Procedural Modeling

Programming of Plants

Computer-assisted simulation of natural growth processes was introduced as early as 1966 – during the time computers became more and more available to researchers. So-called cellular automata, simple computer models, developed by John von Neumann (1903-1957) in the 1950s, were utilized by Stanislaw Ulam in 1966 for the production of branching patterns. The first continuously growing plant model with a branching structure was first published by Dan Cohen in 1967.

The next essential development was pioneered by Aristid Lindenmayer (1925­1989), who in 1968 extended the idea of the string rewriting mechanism to the description of cellular interactions, and also the simulation of branching structures. Hashimoto Honda introduced in 1971 the first parameterized model for the modeling of a three-dimensional tree skeleton.

Outside the botanist community, the process of computer-assisted methods for the production of plants did not, however, receive a high level of attention until the 1980s when increased computer performance allowed for the modeling of complex branching structures and thereby facilitated a more faithful modeling of plants. Parallel to this development, the vastly improved graphics power of computers allowed for the illustration of a larger number of plants in combi­nation with other synthetic objects, and consequently expanded the application area, especially in computer animation.

During the last 25 years a variety of different methods have been developed, more or less successfully. They are mainly divided into two major categories, namely procedural and rule-based methods. Procedural plant creation processes are parameterized algorithms that are designed for the production of a certain type of plant, though often solely for a single specie. Rule-based procedures are based on a rule system, which, using the application of rules, produces from a simple initial state a complex final state.

Of course, the wide range of approaches can be divided further. Prusinkiewicz [161], for example, differentiates between structural and space-oriented mod­els. The first class is based on the assumption that growth is controlled by endogenous mechanisms embodied in the growth structure, while the second

class also includes the interaction between parallel-growing partial structures, thus taking external space-oriented influences into account [165]. For the pur­pose of this book, we divide the methods into procedural and rule-based meth­ods, since the synthesis of both approaches leads to a new method, which is introduced in Chap. 6. So-called rule-based object production combines com­ponents with procedural elements by using a simple rule mechanism. In this way it is flexible and intuitive. First, however, we focus on the main procedural methods, before rule-based procedures are discussed in Chap. 5.

In the following, the procedural processes for plant modeling are listed chrono­logically. Starting from the first models, we can trace the constant improve­ments of the different approaches up to the current efficient modeling methods that are able to generate realistic-looking plants, as will be demonstrated below.