NordiCHI2016_yamanaka_novideo

Scale Effects in the Steering Time Difference
between Narrowing and Widening Linear Tunnels
Shota Yamanaka (Meiji University & JSPS)
Homei Miyashita (Meiji University)
October 25, 2016 Meiji University Japan Society for the
Promotion of Science
1

2
Movement time (MT) measurement on a pen tablet
Steering Task in the Previous Work [Yamanaka+, CHI ’16]

3
Movement time (MT) measurement on a pen tablet
(video)

4
MT for a narrowing tunnel (MTNT) > MT for a widening tunnel (MTWT)

(video)
5
MT for a narrowing tunnel (MTNT) > MT for a widening tunnel (MTWT)

Summary of the Previous Work [Yamanaka+, CHI ’16]
6
• Empirically confirming: MTNT > MTWT
• Modeling the MT difference based on the tunnel parameters
𝐼𝐷Gap=
𝐴(𝑊𝐿 − 𝑊𝑅)
𝑘𝑊𝐿 𝑊𝑅
Tunnel length:
61.2 and 122 mm
Tunnel width
(both left- and right-ends):
2.24, 6.32, and 10.4 mm

Goals of Our Present Work
7
In various scales,
• Confirming whether MTNT is greater than MTWT
• Testing the Validity of our IDGap model
21.5-inch tablet ~iPad ~XperiaZ ~3DS ~LG-W100
1/1 1/2 1/4 1/9 1/12

Background 1/2: Steering Law
8

Accot and Zhai’s Steering Law [Accot+, CHI ’97]
Steering law: 𝑀𝑇 = 𝑎 + 𝑏
𝐴
𝑊
• a and b: empirically determined constants
•
𝐴
𝑊
is called Index of Difficulty (ID)
e.g., a narrower or longer path has a higher ID
that requires a longer MT
9
When navigating a tunnel of width W and amplitude A,
the movement time MT has a linear relationship to A/W
y = 47.666x - 57.524
R² = 0.9984
0
500
1000
1500
2000
2500
0 20 40 60
MT[ms]
ID = A/W [bits]
W
A

𝐼𝐷 =
𝐴
𝑊
is Held to Constant-width Tunnels
10
Constant-width circle
[Accot+, CHI ’99, ’01]
A
WW
A
Constant-width straight tunnel
[Accot+, CHI ’97, ’99, ’01]
𝐼𝐷 =
𝐴
𝑊
𝐼𝐷 =
𝐴
𝑊

Steering Law: Various Devices/Environments
11
VR car driving
[Zhai+, Presence ’04]
Direct-input stylus
[Kulikov+, CHI ’05]
Mouse, touchpad, trackpoint, trackball, indirect-input stylus
[Accot+, CHI ’99]
3D controller [Casiez+, APCHI ’04]

Other Tunnel Shapes: Different ID formulae
12
Narrowing straight tunnel
[Accot+, CHI ’97]
Widening spiral tunnel
[Accot+, CHI ’97]
𝐼𝐷NT =
𝐴
𝑊𝑅 − 𝑊𝐿
ln
𝑊𝑅
𝑊𝐿
𝐼𝐷ST =
2𝜋
2𝜋 𝑛+1
𝜃 + 𝜔 6 + 9 𝜃 + 𝜔 4
𝜃 + 2𝜋 + 𝜔 3 − 𝜃 + 𝜔 3
𝑑𝜃
n : the number of turns
θ : current position (in angle)
ω : width-increasing parameter
WL : left width (start side)
WR : right width (end side)
WL
A
WR

Background 2/2: Scale Effects in GUIs
13

Fitts’ law [Fitts, J. Exp. Psy. ’54]
Performance model for target pointing tasks
14
Target distance A
Size W
(video)
𝑀𝑇 = 𝑎 + 𝑏 log2
𝐴
𝑊
+ 1

Fitts’ law
MT depends on the ratio of A/W
→ Visual size or cursor speed setting would not affect the performance
In fact, such configurations affect the performance
15
y = 127.52x + 170.47
R² = 0.9738
0
200
400
600
800
1000
0 2 4 6
MT[ms]
ID = log2(A/W+1) [bits]
Target distance A
Size W
𝑀𝑇 = 𝑎 + 𝑏 log2
𝐴
𝑊
+ 1

Visual Scale Effect
e.g., Magnifier tool changes only the visual scale on the display
Fitts’ difficulty does not change, but the performance changes
16
(video)
Magnify
(video)

Visual Scale Effect [Browning+, CHI ’14]
A very small display size decreases the pointing performance
Fitts’ law fitness also decreases (R2 = 0.89)
→ Performance model fitness can be affected by the visual scale
17

Motor Scale (Mouse Gain) Effect [Chapuis+, TOCHI ’11]
18
(video)
Very slow Very fastNeutral speed
Too low and too high speed decrease the GUI operation performance
→ Pointing performance can be affected by the visual and motor scales

19
(video)
Too low and too high speed decrease the GUI operation performance

20
(video)
Too low and too high speed decrease the performance

Scale Effects in Steering Tasks [Accot+, CHI ’01]
Steering law suggests that MT depends on the ratio of A/W
e.g., MT for (A = 500 & W = 50) equals to MT for (A = 100 & W = 10)
21
Steering law: 𝑀𝑇 = 𝑎 + 𝑏
𝐴
𝑊

Motor Scale Effects in Steering Tasks [Accot+, CHI ’01]
22
1/1 condition 1/2 condition
24-inch display
24-inch pen tablet

Scale Effects in Steering Tasks: Result
• Too large or too small input areas
degraded the steering performance
• The medium sizes (~A5) was the best
23
Tested motor scales: 1/1 to 1/16 scales
U-shaped
function

Scale Effects in Mouse Steering Tasks [Senanayake+, DHM ’13]
Motor scale was changed by cursor speed congifuration
→ Medium speed was the best
24
W
A

Summary of Previous Studies
• Scaling affects the performance in GUIs (pointing and steering)
• Even for a robust Fitts’ law, the model fitness decreases in a certain scale
→ We have to test the validity of our model IDGap in various scales
25

26
A Model for Steering Time Difference between
Narrowing and Widening Tunnels

Revisiting ID for a Narrowing Straight Tunnel [Accot+, CHI ’97]
Navigating a narrowing tunnel can be converted to
navigating the infinite number of constant-width infinitesimal-length tunnels
𝐼𝐷NT =
0
𝐴
𝑑𝑥
𝑊 𝑥
=
0
𝐴
𝑑𝑥
𝑊𝐿 +
𝑥
𝐴
=
𝐴
ln
𝑊𝑅
𝑊𝐿
W
A
𝐼𝐷 =
𝐴
𝑊
WR
Start line
End line
WL
A
W(x)
dx
x
constant-width linear tunnel
27

ID for a Widening Straight Tunnel
• Integration does not take account of the left/right direction
• The same calculation of IDNT can be used to derive IDWT
𝐼𝐷NT = 𝐼𝐷WT =
𝐴
ln
𝑊𝑅
𝑊𝐿
WR
Start line
End line
WL
A
W(x)
dx
x
WR
End line
Start line
WL
A
W(x)
dx
x
Narrowing direction Widening direction
28
This does not reflect our observation:
MTNT > MTWT

Difficulty of One Movement
Our model
Acceptable slippage on y-axis is affected by the goal-side width
The current strategy is limited by the width at a little forward
Narrowing tunnel: users cannot use
the wider (start) side efficiently
Widening tunnel: users can use the
full width of the wider (end) side
29
Speed-down Speed-up

Deriving IDNT Based on Our Hypothesis
For simplicity, we assume that there are three movement corrections at
regular distance intervals
WR
Start line
End line
WL
A/3 A/3 A/3
e.g.) ID for ① is
𝐴/3
𝑊1
=
𝐴/3
(2𝑊 𝐿+𝑊 𝑅)/3
=
𝐴
2𝑊 𝐿+𝑊 𝑅
𝐼𝐷NT(3) =
𝐴
2𝑊𝐿 + 𝑊𝑅
+
𝐴
𝑊𝐿 + 2𝑊𝑅
+
𝐴
3𝑊𝑅
Narrowing direction
30
W1 W2 W3
① ② ③
① ② ③

Deriving IDWT Based on Our Hypothesis
As the same manner, IDWT(3) can be derived:
WR
End line
Start line
WL
A/3 A/3 A/3
Widening direction
31
W1 W2 W3
𝐼𝐷WT(3) =
𝐴
3𝑊𝐿
+
𝐴
+
𝐴

Deriving the ID Difference (IDGap)
𝐼𝐷 )Gap(3 = 𝐼𝐷 )NT(3 − 𝐼𝐷WT 3
=
𝐴
3𝑊𝑅
−
𝐴
3𝑊𝐿
=
3𝑊𝐿 𝑊𝑅
=
𝐴
+
𝐴
+
𝐴
3𝑊𝑅
−
𝐴
3𝑊𝐿
+
𝐴
+
𝐴
32
WR
Start line
End line
WL
A/3 A/3 A/3
Narrowing direction
W1 W2 W3
① ② ③
WR
End line
Start line
WL
A/3 A/3 A/3
Widening direction
W1 W2 W3
3 → N to generalize

Generalizing IDGap
Users’ strategies may depend on some conditions:
• Tunnel parameters: A, WL, WR, and the degree of change of W
• Current width: one movement becomes shorter under a narrower W
• Current speed: the lower speed is, the more re-thinking occurs in a certain distance
33
WRWL
A
N
A
N
A
N
A
N
A
N
WRWL
𝑎% 𝑏% 𝑐% 𝑑% 𝑒%
𝐼𝐷Gap(𝑁)=
𝑁𝑊𝐿 𝑊𝑅
If users perform movement corrections N times at regular distance intervals,

Our model IDGap
Replacing the number of equal partitions N with a free weight k
that reflects the experimental conditions and tunnel parameters
34
𝐼𝐷Gap(𝑘)=
Our final model:
IDGap(k)
Narrowing Widening
Consistency of our model and the constant-width model: When WL → WR, IDGap(k) → 0
“When the width becomes constant, the time difference between MTNT and MTWT becomes 0”
✔

Question: Steering Time Difference in Various Scales
• Is the time difference always observed in various scales?
• Does the IDGap model [Yamanaka+, CHI ’16] hold in various scales?
36
Longer MT
Shorter MT
Longer MT?
Shorter MT?

(video) (video)
Scale Effects in Narrowing and Widening Tunnels
38
1/1 (48×27 cm) 1/2 (24×13 cm) 1/4 (12×6.7 cm) 1/9 (5.2×3.0 cm) 1/12 (4.0×2.2 cm)
* In this setup, both of visual and motor scales change

Experiment (Design)
A 300, 600 pixels
(= 61.2, 122.4 mm)
WL & WR 11, 31, 51 pixels
( = 2.2, 6.3, 10.4 mm)
Scale (S) 1, 2, 4, 9, 12
2 (A) × {3 (WL) × 3 (WR) － 3 (WL = WR)}× 4 (repetition) = 48 trials per 1 scale
Only WL ≠ WR (not constant-width) conditions were selected
39
Tunnel type (narrowing/widening) was defined by the combination of {WL , WR}
Stroking direction was always to the right

Experiment (Device, Participants, Procedure, Data)
Device: direct-input 21.5-inch pen-tablet
Wacom Cintiq 22HD, 475.2× 267.3 mm, 1920 × 1080 pixels
Participants: ten local university students (within-participant)
Two female, eight male, all right-handed, Mean ± SD = 21.9 ± 2.27 years
Each participant performed 12 warm-up and 48 actual trials for 1 scale:
48 trials × 5 scales × 10 participants = 2400 data points
Recorded data
MT, error rate, time-stamped cursor trajectory
40

Result: MT (repeated measures ANOVA and the Bonferroni post hoc test)
Main effects: ・Scale (F4, 36 = 6.632, p < .001),
・Tunnel type (F1, 9 = 15.664, p < .01)
・ID (F5, 45 = 29.756, p < .001)
Post hoc test: MTNT > MTWT
(p < .01; 821 ms vs. 585 ms)
41
0
200
400
600
800
1000
1200
1 2 4 9 12
MT[ms]
Scale
Narrowing
Widening
For all scale S conditions, the relationship of
MTNT > MTWT was observed (at least p < .05)
Is the time difference always
observed in various scales?
ー Supported
* See our paper for details of error rate,
speed profile, and index of performance (IP)
analyses

No Clear U-shaped Function
For narrowing:
MT increased as the scale became smaller
→ Our results showed a monotonously increasing function
For widening:
A weak U-shaped function is observed,
but not clear
“MT monotonically increases as the stroke
length increases in open-loop operations”
[Cao+, CHI ’08]
→ Our W values were likely large for steering tasks
42
0
200
400
600
800
1000
1200
1 2 4 9 12
MT[ms]
Scale
Narrowing
Widening

Model Fitness: Conventional Steering Law [Accot+, CHI ’97]
Tunnel type (narrowing or widening) is separated
→ R2 > 0.94
43
Scale 1/1
Tunnel type (narrowing or widening) is NOT separated
→ R2 > 0.90
y = 56.702x - 22.815
R² = 0.9648
y = 41.591x + 25.525
R² = 0.94480
500
1000
1500
2000
2500
0 5 10 15 20 25 30 35
ID [bits]
MT[ms]
y = 49.146x + 1.3549
R² = 0.9002
0
500
1000
1500
2000
2500
0 5 10 15 20 25 30 35
ID [bits]
MT[ms]
Narrowing
Widening

Model Fitness: Conventional Steering Law [Accot+, CHI ’97]
44
y = 106.73x - 191.06
R² = 0.975
y = 77.898x - 162.3
R² = 0.97990
500
1000
1500
2000
2500
0 5 10 15 20 25 30 35
ID [bits]
y = 86.108x - 124.87
R² = 0.9513
y = 59.193x - 87.076
R² = 0.99450
500
1000
1500
2000
2500
0 5 10 15 20 25 30 35
ID [bits]
y = 64.099x - 56.995
R² = 0.9639
y = 48.409x - 84.142
R² = 0.99240
500
1000
1500
2000
2500
0 5 10 15 20 25 30 35
ID [bits]
y = 61.571x - 28.284
R² = 0.9809
y = 45.9x - 59.736
R² = 0.98530
500
1000
1500
2000
2500
0 5 10 15 20 25 30 35
ID [bits]
y = 56.702x - 22.815
R² = 0.9648
y = 41.591x + 25.525
R² = 0.94480
500
1000
1500
2000
2500
0 5 10 15 20 25 30 35
ID [bits]
MT[ms]
Narrowing
Widening
y = 92.312x - 176.68
R² = 0.8958
0
500
1000
1500
2000
2500
0 5 10 15 20 25 30 35
ID [bits]
y = 72.651x - 105.97
R² = 0.8619
0
500
1000
1500
2000
2500
0 5 10 15 20 25 30 35
ID [bits]
y = 56.254x - 70.569
R² = 0.8848
0
500
1000
1500
2000
2500
0 5 10 15 20 25 30 35
ID [bits]
y = 53.735x - 44.01
R² = 0.8814
0
500
1000
1500
2000
2500
0 5 10 15 20 25 30 35
ID [bits]
y = 49.146x + 1.3549
R² = 0.9002
0
500
1000
1500
2000
2500
0 5 10 15 20 25 30 35
ID [bits]
MT[ms]
Scale 1/1 Scale 1/2 Scale 1/4 Scale 1/9 Scale 1/12
For the conventional steering law, R2 = 0.86 is the worst case
We had better separate the tunnel type to predict MT

Our Model Fitness [Yamanaka+, CHI ’16]
The fitness improves with our model (R2 > 0.95)
Our model can predict MT without tunnel type separation in various scales
45
y = 79.098x - 158.42
R² = 0.9766
k = 4.48
0
500
1000
1500
2000
2500
0 5 10 15 20 25 30 35
ID [bits]
y = 59.888x - 88.343
R² = 0.979
k = 3.51
0
500
1000
1500
2000
2500
0 5 10 15 20 25 30 35
ID [bits]
y = 46.845x - 57.568
R² = 0.9937
k = 3.73
0
500
1000
1500
2000
2500
0 5 10 15 20 25 30 35
ID [bits]
y = 44.824x - 31.708
R² = 0.9881
k = 3.76
0
500
1000
1500
2000
2500
0 5 10 15 20 25 30 35
ID [bits]
y = 43.623x + 8.9899
R² = 0.9503
k = 5.91
0
500
1000
1500
2000
2500
0 5 10 15 20 25 30 35
ID [bits]
MT[ms]
Scale 1/1 Scale 1/2 Scale 1/4 Scale 1/9 Scale 1/12
k ranges 3.5 to 5.9
k was originally inserted as the number of movement corrections
Let us check the consistency of the role of k

The Role of k
(1) Result:
MT ranged 500 to 1100 ms
(2) Discrete sub-movement hypothesis (by Schmidt ’78 & ’79):
・“Humans’ reaction time is ~200 ms”
・“Humans make four or five corrections in a 900-ms movement”
(3) Within 500 to 1100 ms, humans are assumed to perform 2 to 6 corrections
The results show that k ranges 3.5 to 5.9
This weakly holds the consistency with the original role of k
46
0
200
400
600
800
1000
1200
1 2 4 9 12
MT[ms]
Scale
Narrowing
Widening
* Continuous movement corrections are also believed by HCI researchers

(video here)
Summary
47
This PowerPoint file will be available at http://www.slideshare.net/shotayamanaka35
In various scales (1/1 to 1/12 of the 21.5-inch pen tablet),
(1) MTNT was longer than MTWT (p < .01)
(2) The data supported that IDGap model described a relationship between IDNT and IDWT
(3) U-shaped function (i.e., medium size is the best) was not observed
0
200
400
600
800
1000
1200
1 2 4 9 12
MT[ms]
Scale
Narrowing
Widening
𝐼𝐷Gap(𝑘)=
Contact: Shota Yamanaka, Meiji University (stymnk@meiji.ac.jp)

Detailed Analysis: Akaike Information Criteria (AIC)
Our model has additional free parameter k
→ the model fitness naturally increases compared to the conventional model,
→ overfitting is introduced, which results in inaccurate predictions of MT
AIC can balance the following two factors:
(1) the complexity of the model (i.e., number of free parameters), and
(2) the model fitness
Better model has LOWER AIC value
→ statistically our model improves the prediction capability
48
Model Scale 1/1 Scale 1/2 Scale 1/4 Scale 1/9 Scale 1/12
Conventional 154.620 159.098 159.798 168.426 170.336
Proposed 148.271 133.516 126.862 147.847 154.434

Speed Profile Analysis (A = 600 pixels)
"Turnover" points of the speed appear around 25% on the x-axis
SpeedWT is higher than SpeedNT in 75% of the tunnel length
49
0
0.5
1
1.5
2
2.5
3
3.5
0 150 300 450 600
0
0.5
1
1.5
2
2.5
3
3.5
0 75 150 225 300
0
0.5
1
1.5
2
2.5
3
3.5
0 37.5 75 112.5 150
0
0.5
1
1.5
2
2.5
3
3.5
0 16.5 33 49.5 66
0
0.5
1
1.5
2
2.5
3
3.5
0 12.5 25 37.5 50
Cursor progress on the x-axis [%]
Velocity[pixels/ms]
Narrowing
Widening
0 25 50 75 1000 25 50 75 1000 25 50 75 100 0 25 50 75 100 0 25 50 75 100
1/1 1/2 1/4 1/9 1/12

Result: Error Rate
50
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
1 2 4 9 12
Errorrate
Scale
Narrowing
Widening
Main effects: ・Scale (F4, 36 = 11.289, p < .001),
・Tunnel type (F1, 9 = 7.579, p < .05)
・ID (F5, 45 = 9.151, p < .001)
Post hoc test: ErrorRateNT > ErrorRateWT
(p < .05; 7.48% vs. 3.15%)
Navigating narrowing tunnels is
more difficult than widening tunnels

Does the Performance Decrease as the Scale Decreases?
No established theory: researchers have claimed different opinions
• Hess:
Inversed U-shape function (medium scale is the best) in joystick pointing tasks
• Gibb:
Linear function: a smaller scale is worse
• Jellinek and Card
Mouse cursor speed setting has no scale effect
51

Steering Law [Rashevsky 1959, Drury 1971, Accot & Zhai 1997]
52
𝑠𝑝𝑒𝑒𝑑 =
𝑊 − 2𝛿 − 𝑐
𝜃𝑡
𝑡𝑖𝑚𝑒 =
𝐴𝜃𝑘𝑡
𝑊
𝑡𝑖𝑚𝑒 = 𝑎 + 𝑏
𝐴
𝑊
Discovered independently three times
Key point:
In a wide path tolerance, the speed is high, and the time required is shortened
Rashevsky’s model (for car driving)
Drury’s model (for real pen operations)
Accot and Zhai’s model (for GUIs)

NordiCHI2016_yamanaka_novideo

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