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 & Shumin Zhai 고려대학교 정보경영공학부 사용자인터페이스 연구실 . Contents. Introduction Experiment 1 : Goal Passing Experiment 2 : Increasing Constraints Experiment 3 : Narrowing Tunnel Experiment 4 : Spiral Tunnel Discussion

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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

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

Johnny Accot & ShuminZhai

고려대학교 정보경영공학부

사용자인터페이스 연구실


Contents

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

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


Introduction 2 2

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

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

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

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.


Experiment 2 increasing constraints 2 2

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

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


Experiment 3 narrowing tunnel 2 2

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

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

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

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

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

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

Deriving A Local Law (3/3)

  • For experiment 3 & 4

    • Shows the linear relationship between the path width and the stylus speed


Discussion

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


    Design implications

    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

    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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