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

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

Contents

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

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

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

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

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

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

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

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

- 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.

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

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

- 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

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%

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)

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

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.

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

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.

Deriving A Local Law (3/3)

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

Discussion The local law can be modified to take path curvature into account The starting position clearly influences the difficulty of a steering task

- 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

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

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.

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