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

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

Johnny Accot & ShuminZhai

고려대학교 정보경영공학부

사용자인터페이스 연구실

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

- 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

- To model for today’s input device : trajectory-based tasks

Target width : W, Distance : A, a & b : Constant

- 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

- 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

- 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

- 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

- Is same as experiment 1 but more “Goals” on the trajectory

- 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.

- 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

- 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

- Is same as experiment 2 but not constant path width
- 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

- 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%

- 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)

- 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

- 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.

- 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

- 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.

- For experiment 3 & 4
- Shows the linear relationship between the path width and the stylus speed

- 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

- 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

- 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

- 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.