Behavioural Simulation in Voxel Space

Hongwen Zhang Brian Wyvill

SAGE Systems Division Department of Computer Science

Valmet Automation University of Calgary

Calgary, Alb erta, Canada T2W 3X6 Calgary, Alb erta, Canada T2N 1N4

In the later literature [5], the mo deling and the simula- Abstract

tion steps in b ehavioural animation are referred to as

In this paper we present a framework for be-

behavioural simulation. Compared with b ehavioural

havioural simulation. A uniform voxel spacerepre-

animation, the concept of b ehavioural simulation has

sentation is used to implement the environment mech-

a larger scop e. It not only includes b ehavioural ani-

anism of the framework. An example environment

mation, but also includes those applications that use

is presented where actors with olfactory sensors are

similar mo deling and simulation principles to pro duce

able to direct their motions according to a scent of the

complex and static images, suchas[4].

chemicals in the voxel spacebased on mass transfer

The key problems in b ehavioural simulation are :

theory. Objects in the enviroment arescan converted

to the voxel representation to facilitate col lision detec-

1 Collecting b ehavioural data from the observation

tion. An example of using the framework to simulate

of living systems.

the behaviour of a group of arti cial butter ies is used

to demonstrate the ideas of this research.

2 Behaviour representation. This concerns howto

b etter represent the observed b ehaviour in a com-

1 Intro duction

puter system.

Complex images of a p opulation of ob jects can

b e automatically generated by mo deling the simple

3 Mo deling the world view and the asso ciated sens-

b ehaviour of each individual ob ject and the interac-

ing mechanism for each individual ob ject.

tion b etween the ob jects. This approach is termed

by Craig W. Reynolds as behavioural animation [12].

4 Path generation by reasoning on the b ehaviour

Reynolds noticed that scripting the paths of a large

representation with the sensed information.

numb er of individual ob jects such asa ock of birds

is a very dicult and tedious task in computer ani-

5 The attachment of the details of the motion with

mation. He demonstrated that b ehavioural animation

the generated path, such as the wing ip of birds

is a more ecient and robust way to accomplish this

and the gaits and b o dy swing of a dancer, etc.

task. The basic idea of b ehavioural animation is that

the complex paths can b e generated by the interac-

This pap er addresses the ab ove third problem. There

tion b etween the individual ob jects. Hence only the

are two related sub-problems. The rst is how to pro-

b ehaviour of each individual ob ject needs to b e mo d-

vide a world view for each ob ject. Any solution to this

eled. The paths can then b e generated by simulating

problem has to provide a mechanism to represent the

these mo dels. This di ers from the more conventional

neighb orho o d of each ob ject. The second sub-problem

computer animation metho ds which only mo dels the

concerns how an ob ject obtains information from the

shap e and physical prop erties of the characters. When

outside world. In order to solve this problem, a sensing

visualized, a simulation of a b ehaviour mo del can gen-

mechanism has to b e implemented for all the ob jects.

erate a sequence of dynamic, intentional, and complex

Many previous approaches use a database to store

pictures. This makes b ehavioural animation a very at-

geometric information ab out the ob jects in the system.

tractive high level mo deling metho d in computer ani-

This database provides a world view which is shared

mation.

by the ob jects. Each ob ject can then abstract informa-

Generally sp eaking, a b ehavioural animation pro-

tion ab out its environmentby querying the database

cess includes three related steps. They are :

and computing its relationship with all the other ob-

jects. This pro cess has to b e applied to all the ob jects

mo deling the b ehaviour of each individual ob ject,

in the system. It is an exp ensive op eration which has a

complexityof On , where n is the numb er of ob jects.

simulating a p opulation of these b ehaviour mo d-

To reduce this complexity, Ned Greene [4] used a voxel

els,

space to provide a sub dividing strategy for geometric

information. A voxel space is a region of three di-

visualizing the simulation pro cesses. mensional space partitioned into identical cub es. Each

cub e is called a voxel. His approach e ectively re-

duces the ab ove complexityto On. However, his

original metho d is mainly concerned with using voxel

space for the purp ose of generating static images of

e plants. The plants havevery simple geo-

vine lik Clock

metric shap es. Their b ehaviour is mainly a ected by the geometric information distribution in the neigh-

borhood. Actors

In this researchwe prop ose a framework for b e-

havioural simulation. The framework not only em- 333

33 333 ys vision p erception but also olfaction p erception plo 33 333 33 333 33

h is otherwise very dicult to implementina whic 33 33

ventional approach. By using voxel space, the com- con 33

plexity of the p erception pro cess of each ob ject is re-

duced to linear, within the limitation of a voxel space's

resolution.

A FRAMEWORK FOR

2 Behavioural System

VIOURAL SIMULATION

BEHA Environment

2.1 THE IMPORTANT CONCEPTS

Behaviour simulation assumes that the complex

phenomena of a large system is caused by the interac-

Figure 1: A b ehavioural system

tions of its comp onents. Hence only these comp onents

need to b e explicitly mo deled. The global phenomena

of the large system can b e generated automatically by

simulating a group of explicitly mo deled comp onents.

Each mo del of such a comp onent is called an actor.

One lo osely de ned concept in b ehavioural simula-

tion is the environment. It is used here to refer to

the mechanism that represents all the outside factors

for each individual actor. These factors are ltered

and transformed by each actor to its internal repre-

sentation of its neighb orho o d. The mechanism that yp e of

an actor uses to lter and transform a certain t sense Images

information from the environment is called the sen-

sor of that typ e of information. In a simulation, a set

of actors are coupled by their environment. The set

vironment is called a be-

of these actors and the en Sensors State interpolate

havioural system.

The b ehaviour of an actor is the internal repre-

tation of our observation of the corresp onding dy-

sen interpret

namic ob ject. This internal representation is used in a ulation to map the sensed information and the cur-

sim Actuator update

t state of the actor to a path of state changes. This

ren Behaviour Reasoning

mapping is referred to as path planning. Actuators

are used to execute these state changes byinterpreting

and/or interp olating the path. In b ehavioural simulations that di-

tion, these are usually programs or fun Actor Path

rectly manipulate the state parameters of actors. The

examples of actuators are the motor controller in [15],

or the muscles in [17].

2.2 THE FRAMEWORK

ve discussion, this research estab-

Based on the ab o Environment

lishes a framework for building b ehavioural simulation

applications. The framework is comp osed of two lev-

els. The rst level is the mo del of b ehavioural sys-

tems Figure 1. It has a set of actors, an environ-

Figure 2: An actor

ment shared by all the actors, and a global clo ck for

controlling the animation frequency and synchroniz-

ing each actor with the changes in the environment.

The second level is the mo del of actors Figure 2.

An actor senses the environment to detect any signif-

icantchanges. The path planning mechanism plans

the path according to the sensed information and the

current state of the actor. The actuators interpret and

interp olate the path by reading and setting the cur-

rent state. Images can b e generated by rendering the

state.

The b ehaviour reasoning mechanism can b e imple-

mented by using heuristic rules [3], a network of no des

[20,16], a genetic algorithm [10], or a hybrid approach

using b oth a genetic algorithm and a network of no des

[14]. The path can b e represented as qualitative terms

or a set of parameters to drive the actuators. The im-

plementation of the actuators can range from simply

interpreting the qualitative terms, to the interp ola-

tion of the actors state with key-framing or physically-

based mo deling techniques [15].

The environment and the sensors are implemented

in this research with voxel space representation.

3 VOXEL SPACE AS THE ENVI-

RONMENT

The central idea of using a voxel space as the en-

vironment is to distribute the information ab out each

actor in the voxels. This way, an actor can get infor-

mation ab out anychanges in its neighb orho o d, suchas

an approaching obstacle, a fo o d source, etc., by sens-

Figure 3: A glass temple de ned in Op enInventor

ing the neighb oring voxels. An actor can also let its

activity b e known to others by leaving its \fo otprint"

in the voxel space. In our approach, eachvoxel can

scene graph is used as the data structure to represent

hold a list of information parcels. Each information

a hierarchical geometric shap e. A scene graph con-

parcel corresp onds to a typ e of information. The typ es

sists of one or more no des, each of which represents

of information currently b eing mo deled are geometric

a geometry, prop erty e.g material, etc., transforma-

information and olfactory information. Each informa-

tion, or grouping ob ject. Hierarchical scenes are cre-

tion parcel is represented as the following triplet :

ated by adding no des as children of grouping no des,

resulting in a directed acyclic graph. Figure 3 shows a

t; i; ids

glass temple constructed with an Op enInventor scene

where :

graph.

The algorithm for scan converting a scene graph in

t | the information typ e. Currently, it is either ge-

the voxel space is describ ed as the following :

ometry or olfaction.

i | the intensity of the information. For geometric

scanConvertGroupNode gNode,

information, i is always 0 or 1, which indicates

Transformation aMatrix{

the voxel is empty or o ccupied. For olfactory in-

for each child x of gNode{

formation, i is the combined scentintensityofthe

m = the transformation of x

actors that contribute their scent in this voxel.

under gNode;

//Calculate the combined

ids | A set of actor identi ers. Each actor in this set

//transformation

has contributed to the intensity of the information

m = m*aMatrix;

in this parcel.

switchthe node type of x{

case GroupNode :

When sensing the neighb orho o d, an actor only

scanConvertx, m;

needs to search the list of parcels asso ciated with each

break;

voxel.

case ShapePrimitive :

3.1 GEOMETRIC INFORMATION IN

x.transformm;

VOXEL SPACE

//Use Kaufman algorithms

x.scanConvert; A set of elegant algorithms for distributing the geo-

break; metric primitives such as three dimensional lines, p oly-

default : gons, p olyhedra, circles, cylinders, etc. were devised

break; by Arie Kaufman [7, 6]. These algorithms are used in

} //end switch this research to scan convert geometric primitives.

} //end for loop Complex shap es can b e constructed hierarchically

} //end scanConvert by using these primitives. The Op enInventor [19]

Now the question is how to calculate the molar con-

centration in eachvoxel. The answer can b e found in

the mass transfer theory [8]. The mass balance of a

chemical A in a voxel is mo deled as:

5N + R =0 1

A A

where :

@ @ @

5| the di erential op erator, + +

@x @y @z

N | the molar ux at time t. The molar ux

of A is de ned as the numb er of moles of A that

pass through a unit area p er unit time.

C | the molar concentration of A in the voxel.

R | the rate of repro duction of A p er unit vol-

ume. It is non-zero in the voxels that contain the

sources of A and zero elsewhere.

If we only consider the di usion in the static air, then

the molar ux N is governed by the Fick's law of

di usion :

@C @C @C

A A A

; D ; D 2 N =D

Figure 4: The glass temple in voxel space A

@x @y @z

where D is the mass di usive co ecientofAin the

air. It is a constant if the temp erature and pressure

Figure 4 is the scan converted glass temple in the

are all constant.

voxel space with a 75 75 75 resolution.

Solving equation 1 and equation 2 for C with the

3.2 OLFACTORY INFORMATION IN

Forward Time Center SpaceFTCS metho d [11], we

VOXEL SPACE

have:

t+1 t+1

t t

Olfactory information asso ciated with searching for

+ C + =tR C F

Ai;j;k s Ai;j;k

Ai;j;k Ai;j;k

fo o d, nding a mate, or avoiding a predator plays

where:

an imp ortant role in the activities of many ani-

mals. The following is a vivid depiction of how the

C | the molar concentration of A in the

Ai;j;k

African hyaena uses olfactory information to guide it-

voxel i; j; k at time t.

self through the darkness [1] :

\With a sni a hyaena can p erceive not only

R | the repro duction rate of A in the voxel

Ai;j;k

here and now but, simultaneously, a whole

i; j; k at time t.

series of events stretching backinto the past.

.... The pasted patches of grass must shine in

s | the size of eachvoxel.

the distance like lighthouses and the pack's

trails, p erfumed by their paws, must stretch F | the net ux of A in the voxel i; j; k .

Ai;j;k

ahead like lines of re ector studs down the

middle of a motorway."

The net ux of A can b e expressed as

Previous approaches in b ehaviour simulation applica-

t t t

F = C 6C

Ai;j;k Ai+m;j +n;k +p Ai;j;k

tions have not mo deled the e ect of olfactory informa-

m;n;p2f1;1g

tion on the actors.

According to physics [13], givenachemical source,

Figure 5 illustrates the scent distribution of a p oint

its scentintensityatany p oint in a three dimensional

chemical source in the voxel space.

space is determined by the molar concentration of this

In a complex scene, geometric information can in-

chemical at the p oint. The molar concentration of a

terfere with olfactory information, e.g. a scent will

chemical A is de ned as the numb er of moles of A per

spread a gas around an ob ject. To approximate this

unit volume. We assume that the molar concentration

e ect, the net ux is mo di ed into :

of anychemical substance within a voxel is constant,

whilst di erentvoxels mayhave di erent molar con-

t t t

F = T C

Ai;j;k i+m;j +n;k +p Ai+m;j +n;k +p

centration. If the air is static, i.e. no wind, the dif-

m;n;p2f1;1g

ference of the molar concentration b etween the neigh-

b oring voxels will suggest the direction of the chemical

t t

T C

i+m;j +n;k +p Ai;j;k

source. Hence, an actor can reach the source by \sni -

m;n;p2f1;1g

ing" a set of voxels.

Figure 5: The scent distribution of a p oint source See

colour slide

Figure 6: Interfering scent distribution with geometric

information

where T 2f0;1g. It is 1 if the voxel i; j; k is

i;j;k

not o ccupied. Otherwise, it is 0.

Figure 6 shows the result of putting the same p oint

source in the center of a b ox with an op en gap on one

end. Figure 7 only shows the scent distrubution of

Figure 6. Note that it is shap ed by the b ox.

4 THE SENSORS

A set of sensors are implemented. An actor can

use these sensors to get stimuli from its neighb oring

voxels. This is achieved by scanning the information

parcels in those voxels. The action of the actor can

then b e planned. Hence b oth the principles of the

stimuli/resp onse paradigm and the spatial lo cality are

enforced.

4.1 THE VISION SENSOR

The vision sensors are used to get images of the

actor's neighb orho o d and to extract abstract infor-

mation, e.g. collision, found fo o d, etc., from these

images with some simple p erceptual pro cesses. Each

vision sensor is constrained by its view angle and view

range.

The image obtained by a vision sensor is a 2D

latitude-longitude array.Aray is cast from the sensor

center towards each element of this array. This ray

casting can b e accomplished by a simple 3D version

DDA algorithm [2]. If the ray passes through an o ccu-

pied voxel within the view range, the reference of this

voxel will b e recorded in the corresp onding elementof

the latitude-longitude image. Otherwise, a null value

Figure 7: Olfactory information distribution is shap ed

is assigned to the element. Figure 8 illustrates a vision

by geometric information

sensor.

The p erceptual pro cesses are task oriented. For ex-

ample, if the task is to avoid collision, the asso ciated

pro cess will scan the latitude-longitude arraytolook 5 @@4@@@@6 @@@@@@ @@3 @@4@@5 @@@@@@ @@2 @@3@@4 @@@@@@

@@ @@ --- the smell-detecting cell

--- the gradient of the intensity

Figure 9: The olfactory sensor in a 2D voxel space

avoid collision It should avoid y into the other

digi ies or any obstacles. There is one exception

to this rule, that is a hungry digi y can collide

with its fo o d, i.e. the owers.

seek fo o d The energy level of each digi y drops with

the passage of time. When this level is b elowa

threshold, the digi y will b egin to seek for fo o d.

If it can \see" a ower, it will y towards the

ower. If it can \smell" the fo o d, it will y to the

Figure 8: The vision sensor

direction of the fo o d.

eat fo o d If the tactile sensor detects that the digi y

touchesa ower, the digi y will recharge itself,

for an area with enough null elements that will allow

i.e. set its energy level to a maximum value. It

the whole b o dy of the actor to pass through. This is

will then y away.

actually a very easy task in the simulated environment

of a voxel space since all the information contained in a

y towards other digi ies When the digi y do es

voxel, e.g. depth, who o ccupies it, etc. are readily ac-

not detect any collision and it is not hungry or

cessible through the elements in the latitude-longitude

can not nd any fo o d, it will y towards the cen-

array.

ter of other digi ies that are detected by its vision

4.2 THE TACTILE SENSOR

sensor.

The tactile sensor simply tests if the voxel at the

sensor center is o ccupied or not.

random ight When none of the ab ove rules are

triggered, a lonely digi y will randomly change

4.3 THE OLFACTORY SENSOR

its heading direction to wander around.

The olfactory sensor is a simulated nose. It is com-

p osed of a set of smell-detecting cells with one cell at

The b ehavioural simulation framework develop ed in

the sensor center. Each cell can get the scentinten-

this research allows the ab ove rules to b e formally

sity of the asso ciated voxel. The intensity gradient

sp eci ed with symb olic expressions of CCS, the calcu-

can b e approximated with a vector which p oints from

lus of communicating systems [9]. In the simulation,

the sensor center to the cell that detects the biggest

these rules will b e triggered according to the lo cal cir-

intensityvalue. Figure 9 illustrates an olfactory sensor

cumstance of each digi y.

ina2Dvoxel space. Sensors that detects the gradient

A scene containing the glass temple in Figure 3 and

of a chemical concentration can b e found in the living

a ower in a glass b ox is used. There is a gap on the

systems. For example, Caenorhabditis elegan,atyp e

top side of the b ox. When a set of digi ies are released

of nemato de, can sense the concentration gradientof

into the scene, one should exp ect that those digi ies

the chemical released by its fo o d and move along the

will o cktowards the b ox, y through the gap, eat the

gradient [18].

fo o d, and y away. This is exactly what happ ened into

the simulation. Figure 10 shows the tra jectory of two

5 AN EXAMPLE | THE JOURNEY

digi ies in the scene. Figure 11 is a snapshot of a

OF THE DIGIFLIES

group of sixty digi ies.

As an example, a set of arti cial butter ies called

digi ies are simulated. Each digi y is equipp ed with a

vision sensor, an olfactory sensor, and a tactile sensor.

The hardware used in this research are the Silicon The b ehaviour of the digi y is de ned by the following

Graphics Indigo workstations. The Op enInventor is rules :

used as the graphical system. The visualization of the

scent distribution is achieved by the SGI Explorer.

The program is written in C++.

6 CONCLUSION

Wehave presented a uni ed framework which en-

dorses the imp ortant concepts in b ehaviour simula-

tion. Wehave shown how this framework which uses

avoxel space representation can b e applied to a group

of actors exhibiting emergent b ehaviour.

As demonstrated in this research, there are several

advantages to our approach. Firstly,itisintuitive. A

living system knows it touches an obstacle by sens-

ing that the touching p oint is o ccupied by the obsta-

cle, not by solving equations. Hence, it is easy to b e

used in the b ehavioural simulations that use empir-

ical knowledge. Secondly, the data structure of the

voxel space is very simple. Any geometric mo dels can

b e converted into the voxel representation. This im-

plies that the actors do not havetohave the same

geometric data structure in order for them to interact

with each other. Therefore, the voxel representation

can serve as a common ground for di erent parties to

work collectively to build a complex scene animation.

These advantages must b e traded against the loss

of precision since voxel space mo deling op erates in dis-

crete space. It is p ossible to generate undesired anima-

tions. For example, the feet of a walking animal may

Figure 10: The tra jectory of two digi ies

sometimes p enetrate slightly into the ground or oat

ab ove the ground. Our future work will lo ok at adap-

tivevoxel sub division and other p ossible approaches

to ameliorating this problem as well as optimizing the

existing algorithms to enable the use of actors with

more complicated structures and b ehaviour.

Acknowledgments

The authors would like to thank the many students

and faculty memb ers who have contributed towards

the GraphicsJungle pro ject at the University of Cal-

gary. This work is partially supp orted by the Natural

Sciences and Engineering Council of Canada. Hong-

wen Zhang would like to thank the SAGE Systems

Division of Valmet Automation for sp onsoring him to

present this pap er to Computer Animation 97.

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