Environmental Engineering Reference
In-Depth Information
in graphs. RGG are called “relational” grammars because several types of edges
(relations between nodes) are possible.
The RGG approach allows to model arbitrary relations and networks. It can also
be used to represent genes, genetic processes and the development of the phenotype
in one and the same formalism (Kniemeyer et al. 2004). The weakness of L-systems
concerning software engineering is addressed by permitting RGG rules as construc-
tion elements in a programming language, called XL (eXtended L-system language),
which at the same time is an extension of the object-oriented language Java, and by
allowing Java objects to be nodes of the graphs which are rewritten. A similar
approach led to the language “L+C” (Karwowski and Prusinkiewicz 2003), which
is an extension of C++ by L-system rules, but this language does not include graph
transformations. An exact mathematical definition of RGG and a precise description
of the language XL was given by Kniemeyer (2008).
The general form of an RGG rule is as follows:
L, (* C *), (E)
R {P};
where L is the left-hand side proper of the rule, i.e. a search pattern for a set of
subgraphs to be replaced by the right-hand side, R, which specifies also a set of
graphs. C is a set of graphs which must be present as a
context
of L in order to make
the rule applicable, and E is a condition for applicability of the rule, specified by a
logical
expression
which can contain parameters referring to nodes from L and C (or
to their attributes). P is a piece of imperative code which is executed when the rule is
applied. C, E and P are optional parts. An RGG is composed of such rules, which are
usually simultaneously applied to a given graph, similar to L-system rules.
The inclusion of imperative code allows an easy link to process-oriented
models, e.g., for light interception, photosynthesis and carbon allocation. As an
example, Fig.
11.5
shows the simulation results of three virtual beech trees (
Fagus
¼¼>>
Fig. 11.5 A virtual beech tree grown under three different light conditions (incident radiation
increasing from
left
to
right
). The simulation was done with GroIMP using an RGG (from
Kniemeyer 2008, p. 325)
