beyond fitt’s law : model for trajectory-based hci tasks

Korea Univ.Department of Information Management Engineering

User Interface Lab.

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

Johnny Accot & Shumin Zhai

고려대학교 정보경영공학부사용자인터페이스 연구실


User Interface Lab.

Contents

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

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User Interface Lab.

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 in-

sertion) • 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

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Target width : W, Distance : A, a & b : Con-stant


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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 draw-

ings on the computer monitor

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Target width : tunnel widthAmplitude : tunnel length


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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

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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.

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※ # 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


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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

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• 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 “tun-nel traveling” task.


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Procedure and design• a fully-crossed, within-subjects factorial design with repeated • 13 subjects• Independent variables (32 A-W conditions, 5 trials in each condi-

tion) 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

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Experiment 2 : Increasing Constraints (2/2)


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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

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User Interface Lab.

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 condi-

tion) 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%

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A Generic Approach : Defining a Global Law

New concept• The narrowing tunnel study brought the new concept of integrat-

ing the inverse of the path width along the trajectory• It is possible to propose an extension of this method to complex

path.

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• if C is a curved path, we de-fine the ID for steering through this path as the sum along the curve of the ele-mentary 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)


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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)

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n : # of turns of the spiralw : influencing the increase of the widthS n, w in polar coordinates

Width of the path for a given angle θ

Apply equation 12 and make a summation of elementary IDs


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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 condi-

tion) 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.

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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

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ν(s) : velocity of the lime at the point of curvilinear ab-scissa s W(s) : width of the path at the same pointτ : empirically determined time constant

τ c : time needed to steering through a path cν = ds/dt , so that dt = ds/ν


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In order to check Local law equation’s validity• used the data from previous experiments and plotted speed ver-

sus path width to check the linear relationship.For experiment 2

• Shows the linear relationship between the path width and the sty-lus speed

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Small intercept can be neglected, which is coherent with local law.



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For experiment 3 & 4• Shows the linear relationship between the path width and the sty-

lus speed

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Discussion

There are various limitation to these simple laws1. Due to human body limitation there are upper bound lim-

its to the path width can be correctly modeled by the these simple laws• Exceeding these limits leads to the saturation of the laws

2. The local law can be modified to take path curvature into account

3. 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.

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ρ : Radius of curva-ture


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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

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Two linear steering task 1) vertical steering to select a parent item 2) horizontal steering to select a sub item


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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 “tun-nel” 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.

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beyond fitt’s law : model for trajectory-based hci tasks

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