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 combine into plant communities of various kinds and in this way populate typical forms of landscapes that are called aerials.

This type of classification is also logical for the computer graphics community, since the modeling methods for the different stages clearly vary. Geometrical details play a large role with individual plants. Plant populations, however, are viewed more or less statistically, which makes geometrical characteristics, such as shading conditions, less significant. With plant communities and aerials, this effect is strengthened: here only statistical aspects, in combination with biotic and abiotic environmental factors, are considered.

When a virtual landscape is created, starting with the overall description of the aerial, a number of spatial refinements have to be created, finally ending in the geometric design of each individual plant. Already at this point, the abundance of geometrical and formative complexity of this global task becomes apparent. This complexity is also evidenced with the design of an individual plant. The existing approaches can be divided into procedural and rule-based methods. Procedural methods are parameterized algorithms for generating special mod­els, while rule-based methods use a formal rule base, which produces a com­plex final state by application of rules starting with a simple initial state. The advantages and disadvantages of both approaches are analyzed. Then, we are describing a procedure that combines the benefit of both methods through merging rule-based and procedural elements.

Since the individual modeling methods use completely different parameters for the description of plants, it is an interesting question whether there is not a more fundamental universal parameter set and/or a general description that would approximate the many different procedures. Though such a description does not have to exist, not even in the mathematical or algorithmic sense, even a simple method for limiting the producible forms to what is meaningful in botany would make modeling a great deal easier.

Once the geometric data of a single plant model is generated, we are con­fronted with the difficulty of managing the massive amount of needed data for most models. To reduce the excess data, model representations must be created that depict a plant at different levels of detail. When displayed on the screen, depending on the projected size of the plant, the appropriate representation is used, which allows for a drastic reduction of the amount of data that has to be worked with.

Chapter 1 First, however, efficient procedures must be found that can approximate what Computer-Generated Plants is actually visible for a potential viewer. If, for example, a virtual visitor strolls

through a synthetically generated forest, it will not be necessary to show the trees in the hundredth row, since they most likely are covered up by those in front. Corresponding procedures for the deletion of such objects are used with success in other areas of computer graphics and must be adapted for synthetic landscapes.

Next we will deal with plant communities. In botany most often descriptive models are used instead of algorithmic ones to define plant populations and plant communities. Mathematicians, on the other hand, are more concerned with the description and simulation of interacting sets of discrete objects and the application of the results to plant populations.

By contrast, researchers in computer graphics are only interested in the descrip­tive models, and weather they can be converted into efficient algorithms. The same is true for the mathematical procedures, which often are found in ecol­ogy and that cannot be integrated easily. For example, the simulation processes used here are often too complex for application. Therefore, efficient procedures for the specification of plant populations must be found and, at the same time, the different conditions for the plant habitats, such as the availability of water and light, have to be taken into account.

An essential difference between the methods employed in computer graph­ics and those used by botanists is the complexity of the required systems. In botany, rather small areas are being examined and analyzed, and large amounts of data are simplified by means of abstraction. For image production, however, also large aerials of several square miles must be produced with visible details. Here, simply storing the locations of the corresponding plants can present a problem, since billions of positions have to be recorded. A challenge in com­puter graphics is to record the positions only if necessary and to disregard them as soon as a plant is no longer visible. This kind of “on-the-fly” computation raises a number of interesting questions.

Another challenge is to efficiently represent geometrical models of plant pop­ulations and plant communities. For example, it is necessary to find out what are visually essential elements in a plant community and how these essential elements can be depicted with the smallest possible geometric resolution. Al­though not all of these questions are addressed in this book, we will introduce approaches that at least let us insinuate the overall picture.

At this point it should be mentioned that the rapid development of computer graphics hardware most likely will not make procedures for the minimization of geometry obsolete, at least not during the next few years. The past decades have shown that the desired model complexities increased more rapidly than the corresponding developments in computer hardware. Of course, it is possible that at one point in the future, all essential requirements with respect to the graphical performance of computers will be satisfied, but for right now this is absolutely not the case.