = 8, 16, 32 pixels (0.4, 0.8, 1.6 cm) • 9 A-W conditions, 10 trials in each condition

6. Experiment 1 : Goal Passing (2/2) • Result • Goal passing task follows the same law as in Fitts’ tapping task, despite the different nature of movement constraint. ※ # of ID : 5 • 1) 256/8, 512/16, 1024/32 • 2) 512/8, 1024/16 • 3) 256/16, 512/32 • 4) 1024/8 • 5) 256/32

7. Experiment 2 : Increasing Constraints (1/2) • Task • Is same as experiment 1 but more “Goals” on the trajectory • what will the law become if we place infinite number of goals? • The resulting task is the straight tunnel steering task • The bigger N is, the more careful the subject has to be in order to pass through all goals. • If N tends to infinity, the task becomes a “tunnel traveling” task.

8. Experiment 2 : Increasing Constraints (2/2) • Procedure and design • a fully-crossed, within-subjects factorial design with repeated • 13 subjects • Independent variables (32 A-W conditions, 5 trials in each condition) • Amplitude : A= 250, 500, 750, 1000 pixels • Path width : W= 20, 30, 40, 50, 60, 70, 80, 90 pixels • Result • hypothesized model was successful in describing the difficulty of the task and Error rate are considerably higher than those found in Fitt’s law

9. Experiment 3 : Narrowing Tunnel (1/2) • Task • Is same as experiment 2 but not constant path width • a task can also be decomposed into a set of elemental goal passing tasks • New method to computer ID • New approach considers the narrowing tunnel steering task as a sum of elemental linear steering tasks described in experiment 2. (Fig 7) • Index of Difficulty

10. Experiment 3 : Narrowing Tunnel (2/2) • Procedure and design • a fully-crossed, within-subjects factorial design with repeated • 10 subjects • Independent variables (16 A-W conditions, 5 trials in each condition) • Amplitude : A= 250, 500, 750, 1000 pixels • Path width : W1= 20, 30, 40, 50 (1, 1.5, 2, 2.5 ㎝) ; W2= 8 pixels (0.4 ㎝) • Result • The completion time of the successful trials and ID for this task once again forms a linear relationship • Average error rate is close to 18%

11. A Generic Approach : Defining a Global Law • New concept • The narrowing tunnel study brought the new concept of integrating the inverse of the path width along the trajectory • It is possible to propose an extension of this method to complex path. • if C is a curved path, we define the ID for steering through this path as the sum along the curve of the elementary ID • Our hypothesis was then that the time to steer through C is linearly related to IDc, that is: (13) • In horizontal steering (expe’ 2), W(s) is constant and equal to W, so that equation (13) gives: (14)

12. Experiment 4 : Spiral Tunnel (1/2) • Task • In order to test our method for complex path, we studied a new configuration • Subjects were asked to draw a line from the center to the end of the spiral (Fig 10 : S2, 15) n : # of turns of the spiral w : influencing the increase of the width S n, w in polar coordinates Width of the path for a given angle θ Apply equation 12 and make a summation of elementary IDs

13. Experiment 4 : Spiral Tunnel (2/2) • Procedure and Design • a fully-crossed, within-subjects factorial design with repeated • 11 subjects • Independent variables (16 n-ω conditions, 10 trials in each condition) • Spiral turn number : 1, 2, 3, 4 • Width factor : ω= 10, 15, 20, 25 • Results • the prediction of the difficulty of steering tasks is also valid for this more complex task.

14. Deriving A Local Law (1/3) • Instantaneous speed of steering movement • Corresponding global law, local law that models instantaneous speed can be expressed as follows: • The justification of this relationship between velocity and path width comes from the calculation of the time needed to steering ν(s) : velocity of the lime at the point of curvilinear abscissa s W(s) : width of the path at the same point τ : empirically determined time constant τ c : time needed to steering through a path c ν = ds/dt , so that dt = ds/ν

15. Deriving A Local Law (2/3) • In order to check Local law equation’s validity • used the data from previous experiments and plotted speed versus path width to check the linear relationship. • For experiment 2 • Shows the linear relationship between the path width and the stylus speed Small intercept can be neglected, which is coherent with local law.

16. Deriving A Local Law (3/3) • For experiment 3 & 4 • Shows the linear relationship between the path width and the stylus speed

17. Discussion • There are various limitation to these simple laws • Due to human body limitation there are upper bound limits to the path width can be correctly modeled by the these simple laws • Exceeding these limits leads to the saturation of the laws • The local law can be modified to take path curvature into account • The starting position clearly influences the difficulty of a steering task • whether steering is performed from left to right or from right to left, and on both the clockwise / counter clockwise directions of steering. • Steering is then probably related to handedness. ρ: Radius of curvature

18. Design Implications • Modeling interaction time when using menus • Each step in menu selection is a linear path steering task, similar to the one in experiment 2 Two linear steering task 1) vertical steering to select a parent item 2) horizontal steering to select a sub item

19. Conclusion • In this study, We carried the spirit of Fitts’ Law a step forward and explored the possible existence of other robust regularities in movement task. • First, demonstrated that the logarithmic relationship between MT and Tangential width of target in a tapping task also exists between MT and normal width of the target in a “goal passing” task. • Second, increasing constraints experiment lead us to hypothesize that there is a simple linear relationship between MT and the “tunnel” width in steering tasks. • Finally, generalize the relationships in both integral and local forms. • The integral form states that the steering time is linearly related to the ID • The local form states that the speed of movement is linearly related to the normal constraint.