Spatial Phenomenological Models
in such models the focus no longer is on the single plants and their total number, but on the surface used as well as the growth rate. The density of …
Developmental Models
During the simulation of the evolution of a plant population, we must decide in each case to what point of accuracy one wants to control the system being produced, and …
Description of Plant Populations
In Sect. 2.9 we already pointed out that for the description of populations of individual plants as well as of plant associations, statistical models are necessary. In ecology there is …
Phyllotaxis
Phyllotaxis is the term for the regular arrangement of outer plant organs such as leaves, blossoms or seeds along branches or in a bud. In Sect. 2.1 the distribution of …
Trees as Fractal Objects
The theory of fractals allows for new mathematical ways to describe a number of natural objects. At this point, however, we cannot discuss the formalism or the consequences of the …
Branching Structures
We can use a classification system to assign a numerical value to each knot and to each edge of the topological branching structure, called its reference or ordinal number. In …
Geometrical and Topological Models
Already in the preceding chapters, we differentiated between the geometrical and topological characteristics of trees. At this point, we reiterate these differences, for the sake of clarity. In the following …
Some Mathematics
Plants as Mathematical Objects In order to generate a mathematical description of branching structures, we need formulations coming from statistics because of the underlying random processes of parameters such as …
Description Methods for Vegetation
Plants On the rather regional and detailed level of such local ecosystems, a description of the individual vegetation types can be produced by means of so-called plant formations. The description …
Geobotanical Description Methods
Since also entire plant societies are to be modeled later in this book, In this chapter we are also concerned with the description of vegetation. The vegetation geography is the …
Leaves
No matter how leaves evolved, it may be through evolution, as suggested by the telome theory, through planation, and/or deformation, or through other mechanisms, a leaf consists of four main …
Architectural Analysis of Trees
The concepts described so far are the decisive factors for the general construction of branching structures. However, the vast variety of trees found in nature, necessitates a more detailed categorization …
Tropisms
The appearance of a plant is, except for the branch formation, substantially determined by the formation of the shoot axes according to growth preferences, so-called tropism. The direction of the …
Spatial Division
According to its genetic options and the available space, a plant tries to optimize growth. Independent of the branching form, the primary axes grow vertically, the secondary axes rather horizontally. …
Branching Types
The geometry of a branching structure is determined either by the dominant main axis or the side branches. In the first case, we speak of a monopodial form, in the …
Budding
The bud is a propagation system, since each new branch begins in a bud. We differentiate between terminal main buds and side buds in the axis of carrying leaves (bud …
The Shoot Axis
As mentioned earlier, we are mainly concerned with cormophytes, land plants consisting of roots, shoot axes, and foliage. Starting at the shoot, the branch develops through vertical growth. It can …
Plants
For an adequate evaluation and the ability to generate plant geometry, a comparatively small range of botanical methods and descriptive formulas is needed. Computer graphics in most cases works with …
Applications
Some areas of applications for synthetic landscaping have already been mentioned. Particularly in ecology, plant models can also serve as a medium: they transport information about more deeper-lying processes, enabling …
Rendering Issues
Depending upon the area of application, different goals are pursued in landscape visualizations. In botany often only an approximate representation of the model is required. In architecture, and in some …
Modeling of Virtual Landscapes
In botany, vegetation is viewed on different levels of abstraction. Based on the already existing data of individual plants, emphases are put on plant populations, concentrations of similar plants, which …
Computer-Generated Plants
Introduction For over thirty years, botanists and computer scientists have made considerable efforts to develop effective methods to synthetically generate natural objects. As early as in 1966 the first method …
Foreword
It has been over 40 years since Stanislaw Ulam published his pioneering work on computer models of branching structures. In the period that followed, plant modeling has become an area …
Digital Design of Nature
What is computer graphics and what are the conceptual tasks of research in this area? To the average person the term still conveys more or less the design of logos …
