Rule Application

The basic idea of a rule is to replace a shape with a certain shape symbol with a number of new shapes. Formally:

PredecessorShape --> Successor

Let us start with a very simple example:

A --> B

On application on a specific shape with symbol A, the rule above creates a copy of the shape and sets its shape symbol to B. The A shape is now considered done and not processed anymore. If there is no rule matching symbol B the generation process is finished. The resulting structure is called the shape tree and looks like this:

In the (extremely simple) shape tree above, A is the root shape and B is a leaf shape. Leaves are very important because the sum of all leaves represents the generated model. Inner nodes are not visible in the final model.

In this simple example, we assume shape A's geometry, scope and pivot are set up such that the shape represents a unit cube in the origin; because B is a copy of A, B looks exactly the same (see the picture above).

A rule can have more complex successors, e.g., the right side of the rule can consist of multiple shape symbols and so-called shape operations:

A --> B t(3, 0, 0) C

This successor is now executed from the left to the right. Again, B is an identical copy of A. Then the current shape is translated by 3 units in x-direction (i.e., the scope.t is manipulated) and a new shape C is created. The shape tree now has two leaves:

The two leaves B and C make up the final 3D model:

If we add this rule for C:

C --> D s(2, 0.5, 1.75) E

The generation process will add two children, D and E to shape C. Shape D is an exact copy of shape C, but shape E will have a different sized scope (because of the s() shape operation). The shape tree and the associated model look like this:

Note that now, the leaves (B, D, E) are not on the same level (i.e. have different distances to the root shape) but they are all part of the model.

Another shape operation is the insert operation i():

E --> i("cylinder.obj") F

After starting the generation again, shape E is not a leaf anymore but now has a child shape F.

The geometry of shape F is not a cube anymore but was replaced with the mesh read from file "cylinder.obj". Note that the size (i.e. the scope.s vector) of shape F is still the same as the one of shape E.

Terminal Shapes

In the E rule above, F is a so-called terminal shape: because no rule F is defined, the generation is stopped at this point. However, the CGA editor will issue a "Undefined Rule" warning. This can be suppressed by adding a period after F, thus explicitely marking F as a terminal shape:

E --> i("cylinder.obj") F.

Anonymous Leaf Shapes

For convenience, rules like the E rule above can be truncated:

E --> i("cylinder.obj")

In this case (i.e. E has no children), the rule interpreter silently inserts an anonymous leaf with the same name as the rule itself. The shape tree after applying the E rule above looks like this:

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