Curtain Graphs: Using a Floating Baseline for Comparison in a

Two-dimensional Graphical Space

Kassandra Raymond and Andrew Hamilton-Wright

School of Computer Science, University of Guelph, Canada

Keywords:

Relative and Absolute Measurement, Multi-dimensional Data, Floating Baseline, Inter-series Comparison,

Time-series, Data Analysis.

Abstract:

We present a novel visualization tool designed to provide support for the analysis of data sets focused around

deviation from a baseline and including data from multiple series. The incorporation of a ﬂoating baseline

makes the curtain graph distinct from waterfall plots and bar charts. Each data series therefore has a visual

anchor that assists in interpretability, gives focus, and provides a means for easily broadening analysis across

all presented series. The use of this tool in real-world examples based on relative and absolute comparisons is

discussed.

1 INTRODUCTION AND

RELATED WORK

This paper presents a novel tool for inter- and within-

series comparisons where a deﬁning feature of the se-

ries is its relationship to a particular anchor point, rep-

resenting an initial condition or exemplar. This static

graph can be used to visualize comparisons between

multi-dimensional numerical and categorical data.

1.1 Background

The complexity of data analysis is increasing, both in

terms of the complexity of the data sets themselves,

and in the insights expected to be derived from them.

The relationship between multiple variables of dif-

ferent types frequently captures the critical insight

allowing us to understand a multi-dimensional data

problem. This dimensionality, coupled with data of

different types, such as discrete, continuous and cat-

egorical, can create a complicated set of data which

can be difﬁcult to visualize. Moreover, we are often

limited to static plots when creating reports, books or

articles, causing it to be increasingly difﬁcult to dis-

play multi-dimensional data.

The ﬁeld of information visualization has a long

history of both broadly applicable and context spe-

ciﬁc visualization techniques. Great ideas in the ﬁeld

build on the work of pioneers such a Bertin (2001) and

we see books regularly appearing that provide excel-

lent advice in how to proceed both in general and in

speciﬁc cases (Shneiderman, 1996; Tufte, 2001, 1991,

1997, 2006; Cairo, 2012, 2016; Evergreen, 2020).

A central focus within this long history is the iden-

tiﬁcation of tools speciﬁc to a certain decision making

paradigm. Inside of a decision making context, identi-

ﬁcation of a particular narrative (Klanten et al., 2011)

or decision point (Agrawala et al., 2011) allows con-

struction of a context for the speciﬁc data interpreta-

tion needs (Cairo, 2016).

Evaluation of visualization techniques has pro-

ceeded by applying various metrics to elucidate the

understandability, utility and efﬁcacy of the tool (Zen,

2013; Agrawala et al., 2011; Daru, 2001), including

metrics such as the data-ink ratio (Tufte, 2001; In-

bar et al., 2007) and identiﬁcation of patterns driv-

ing our understand such as ‘small multiples’ (Tufte,

1991, pp. 67–80). This analysis has resulted in toolk-

its (Heer et al., 2005; Klimov et al., 2010) and advice

(Shneiderman, 1996; Evergreen, 2020; Hicks, 2009;

Metoyer et al., 2012) based around selecting exactly

the correct visualization for a speciﬁc purpose, result-

ing in tailored visualizations for speciﬁc applications

(de Almeida and Roselli, 2017; Klimov et al., 2010;

Klanten et al., 2011).

In this paper we target a speciﬁc instance of data

set interpretation, focusing on a multi-dimensional

data set whose interpretation is based on the context

of changes relative to a particular exemplar point—

either an initial sample forming a point in time, or a

particular datum from which all of the other points

derive their meaning in some other form.

Raymond, K. and Hamilton-Wright, A.

Curtain Graphs: Using a Floating Baseline for Comparison in a Two-dimensional Graphical Space.

DOI: 10.5220/0008874001250132

In Proceedings of the 15th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications (VISIGRAPP 2020) - Volume 3: IVAPP, pages

125-132

ISBN: 978-989-758-402-2; ISSN: 2184-4321

125

−200

200

400

Initial Sales Refunds Payouts Court LossesCour t Wins Contracts End Cash

desc

type

net

out

Figure 1: Waterfall plot

showing consecutive

changes in a series, from

Few (2006).

banana poacee sorgho triticum

species

value

condition

Nitrogen

Normal

Stress

Figure 2: Stacked barchart

showing series data in sum-

mation, from Holtz (2019).

Figure 3: Hat graphs (rightmost two plots), as related to

barcharts of the same data; reproduced from Witt (2019).

A related visualization technique is the ‘waterfall

chart’ (Metoyer et al., 2012; Few, 2006; Evergreen,

2020), which is constructed as a sequence of bars

with a start and end showing change at an interval de-

scribed on the x axis relative to the previous bar, as

shown in Figure 1, which is reproduced from the data

discussed in Few (2006).

In a waterfall chart, there are three assumptions

that are different from those of our needs:

• the initial value from which the ﬁrst change starts

is assumed to be zero;

• the changes as one works through the series are to

be compared primarily only to their neighbours;

and

• there is only one series in the chart.

Another related visualization is the common

stacked bar chart, as discussed in Talbot et al. (2014)

and shown in Figure 2. In this presentation, data from

several series over a common baseline are combined

into stacks. however the readability within a given

series is compromised in support of an overall under-

standing of the extent of the sum of the series. The

difﬁculty of visually separating a single series from

the stack is evident.

Other work improves on the data-ink ratio of the

bar char, providing the hat graph, shown in Figure 3,

reproduced from the paper developing this technique,

(Witt, 2019). In the hat graph, only the tops of the

bars of a bar chart, providing a ﬂoating appearance of

the relevant data, and using as visual anchor the top of

the ﬁrst bar. This reduces the amount of int required,

to present the same data as the analogous bar chart, as

shown in Figure 3.

1.2 Identifying the Need

We wish to extend the use of the waterfall plot for the

speciﬁc context in which we have multiple series of

data, and where the initial point is the focus of com-

parison across all points on the x axis. We break the

association with a single baseline, allowing various

types of comparisons across and among the data se-

ries within the plot, unifying the whole within a com-

mon y axis.

The next section of this paper will outline our pro-

posed solution to this problem, and outline the deﬁn-

ing features of our idea. Following this we will eval-

uate our tool on several interesting data sets drawn

from real world problems. Finally, we present a dis-

cussion summarizing the data trends, patterns and

comparisons that can be expressed by the curtain

graph.

2 PROPOSED VISUALIZATION

The motivation for this visualization comes from the

desire to represent three-dimensions within a clear

two-dimensional set of axes. The measures along the

x dimension form a series relative to a ﬁxed starting

location, but where this starting location is not nec-

essarily the same for other series within the same x

variable. The y axis provides a common system for

interpretation, and a set of data series arranged hori-

zontally captures a variable in the z axis.

Thus, we present the curtain graph (Figure 4). The

curtain graph is a novel, comprehensible method of

visualizing high dimensional, multivariate data. This

plot allows correlations of various attributes of a data

set involving relative and absolute value comparisons

to be easily identiﬁed on a single plot.

2.1 The Curtain Graph

The fundamental property of the curtain graph is the

inclusion, within a single y axis, of a series of bar-

chart type representations, allowing the visualization

to be especially useful when comparing data with

multiple treatment types. Figure 4 shows a detailed

example of the curtain graph.

In Figure 4, each of the bar chart representations,

which we will now refer to as ‘subplots,’ are placed

vertically in a position on the curtain graph which acts

as an anchor for that subplot. This anchor represents

a common baseline, from which each bar from each

subplot extends. A single subplot is identiﬁed in Fig-

ure 4 within the single line yellow box.

IVAPP 2020 - 11th International Conference on Information Visualization Theory and Applications

126

1 2 3 4 5

Pesticide Type

Number of Plants

type

corn_muck

corn_sand

soybean_muck

soybean_sand

squash_muck

squash_sand

Difference

from Baseline

Curtain Rod

(baseline)

Sequential

data x axis

Subplot - the

sequence

of subplots

captures

a categorial

variable

along the z axis

Figure 4: The anatomy of a curtain graph; colour/line vari-

ations used to show the graphical terminology used to refer

unique areas on the plot. This ﬁgure was rendered from R

using ggplot2 and modiﬁcations to the geom rect func-

tionality.

We will refer to the this ﬂoating baseline as the

‘curtain rod’ as it provides the anchor for the strips

forming the ‘curtain’ to ascend or descend. This ﬂoat-

ing axis rod is shown in Figure 4 enclosed by a blue

double box near the right hand side of the ﬁgure.

The subplot consisting of the ﬂoating curtain rod

axis and the attached bars can be placed in a se-

quence representing some categorical variable. Fig-

ure 4 presents the data obtained when measuring the

response variable “Number of Plants” obtained when

applying one of six (numbered) pesticide preparations

to plants growing in various ‘muck’ and ‘sand’ soils.

For each soil type there is a base expected yield, and

the pesticide performance is measured against this

base yield.

Such a sequence is shown in Figure 4 within the

dotted ellipse identifying the individual bars making

up the curtain running along the rod presented within

the leftmost subplot of the ﬁgure. This sequence of

the bars allows a second variable within an inner x

axis, providing side-by-side comparison of some vari-

able for whom the values form the basis of the most

sensitive consideration in the visualization design (as

opposed to the set of subplots forming the outer, or z

axis, following the advice from Talbot et al. (2014).

In this case, this would be pesticide type.

By placing the bars of the subplots all together at

the same y coordinate, the absolute and relative po-

sition of each of the bar from the curtain rod of the

bars respective subplot can be identiﬁed. Each sub-

plot contains the data for a speciﬁc instance of a vari-

able of interest for which we have performed repeated

measures. The same bar within each curtain then per-

tains to a measure of the same variable within a dif-

ferent data series.

As noted in Cleveland and McGill (1984), posi-

tion along a given access is an easily apprehended

measure, and in particular more easily understood

than data represented purely by length. In the exten-

sive experimentation provided by Talbot et al. (2014),

these conclusions are extended by statements about

relative bar length, separation and position that sup-

port our placement within disparate series.

Because the curtain rod acts as the anchor for

comparison of the variables within each subplot, the

units of measure forming the y axis must be conduc-

tive to measurement within this number line. Each

bar of the curtain provides an easily approachable

measure of the degree of deviation from the baseline,

while the absolute position of the ends of these bars

provides an ability to compare the data across the full

graphic, in absolute terms. This allows both simple

absolute comparisons of values as typically found on

a standard bar chart, or in a waterfall plot, as well

as relative comparisons within the series attached to

each ﬂoating curtain rod baseline.

Note the distinction from the hat graph described

by Witt (2019); while both graph types display an ap-

parently ﬂoating sequence, in the hat graph, this se-

quence is driven by the need to display only the tops

of bars arising in the same direction from a baseline

at an axis. Here, the baseline itself is ﬂoating, and

the potential variability in sign requires us to keep the

bars linking the data with each ﬂoating baseline.

While the properties commonly held on any

number-line axis measurement (such as linear, loga-

rithmic etc.) must be considered for the y axis, the x

axis can be comprised of other variable types such as

ordinal or categorical. The x axis of the curtain graph

is comprised of the axes on the subplots. The number

of labels on each x axis will correspond to the number

of bars extending from each curtain rod. For exam-

ple, with three subplots, each containing six bars, the

x axis would consist of three sequences of multiply

measured variables with six labels.

Curtain Graphs: Using a Floating Baseline for Comparison in a Two-dimensional Graphical Space

127

Back/Frontal Back/Sagittal Head/Frontal Head/Sagittal

Sitting

●

● ● ●

● ●

●

234567 8

● ● ● ● ● ● ●

234567 8

●

● ● ●

234567 8

● ● ● ● ● ● ●

234567 8

S/S45%

●

● ● ●

234567 8

● ● ● ● ● ● ●

234567 8

●

● ●

●

2345678

●

● ●

●

234567 8

Figure 5: Four subplots showing the comparison of ﬁve dimensions of data using the curtain graph. Subplot curtain identiﬁers:

Back Avoid

HS00 HS-1 HS00 HS+1

à à à

Postural state sequence duration and musculoskeletal

disorder marker perception at sit-stand workstations

Kassandra'Raymond¹. Andrew'Hamilton-Wright¹.'Nancy'Black

.'''

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INTRODUCTION

Musculoskeletal disorders (MSDs) account for approximately 43% of all workers

compensation claims in Ontario, costing the government up to 22 billion dollars a year [1].

Prolonged static postures, such as those required in office work, are a known cause of

MSDs [2]. In a past study by Black et al., significant postural gestures that were associated

with perceived pain or fatigue were identified, however duration of postural state was not

considered [3]. Objective: To add duration analysis to a previous study of the

relationship between postural gestures (movements) and participants’ perception of

pain and fatigue during office work.

References

1, Owen, N., Healy, G.N., Mathews, C.E. and Dunstan, D.W. (2010). Too much sitting: The population health science of sedentary behavior. Exercise and Sport Sciences Reviews 38 (3): 105-13

2. Bhanderi D, Choudhary S, Parmar L, Doshi V. A Study of Occurrence of Musculoskeletal Discomfort in Computer Operators. Indian J Community Med Off Publ Indian Assoc Prev Soc Med. 2008 Jan;33(1):65–6.

3. Black N, Hamilton-Wright A, Lange J, Bouet C, Shein MM, Samson M, et al. Postural Deviation Gestures Distinguish Perceived Pain and Fatigue Particularly in Frontal Plane. In: Bagnara S, Tartaglia R, Albolino S, Alexander T, Fujita Y, editors. Proceedings of the 20th Congress of the International Ergonomics Association (IEA 2018). Springer; 2019. p. 495–501.

4. Keyserling, W.M. (1986). Postural analysis of the trunk and shoulders in simulated real time. Ergonomics. 29, 569–583.

5. McAtamney, L., and Corlett, N. (1993). RULA: A Survey Method for the Investigation of Work Related Upper Limb Disorders. Applied Ergonomics, 24(2), 91-99.

METHODOLOGY

(A) Data Collection

• 10 participants completed a 1 hr data entry task at each of 3 workstations (sitting,

S/S30%, S/S45%) and used a 10 point visual analogue scale to mark their perception of

fatigue and neck and back pain

• 16 Hz, 2D inclinometers on the back and neck of each participant measuring angles in

the frontal and sagittal planes

RESULTS & DISCUSSION

Back Frontal Back Sagittal Head Frontal Head Sagittal

SittingS/S30%S/S45%

CHANNEL STATE*

ANGULAR*

RANGE

HS HS

-1

-∞ -5

HS00 -5 10

HS+1 10 20

HS+2 20 ∞

HF HF

-2

-∞ -10

-1

-10 -2

HF00 -2 2

HF+1 2 10

HF+2 10 ∞

BS BS

-2

-∞ -5

-1

-5 10

BS00 10 20

BS+1 20 60

BS+2 60 ∞

BF BF

-2

-∞ -10

-1

-10 -2

BF00 -2 2

BF+1 2 10

BF+2 10 ∞

CONCLUSION & FUTURE DIRECTIONS

While the data are noisy, there is evidence to suggest that there are postural movements that may be

associated with the risk or avoidance of pain and fatigue. Future work will explore subtle movements

based on direct measurements of postural angles to compare found patterns with those reported here

with the RULA paradigm. This study provides a novel method for categorizing human movement

based on raw inclinometer measurements and underscores the importance of understanding

quantization boundaries upon their introduction.

Figure 1: Waterfall plots showing the absolute and relative change in number of postural sequences significantly associated with a

given perception as an MPD filter is applied for each workstation (sitting, S/S30%, S/S45%) and channel (head frontal plane, head

sagittal plane, back frontal plane, back sagittal plane).

(E) Perceptual Features

Black et al.’s (2018) quintile separation method was

used to categorize perceptual data from the visual

analogue scale into the ‘absence’ or ‘presence’ of a

given perception, for each participant and workstation.

q Filtering using a lower MPD filter shows that in 15 cases there is an increase in the number of

patterns found, while filtering with a longer MPD causes a decrease in the number of patterns (Fig 1).

q Mapping of dynamic posture into quantization boundaries can introduce an apparent increase in the

number of postural state changes. When this occurs due to a small overall change in the measured

angle that crosses into a new quantization region and then returns to the original, this small change

may be better ignored.

q While using RULA allows for the quantification of postural movements, smaller movements that are

occurring within a RULA defined region may be lost.

(B) Postural State Quantization

Each raw sample was quantized using the thresholds

adapted from RULA in Table 1.

(D) Postural Sequence Identification

Postural states were linked together to length 4 to

create postural gestures.

A state must have occurred for a minimum number of

samples to be considered a postural state change,

otherwise the sample was assigned to the previous

state. An MPD of 1 through 8 was calculated.

Table 1: Angular thresholds used to assign State

IDs to raw inclinometer angles. Thresholds

adapted from the Rapid Upper Limb Assessment

(RULA) methodology [4][5].

(F) Chi squared contingency test

If the postural gestures for a given perception occurred at least 5 times in both the present

and absence group and the results of the !

contingency comparison resulted in a p < .01,

then the postural gesture was deemed significant

●

● ● ●

● ●

●

23 4 5 6 78

● ● ● ● ● ● ●

23 4 5 6 7 8

●

● ● ●

23 4 5 6 7 8

● ● ● ● ● ● ●

23 4 5 6 7 8

● ● ● ● ● ●

●

23 4 5 6 78

● ● ● ● ● ●

●

23 4 5 6 78

●

● ●

●

23 4 5 6 78

●

● ● ● ● ● ●

23 4 5 6 7 8

●

● ● ●

23 4 5 6 7 8

● ● ● ● ● ● ●

23 4 5 6 7 8

●

● ●

●

234 567 8

●

● ●

●

23 4 5 6 7 8

0 5 10 15

LEGEND

Back'avoid

Back'risk

Fatigue'avoid

Fatigue'risk

Neck'avoid'

Neck'risk

Minimum Persistent Duration

# of Significant Postural Sequences

2 4 6 8

3 5 7

. Back Risk

HS00 HS-1 HS00 HS+1

à à à

Postural state sequence duration and musculoskeletal

disorder marker perception at sit-stand workstations

Kassandra'Raymond¹. Andrew'Hamilton-Wright¹.'Nancy'Black

.'''

!"# $%&''()'*)+',-./01)$%203%04)53260172/8)'*)9.0(-&): ;1<8,'3=>.'?.0(-&@%< !A#)B<%.(/C =D23?C3201204)53260172/C =0)E'3%/'3

INTRODUCTION

Musculoskeletal disorders (MSDs) account for approximately 43% of all workers

compensation claims in Ontario, costing the government up to 22 billion dollars a year [1].

Prolonged static postures, such as those required in office work, are a known cause of

MSDs [2]. In a past study by Black et al., significant postural gestures that were associated

with perceived pain or fatigue were identified, however duration of postural state was not

considered [3]. Objective: To add duration analysis to a previous study of the

relationship between postural gestures (movements) and participants’ perception of

pain and fatigue during office work.

References

1, Owen, N., Healy, G.N., Mathews, C.E. and Dunstan, D.W. (2010). Too much sitting: The population health science of sedentary behavior. Exercise and Sport Sciences Reviews 38 (3): 105-13

4. Keyserling, W.M. (1986). Postural analysis of the trunk and shoulders in simulated real time. Ergonomics. 29, 569–583.

5. McAtamney, L., and Corlett, N. (1993). RULA: A Survey Method for the Investigation of Work Related Upper Limb Disorders. Applied Ergonomics, 24(2), 91-99.

METHODOLOGY

(A) Data Collection

• 10 participants completed a 1 hr data entry task at each of 3 workstations (sitting,

S/S30%, S/S45%) and used a 10 point visual analogue scale to mark their perception of

fatigue and neck and back pain

• 16 Hz, 2D inclinometers on the back and neck of each participant measuring angles in

the frontal and sagittal planes

RESULTS & DISCUSSION

Back Frontal Back Sagittal Head Frontal Head Sagittal

SittingS/S30%S/S45%

CHANNEL STATE*

ANGULAR*

RANGE

HS HS

-1

-∞ -5

HS00 -5 10

HS+1 10 20

HS+2 20 ∞

HF HF

-2

-∞ -10

-1

-10 -2

HF00 -2 2

HF+1 2 10

HF+2 10 ∞

BS BS

-2

-∞ -5

-1

-5 10

BS00 10 20

BS+1 20 60

BS+2 60 ∞

BF BF

-2

-∞ -10

-1

-10 -2

BF00 -2 2

BF+1 2 10

BF+2 10 ∞

CONCLUSION & FUTURE DIRECTIONS

While the data are noisy, there is evidence to suggest that there are postural movements that may be

associated with the risk or avoidance of pain and fatigue. Future work will explore subtle movements

based on direct measurements of postural angles to compare found patterns with those reported here

with the RULA paradigm. This study provides a novel method for categorizing human movement

based on raw inclinometer measurements and underscores the importance of understanding

quantization boundaries upon their introduction.

Figure 1: Waterfall plots showing the absolute and relative change in number of postural sequences significantly associated with a

given perception as an MPD filter is applied for each workstation (sitting, S/S30%, S/S45%) and channel (head frontal plane, head

sagittal plane, back frontal plane, back sagittal plane).

(E) Perceptual Features

Black et al.’s (2018) quintile separation method was

used to categorize perceptual data from the visual

analogue scale into the ‘absence’ or ‘presence’ of a

given perception, for each participant and workstation.

q Filtering using a lower MPD filter shows that in 15 cases there is an increase in the number of

patterns found, while filtering with a longer MPD causes a decrease in the number of patterns (Fig 1).

q Mapping of dynamic posture into quantization boundaries can introduce an apparent increase in the

number of postural state changes. When this occurs due to a small overall change in the measured

angle that crosses into a new quantization region and then returns to the original, this small change

may be better ignored.

q While using RULA allows for the quantification of postural movements, smaller movements that are

occurring within a RULA defined region may be lost.

(B) Postural State Quantization

Each raw sample was quantized using the thresholds

adapted from RULA in Table 1.

(D) Postural Sequence Identification

Postural states were linked together to length 4 to

create postural gestures.

A state must have occurred for a minimum number of

samples to be considered a postural state change,

otherwise the sample was assigned to the previous

state. An MPD of 1 through 8 was calculated.

Table 1: Angular thresholds used to assign State

IDs to raw inclinometer angles. Thresholds

adapted from the Rapid Upper Limb Assessment

(RULA) methodology [4][5].

(F) Chi squared contingency test

If the postural gestures for a given perception occurred at least 5 times in both the present

and absence group and the results of the !

contingency comparison resulted in a p < .01,

then the postural gesture was deemed significant

●

● ● ●

● ●

●

23 4 5 6 78

● ● ● ● ● ● ●

23 4 5 6 7 8

●

● ● ●

23 4 5 6 7 8

● ● ● ● ● ● ●

23 4 5 6 7 8

● ● ● ● ● ●

●

23 4 5 6 78

● ● ● ● ● ●

●

23 4 5 6 78

●

● ●

●

23 4 5 6 78

●

● ● ● ● ● ●

23 4 5 6 7 8

●

● ● ●

23 4 5 6 7 8

● ● ● ● ● ● ●

23 4 5 6 7 8

●

● ●

●

234 567 8

●

● ●

●

23 4 5 6 7 8

0 5 10 15

LEGEND

Back'avoid

Back'risk

Fatigue'avoid

Fatigue'risk

Neck'avoid'

Neck'risk

Minimum Persistent Duration

# of Significant Postural Sequences

2 4 6 8

3 5 7

. Fatigue Avoid

HS00 HS-1 HS00 HS+1

à à à

Postural state sequence duration and musculoskeletal

disorder marker perception at sit-stand workstations

Kassandra'Raymond¹. Andrew'Hamilton-Wright¹.'Nancy'Black

.'''

!"# $%&''()'*)+',-./01)$%203%04)53260172/8)'*)9.0(-&): ;1<8,'3=>.'?.0(-&@%< !A#)B<%.(/C =D23?C3201204)53260172/C =0)E'3%/'3

INTRODUCTION

Musculoskeletal disorders (MSDs) account for approximately 43% of all workers

compensation claims in Ontario, costing the government up to 22 billion dollars a year [1].

Prolonged static postures, such as those required in office work, are a known cause of

MSDs [2]. In a past study by Black et al., significant postural gestures that were associated

with perceived pain or fatigue were identified, however duration of postural state was not

considered [3]. Objective: To add duration analysis to a previous study of the

relationship between postural gestures (movements) and participants’ perception of

pain and fatigue during office work.

References

1, Owen, N., Healy, G.N., Mathews, C.E. and Dunstan, D.W. (2010). Too much sitting: The population health science of sedentary behavior. Exercise and Sport Sciences Reviews 38 (3): 105-13

4. Keyserling, W.M. (1986). Postural analysis of the trunk and shoulders in simulated real time. Ergonomics. 29, 569–583.

5. McAtamney, L., and Corlett, N. (1993). RULA: A Survey Method for the Investigation of Work Related Upper Limb Disorders. Applied Ergonomics, 24(2), 91-99.

METHODOLOGY

(A) Data Collection

• 10 participants completed a 1 hr data entry task at each of 3 workstations (sitting,

S/S30%, S/S45%) and used a 10 point visual analogue scale to mark their perception of

fatigue and neck and back pain

• 16 Hz, 2D inclinometers on the back and neck of each participant measuring angles in

the frontal and sagittal planes

RESULTS & DISCUSSION

Back Frontal Back Sagittal Head Frontal Head Sagittal

SittingS/S30%S/S45%

CHANNEL STATE*

ANGULAR*

RANGE

HS HS

-1

-∞ -5

HS00 -5 10

HS+1 10 20

HS+2 20 ∞

HF HF

-2

-∞ -10

-1

-10 -2

HF00 -2 2

HF+1 2 10

HF+2 10 ∞

BS BS

-2

-∞ -5

-1

-5 10

BS00 10 20

BS+1 20 60

BS+2 60 ∞

BF BF

-2

-∞ -10

-1

-10 -2

BF00 -2 2

BF+1 2 10

BF+2 10 ∞

CONCLUSION & FUTURE DIRECTIONS

While the data are noisy, there is evidence to suggest that there are postural movements that may be

associated with the risk or avoidance of pain and fatigue. Future work will explore subtle movements

based on direct measurements of postural angles to compare found patterns with those reported here

with the RULA paradigm. This study provides a novel method for categorizing human movement

based on raw inclinometer measurements and underscores the importance of understanding

quantization boundaries upon their introduction.

Figure 1: Waterfall plots showing the absolute and relative change in number of postural sequences significantly associated with a

given perception as an MPD filter is applied for each workstation (sitting, S/S30%, S/S45%) and channel (head frontal plane, head

sagittal plane, back frontal plane, back sagittal plane).

(E) Perceptual Features

Black et al.’s (2018) quintile separation method was

used to categorize perceptual data from the visual

analogue scale into the ‘absence’ or ‘presence’ of a

given perception, for each participant and workstation.

q Filtering using a lower MPD filter shows that in 15 cases there is an increase in the number of

patterns found, while filtering with a longer MPD causes a decrease in the number of patterns (Fig 1).

q Mapping of dynamic posture into quantization boundaries can introduce an apparent increase in the

number of postural state changes. When this occurs due to a small overall change in the measured

angle that crosses into a new quantization region and then returns to the original, this small change

may be better ignored.

q While using RULA allows for the quantification of postural movements, smaller movements that are

occurring within a RULA defined region may be lost.

(B) Postural State Quantization

Each raw sample was quantized using the thresholds

adapted from RULA in Table 1.

(D) Postural Sequence Identification

Postural states were linked together to length 4 to

create postural gestures.

A state must have occurred for a minimum number of

samples to be considered a postural state change,

otherwise the sample was assigned to the previous

state. An MPD of 1 through 8 was calculated.

Table 1: Angular thresholds used to assign State

IDs to raw inclinometer angles. Thresholds

adapted from the Rapid Upper Limb Assessment

(RULA) methodology [4][5].

(F) Chi squared contingency test

If the postural gestures for a given perception occurred at least 5 times in both the present

and absence group and the results of the !

contingency comparison resulted in a p < .01,

then the postural gesture was deemed significant

●

● ● ●

● ●

●

23 4 5 6 78

● ● ● ● ● ● ●

23 4 5 6 7 8

●

● ● ●

23 4 5 6 7 8

● ● ● ● ● ● ●

23 4 5 6 7 8

● ● ● ● ● ●

●

23 4 5 6 78

● ● ● ● ● ●

●

23 4 5 6 78

●

● ●

●

23 4 5 6 78

●

● ● ● ● ● ●

23 4 5 6 7 8

●

● ● ●

23 4 5 6 7 8

● ● ● ● ● ● ●

23 4 5 6 7 8

●

● ●

●

234 567 8

●

● ●

●

23 4 5 6 7 8

0 5 10 15

LEGEND

Back'avoid

Back'risk

Fatigue'avoid

Fatigue'risk

Neck'avoid'

Neck'risk

Minimum Persistent Duration

# of Significant Postural Sequences

2 4 6 8

3 5 7

. Fatigue Risk

HS00 HS-1 HS00 HS+1

à à à

Postural state sequence duration and musculoskeletal

disorder marker perception at sit-stand workstations

Kassandra'Raymond¹. Andrew'Hamilton-Wright¹.'Nancy'Black

.'''

!"# $%&''()'*)+',-./01)$%203%04)53260172/8)'*)9.0(-&): ;1<8,'3=>.'?.0(-&@%< !A#)B<%.(/C =D23?C3201204)53260172/C =0)E'3%/'3

INTRODUCTION

Musculoskeletal disorders (MSDs) account for approximately 43% of all workers

compensation claims in Ontario, costing the government up to 22 billion dollars a year [1].

Prolonged static postures, such as those required in office work, are a known cause of

MSDs [2]. In a past study by Black et al., significant postural gestures that were associated

with perceived pain or fatigue were identified, however duration of postural state was not

considered [3]. Objective: To add duration analysis to a previous study of the

relationship between postural gestures (movements) and participants’ perception of

pain and fatigue during office work.

References

1, Owen, N., Healy, G.N., Mathews, C.E. and Dunstan, D.W. (2010). Too much sitting: The population health science of sedentary behavior. Exercise and Sport Sciences Reviews 38 (3): 105-13

4. Keyserling, W.M. (1986). Postural analysis of the trunk and shoulders in simulated real time. Ergonomics. 29, 569–583.

5. McAtamney, L., and Corlett, N. (1993). RULA: A Survey Method for the Investigation of Work Related Upper Limb Disorders. Applied Ergonomics, 24(2), 91-99.

METHODOLOGY

(A) Data Collection

• 10 participants completed a 1 hr data entry task at each of 3 workstations (sitting,

S/S30%, S/S45%) and used a 10 point visual analogue scale to mark their perception of

fatigue and neck and back pain

• 16 Hz, 2D inclinometers on the back and neck of each participant measuring angles in

the frontal and sagittal planes

RESULTS & DISCUSSION

Back Frontal Back Sagittal Head Frontal Head Sagittal

SittingS/S30%S/S45%

CHANNEL STATE*

ANGULAR*

RANGE

HS HS

-1

-∞ -5

HS00 -5 10

HS+1 10 20

HS+2 20 ∞

HF HF

-2

-∞ -10

-1

-10 -2

HF00 -2 2

HF+1 2 10

HF+2 10 ∞

BS BS

-2

-∞ -5

-1

-5 10

BS00 10 20

BS+1 20 60

BS+2 60 ∞

BF BF

-2

-∞ -10

-1

-10 -2

BF00 -2 2

BF+1 2 10

BF+2 10 ∞

CONCLUSION & FUTURE DIRECTIONS

While the data are noisy, there is evidence to suggest that there are postural movements that may be

associated with the risk or avoidance of pain and fatigue. Future work will explore subtle movements

based on direct measurements of postural angles to compare found patterns with those reported here

with the RULA paradigm. This study provides a novel method for categorizing human movement

based on raw inclinometer measurements and underscores the importance of understanding

quantization boundaries upon their introduction.

Figure 1: Waterfall plots showing the absolute and relative change in number of postural sequences significantly associated with a

given perception as an MPD filter is applied for each workstation (sitting, S/S30%, S/S45%) and channel (head frontal plane, head

sagittal plane, back frontal plane, back sagittal plane).

(E) Perceptual Features

Black et al.’s (2018) quintile separation method was

used to categorize perceptual data from the visual

analogue scale into the ‘absence’ or ‘presence’ of a

given perception, for each participant and workstation.

q Filtering using a lower MPD filter shows that in 15 cases there is an increase in the number of

patterns found, while filtering with a longer MPD causes a decrease in the number of patterns (Fig 1).

q Mapping of dynamic posture into quantization boundaries can introduce an apparent increase in the

number of postural state changes. When this occurs due to a small overall change in the measured

angle that crosses into a new quantization region and then returns to the original, this small change

may be better ignored.

q While using RULA allows for the quantification of postural movements, smaller movements that are

occurring within a RULA defined region may be lost.

(B) Postural State Quantization

Each raw sample was quantized using the thresholds

adapted from RULA in Table 1.

(D) Postural Sequence Identification

Postural states were linked together to length 4 to

create postural gestures.

A state must have occurred for a minimum number of

samples to be considered a postural state change,

otherwise the sample was assigned to the previous

state. An MPD of 1 through 8 was calculated.

Table 1: Angular thresholds used to assign State

IDs to raw inclinometer angles. Thresholds

adapted from the Rapid Upper Limb Assessment

(RULA) methodology [4][5].

(F) Chi squared contingency test

If the postural gestures for a given perception occurred at least 5 times in both the present

and absence group and the results of the !

contingency comparison resulted in a p < .01,

then the postural gesture was deemed significant

●

● ● ●

● ●

●

23 4 5 6 78

● ● ● ● ● ● ●

23 4 5 6 7 8

●

● ● ●

23 4 5 6 7 8

● ● ● ● ● ● ●

23 4 5 6 7 8

● ● ● ● ● ●

●

23 4 5 6 78

● ● ● ● ● ●

●

23 4 5 6 78

●

● ●

●

23 4 5 6 78

●

● ● ● ● ● ●

23 4 5 6 7 8

●

● ● ●

23 4 5 6 7 8

● ● ● ● ● ● ●

23 4 5 6 7 8

●

● ●

●

234 567 8

●

● ●

●

23 4 5 6 7 8

0 5 10 15

LEGEND

Back'avoid

Back'risk

Fatigue'avoid

Fatigue'risk

Neck'avoid'

Neck'risk

Minimum Persistent Duration

# of Significant Postural Sequences

2 4 6 8

3 5 7

. Neck Avoid

HS00 HS-1 HS00 HS+1

à à à

Postural state sequence duration and musculoskeletal

disorder marker perception at sit-stand workstations

Kassandra'Raymond¹. Andrew'Hamilton-Wright¹.'Nancy'Black

.'''

!"# $%&''()'*)+',-./01)$%203%04)53260172/8)'*)9.0(-&): ;1<8,'3=>.'?.0(-&@%< !A#)B<%.(/C =D23?C3201204)53260172/C =0)E'3%/'3

INTRODUCTION

Musculoskeletal disorders (MSDs) account for approximately 43% of all workers

compensation claims in Ontario, costing the government up to 22 billion dollars a year [1].

Prolonged static postures, such as those required in office work, are a known cause of

MSDs [2]. In a past study by Black et al., significant postural gestures that were associated

with perceived pain or fatigue were identified, however duration of postural state was not

considered [3]. Objective: To add duration analysis to a previous study of the

relationship between postural gestures (movements) and participants’ perception of

pain and fatigue during office work.

References

1, Owen, N., Healy, G.N., Mathews, C.E. and Dunstan, D.W. (2010). Too much sitting: The population health science of sedentary behavior. Exercise and Sport Sciences Reviews 38 (3): 105-13

4. Keyserling, W.M. (1986). Postural analysis of the trunk and shoulders in simulated real time. Ergonomics. 29, 569–583.

5. McAtamney, L., and Corlett, N. (1993). RULA: A Survey Method for the Investigation of Work Related Upper Limb Disorders. Applied Ergonomics, 24(2), 91-99.

METHODOLOGY

(A) Data Collection

• 10 participants completed a 1 hr data entry task at each of 3 workstations (sitting,

S/S30%, S/S45%) and used a 10 point visual analogue scale to mark their perception of

fatigue and neck and back pain

• 16 Hz, 2D inclinometers on the back and neck of each participant measuring angles in

the frontal and sagittal planes

RESULTS & DISCUSSION

Back Frontal Back Sagittal Head Frontal Head Sagittal

SittingS/S30%S/S45%

CHANNEL STATE*

ANGULAR*

RANGE

HS HS

-1

-∞ -5

HS00 -5 10

HS+1 10 20

HS+2 20 ∞

HF HF

-2

-∞ -10

-1

-10 -2

HF00 -2 2

HF+1 2 10

HF+2 10 ∞

BS BS

-2

-∞ -5

-1

-5 10

BS00 10 20

BS+1 20 60

BS+2 60 ∞

BF BF

-2

-∞ -10

-1

-10 -2

BF00 -2 2

BF+1 2 10

BF+2 10 ∞

CONCLUSION & FUTURE DIRECTIONS

While the data are noisy, there is evidence to suggest that there are postural movements that may be

associated with the risk or avoidance of pain and fatigue. Future work will explore subtle movements

based on direct measurements of postural angles to compare found patterns with those reported here

with the RULA paradigm. This study provides a novel method for categorizing human movement

based on raw inclinometer measurements and underscores the importance of understanding

quantization boundaries upon their introduction.

Figure 1: Waterfall plots showing the absolute and relative change in number of postural sequences significantly associated with a

given perception as an MPD filter is applied for each workstation (sitting, S/S30%, S/S45%) and channel (head frontal plane, head

sagittal plane, back frontal plane, back sagittal plane).

(E) Perceptual Features

Black et al.’s (2018) quintile separation method was

used to categorize perceptual data from the visual

analogue scale into the ‘absence’ or ‘presence’ of a

given perception, for each participant and workstation.

q Filtering using a lower MPD filter shows that in 15 cases there is an increase in the number of

patterns found, while filtering with a longer MPD causes a decrease in the number of patterns (Fig 1).

q Mapping of dynamic posture into quantization boundaries can introduce an apparent increase in the

number of postural state changes. When this occurs due to a small overall change in the measured

angle that crosses into a new quantization region and then returns to the original, this small change

may be better ignored.

q While using RULA allows for the quantification of postural movements, smaller movements that are

occurring within a RULA defined region may be lost.

(B) Postural State Quantization

Each raw sample was quantized using the thresholds

adapted from RULA in Table 1.

(D) Postural Sequence Identification

Postural states were linked together to length 4 to

create postural gestures.

A state must have occurred for a minimum number of

samples to be considered a postural state change,

otherwise the sample was assigned to the previous

state. An MPD of 1 through 8 was calculated.

Table 1: Angular thresholds used to assign State

IDs to raw inclinometer angles. Thresholds

adapted from the Rapid Upper Limb Assessment

(RULA) methodology [4][5].

(F) Chi squared contingency test

If the postural gestures for a given perception occurred at least 5 times in both the present

and absence group and the results of the !

contingency comparison resulted in a p < .01,

then the postural gesture was deemed significant

●

● ● ●

● ●

●

23 4 5 6 78

● ● ● ● ● ● ●

23 4 5 6 7 8

●

● ● ●

23 4 5 6 7 8

● ● ● ● ● ● ●

23 4 5 6 7 8

● ● ● ● ● ●

●

23 4 5 6 78

● ● ● ● ● ●

●

23 4 5 6 78

●

● ●

●

23 4 5 6 78

●

● ● ● ● ● ●

23 4 5 6 7 8

●

● ● ●

23 4 5 6 7 8

● ● ● ● ● ● ●

23 4 5 6 7 8

●

● ●

●

234 567 8

●

● ●

●

23 4 5 6 7 8

0 5 10 15

LEGEND

Back'avoid

Back'risk

Fatigue'avoid

Fatigue'risk

Neck'avoid'

Neck'risk

Minimum Persistent Duration

# of Significant Postural Sequences

2 4 6 8

3 5 7

. Neck Risk

HS00 HS-1 HS00 HS+1

à à à

Postural state sequence duration and musculoskeletal

disorder marker perception at sit-stand workstations

Kassandra'Raymond¹. Andrew'Hamilton-Wright¹.'Nancy'Black

.'''

!"# $%&''()'*)+',-./01)$%203%04)53260172/8)'*)9.0(-&): ;1<8,'3=>.'?.0(-&@%< !A#)B<%.(/C =D23?C3201204)53260172/C =0)E'3%/'3

INTRODUCTION

Musculoskeletal disorders (MSDs) account for approximately 43% of all workers

compensation claims in Ontario, costing the government up to 22 billion dollars a year [1].

Prolonged static postures, such as those required in office work, are a known cause of

MSDs [2]. In a past study by Black et al., significant postural gestures that were associated

with perceived pain or fatigue were identified, however duration of postural state was not

considered [3]. Objective: To add duration analysis to a previous study of the

relationship between postural gestures (movements) and participants’ perception of

pain and fatigue during office work.

References

1, Owen, N., Healy, G.N., Mathews, C.E. and Dunstan, D.W. (2010). Too much sitting: The population health science of sedentary behavior. Exercise and Sport Sciences Reviews 38 (3): 105-13

4. Keyserling, W.M. (1986). Postural analysis of the trunk and shoulders in simulated real time. Ergonomics. 29, 569–583.

5. McAtamney, L., and Corlett, N. (1993). RULA: A Survey Method for the Investigation of Work Related Upper Limb Disorders. Applied Ergonomics, 24(2), 91-99.

METHODOLOGY

(A) Data Collection

• 10 participants completed a 1 hr data entry task at each of 3 workstations (sitting,

S/S30%, S/S45%) and used a 10 point visual analogue scale to mark their perception of

fatigue and neck and back pain

• 16 Hz, 2D inclinometers on the back and neck of each participant measuring angles in

the frontal and sagittal planes

RESULTS & DISCUSSION

Back Frontal Back Sagittal Head Frontal Head Sagittal

SittingS/S30%S/S45%

CHANNEL STATE*

ANGULAR*

RANGE

HS HS

-1

-∞ -5

HS00 -5 10

HS+1 10 20

HS+2 20 ∞

HF HF

-2

-∞ -10

-1

-10 -2

HF00 -2 2

HF+1 2 10

HF+2 10 ∞

BS BS

-2

-∞ -5

-1

-5 10

BS00 10 20

BS+1 20 60

BS+2 60 ∞

BF BF

-2

-∞ -10

-1

-10 -2

BF00 -2 2

BF+1 2 10

BF+2 10 ∞

CONCLUSION & FUTURE DIRECTIONS

While the data are noisy, there is evidence to suggest that there are postural movements that may be

associated with the risk or avoidance of pain and fatigue. Future work will explore subtle movements

based on direct measurements of postural angles to compare found patterns with those reported here

with the RULA paradigm. This study provides a novel method for categorizing human movement

based on raw inclinometer measurements and underscores the importance of understanding

quantization boundaries upon their introduction.

Figure 1: Waterfall plots showing the absolute and relative change in number of postural sequences significantly associated with a

given perception as an MPD filter is applied for each workstation (sitting, S/S30%, S/S45%) and channel (head frontal plane, head

sagittal plane, back frontal plane, back sagittal plane).

(E) Perceptual Features

Black et al.’s (2018) quintile separation method was

used to categorize perceptual data from the visual

analogue scale into the ‘absence’ or ‘presence’ of a

given perception, for each participant and workstation.

q Filtering using a lower MPD filter shows that in 15 cases there is an increase in the number of

patterns found, while filtering with a longer MPD causes a decrease in the number of patterns (Fig 1).

q Mapping of dynamic posture into quantization boundaries can introduce an apparent increase in the

number of postural state changes. When this occurs due to a small overall change in the measured

angle that crosses into a new quantization region and then returns to the original, this small change

may be better ignored.

q While using RULA allows for the quantification of postural movements, smaller movements that are

occurring within a RULA defined region may be lost.

(B) Postural State Quantization

Each raw sample was quantized using the thresholds

adapted from RULA in Table 1.

(D) Postural Sequence Identification

Postural states were linked together to length 4 to

create postural gestures.

A state must have occurred for a minimum number of

samples to be considered a postural state change,

otherwise the sample was assigned to the previous

state. An MPD of 1 through 8 was calculated.

Table 1: Angular thresholds used to assign State

IDs to raw inclinometer angles. Thresholds

adapted from the Rapid Upper Limb Assessment

(RULA) methodology [4][5].

(F) Chi squared contingency test

If the postural gestures for a given perception occurred at least 5 times in both the present

and absence group and the results of the !

contingency comparison resulted in a p < .01,

then the postural gesture was deemed significant

●

● ● ●

● ●

●

23 4 5 6 78

● ● ● ● ● ● ●

23 4 5 6 7 8

●

● ● ●

23 4 5 6 7 8

● ● ● ● ● ● ●

23 4 5 6 7 8

● ● ● ● ● ●

●

23 4 5 6 78

● ● ● ● ● ●

●

23 4 5 6 78

●

● ●

●

23 4 5 6 78

●

● ● ● ● ● ●

23 4 5 6 7 8

●

● ● ●

23 4 5 6 7 8

● ● ● ● ● ● ●

23 4 5 6 7 8

●

● ●

●

234 567 8

●

● ●

●

23 4 5 6 7 8

0 5 10 15

LEGEND

Back'avoid

Back'risk

Fatigue'avoid

Fatigue'risk

Neck'avoid'

Neck'risk

Minimum Persistent Duration

# of Significant Postural Sequences

2 4 6 8

3 5 7

3 REAL-WORLD APPLICATIONS

The applications of the curtain graph are very robust;

it can be used in many ﬁelds, with different types and

dimensionalities of data. To understand the type of

data that can be expressed using the curtain graph, we

outline three real-world examples of the visualization.

3.1 Example: Posture Data

The data analysis problem which spurred our inter-

est in this type of visualization is a problem in pos-

tural data analysis. (This data and the soil type

data available at the authors’ website https://qemg.

uoguelph.ca/data/.) This data analysis is charac-

terized by evaluating observations regarding percep-

tion (‘perception’) across multiple channels simulta-

neously (‘channel’), as well as across multiple exper-

imental setups (‘modality’). For each of these, we

needed a visualization to explore the relationship be-

tween the effects of progressive degrees of applica-

tion of a new ﬁlter (‘ﬁltering’) and the response vari-

able, which in this case was the number of patterns

obtained under the ﬁltering strategy (‘number of pat-

terns’).

The dataset: Researchers are studying sedentary

behaviour in ofﬁce workers and are concerned with

understanding gestures that are associated with the

risk and avoidance of back pain, neck pain and fatigue

in four different bodily modalities at three different

workstations. The results of this work were presented

at the July 2019 meeting of the Canadian Association

of Ergonomists (Raymond et al., 2019).

The data consists of angular data obtained from

the head and neck measured as an incline from ver-

tical. This data was obtained for a the set of per-

ceptions mentioned above (risk and avoidance of fa-

tigue and of pain at the neck, and of pain at the back),

and under experimental modalities of controlled sit-

ting and standing alternating within a 20 minute cy-

cle. Example data shown here includes at 45% stand-

ing (S/S45%) and sitting, for several channels. Only

the channels ‘Head/Sagittal’ and ‘Back/Frontal’ are

reproduced here, due to space constraints.

This results in a numerical y axis with a numeri-

cal x axis along each curtain rod and a categorical z

between the series of bars (Figure 5).

In Figure 5 the curtain graphs are arranged in a

grid table similar to a matrix. Note that the axes, and

colour/pattern in each curtain graph is consistent with

the other curtain graphs. The column and rows of the

matrix are based on the planes of the body and each

workstation, respectively.

Representation of this ﬁve dimensional problem

gave birth to this visualization strategy through the

observation that the critical comparison was the itera-

tive application of the ‘ﬁltering’ factor. As the ﬁlter-

ing is occurring relative to the state of a baseline data

set, new values for ﬁltering are understood only in the

context of observations given in relation to the initial

IVAPP 2020 - 11th International Conference on Information Visualization Theory and Applications

128

or base point for that series — we can see any changes

as a reﬁnement of an initial setup. Applying succes-

sively greater amounts of ﬁltering yields a series of

points in a logical progression. This requires a lo-

cal display space in order to be coherently understood

relative to the base position, but which also require

comparison with our other variables.

As shown in Figure 5, the curtain plot displays this

data in order of comparison precedence, moving up

from the number of patterns obtained through succes-

sive ﬁltering through data channel and experimental

modality. Speciﬁcally:

1. In a typical multi-plot grid, the two least critical

variables lay out a grid of inner plots, indexed by

channel and experimental modality. This reduces

the remaining visualization dimensionality needs

to three.

2. Within each plot, we can then associate the num-

ber of patterns on the y axis with both perception,

shown as the group of measures within a given

series placed along a speciﬁc curtain rod, and the

ﬁltering values arranged along the rod.

The ﬁltering setting is the experimental variable

that we wish to fall under the closest scrutiny. By set-

ting these within the adjacent bar sequence arranged

along each ‘curtain rod’ we easily see the effects of

increasing the ﬁltering control, moving from no ﬁlter-

ing at the leftmost end of the rod through to a ﬁlter

setting of 8 units at the rightmost end of each series.

The curtain rod bars themselves ﬂoat in space at the

baseline position provided by no ﬁltering, which al-

lows easy and direct comparison of any of the num-

ber of patterns obtained by different ﬁltering settings

within a series to the number obtained at baseline.

For example, in the lower leftmost plot in Fig-

ure 5 (S/S 45%, Back/Frontal) the sequences for ‘back

avoid’ and ‘back risk’ are easily recognized as hav-

ing little change relative to their baseline position,

and also immediately indicate that the direction of the

changes that are seen are in opposite sign to one an-

other, back avoid projecting upwards from the rod,

while back risk descends. The relative position of

these two rods in this plot show that while the range

is the same, the opposite change is shown. Compar-

ing these two series to the other series in the plots,

we can easily locate those where signiﬁcant change is

apparent, as well as the overall trend of the change.

In the display for both experimental modalities of

the Head/Frontal data large visible trends of decreas-

ing measures are shown. The cascade of bars down

from the curtain rod gives us the name for the tool.

Again, several insights are easily captured here that

would not be available without the relative position-

ing of the curtain rod chart:

• the similarity of structure across all the subplots;

• the right shifting along the rod of ‘back risk’ and

‘fatigue risk’ within S/S45%; and

• the similar trend but different initial sign in ‘back

avoid’.

Turning to the Back/Sagittal column, we easily

see here the consistency of the changes noted, as well

as the distinct representation of an unﬁlled baseline

curtain rod. While in this data all of the empty rods

happen to be at the y = 0 axis, it is easy to imagine

plots in which they might be scattered.

Overall, this plot type employs the type of imme-

diate insight described as ‘small multiples’ by Tufte

(1991, pp. 67–80) which allows immediate recogni-

tion of visually accessible patterns within the display.

As the purpose here is to facilitate recognition of both

overall trends as well as patterns of association of the

‘number of patterns’ variable across the many plots,

the concept of the small multiple is particularly im-

portant here. For example, the power of the plot

is shown in particularly striking fashion by the way

that ‘neck avoid’ on the lower right plot leaps from

the page (S/S 45%, Head/Sagittal), showing how un-

usual cases are easily recognized relative to the ﬂoat-

ing baseline.

Movement along the x axis can be identiﬁed as

progression when labels are numerically and tempo-

rally sequential in Figure 5. Here, the progression in

the x axis corresponds to the increase in the length of

the minimum persistent duration ﬁlter. Further, when

the curtain graphs are grouped together in a matrix,

the patterns of different combinations of data can be

easily identiﬁed.

3.2 Example: Crop Data

The curtain graph can also be used to visualize a

data set consisting of multiple categorical factors as

well as numerical data. Several modiﬁcations to

colour/pattern and symbols are shown to emphasize

speciﬁc trends in the data set.

The dataset: Researchers are interested in study-

ing the survival rate of three crops, in two different

soil types after the application of ﬁve pesticides com-

pared to when there are no pesticides applied. The

crops are soybean, corn and wheat and the soil types

are sandy and muck soil (sapric organic soils). The

pesticides used are simply labelled one to ﬁve, and

zero (for no pesticide applied).

Figure 6 displays the data on the curtain graph.

Colours are used to distinguish the subplots which

represent the different soil/crop types. Each bar

within a subplot shows the plant survival rate of the

crop it represents in comparison to the baseline. Here,

Curtain Graphs: Using a Floating Baseline for Comparison in a Two-dimensional Graphical Space

129

1 2 3 4 5

Pesticide Type

Number of Plants

type

corn_muck

corn_sand

soybean_muck

soybean_sand

squash_muck

squash_sand

Figure 6: A curtain plot showing the data from the “crop”

data set.

1 2 3 4 5

Pesticide Type

Number of Plants

type

corn_muck

corn_sand

soybean_muck

soybean_sand

squash_muck

squash_sand

Figure 7: A curtain plot showing the data from the “crop”

data set, with updated colour scheme to emphasize soil type.

pesticide level zero (no pesticide applied), acts as the

curtain rod (baseline), which is the solid black line

on each subplot. The extension of the bars from the

curtain rod therefore represents the absolute and rela-

tive difference in survival rate from when there is no

pesticide applied.

Note that while here, ‘no pesticide applied’, acts

as the curtain rod, if the researcher was interested in

the difference in survival rate from a gold standard

pesticide, they could simply use that pesticide as the

curtain rod anchor point.

The curtain graph can be modiﬁed using colour,

pattern or symbols to visually emphasize different

trends or patterns in the data. For example, the vari-

ation in pattern between soil type can be explored in

this manner. From Figure 6, the viewer can conclude

that for this experience, the baseline survival rate of

all crops was higher when plants were grown in the

soil type identiﬁed as muck soil, compared to sandy.

To easily distinguish this trend, the curtain plot could

be reﬁned using shades of the same colour or varieties

of the same pattern, to show which that these crops

were all grown in the same soil type (Figure 7).

3.3 Example: Non-linear Axes

The curtain graph is robust in its ability to accommo-

date non-linearity in the y axis, in spite of the need to

support both relative and absolute data comparisons.

For example, the curtain graph can be used with a log-

arithmic axis.

The dataset: This UNICEF (2019) dataset (avail-

able from UNICEF at https://mics.unicef.org)

consists of the estimated number of deaths by diar-

rhoeal disease in children under ﬁve in the year 2000

1e+02

1e+03

1e+04

1e+05

SA−PER

SA−BRA

SA−CRI

SA−ECU

SA−GTM

A−ETH

A−NGA

A−LBR

A−RWA

A−ZAF

AS−IND

AS−BGD

AS−PAK

AS−AFG

AS−THA

Countries

Number of Mortalities

A−ETH

A−LBR

A−NGA

A−RWA

A−ZAF

AS−AFG

AS−BGD

AS−IND

AS−PAK

AS−THA

SA−BRA

SA−CRI

SA−ECU

SA−GTM

SA−PER

Figure 8: A curtain plot showing the data from the

‘UNICEF’ data set. Sublots with data beginning ‘SA-’ are

South America, ‘A-’ are Africa, and ‘AS-’ are Asia. Coun-

tries are rendered in shades of red, green and blue respec-

tively.

by country. The countries used were organized into

geographic region. South America is represented by

Peru (SA-PER), Brazil (SA-BRA), Costa Rica (SA-

CRI), Ecuador (SA-ECU) and Guatemala (SA-GTM).

Africa is represented by Ethiopia (A-ETH), Nige-

ria (A-NGA), Liberia (A-LBR), Rwanda (A-RWA)

and South Africa (A-SA) and Asia consists of data

from India (AS-IND), Bangladesh (AS-BGD), Pak-

IVAPP 2020 - 11th International Conference on Information Visualization Theory and Applications

130

istan (AS-PAK), Afghanistan (AS-AFG) and Thai-

land (AS-THA).

Figure 8 shows the described UNICEF dataset us-

ing a log

y axis. Here, each subplot represents a

geographic region, while the bars each represent a

different country within that region. Visually, each

geographic region is a different colour, with the bars

consisting of different hues of this colour. The coor-

dinates of the curtain rod were calculated by taking

the mean mortality rate of children under ﬁve due to

diarrhea in the region.

We chose the mean as the anchor point for the cur-

tain rod baseline to provide an example of a differ-

ent type of analysis, where variation around a central

theme, rather than a series based on initial conditions,

is the focus of the visualization.

As there is still a common space deﬁned by the

y axis, and there is a meaning to the anchor point

and the extent of the curtain bars, all of our previ-

ous observations on interpretability still hold in this

scenario.

4 DATA PROPERTIES

The fundamental property of this graph is the inclu-

sion, within a single y axis, of a series of bar chart

type representations, where the vertical position of the

baseline of each of the individual sub-charts is placed

at a position representing the anchor of that data se-

ries. By placing these together within the same set of

coordinate systems, both the absolute and relative po-

sition of each of the bars within the various sub-charts

correctly represents the data changes both across and

between the data series.

The units of the measure forming the y axis must

therefore be conducive to measurement within this

number line, so this measure must obey the proper-

ties of a metric space — in other words the properties

of a distance measurement must hold:

• points falling at the same position must indicate

that there is no difference in the measurement

(there must be only one measured value that falls

at each point);

• the distance between any two points mapped to

the y axis must be the same regardless whether

measured in the positive or negative direction; and

• the triangle inequality must hold, such that the

sum of two consecutive distances on this line must

represent a difference at least as large as that be-

tween the two end points.

These properties commonly hold on any number

line based axis measurement, such as linear, logarith-

mic, etc. The other axes within the visualization are

free to be other non-metric types, such as ordinal or

categorical.

The motivation for this visualization comes from

the desire to represent three dimensional data within

a clear two-dimensional plotting space. We are inter-

ested in the case where the measures along our x di-

mension form a series relative to a ﬁxed starting loca-

tion, but where this starting location is not necessarily

the same for the other series within the x variable. The

existing waterfall chart also presents a series of values

relating to a ﬁxed starting point, but in that case, the

starting point must be y = 0. In addition, we com-

bine multiple series with different starting points in

the same plot.

5 CONCLUSIONS AND FUTURE

WORK

The visualization tool presented allows for the visu-

alization of high-dimensional multivariate data in one

conceptual two-dimensional plot. We are deliberate

with the layout of the curtain graph such that it allows

for comparisons between and within the interrelated

data groupings of a given data set. The curtain graph

is ﬂexible in its ability to accommodate data of differ-

ent types; while the y axis must be numerical, while

the x and z axes can be categorical, ordinal or numer-

ical.

In this paper, we outline three different real-world

examples from different disciplines and data sets, pro-

viding the reader examples of the beneﬁts of using the

curtain graph and its ability to visualize information

in a fashion that was not previously as coherent. Fur-

ther, we provide the properties of data that must be

true for an individual to use the curtain graph.

Future work will consist of creating a software

package for the creation of the curtain graph. We

currently use modiﬁcations to the ‘geom-rect’ func-

tionality in R’s ggplot2 package (Wickham, 2016)

to create the graphs. Ideally, this would allow a user

to simply format their data in a data frame and curate

the graph using a function call. This will allow for use

of the visualization from a broader audience.

ACKNOWLEDGEMENTS

We would like to thank Nancy Black of the Univer-

sity of Moncton, New Brunswick, for providing us

with the data that inspired the early workings of our

visualization. Further, thank you to Jack Johnson for

motivating the use of the term ‘subplots’ in our work.

Curtain Graphs: Using a Floating Baseline for Comparison in a Two-dimensional Graphical Space

131

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