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 2 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 33 h is otherwise very dicult to implementina whic 33 33 33 ventional approach. By using voxel space, the com- con 33 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 simula- tions 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.