Behavior of animation characters is defined by describing state-transition diagrams on the editor. Figure 1 is a screenshot of the editor. A state represented by an oval has actions for the character to take in the state. Actions are selected out of geometric actions such as parallel translations and rotations or logical ones such as forking other characters. A transition represented by an arrow means that the character shifts its state to the pointed one on condition written along the arrow. In Figure 1, the diagram is attached

to the character so that it turns left or right when an arrow key is pressed.

A character can be recursively composed of lower-level characters as illustrated in Figure 2. Each character encapsulated in an orange oval has its shape in the blue oval and definition of behavior represented by the yellow box being a set of state-transition diagrams.

The original character on the top level has its appearance composed of other characters representing its head, body, right and left hands, and feet. This character has a hammer in the right hand so that the right arm is defined as an upper-level character composed of an arm character and a hammer character. The 3D objects representing the bottom-level characters are called atom 3D objects hereafter.

This hierarchical structure is nothing special but a standard model for composing 3D objects. The lower-level characters behave relative to the local coordinate system of the upper-level character. The top-level characters behave relative to the global coordinate system.

Actions are selected out of geometric actions such as parallel translations and rotations or logical ones such as forking other characters and sending messages. A state can have

both geometric action and logical action.

Events include key press, messages, and collisions with other characters or walls that condition transition of the states.

The definition of animation includes the shapes of atom 3D objects, character definitions composed of state-transition diagrams and references to lower-level characters with their initial relative positions, and groups of characters to be forked at the same time. Those data are stored in an XML-based format as their example in Figure 3.

An atom 3D object’s shape is expressed in a digital asset exchange (DAE) file in the Collada format [10] to be referred to by its file name. Its example is the light blue block in Figure 3.

A character definition in the orange block of Figure 3 has a name, a set of state- transition diagrams as in the yellow block of Figure 3. A bottom-level character has its appearance specified by a DAE file name in the light blue block in Figure 3. An upper-level character has its appearance specified by a list of lower-level character names and their relative initial positions in the blue block of Figure 3. Figure 4 is an expanded form of the yellow block in Figure 3. Diagram 1 is the expression of the state-transition diagram in Figure 1 that specifies horizontal rotation of the character according to the left and right arrow keys. Diagram 2 is the one for moving forward or backward according to the up and down arrow keys. A state-transition diagram in the yellow block has the orange block where names of states are listed together with the actions to be taken in the state. In the green block, transitions are listed each of which is a triple of the condition, the source and destination states.

An upper-level character has its appearance specified in the blue block of composing definition in Figure 3. There the lower-level characters are listed with their initial relative positions to form the upper-level character and also with their initial states.

A group comprises pairs of a character name and its initial state. By the “fork” action, we can create their instances at the same time in the specified initial states. There is at least one group named main group, which is the set of characters to start up the animation as in the part of group definition in Figure 3.

The space where characters play inside is defined with its dimensions, type, background color, and the transition time interval as the part of the world definition in Figure 3. The type can be chosen out of a space having no boundaries, a ground with a

boundary on the floor, and a room that has six surrounding boundaries.

In a translation into AS3 code, actions and state transitions take place in the following steps.

1. A class for mediating the whole animation watches the timer until the next timing for actions and state transitions.

2. The mediator class calls the function for taking action and shifting states implemented in each of the top-level characters. The function call is accompanied by events conditioning the state transition.

3. Each character takes actions and shifts states on events.

4. If the character retains its children (lower-level characters), it calls the function of its children for taking action and shifting states with the events.

5. Repeat 3 and 4 until all the bottom-level characters take actions and shift states.

In that way, all the characters keep taking their actions shifting their states by a regular interval.

In order to implement the hierarchical structure as illustrated in Figure 2, we introduce a class named Performer. One instance of this class encapsulates that of any character. As indicated in the top line of Figure 5, this class inherits the DisplayObject3D class of the Papervision3D library that is the fundamental class for any kinds of 3D objects. Among the properties of the DisplayObject3D class, the Performer class especially utilizes the following: Multiple instances of the DisplayObject3D class can be retained in an instance of the DisplayObject3D class as its children. The children instances behave relative to the local coordinate system of their parent instance to constitute the appearance of the parent. The DisplayObject3D retains all the parameters for three-dimensional manipulation of objects such as vertex coordinates, local and global coordinate systems, and the rotation angles. It has also the function for transforming pose and position of 3D objects by manipulating those parameters.

In the light blue ovals, the Performer class retains a reference to an instance of the class for an atom 3D object in the case of bottom-level character or to a list of instances of the Performer class in the case the character is made up of lower-level characters. In that way, the hierarchical structure of the characters can naturally be implemented. It is even capable of communicating with the children, which provides a natural means to control the children.

The character represented by the yellow box in Figure 5 is an instance of the Character class of which detail will be described later. The Character class describes how a character should behave in accordance with the state-transition diagrams. Encapsulated in the Performer class, this class implements functions for state transitions and geometrically manipulating the Performer class instance as a 3D object.

In order to cause actions and state transitions according to events, we introduce a class named Mediator that is marked in pink in Figure 5. It uses the ObjetCollision and WallCollision classes as schematized in Figure 6 for detecting collisions.

The mediator class controls the progress of whole animation by watching the timer and calling the function for taking actions implemented in the top level character by a constant time interval. When calling the function, events such as key press, messages, and collisions are sent to the function, which recursively calls that of the lower-level characters as indicated by the light blue arrows in Figure 5.

We describe how to convert the Islay 3D animation definition in Figure 3 into the form of object class definitions in AS3.

In order to implement the atom 3D object definition such as the one in the light blue block of Figure 3, we introduce the Object class. This Object class inherits from the Objects class of the Papervision3D library its functions such as creating an instance of an atom 3D object and creating an instance of bounding box object for collision detection.

In Figure 7, the BoundingVolume class retains data fields of the oriented bounding box for collision detection. The ExtendedDAE class creates an atom 3D object as an instance of itself. An atom 3D object being a DAE file is parsed by the ExtendedDAE class extending the DAE class of Papervision3D to create an instance of the atom 3D object and embed it to be available in the animation.

In order to implement the character definition including actions and state transitions, we introduce the Character class that inherits the Characters class as illustrated in Figure 8.

The Characters class includes common functions for applying actions to the per-

former class and a function to remember the current state. Inheriting the Characters class, the Character class implements the state transition diagrams in the form illustrated in Figure 9 for the example character definition in Figure 4. As in the red block of Figure 8, each state is represented by a function that applies actions in the state to the 3D object which is appearance of the Performer class, and returns the name of the next state at the parts underlined in blue. In the green block, the destination state is determined as the return value according to the transition conditions. If no conditions match, the state remains the same (for the null return value).

The Character class retains the name of its appearance by which the Performer class

gets an instance of the PartsFactory class (described later). The Performer class, called by the Mediator class by a regular time interval, calls the function representing the current state of the encapsulated Character class to apply the actions to its appearance. The return value of the function updates the current state if not null.

The PartsFactory class creates instances of the Object class in accordance with the atom 3D object definition and also composes the appearances of upper-level characters in accordance with the composing definition such as in Figure 3.

When the instance of the Performer class is created, 3D object name for specifying its appearance is passed to this class. Example atom 3D object names are listed in the light blue block in Figure 3. In the blue block of composing definition in Figure 3, the lower-level characters are registered with their relative positions to compose the upper-level character and also with their initial states.

The PartsFactory class creates (3D) Object instances, sets their initial positions, and returns these to the Performer class instance as illustrated in Figure 10. In the case that the Performer class instance represents a bottom-level character, this class returns an Object class instance. In the case that the Performer class instance represents an upper-level character, this class returns a set of Performer class instances.

The groups class retains pairs of a character and its initial state and creates instances of the Performer class retaining those characters when the they are forked. The group of characters in Figure 11 is the initial performers in this example animation.

The Main class sets a space where characters play inside in accordance with the world definition such as in Figure 3. As illustrated in Figure 12, the Main class inherits from the IslayBasicView class its auxiliary functions for displaying walls and catching user events such as key input and mouse click. The IslayViewport3D class displays the walls. The IslayInteractiveSceneManager class makes it possible to catch the mouse event.