Hydra and Wreath Components
The hydra component multiplies all components attached to the p-graph and places them in a star-shaped arrangement. With the hydra component, the user can define the number and size of …
Horn Component
The geometry produced with the horn component is used as the basis for all types of stems, branches or trunks, and it can additionally be used for the rendering of …
Surface of Revolution Component
This component generates an additional geometrical primitive: a surface of revolution. The user can edit the silhouette as a polygonal curve as well as determine the resolution in the direction …
Camera Component
The camera component is the root component of every plant description, thus it must always be the first element in the structure tree. It accommodates all parameters that are needed …
Algorithmic Multiplication
If a multiplication component is part of a p-graph, then during the production of the i-tree the corresponding subtree is generated as many times as is indicated by the corresponding …
Rule-Based Object Production
Interactive Modeling The previous chapter demonstrated that rule-based procedures are a very powerful method for the production of a variety of plants. Nevertheless, there are many alternative modeling procedures. On …
. Categorizing the Methods
Rule-based systems and in particular L-systems provide possibilities for modeling plants in extremely compact ways. The fundamental formalism of L-sys - tems is simple and has its aesthetic attraction. using …
CSG-Based Modeling
object instancing is also used in CSG graphs (Constructive Solid Geometry), a common type of representation for objects within the CAD domain. A CSG expression is a set operation with …
Object Instancing
To model branching structures, often tree-like data structures are used. We saw this already in some procedural methods in Chap. 4. In the case of L-systems, the tree is represented …
Iterated Function Systems
The method proposed by Barnsley and Demko [10, 35] for modeling natural objects does not work with geometric data, but rather with two - or higherdimensional point sets. The structures …
Use of Position Information
Similarly to how environmental information is incorporated into the production of the branching structures, geometrical aspects of modeling can be integrated as well [167]. Instead of a communication module, user-defined …
Animation of L-Systems
In [166] and later in [164] Prusinkiewicz et al. introduced extensions for L - systems which allow for the animation of growth processes in static models. The most important extensions …
Modeling of Phyllotaxis
Phyllotaxis is the spatial arrangement of leaves in blooms and was introduced in Sect. 3.4. Also, we previously discussed different procedures for the production of phyllotaxial patterns. In the following, …
Context-Sensitive Systems
As already mentioned at the beginning of this chapter, in a context-sensitive system the use of a production is made dependent on the local environment of a character. The left …
Stochastic and Parameterized Systems
The L-systems introduced so far are deterministic, and thus always produce the same branching structures. In order to replicate the variability of nature, probabilistic influences must be brought into the …
Three-Dimensional Commands
The commands operated so far on a two-dimensional plane. However, they can easily be extended to a three-dimensional space. Aside from the third coordi- nate, the only difference is the …
Branching Structures
For the modeling of branching structures, L-systems have to be extended. The processing of the string sequence is now accomplished by means of a so-called pushdown automaton. This method contains …
Lindenmayer Systems
Lindenmayer systems or L-systems, are one kind of string rewriting mechanism, consisting of a set of rules and symbols that model growth processes. An initial string or symbol, the axiom, …
Rewriting Systems
The general mechanism of a rewriting system can best be illustrated with the so-called snowflake curve or von Koch curve. This curve is actually the classic example of a rewriting …
Rule-Based Modeling
Single Plants Are “Emerging” Aristid Lindenmayer’s approach to describing morphological forms of plants using so-called string rewriting systems [117, 118, 119] opened a broad scientific field in botany as well …
Remaining Questions
The number and variety of algorithmic methods that can be applied to model plants and in particular trees convincingly faithfully, is indeed surprising. It may be due to the relatively …
Modeling of Phyllotaxis
In Sect. 3.4 we already mentioned the remarkable effect that the mathematical method using the Golden Angle describes the arrangement of the seeds in many flowers very well, but that …
Growth in Voxels
The last procedural method discussed in this chapter generates climbing plants, which are actually in an entirely different category. Ned Greene [77] deals with the question of how the interaction …
Approximate Modeling
While these approaches, with the exception of the particle-based procedure of Reeves and Blau, endeavor to model trees as realistically as possible, it is the affirmed goal of Weber and …
Tree Modeling Using Strands
Leonardo da Vinci assumed that for trees in a branch bifurcation, the crosssection of the father branch equals the sum of the cross-sections of his children. This was already discussed …
Combinatorial Approach
In Sect. 3.2, we already addressed the Strahler analysis of trees and other networks. Vannimenus and Viennot [222] extend this subject with the goal to find a combinatorial mechanism for …
An Approach Based on Budding
An approach oriented on botanical growth rules was pioneered by De Reffye et al. [34]. The authors simulated the growth of the shoot axes in discrete time steps from node …
Geometric Modeling
Bloomenthal [17, 18] focuses on the geometrical aspects of tree modeling. The approach is demonstrated with a tree example that shows a branching structure generated by a recursive algorithm. Unfortunately, …
Generation Using Particle Systems
Compared with the previous achievements in this area, the works of Reeves [171] as well as Reeves and Blau [172] illustrate the different motivations underlying the modeling of plants. Reeves, …
Regulation of the Branching Process
Ten years after their first work, Honda et al. [92] examined how a branching procedure can be controlled by rule mechanisms. They found that with plants that have dense branching …
Three-Dimensional Procedural Models
Honda [91] and Fisher [62, 63] also came from a botany background. Their approach is to simulate the branching structures of trees and other plants using another procedural model. Here, …
A First Continuous Model
Independently of the discrete cellular automata, Dan Cohen, a botanist, implemented the first procedural method for the modeling of branching structures [29]. For each branching pattern a Fortran program was …
Cellular Automata
Stanislaw Ulam [220] worked with John von Neumann and became inspired by von Neumann’s concept of cellular automata. In this concept, the space, either an arbitrary dimensional abstract space or …
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, …
Spatial Mechanistic Models
contrary to the phenomenological models, mechanistic models are based on ecological parameters of individual system components, which are defined independently. The result of the simulation is determined by these parameters, …
