Particle systems make an excellent tool for creating tracks (which we call strokes) in vector fields. The question addressed in this paper is how such tracks should be made to vary in size and colour in order to reveal properties such as local direction and strength of the field. We find that for strokes that vary from large to small, direction is indicated by the large end. We also find that for strokes that vary in colour, the colour of the background is the most important determinant of perceived direction

Fowler, David

Ware, Colin

English

UNH Scholars' Repository

University of New HampshireUniversity of New Hampshire Scholars' RepositoryCenter for Coastal and Ocean Mapping Center for Coastal and Ocean Mapping6-1989Strokes for Representing Univariate Vector FieldMapsDavid FowlerUniversity of New BrunswickColin WareUniversity of New Hampshire, Durham, colin.ware@unh.eduFollow this and additional works at: https://scholars.unh.edu/ccomPart of the Computer Sciences Commons, and the Oceanography and Atmospheric Sciences andMeteorology CommonsThis Conference Proceeding is brought to you for free and open access by the Center for Coastal and Ocean Mapping at University of New HampshireScholars' Repository. It has been accepted for inclusion in Center for Coastal and Ocean Mapping by an authorized administrator of University of NewHampshire Scholars' Repository. For more information, please contact nicole.hentz@unh.edu.Recommended CitationFowler, David and Ware, Colin, "Strokes for Representing Univariate Vector Field Maps" (1989). Graphics Interface. 769.https://scholars.unh.edu/ccom/769249 Strokes for Representing U nivariate Vector Field Maps David Fowler Colin Ware School of Computer Science University of New Brunswick P.O. Box 4400 Fredericton, New Brunswick CAN ADA E3B 5A3 bitnet: cware@UNB.ca Abstract Particle systems make an excellent tool for creating tracks (which we call strokes) in vector fields. The question ad-dressed in this paper is how such tracks should be made to vary in size and colour in order to reveal properties such as local direction and strength of the field. We find that for strokes that vary from large to small, direction is indicated by the large end. We also find that for strokes that vary in colour, the colour of the background is the most important determinant of perceived direction. [( eywords: Data Display, Vector Fields. 1 Introd uction An early example of the use of line segments to represent vector field data is a 17th century map by Edmond Halley (discussed in Tufte, 1983) which shows trade winds over the Atlantic Ocean (see Figure 1). Halley's elegant pen strokes are shaped like long narrow airfoils oriented to the flow,with the wind direction being given the blunt end. While vector field plots have become more accurate in intervening years, they have also simultaneously become less easily read and less attractive. A standard computer plotting method for displaying vector fields is to provide a regular two dimen-sional array of line segments which by their orientation dis-play direCtion and by their length display magnitude. It is also possible to use the density of line segments in order to display an additional field parameter (Lavin and Cerveny, 1987). Of course, line segments are ambiguous as to direction - hence the common use of arrows which are strokes em-bellished with arrowheads (Lueptow, 1988). But even ar-rows may not give the correct impression according to Bertin (1983) who advocates broadening the stroke towards the head of the arrow in order to get the correct impression of direction. A disadvantage of arrows is that the arrowheads often clutter up the map, especially when the line segments are dense and certainly when drawn by computer. Recently there have been attempts to break away from the simple line segment with or without an arrowhead. Hib-bard (1986) used flow lines, generated in a computer graphics system, which are represented by cylindrical pipes twisting through a three dimensional space and rendered in perspec-tive. He also used strokes, whose tails fade to transparency, to great effect. The Particle Systems technique (Reeves, 1983,1985) was recently invented to model such phenomenon as fire and clouds. Particle systems have obvious application in pro-viding tools to visualize vector field maps. The essence of the method we use is as follows: We scatter particles on the vector field where they immediately begin to move in the direction indicated by the local field. As the particles move they age, and as they age they may change their character-istics in a number of ways. We define a "stroke" as the trace left by a particle over the course of its life. The purpose of this paper is to report on an attempt to develop guidelines on how to design strokes in order to best reveal properties of the vector field. Once we depart from the notion of a stroke as a uniform width variable length line segment, a large number of possi-bilities offer themselves. Strokes may vary in colour or size as they age, or they can vary in colour or size to reflect aspects of the field they are to represent. Moreover, strokes may be made to vary in colour in a variety of different ways. They may be made to vary, for example, in luminance, or in hue, and they may be made to vary cyclically or monotonically. In this paper we present the results of a study designed to examine how people perceive direction and magnitude using some of the simplest strokes. - ---- - -Figure 1. A copy of the pen strokes used by Edmond Halley (1686) to represent the trade winds of the North Atlantic. Halley described the wind direction as being given by" ... the sharp end of each little stroak pointing out that part of the Horizon, from whence the wind continually comes". Halley's map is discussed in Tufte (1983). Graphics Interface '89 1.1 Colour and Size We decided to study the perception of strokes which change linearly in size, either getting smaller or larger, and strokes which change in colour as they age, either changing from white to black, from black to white, or from red to green. We also investigated strokes which had a constant size and strokes which had a constant colour (black) . These strokes were used to display a circular vector field . We asked two basic questions of our observers. 1. In which direction is the vector field oriented? That is, does the flow appear to be clockwise or counter clock-wise? 2. How strong is the impression of flow? Note that we described the images as representing flow to our subjects, but we presume that the results will apply to the perception of other vector fields . 2 Experimental Design 2.1 Stimuli The stimulus pattern was generated using a synthetic circu-lar field. The field was descibed by bx = O.Olsin(Yf) by = -0.01 sin( T) where bX, by gives the distance between successive positions of a particle as it traces out a path over the course of its lifetime. Particles aged through 25 steps and then disap-peared. To create the stimulus pattern a virtual square was randomly seeded with 150 particles which were allowed to age to extinction. The particles were generated using a uni-form random function in a virtual square with lower left hand corner having coordinates (-1.1,-1.1) and uppper right hand corner having coordinates (1.1,1.1). The space in which the particles were generated was clipped to (-1.0,-1.0), (1.0,1.0) and the square was mapped to a 22 by 22 cm window cen-tered on the monitor. 2.1.1 Stroke Shape The shape of the strokes was achieved by making the particle size a function of the particle's age. Three functions were investigated. 1. Particles could start off having a diameter of 1 mm and linearly increase in size to 4 mm at their death. 2. Particles could maintain the same diameter of 2.5 mm over the course of their lifespan. 3. Particles could start off having a diameter of 4 mm and linearly decrease in size to 1 mm at their death. 2.1.2 Stroke Colour The colour gradient of a stoke was achieved by making the 250 colour a function of the particle's age. Three functions were investigated. 1. Particles could start off black and change to white us-ing the following function. L = (age/25?13 if we consider L to be luminance that varies over [0,1]. We chose this exponent for our grey scale function be-cause under the display conditions of the experiment (at least with a grey background) this produced the most perceptually linear gradient from black to white. 2. Particles could start off white and change to black us-ing the equation. L = (1 - age/25?13 3. Particles could start of red and change to green using a linear interpolation between monitor red and monitor green. The eIE chromaticity coordinates and maxi-mum luminance values (x, y, Y) for the monitor guns x y Y R 0.610 0.342 15.72 are: G 0.298 0.588 33.80 B 0.151 0.063 6.14 2.1.3 Background Colour The colour of the background was set to one of the following three values: 1. The start of the colour gradient as described above (this could be one of black, white, or red). 2. The middle of the colour gradient described above (this could be one of grey or beige). 3. The end of the colour gradient as described above (this could be one of black, white, or green). The basic design was a three by three by three facto-rial experiment consisting of all twenty-seven combinations of the above factors. In addition there were three other ex-perimental conditions consisting of each of the three stroke shapes defined above in solid black on a white background. The resulting thirty conditions are summarized in figure 2. Three of the stimulus patterns are illustrated in figure 3. 2.2 Measures The subject was required to observe thirty trials and record observations about them with respect to the direction and strength. The subject indicated direction by stating either "clockwise" or "counter clockwise". This was a forced choice decision in that the subject was forced to respond with one of the above even if no direction was apparent. Strength of perceived direction was assessed using a five point rating scale (0 .. .4). Trials were presented to each subject in random order. Graphics Interface '89 Table la Inc Same Dec first 13 11 12 (black) 3.54 2.31 3.15 Black -+ White middle 6 1 1 (grey) 0.07 1.85 2.54 last 0 0 1 (white) 3.61 3.54 3.00 Table lb Inc Same Dec first 12 13 13 (white) 3.38 3.00 3.46 White -+ Black middle 11 9 4 (grey) 2.62 0.77 1.00 last 1 0 0 (black) 2.92 2.62 3.31 Table le Inc Same Dec first 12 12 13 (red) 3.15 2.69 3.46 Red -+ Green middle 8 4 0 (beige) 0.46 0.46 2.00 last 1 1 0 (green) 3.00 3.00 3.54 Table ld Inc Same Dec Solid Black 13 5 1 (white) 3.00 0.00 2.54 4 Results and Discussion The strongest factor in determining the direction of flow was an interaction between the color of the background and the colour sequence used. The direction of perceived flow was away from the end of the stroke which matched the back-ground colour. These can be determined by examining the top and bottom rows of the Tables la, 1b, and 1c which con-tain a total of 234 observations. Out of these observations only ten deviate from the above rule. Of these deviations five were contributed by a single subject. The effect occurs irrespective of the shape of the stroke and irrespective of the colour sequence. The effect of stroke shape was studied in the conditions where the strokes were a constant black on a white back-ground. In these cases (see Table Id) the direction of mo-tion was perceived as towards the larger end of the stroke, no matter which way the stroke was drawn. This finding is consistent with the phenomenological observations of Halley (1686) and of Bertin (1983). A complex picture emerges when we examine the effects of colour sequences and grey sequences on a neutral back-ground. In the grey scale conditions with a neutral back-251 ground (center cell in tables la and Ib), the subjects tended to find the particles to be moving towards the darker end of the stroke. This is most evident from the constant size trials. However when size is brought into consideration, the tendency of the subjects to perceive direction towards the large end of the stroke would either enhance or conflict with this. Thus when the dark end coincides with the large end of the stroke, a stronger perceived flow rating was obtained compared with the constant size condition. Conversely, if the dark end coincided with the small end of the stroke, a very weak rating was obtained. The red-green colour gradient on a neutral background also produced some interesting results. It appears that the colour red is the dominating colour. When the large end of the stroke is red, the subjects unanimously agreed on a direction, although did not rate it as strong. In the other two stroke categories, the subjects did not agree on the direction of flow. The study presented here only begins to tap the pos-sibilities for designing strokes using particle systems. An idea which we are currently exploring is the presentation of more dimensions simultaneously. Thus we can use hue, for example, to represent temperature in a vector field, while value (lightness) represents age. Another idea is to use par-ticle size to represent exaggerated depth in a slice through a three-dimensional vector field. 5 Acknowledgements We wish to thank Serge Limoges for his preliminary research into the use of particle systems for the representation of flow data. 6 References Bertin, Jacques., Trans. by William J . Berg. Semiology of Graphics, The University of Wisconsin Press, 1983, p. 342-355. Halley, Edmond, An Historical Account of the Trade Winds, and Monsoons, Observable in the Seas Between and Near the Tropicksj With an Attempt to Assign the Phisical Cause of Said Winds, Philosophical Transac-tions, Vol183, 1686 p. 153-168. Hibbard, William L., 4-D Display of Meteorological Data, Proc. 1986 Workshop on Interactive 3D Graphics, F . Crow and S. M. Pizar, eds., ACM, New York, p. 23-36 Lavin, S., and Cerveny, R., Unit-Vector Density Mapping, The Cartogmphic Journal, Vol. 24(December 1987), p. 131-141 Lueptow, Richard M., Software for Computational Fluid Flow and Heat Transfer Analysis, Compute rs in Me-chanical Engineering, Vol. 6, No. 5(March/ April 88), p. 10-17 Graphics Interface '89 Also, the direction in which the strokes were drawn was de-termined randomly to be one of clockwise or counter-clockwise. 2.3 Subjects There were thirteen subjects. Each subject was colour nor-mal according to Ishihara Pseudo isochromatic plates and had (at least) 20/20 vision by a Snellen eye chart. Stroke Shape ./ ./ /' /' ./ /' /' ./ /' /' ./ ~ BlaCk ~ White ~ ~ White ~ Black U .. -'" ~ U) Red --t Green ./ V ./ V ./ ./ V~. ./ ~. ~ -c ~ <' .$"V 'it $ 252 A.~"'y;< ~ ~ Background t::)Jf Colour. ,...--,--,----, Solid Black White Figure 2. A visual representation of the 3 by 3 by 3 factorial experiment with 3 additional conditions. 3 Results and Discussion In order to derive a value for the strength of movement which took into account the direction of perceived movement we devised the following metric. where d; = { ILi~ld;x;1 13 subject; matched direction -1 subject; did not match direction and Xi represents the rating scale response by each subject. The strength ratings, averaged across subjects, are given in the lower half of each cell in Tables la, 1 b, lc and Id which summarize the results from all thirty experimental condi-tions. The integer in the upper half of each cell is the total number of subjects out of thirteen who reported that ·the di-rection displayed matched the direction in which the strokes were drawn. These tables correspond to planes in Figure 2. 7':'-.,-, , a b c Figure 3. Photographs showing a small portion of each of three of the stimulus patterns. All three utilize the black ~ white colour sequence. ( a) appears on a black background and was constructed using particles which decrease in size. (b) appears on a grey background and was constructed using particles of a constant size. (c) appears on a white background and was con-structed using particles which increase in size. Graphics Interface '89 Reeves, WilIiam T., Particle Systems - A Technique for Modeling a Class of Fuzzy Objects Computer Graphics VoJ. 17,No. 3 (July 1983), pp. 359-376 Reeves, Wand Blau, R., Approximate and Probabilistic Al-gorithms for Shading and Rendering Structured Parti-cle Systems, Proc. SIGGRAPH '85, Computer Graph-ics Vol. 19,No. 3(July 1985) p. 313-322. Tufte, Edward R. The Visual Display of Quantitative Infor-mation, Graphics Press, Cheshire, Conneticut, 1983. 253 Graphics Interface '89 

Strokes for Representing Univariate Vector Field Maps

University of New Hampshire

University of New Hampshire
University of New Hampshire Scholars' Repository
Center for Coastal and Ocean Mapping Center for Coastal and Ocean Mapping
6-1989
Strokes for Representing Univariate Vector Field
Maps
David Fowler
University of New Brunswick
Colin Ware
University of New Hampshire, Durham, colin.ware@unh.edu
Follow this and additional works at: https://scholars.unh.edu/ccom
Part of the Computer Sciences Commons, and the Oceanography and Atmospheric Sciences and
Meteorology Commons
This Conference Proceeding is brought to you for free and open access by the Center for Coastal and Ocean Mapping at University of New Hampshire
Scholars' Repository. It has been accepted for inclusion in Center for Coastal and Ocean Mapping by an authorized administrator of University of New
Hampshire Scholars' Repository. For more information, please contact nicole.hentz@unh.edu.
Recommended Citation
Fowler, David and Ware, Colin, "Strokes for Representing Univariate Vector Field Maps" (1989). Graphics Interface. 769.
https://scholars.unh.edu/ccom/769
249 
Strokes for Representing U nivariate 
Vector Field Maps 
David Fowler 
Colin Ware 
School of Computer Science 
University of New Brunswick 
P.O. Box 4400 
Fredericton, New Brunswick 
CAN ADA E3B 5A3 
bitnet: cware@UNB.ca 
Abstract 
Particle systems make an excellent tool for creating tracks 
(which we call strokes) in vector fields. The question ad-
dressed in this paper is how such tracks should be made to 
vary in size and colour in order to reveal properties such as 
local direction and strength of the field. We find that for 
strokes that vary from large to small, direction is indicated 
by the large end. We also find that for strokes that vary in 
colour, the colour of the background is the most important 
determinant of perceived direction. 
[( eywords: Data Display, Vector Fields. 
1 Introd uction 
An early example of the use of line segments to represent 
vector field data is a 17th century map by Edmond Halley 
(discussed in Tufte, 1983) which shows trade winds over the 
Atlantic Ocean (see Figure 1). Halley's elegant pen strokes 
are shaped like long narrow airfoils oriented to the flow,with 
the wind direction being given the blunt end. While vector 
field plots have become more accurate in intervening years, 
they have also simultaneously become less easily read and 
less attractive. A standard computer plotting method for 
displaying vector fields is to provide a regular two dimen-
sional array of line segments which by their orientation dis-
play direCtion and by their length display magnitude. It is 
also possible to use the density of line segments in order to 
display an additional field parameter (Lavin and Cerveny, 
1987). 
Of course, line segments are ambiguous as to direction 
- hence the common use of arrows which are strokes em-
bellished with arrowheads (Lueptow, 1988). But even ar-
rows may not give the correct impression according to Bertin 
(1983) who advocates broadening the stroke towards the 
head of the arrow in order to get the correct impression of 
direction. A disadvantage of arrows is that the arrowheads 
often clutter up the map, especially when the line segments 
are dense and certainly when drawn by computer. 
Recently there have been attempts to break away from 
the simple line segment with or without an arrowhead. Hib-
bard (1986) used flow lines, generated in a computer graphics 
system, which are represented by cylindrical pipes twisting 
through a three dimensional space and rendered in perspec-
tive. He also used strokes, whose tails fade to transparency, 
to great effect. 
The Particle Systems technique (Reeves, 1983,1985) was 
recently invented to model such phenomenon as fire and 
clouds. Particle systems have obvious application in pro-
viding tools to visualize vector field maps. The essence of 
the method we use is as follows: We scatter particles on the 
vector field where they immediately begin to move in the 
direction indicated by the local field. As the particles move 
they age, and as they age they may change their character-
istics in a number of ways. We define a "stroke" as the trace 
left by a particle over the course of its life. The purpose of 
this paper is to report on an attempt to develop guidelines 
on how to design strokes in order to best reveal properties of 
the vector field. 
Once we depart from the notion of a stroke as a uniform 
width variable length line segment, a large number of possi-
bilities offer themselves. Strokes may vary in colour or size as 
they age, or they can vary in colour or size to reflect aspects 
of the field they are to represent. Moreover, strokes may be 
made to vary in colour in a variety of different ways. They 
may be made to vary, for example, in luminance, or in hue, 
and they may be made to vary cyclically or monotonically. 
In this paper we present the results of a study designed to 
examine how people perceive direction and magnitude using 
some of the simplest strokes. 
- ---- - -
Figure 1. A copy of the pen strokes used by Edmond Halley 
(1686) to represent the trade winds of the North Atlantic. Halley 
described the wind direction as being given by" ... the sharp end 
of each little stroak pointing out that part of the Horizon, from 
whence the wind continually comes". Halley's map is discussed 
in Tufte (1983). 
Graphics Interface '89 
1.1 Colour and Size 
We decided to study the perception of strokes which change 
linearly in size, either getting smaller or larger, and strokes 
which change in colour as they age, either changing from 
white to black, from black to white, or from red to green. 
We also investigated strokes which had a constant size and 
strokes which had a constant colour (black) . These strokes 
were used to display a circular vector field . We asked two 
basic questions of our observers. 
1. In which direction is the vector field oriented? That is, 
does the flow appear to be clockwise or counter clock-
wise? 
2. How strong is the impression of flow? 
Note that we described the images as representing flow to 
our subjects, but we presume that the results will apply to 
the perception of other vector fields . 
2 Experimental Design 
2.1 Stimuli 
The stimulus pattern was generated using a synthetic circu-
lar field. The field was descibed by 
bx = O.Olsin(Yf) 
by = -0.01 sin( T) 
where bX, by gives the distance between successive positions 
of a particle as it traces out a path over the course of its 
lifetime. Particles aged through 25 steps and then disap-
peared. To create the stimulus pattern a virtual square was 
randomly seeded with 150 particles which were allowed to 
age to extinction. The particles were generated using a uni-
form random function in a virtual square with lower left hand 
corner having coordinates (-1.1,-1.1) and uppper right hand 
corner having coordinates (1.1,1.1). The space in which the 
particles were generated was clipped to (-1.0,-1.0), (1.0,1.0) 
and the square was mapped to a 22 by 22 cm window cen-
tered on the monitor. 
2.1.1 Stroke Shape 
The shape of the strokes was achieved by making the particle 
size a function of the particle's age. Three functions were 
investigated. 
1. Particles could start off having a diameter of 1 mm and 
linearly increase in size to 4 mm at their death. 
2. Particles could maintain the same diameter of 2.5 mm 
over the course of their lifespan. 
3. Particles could start off having a diameter of 4 mm and 
linearly decrease in size to 1 mm at their death. 
2.1.2 Stroke Colour 
The colour gradient of a stoke was achieved by making the 
250 
colour a function of the particle's age. Three functions were 
investigated. 
1. Particles could start off black and change to white us-
ing the following function. 
L = (age/25?13 
if we consider L to be luminance that varies over [0,1]. 
We chose this exponent for our grey scale function be-
cause under the display conditions of the experiment 
(at least with a grey background) this produced the 
most perceptually linear gradient from black to white. 
2. Particles could start off white and change to black us-
ing the equation. 
L = (1 - age/25?13 
3. Particles could start of red and change to green using a 
linear interpolation between monitor red and monitor 
green. The eIE chromaticity coordinates and maxi-
mum luminance values (x, y, Y) for the monitor guns 
x y Y 
R 0.610 0.342 15.72 
are: G 0.298 0.588 33.80 
B 0.151 0.063 6.14 
2.1.3 Background Colour 
The colour of the background was set to one of the following 
three values: 
1. The start of the colour gradient as described above 
(this could be one of black, white, or red). 
2. The middle of the colour gradient described above (this 
could be one of grey or beige). 
3. The end of the colour gradient as described above (this 
could be one of black, white, or green). 
The basic design was a three by three by three facto-
rial experiment consisting of all twenty-seven combinations 
of the above factors. In addition there were three other ex-
perimental conditions consisting of each of the three stroke 
shapes defined above in solid black on a white background. 
The resulting thirty conditions are summarized in figure 2. 
Three of the stimulus patterns are illustrated in figure 3. 
2.2 Measures 
The subject was required to observe thirty trials and record 
observations about them with respect to the direction and 
strength. The subject indicated direction by stating either 
"clockwise" or "counter clockwise". This was a forced choice 
decision in that the subject was forced to respond with one 
of the above even if no direction was apparent. Strength 
of perceived direction was assessed using a five point rating 
scale (0 .. .4). 
Trials were presented to each subject in random order. 
Graphics Interface '89 
Table la 
Inc Same Dec 
first 13 11 12 
(black) 3.54 2.31 3.15 
Black -+ White middle 6 1 1 
(grey) 0.07 1.85 2.54 
last 0 0 1 
(white) 3.61 3.54 3.00 
Table lb 
Inc Same Dec 
first 12 13 13 
(white) 3.38 3.00 3.46 
White -+ Black middle 11 9 4 
(grey) 2.62 0.77 1.00 
last 1 0 0 
(black) 2.92 2.62 3.31 
Table le 
Inc Same Dec 
first 12 12 13 
(red) 3.15 2.69 3.46 
Red -+ Green middle 8 4 0 
(beige) 0.46 0.46 2.00 
last 1 1 0 
(green) 3.00 3.00 3.54 
Table ld 
Inc Same Dec 
Solid Black 13 5 1 
(white) 3.00 0.00 2.54 
4 Results and Discussion 
The strongest factor in determining the direction of flow was 
an interaction between the color of the background and the 
colour sequence used. The direction of perceived flow was 
away from the end of the stroke which matched the back-
ground colour. These can be determined by examining the 
top and bottom rows of the Tables la, 1b, and 1c which con-
tain a total of 234 observations. Out of these observations 
only ten deviate from the above rule. Of these deviations 
five were contributed by a single subject. The effect occurs 
irrespective of the shape of the stroke and irrespective of the 
colour sequence. 
The effect of stroke shape was studied in the conditions 
where the strokes were a constant black on a white back-
ground. In these cases (see Table Id) the direction of mo-
tion was perceived as towards the larger end of the stroke, 
no matter which way the stroke was drawn. This finding is 
consistent with the phenomenological observations of Halley 
(1686) and of Bertin (1983). 
A complex picture emerges when we examine the effects 
of colour sequences and grey sequences on a neutral back-
ground. In the grey scale conditions with a neutral back-
251 
ground (center cell in tables la and Ib), the subjects tended 
to find the particles to be moving towards the darker end 
of the stroke. This is most evident from the constant size 
trials. However when size is brought into consideration, the 
tendency of the subjects to perceive direction towards the 
large end of the stroke would either enhance or conflict with 
this. Thus when the dark end coincides with the large end 
of the stroke, a stronger perceived flow rating was obtained 
compared with the constant size condition. Conversely, if 
the dark end coincided with the small end of the stroke, a 
very weak rating was obtained. 
The red-green colour gradient on a neutral background 
also produced some interesting results. It appears that the 
colour red is the dominating colour. When the large end 
of the stroke is red, the subjects unanimously agreed on a 
direction, although did not rate it as strong. In the other two 
stroke categories, the subjects did not agree on the direction 
of flow. 
The study presented here only begins to tap the pos-
sibilities for designing strokes using particle systems. An 
idea which we are currently exploring is the presentation of 
more dimensions simultaneously. Thus we can use hue, for 
example, to represent temperature in a vector field, while 
value (lightness) represents age. Another idea is to use par-
ticle size to represent exaggerated depth in a slice through a 
three-dimensional vector field. 
5 Acknowledgements 
We wish to thank Serge Limoges for his preliminary research 
into the use of particle systems for the representation of flow 
data. 
6 References 
Bertin, Jacques., Trans. by William J . Berg. Semiology of 
Graphics, The University of Wisconsin Press, 1983, p. 
342-355. 
Halley, Edmond, An Historical Account of the Trade Winds, 
and Monsoons, Observable in the Seas Between and 
Near the Tropicksj With an Attempt to Assign the 
Phisical Cause of Said Winds, Philosophical Transac-
tions, Vol183, 1686 p. 153-168. 
Hibbard, William L., 4-D Display of Meteorological Data, 
Proc. 1986 Workshop on Interactive 3D Graphics, F . 
Crow and S. M. Pizar, eds., ACM, New York, p. 23-36 
Lavin, S., and Cerveny, R., Unit-Vector Density Mapping, 
The Cartogmphic Journal, Vol. 24(December 1987), p. 
131-141 
Lueptow, Richard M., Software for Computational Fluid 
Flow and Heat Transfer Analysis, Compute rs in Me-
chanical Engineering, Vol. 6, No. 5(March/ April 88), 
p. 10-17 
Graphics Interface '89 
Also, the direction in which the strokes were drawn was de-
termined randomly to be one of clockwise or counter-clockwise. 
2.3 Subjects 
There were thirteen subjects. Each subject was colour nor-
mal according to Ishihara Pseudo isochromatic plates and 
had (at least) 20/20 vision by a Snellen eye chart. 
Stroke Shape 
./ ./ /' /' 
./ /' /' ./ 
/' /' ./ 
~
BlaCk ~ White 
~ 
~ White ~ Black 
U .. 
-'" 
~ 
U) Red --t Green 
./ 
V 
./ 
V 
./ 
./ 
V~. 
./ ~. ~ -c ~ <' 
.$"V 'it $ 
252 
A.~"'y;< 
~ 
~ Background 
t::)Jf Colour. 
,...--,--,----, 
Solid Black White 
Figure 2. A visual representation of the 3 by 3 by 3 factorial 
experiment with 3 additional conditions. 
3 Results and Discussion 
In order to derive a value for the strength of movement which 
took into account the direction of perceived movement we 
devised the following metric. 
where 
d; = { 
ILi~ld;x;1 
13 
subject; matched direction 
-1 subject; did not match direction 
and Xi represents the rating scale response by each subject. 
The strength ratings, averaged across subjects, are given in 
the lower half of each cell in Tables la, 1 b, lc and Id which 
summarize the results from all thirty experimental condi-
tions. The integer in the upper half of each cell is the total 
number of subjects out of thirteen who reported that ·the di-
rection displayed matched the direction in which the strokes 
were drawn. These tables correspond to planes in Figure 2. 
7':'-.,-, 
, 
a 
b 
c 
Figure 3. Photographs showing a small portion of each of three 
of the stimulus patterns. All three utilize the black ~ white 
colour sequence. ( a) appears on a black background and was 
constructed using particles which decrease in size. (b) appears 
on a grey background and was constructed using particles of a 
constant size. (c) appears on a white background and was con-
structed using particles which increase in size. 
Graphics Interface '89 
Reeves, WilIiam T., Particle Systems - A Technique for 
Modeling a Class of Fuzzy Objects Computer Graphics 
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Strokes for Representing Univariate Vector Field Maps

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