UNIVERZITA KOMENSKÉHO V BRATISLAVE
FAKULTA MATEMATIKY, FYZIKY A
INFORMATIKY
RNDr. Jana Běhal Dadová
Autoreferát dizertačnej práce
Cellular Automata and Particle
Systems for Crowd Simulation
in Selected Environments
na získanie akademického titulu philosophiae doctor
v odbore doktorandského štúdia: 9.1.7 Geometria a topológia
Bratislava 2014
Dizertačná práca bola vypracovaná v dennej forme doktorandského štúdia na Katedre
algebry, geometrie a didaktiky matematiky, Fakulty matematiky, fyziky a informatiky
Univerzity Komenského v Bratislave.
Predkladateľ:
RNDr. Jana Běhal Dadová
Katedra algebry, geometrie a didaktiky matematiky
FMFI UK, Mlynská dolina, 842 48 Bratislava
Školiteľ:
doc. RNDr. Andrej Ferko, PhD.
Katedra algebry, geometrie a didaktiky matematiky
FMFI UK, Mlynská dolina, 842 48 Bratislava
Oponenti:
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Obhajoba dizertačnej práce sa koná ..................... o ............. h
pred komisiou pre obhajobu dizertačnej práce v odbore doktorandského štúdia vymenovanou predsedom odborovej komisie ........................................
9.1.7 Geometria a topológia
na Fakulte matematiky, fyziky a informatiky Univerzity Komenského
Mlynská dolina, 842 48 Bratislava
Predseda odborovej komisie:
Prof. RNDr. Július Korbaš, CSc.
Katedra algebry, geometrie a didaktiky matematiky
FMFI UK, Mlynská dolina, 842 48 Bratislava
Cellular Automata and Particle Systems
for Crowd Simulation in Selected
Environments
1 Introduction
Adding crowds to the computer games and motion picture is more and more possible
thanks to the available computational power. Crowds are interesting not only visually,
but they create more believable, life-like scenes. In interactive computer games and
virtual museum tours crowds influence user personal emotions of the environments.
Moreover, analyzing human behavior in selected environments can be used for safety
purposes, to identify best evacuation routes and exits to avoid traffic jams during
evacuation. Even positions for exhibits in museum can be properly set if the virtual
crowd in museum shows some problems with them.
There are two main goals of this work, each of them is related to the crowd simulation field in a group of selected environments. We choose following environments:
museum with interesting objects, exhibition hall and city square for their relation to
the cultural heritage, presence of attractive objects and interesting human behavior.
For this group of environments we analyze human behavior and try to set our simulation method according to the results from the analysis. Visualized representation
of virtual human characters is simplified to the simple point. What is important are
movements of these characters and their positions in time.
Another group of environments includes stadium, rock concert and disco. We choose
them, because people usually do not change their position often, but there are motions
of characters that are important. We also analyzed behaviors in these environments
and set our simulation to create believable crowd. On the other hand, here positions
of characters were not so much important as were their motions. We try to use more
automated techniques to create new sequences of motions with few pre-modeled ones.
For the first group (museum, exhibition, historic city square), there are many possible techniques that can be used to simulate a crowd. The most interesting from
our perspective are cellular automata, because of their collision detection handling
and particle systems for their unconstrained movement. Both have advantages and
disadvantages and are suitable for different environments, we discuss these problems
through the whole work and also compare these techniques.
3
2. RELATED WORK
The second group addresses both the problem of crowd simulation and also the problem of motion retargeting as adaptable sequences motions need to be created. These
sequences should then be applied also to new, different characters. There are already
methods that try to solve this problem, we discuss them in related work section, but
purpose of this work is to find unique solution for this problem and show it in different
environments.
2 Related Work
Topics discussing crowd simulation, according to Thalmann and Musse [TM13] are
divided into six broad categories: Generation of virtual individuals, Crowd animation,
Crowd behavior generation, Interaction with virtual crowds, Virtual crowd rendering
and Integration of crowds in virtual environments. We focus to: Crowd animation,
Crowd behavior generation and Integration of crowds in virtual environments.
Firstly, real crowds need to be studied and analyzed to understand how real people
behave, mostly behavior is closely bound with movement and positions of the people.
Therefore their paths, speed, goals and interactions are observed. Then methods
that simulate these behaviors are suggested. Mostly pedestrians are analyzed in the
psychological studies [Fru71], [BA00], [Sti00], [SHT09] or from acquired video and
images [MJJB07], [LCHL07]. Patterns found in crowd with pedestrians are common
also to the behavior and movement of more general crowd.
One of the psychological aspects is idea of personal space, which is a minimal space
that needs to be maintained among the agents and should not be penetrated by other
agents or obstacles [Hal90]. The space shape may vary according to the crowd density,
personal preferences or situation.
Another aspect is Least Effort movement. A pedestrian chooses generally the fastest
way to achieve his goal and tries to satisfy Law of Minimal Change [SHT09] and Least
Effort [Sti00]. Law of Minimal Change is satisfied when pedestrian chooses the
straightest way, with the minimum of changing direction, the most attractive and the
less noisy [BEHG11]. Moreover a pedestrian typically prefers not to take detours.
When creating crowd simulation, not only preferred path is important, but also dealing with collisions. There are three types of problems: Collision Detection, Collision
Prediction and Collision Avoidance. All of them consider collisions with static and
dynamic objects, including other individuals, but difference between them is how
early is an action taken to avoid collision. Collision detection usually results in ur-
4
3. CELLULAR AUTOMATA FOR MOTION CONTROL
gent collision avoidance strategy and collision prediction results in smooth collision
avoidance strategy. In urgent collision avoidance strategy, agent rapidly decelerate or
sharply veer by side stepping. In smooth collision avoidance strategy agent gradually
steer to the sides when, because there is enough time [RD05].
Moreover, to simulate crowd with the correctly set behavior, also perception and
memory are important, because they influence behavior and decision. Perception
can be defined as the awareness of the elements in the environment through physical
sensation [TMK00]. Usually, human sensing system is constrained to only visual
information, (visual system). Variables from visual system include Field of View
(FOV), visible distance, height of a person (height from which other objects are
observed), refresh rate, sometimes memory and others [RD05], [BEHG11].
Synthesized memory has an important role in a realistic behavior simulation, because
agents without any memory appear to be stupid. Another mistake that is commonly
used in the virtual memory simulation is giving all possible information about the
environment to the agents. This is not plausible, it is even supernatural, because
real people do not have all information about the environment due to the occlusion,
obstacles and forgetting [PO02].
3 Cellular Automata for Motion Control
Usually, cellular automata are used for path planning, where cells are part of the
environment and agents occupy these cells. In methods presented in this section we
use cellular automata as a tool to create automated motion of a group members from
the predefined set of motions.
Firstly, we define special mapping between agents and the cells of the automaton. In
our solution, agents are positioned in the environment on the grid created by cellular
automaton. One agent at the most for each cell. Mapping is then straightforward,
agent to the cell that occupies and cell to the agent that occupies it, see fig. 1.
Because there is no restriction for the grid dimensions in cellular automata, we could
use as many figures as needed.
Another mapping is between values and motion clips from the database of motions.
Database is created from one longer animation sequence or set of sequences that
are then applied to the figures in the crowd. These motions are indexed in the
database. Which motion to use from the database is defined by the properties of
motion - depending on what the topology of characters is, what kind of motion and
5
3. CELLULAR AUTOMATA FOR MOTION CONTROL
(a)
(b)
Figure 1: Our mapping in a nutshell. (a) from left to right: Moore neighborhood
(8-neighborhood) of a cell with neighbors in black, one step of an automaton (3x3
grid), mapping to movements of a group (b) final render
what diversity of a group is needed. Current solution allows only transitions between
motions that have the same beginning and ending transformations. This way we
could use any permutations of them. Those are input parameters.
Afterwards we suggested various automaton rules, that are suitable for different scenarios. Very simple one is mapping, where we choose 9 different motions as our
motion database. Number 9 is because as index, we use sum of occupied cells from
the 8-neighborhood, which means 0-8 values. These values means indices to the sorted
and indexed motions from the database. After this basic solution, we defined rules
to be suitable for the flash mob scenario. The Flash Mob is when group of informed
people suddenly gather in the public space and start to move evenly. Movement of
an individual depend on the surrounding people. At first there are some seeds - cells
that are informed. Other cells are uninformed and become informed when there are
some informed cells in the previous step in their neighborhood. We enhanced this
solution also with looking orientation of agents and informed cells from the previous
step are calculated only for the cells, that are in the field of view of an agent.
Third scenario includes performance of a mexican wave in the stadium. Wave propagates also based on the field of view and informed cells spread by changing uninformed
ones, similarly to previous solution, but the neighborhood is different. Also there are
various states of an automaton, that are considering, not only (0-1) value as in previous solution. 0 - uniformed cell, 1 - standing motion, 2 - performing wave, 3 - sitting,
4 - stays informed, but the motion is sitting. We also introduces personality function, that are based on probability in which agent will attend the performance. In
these scenarios we showed that cellular automata could be used for automatic motion
control for the crowd instead of other techniques.
6
4. CELLULAR AUTOMATA FOR PATH PLANNING
4 Cellular Automata for Path Planning
Use of cellular automata for path planning is not novel, but we would like to discuss enhancement possibilities and advantages and disadvantages of their use. Firstly
we decided to use regular rectangular cellular automaton, as standard type of an
automaton in similar solutions [BKSZ01], [LM03], [DDW06]. Moreover we also simulate basic behavior of the agents for the exhibition hall scenario. There are some
attractive objects (displayed art objects, exhibits, etc.) similarly to real museum and
according to the psychological studies in such environment, visitors are approaching
these objects and observe them, then when level of fatigue is hight enough they leave
the space. Movement of agents is limited to the grid, because they move from cell to
cell in each step. Cell is size of a 0.5m x 0.5m which is standard personal space for a
person. With use of the grid we have simple access to the neighborhood of the agents
and finding nearest neighbors is trivial. For the collision avoidance we use prioritized
detour and stopping method, where colliding agents try to detour object or another
agent in two directions, when none of them is possible, than they stop for one step
and their priority in the next step is higher. Personal goal of an agent is influenced by
the attractor and they stop to observed these objects. Therefore also agents appear
to be stuck near these objects as is case also in real museums, see fig. 2.
Figure 2: Various stages of the simulation.
(left) initial step, (right) step during movement. Blue spheres represent participants
that are interested in objects (yellow cylinders) and are grouped around these
interesting objects.
With this solution there was problem of using rectangular grid, because movement
in diagonal direction is faster than movement in axis aligned directions, it is called
diagonal problem. Therefore we analyzed use of hexagonal grid instead of rectangular, which eliminated this problem. On the other hand, there were still problems
with the hexagonal grid as constrained movement in to the 6 directions (there are 6
neighborhood cells) and in other directions movement violates minimal change law
7
5. PARTICLE SYSTEMS FOR CROWD CONTROL
and least effort movement, see fig. 3. Moreover also implementation of a rectangular
grid is more native to the programming, where 2-dimensional arrays are one of the
basic structures. With these structures rectangular grid is trivially implemented and
hexagonal grid is also possible but with some differences.
(a)
(b)
(c)
Figure 3: Movement on the grid vs. least effort movement. A is starting point,
B is end point. (a) movement on hexagonal grid (b) movement on rectangular grid
(c) difference between least effort path (black), hexagonal path (red) and rectangular
path (green)
The problem with the movement on the grid is that agent’s position are centered
on the cell centers, therefore their movement is restricted and unnatural. It does
not matter, if the grid is hexagonal or rectangular, the movement is unnatural. It
is suitable for some situations, where precise movement is not important, only flow
of people matters. Also this solutions are not suitable for the dense crowd, because
agents on the grid cannot get closer to each other than is the cell size.
5 Particle Systems for Crowd Control
Cellular automata solutions create unrealistic movement, because it is constrained to
the center of the cells. Therefore in this section, we would like to discuss particle
system solution, where agents are represented by simple objects and their behavior
is rule based. Moreover we also use grid for the environment and easier access to the
neighborhood of the cells, but the movement is not restricted to the centers of the
cells. Particle systems were originally created to render fuzzy objects, such as smoke
and fire [Ree83], but they were also already applied to crowd simulation problems
[TCP06], [HM95]. Lifecycle of each particle includes three stages: Generation of
particles, Particle dynamics and Extinction. It possible to use particle system with
various algorithms that define behavior or path calculation. In this section, we discuss
our solution for a crowd simulation with use of these systems.
8
5. PARTICLE SYSTEMS FOR CROWD CONTROL
5.1
Potential Fields and Fuzzy Logic
Our environment is divided in the regular rectangular cell grid for easier movement
calculation, where cells are twice as large as radius of an agent representation to
avoid unnatural movement. There are different types of cells, entrance (blue), exit
(red), interesting art object (yellow, attractor with different attraction value) and
walls (green). We calculate potential field for each interesting object separately using
the following equation (1):
y =I −2
x.c
I
,
1 where x is euclidean distance from the interesting object, I is attraction at the interesting object, y is resulting attraction at current cell and c is constant global value
that defines attractor influence. Result of the potential field calculation is shown on
the fig. 4.
Figure 4: Results of potential fields calculation with direction to the attractors. More
than one direction vector could be associated to a single cell (red cells).
The final path for an agent is calculated by decision process in each step. Agent
starts at entrance point (blue cell) and path is goal directed. Decision process is
influenced by the behavioral patterns that are result of the crowd analysis in sec.
5.2. Agent has preferred direction (to the exit, or to the next interesting object from
the list of objects) and direction to the interesting objects which is influences by the
potential field calculation. Which if these two is selected is based on the fuzzy logic
decision process. Inputs to this process are values that increase, decrease during the
time and values that are set at the beginning of the simulation are represent personal
9
5. PARTICLE SYSTEMS FOR CROWD CONTROL
preferences of an agent. Afterward we defined various membership function for these
values and fuzzified them. With the defuzzification we came to the crisp values, that
tell in which direction agent finally moves.
(a)
(b)
(c)
Figure 5: Smoothing with Bèzier curve. (a) pre-calculated path (b) smoothed path
(black dots as representation of an agent have smaller radius to make changes in the
path more visible) (c) both paths together
The problem with such path is that abrupt change in the movement may occur, which
is without stopping not natural. We solve this problem by pre-calculating next few
steps (in our case 4) and smoothing path created with these steps. For the smoothing
we used standard cubic Bèzier curve [Far02], where control points are pre-calculated
positions in time. We use only 4 control points (positions from the previous steps) and
smoothing that we needed is not in large area, therefore special curves are not needed.
When the curve is calculated we find smoothed positions on the curve with the respect
to the distance between positions in the pre-calculated curve. Positions of smoothed
points and pre-calculated positions will be in the convex hull of pre-calculated points,
from the definition of the Bèzier curve, because pre-calculated points are same as
control points, see fig. 5.
5.2
Observation of a Real Crowd
Firstly, we tracked positions of the visitors in the city during their visit using GPS
(Global Positioning System) tracking system. For this tracking to be possible, tracked
visitor used GPS tracking application for the mobile devices. Mostly, these applications are used to track sport workouts (running, walking, bicycling). After tests,
where we tested accuracy of the tracked path and available exporting options, we decided to use Endomondo. We tracked visitors in two different, historically interesting
locations in Bratislava: Hviezdoslavovo námestie a Hlavné námestie. Another option
that we used to observe behavior of a visitors was video capture from various locations. There are two different outdoor locations - Michalská ulica a Hlavné námestie
10
5. PARTICLE SYSTEMS FOR CROWD CONTROL
(a)
(b)
(c)
(d)
Figure 6: Time steps: t1 = 1 : 20, t2 = 1 : 28, t3 = 1 : 44, t4 = 1 : 52 average speed:
1.66 km/h
and indoor locations of the Malokarpatské múzeum Pezinok (The Small Carpathian
Museum in Pezinok)1 . We observed visitors in these locations, their average and
maximal speed, they path and behavior patterns they did during their visit, such as
taking pictures, observing the object, reading a text.
There are two main categories that will enhance simulation of visitors behavior. These
include different zones of influence and different path patterns for each behavior.
Zones of influence define circle around the object where people show predefined behavior, different for each zone. We observed four different zones: read zone (when
some text is on the interesting object visitors stops to read it), observe zone (visitor
stops or slow down to observe the object), take picture zone (visitor stops to take
picture of an object, or walk back to this zone to take a picture), be on the picture
zone (visitor come closer to fit him/her with the object in the camera held by another
person). These zones are different for the small indoor museum and larger outdoor
environment. Also they are different for the smaller and larger objects. Because
visitor need to be further away to fit object in the camera.
1
http://www.muzeumpezinok.sk/en/
11
5. PARTICLE SYSTEMS FOR CROWD CONTROL
entrance
entrance
entrance
entrance
exit
exit
exit
exit
(a)
(b)
(c)
(d)
entrance
exit
(e)
Figure 7: Behavior of the people on the square. (a) citizen, that only crosses the
square (b) visitors, that stops to take picture, or observe object (c) visitor, that comes
closer to the object for observation, or wants to be on the picture (d) visitor, that
comes closed to the object and stops to read information (e) visitor, that walks back
to take picture of an object
Moreover, we came to the following path patterns (see fig. 7, but not all of them
can be incorporated in our current solution. Currently our solution does not allow
to create smaller groups, not even two people as a separate group, therefore last
path, where person walks back to take picture of another person is not possible with
our current solution. However, the same path is created when person discovers that
object would not fit camera field of view and need to walk back. Patterns that we
discovered for the tourists in the city and visitors in the museum should significantly
enhance our simulation when incorporated in it.
5.3
Results
For the implementation purpose we used architecture that is proposed by Pelechano
et al. [PAB07]. We have used various environments with various exits and entrance
points to show our solution. However, all of them are simplification of room in a
small museum, or exhibition hall (rectangular shape, entrance points, exit points,
with walls and interesting objects) or a simplification of a city square (rectangular
shape, entrance points, exit points, surrounding buildings and interesting objects).
After study of the human navigation behavior, we modified our method to include
12
5. PARTICLE SYSTEMS FOR CROWD CONTROL
Figure 8: Example of the final path influenced by collision avoidance. Black dots are
representations of agents, blue dots are positions of one agent during the simulation.
behavioral patterns according to this study. It is possible to set each interesting
object as large object, such as fountain, or building, which are more common in
outdoor environment. It is also possible to set each interesting object as a text
object, where it is possible to read some information, which is more common in
indoor environment, such as museums. These settings allow us to create scalable
behavior, suitable for the museums and also for the city squares. Moreover, it was
necessary to create decision process based on finite state machines. In this decision
process visitor chooses behavioral pattern that is suitable for him and surrounding,
when he approaches interesting objects. The suitable behavioral pattern is agents
intention, which is a high-level goal that an agent is committed to achieve and agent
has exactly one intention at any given time [TM13]. Final crowd simulation for one
time step and the whole path for one agent during the simulation is shown on fig. 9.
With this decision process, it depends on the visitors actual preference if picture of
the object will be taken. It is not a deterministic process, where, if visitors is near and
has the camera then he/she will take the picture. In each node in the decision graph,
where question is asked, visitors decide with personal preference in current moment
if he/she is willing to take the picture. Personal preference for each question from the
graph is set at the beginning of the simulation for each agent and it is a percentage
value that will tell how much is agent willing to do something. Pseudocode for the
whole approach is in algorithm 1.
For comparison of results from our method and data from the observation of a real
humans we used graph, where we compared statistical data for various options. We
created two different scenarios, the historical city square, see fig. 9(a) and the mu13
5. PARTICLE SYSTEMS FOR CROWD CONTROL
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(b)
Figure 9: Comparison of our results and observed data. Observing objects shows
the percentage of objects that were observed by some people/agents, and observed
people shows the percentage of people comparing to all analyzed people/agents. (a)
yellow - observed data from the historical city square, blue - observed data, where
only observing visitors are taken into account, green - data from our application (b)
yellow - observed data from the museum, green - data from our application
seum, see fig. 9(b). In both we set various parameters to be as accurate as possible
to the analyzed data. There are still differences, because parameters set only probability that some behavior pattern will be present and in the graph are measured data.
In each measured element we show average percentage, where 100% is the maximal
measured value for each element. We used same elements for both situations, but
some of them are not available in both (e.g. taking pictures was not allowed in the
museum). Moreover there were lot of people in the city square that were only crossing
the square and were not visitors. Therefore the resulting polyline is different to our
results, where we set parameters mostly according to the visitors. We also showed in
this scenario also observed data that took only visitors into account (those people,
who observed something, or took a picture). There were also people that brought
non-standard results, such as bicyclists and distorted the results. In our solution we
did not take into account such people, therefore is our curve different.
Our results proof, that our solution is scalable enough to be used with different
scenarios. The average difference between analyzed data and measured from our
application (if we take into account more visitors, than crossing people) is less than
10% for the museum scenario and less than 15% for the square scenario, which is
small enough to be proof our solution.
14
5. PARTICLE SYSTEMS FOR CROWD CONTROL
Algorithm 1 CalculateNextStep
Require: agent
Require: automaton
Require: markers
Require: criticalAngle
Require: guide
cell ← automaton.cells[agent.cell]
goal ← agent.goal {preset selected exit for the agent}
neighbors ← cell.getN eighborAgents()
interest ← cell.getInterestV ector() {vector from potential field calculation}
if agent.currentGuideGoal.visited() then
agent.currentGuideGoal ← guide.getGoal(agent) {change goal from guide if
current was already visited}
end if
destination ← agent.calculateF uzzy(guideGoal, goal, interest) {decision of the
destination vector}
if destination.cell.hasInterestingObject then
destination ← agent.behaviorAvoidance(destination) {behavior decision near
interesting object}
end if
if not neighbors.isEmpty then
destination ← agent.collisionAvoidance(destination, markers) {collision
avoidance using markers}
end if
if criticalAngle < getAngle(agent.previousSteps, agent.newP os) then
agent.smooth(agent.previousSteps) {smoothing using Bézier curves}
end if
agent.newP os ← destination
15
6. CONCLUSION
6 Conclusion
In this thesis I focused on behavioral crowd simulation and presented my original,
more formal definition of a crowd model and other terms that are mostly used in this
topic. Such general formalism is needed for better understanding and is not available
in referenced literature. I explained related well known methods, that I use in this
thesis such as cellular automata and fuzzy logic.
My main focus was on the two small areas, that were result of my Project of Dissertation: use of cellular automata for non standard problems and crowd
simulation for a museum environment. The other two areas that were part of
the Project of Dissertation are also discussed in my thesis, but are not major. These
areas are: classification of methods according to the memory and use of
hexagonal grid for crowd simulation.
The main contribution of this thesis is in the following areas:
• formal definition of a model crowd simulation
• classification of methods according to the memory
• discussion of suitable grid solution for crowd simulation
• various models of cellular automata for motion control
• analysis of human behavior and paths in museums and city squares
• behavioral model based on the real human behavior for museum, exhibition
halls and city squares
• scalable application for crowd movement control
As for the future work, it is still possible to define better cellular automata for more
general purposes for crowd motion and not only motion itself but also incorporate
change of the position from cell to cell. Our current solution is scalable, but it still
needs analysis of the situation to define automaton rules. Moreover not all situations
are suitable for the use with our proposed solution.
Our first idea of the crowd simulation for a museum environment at it was proposed
in the Project of Dissertation was to use virtual terrain as the function of attraction to
control the behavior of the crowd. In this thesis we used potential fields as well known
representation of attraction or repulsion to implement procedural analogy of terrains.
16
6. CONCLUSION
Moreover I set properties of the behavior in the model according to the crowd analysis
I did in the museum and city square. Path calculation and behavior of a crowd use
fuzzy logic and other decision techniques as well as markers as a modern technique
for collision avoidance. What I leave for the future work is behavior of the pairs and
subgroups, which are part of the real crowd in discussed environments. Subgroups
would allow us to incorporate even more complicated and realistic behavior, which
would improve my solution. On the other hand, current solution is still scalable
enough to analyze crowd behavior for the purposes of the museum exhibits setup to
avoid traffic jams and to get best positions for the most attractive objects.
Most of the novel ideas from this thesis were already published as is mentioned through
the thesis and list of my all publications is in the List of Publications. I also supervised students on bachelor (6 students) and master levels (1 student), who successfully
defended their theses. During my PhD studies I was also part of the following research and grant projects: Slovak Ministry of Education, VEGA grant No. 1/0763/09
and VEGA grant no. 1/1106/11, Comenius University, Bratislava, Slovakia grant
no. UK/364/2012 and UK/288/2013, ASFEU project OPVaV-2011/4.2/07-SORO:
Comeniana, methods and tools of presentation and 3D digitization of cultural heritage
objects.
17
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List of Publications
[1] Jana Běhal Dadová. Crowd Simulation Using Potential Fields and Markers. In
Current Issues of Science and Research in the Global World. Kluwer. 2014. (in
a review process)
[2] Jana Běhal Dadová, Tomáš Dado, Andrej Ferko. How to Build a Model for
Crowd Simulation. In Slovenský časopis pre geometriu a grafiku. Vol. 1. 2014.
(in a review process)
[3] Martin Madaras, Jana Běhal Dadová, et al. Skeleton-based Matching for Animation Transfer and Joint Detection. In Spring Conference on Computer Graphics
2014. 2014. (accepted)
[4] Jana Dadová, et al. Use of cellular automaton in crowd animation. In Information
Technology Applications Vol. 2. 2013. pp. 79-84
[5] Stanislav Stanek, Jana Dadová, et al. SPINKLAR-3D: motion capture interaction and cooperation between people and avatars in 3D augmented reality and
virtual reality. In Information Technology Applications = Aplikácie informačných
technológií. Vol. 2. 2013. pp. 46-53
[6] Jana Dadová. Simple crowd simulation of a Mexican wave. In Študentská vedecká
konferencia FMFI UK: Zborník príspevkov, Fakulta matematiky, fyziky a informatiky UK, Bratislava 2013. pp. 304
[7] Jana Dadová, Andrej Ferko. Cellular automata based crowd simulation of mexican wave. In Spring Conference on Computer Graphics SCCG 2013: Conference
Materials and Posters. 2013. pp. 32-35
[8] Jana Dadová Importance of Procedural Animation and Modeling. In Katedra geometrie 50 rokov založenia - Pamätnica k 50. výročiu vzniku KG na UK
Bratislava a zborník abstraktov. Research Stream, Knižničné a edičné centrum
FMFI UK. Bratislava. 2012. pp. 46
[9] David Běhal, Jana Dadová. Interactive video and camera position for virtual environment. IADIS International Journal on Computer Science and Information
Systems. Vol. 7, No. 2 (2012), pp. 167-177
[10] David Běhal, Jana Dadová. Interactive video and camera position for virtual
environment. In Proceedings of the IADIS International Conference Graphics,
Visualization, Computer Vision and Image Processing 2012, IADIS Press. Lisbon. 2012. pp. 19-26.
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LIST OF PUBLICATIONS
[11] Jana Dadová, Andrej Ferko, David Běhal. Crowd simulation in an exhibition
environment. In Proceedings of the IADIS International Conference Graphics,
Visualization, Computer Vision and Image Processing 2012, IADIS Press. Lisbon. 2012. pp. 127-131.
[12] Jana Dadová, Roman Franta, Andrej Ferko. Motion Control in a Group Based
on Cellular Automaton. In Spring Conference on Computer Graphics SCCG
2010: Conference Materials and Posters. 2012.
[13] Jana Dadová Cellular Automata Approach for Crowd Simulation. Rigorous
Thesis. FMFI Comenius University. Bratislava. 2012.
[14] Jana Dadová. Virtuálna populácia. In Virtuálny svet 2012 : Myv́slienky, kontext,
tvorivé dielne a postery pre vedeckú výstavu (DVD). , Knižničné a edičné centrum
FMFI UK. ISBN 978 - 80 - 89186 - 95 Bratislava. 2011. pp. 91-93.
[15] Jana Dadová, Roman Franta, Andrej Ferko. Motion Control in a Group Based
on Cellular Automaton. Eurographics 2011, [s.l.]: The Eurographics Association.
2011. (accepted, unpublished)
[16] Jana Dadová. Flash mob Like Group Formation Control. In Študentská vedecká
konferencia FMFI UK: Zborník príspevkov, Fakulta matematiky, fyziky a informatiky UK, Bratislava 2011.
[17] David Běhal, Jana Dadová, Ivana Uhlíková 3D extension of web. In WSCG 2011
- Poster Papers Proceedings, pp 37-40. Václav Skala - Union Agency. Plzeň.
2011.
[18] Jana Dadová Animation of Flocks and Herds (Supervised by Andrej Ferko).
Master Thesis. FMFI Comenius University. Bratislava. 2010.
[19] Jana Dadová Force-based group formation control. In Spring Conference on
Computer Graphics SCCG 2010 : Conference Materials and Posters. Comenius
University. Bratislava. 2010. pp 31-33
[20] Jana Dadová Automatic animation of representative shapes with particle systems. In Študentská vedecká konferencia FMFI UK: Zborník príspevkov, Fakulta
matematiky, fyziky a informatiky UK, page 329. Bratislava 2010.
[24] Jana Dadová Obloha ako informačný bilboard. (Supervised by Andrej Ferko).
Bachelor Thesis. FMFI Comenius University. Bratislava. 2008.
21