A GroupGO.T is a geometric object that contains a collection of other geometric objects.

Groups serve two purposes: They allow the user to group indiviual geometric objects together, and they provide a mechanism for property inheritance.

Groups allow the user to organize individual geometric objects into a graph structure. A {\em scene} is described by a {\em root node} (a \type{RootGO}{T}, which is a subtype of GroupGO.T), and contains all the geometric objects reacheable from the root. Usually, this structure forms a tree. However, geometric objects may occur in more than one group, so in general, the objects in a scene form a DAG (the rendering process does not terminate for cyclic graphs).

During rendering, the DAG is travered in a depth-first fashion. Whenever a node o is visited, there is a unique traversal path between o and the root. We call the nodes on this path the {\em ancestors} of o.

Associated with each geometric object o is a property mapping $M_o$, a partial function from property names $n$ to property values $n$ (see the \interface{GO} interface for details). When the scene is traversed, the property mappings of the nodes on the traversal path are composed together. Composition of property mappings is defined as follows: \[ (M_i \circ M_{i+1})(n) = \left\{ \begin{array}{ll} M_i(n) & \mbox{if $M_{i+1}(n)$ is undefined} \\ M_{i+1}(n) & \mbox{if $M_i(n)$ is undefined} \\ M_i(n) \oplus M_{i+1}(n) & \mbox{otherwise} \end{array} \right. \] $\oplus$ is the {\em property value composition operator}. Its semantics depends of the type of the property values. At the moment, for all properties except transformation properties, $v \oplus v' = v'$. A transformation property value $v$ is internally described by a $4\times4$ matrix $A_v$. For transformation property values, $v \oplus v' = v''$ where $A_{v''} = A_v A_{v'}$.

Here is an example of how this property inheritance mechanism works: \begin{center} \begin{tabular}{c} \psfig{figure=images/PropInheritance.ps,width=4in,silent=} \end{tabular} \end{center} The actual scene contains three objects, a sphere, a box, and a cone. The sphere and the box are red, while the cone is blue.

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INTERFACE GroupGO;

IMPORT GO;

EXCEPTION BadElement;

TYPE
  T <: Public;
  Public = GO.T OBJECT
  METHODS
    init (initSize := 5) : T;
    add (o : GO.T);
    remove (o : GO.T) RAISES {BadElement};
    flush ();
    content () : REF ARRAY OF GO.T;
  END;

g.init(size) initializes and returns a new group g. Initially, g has room for size elements; whenever g fills up, its size doubles.

g.add(o) adds a new geometric object o to the group g.

g.remove(o) removes the geometric object o from the group g. If o is not contained in g, the exception BadElement is raised.

g.flush() removes all geometric objects from g.

g.content() returns an array containing all the elements of g.

PROCEDURE New (initSize := 5) : T;

END GroupGO.