Saito and Takahashi  recognized the importance of depth-buffer-differences for obtaining important lines. The models they dealt with are, however, smooth surfaces in contrast to the decayed surfaces of foliage. In the same way as discontinuities of the first and second order are appropriate for the production of important lines on smooth objects, discontinuities of zero order, i. e., simple differences, can be used for defining important lines of decayed objects, such as trees and fractals: the contour of a drawing primitive is only drawn if the difference to the depth of the primitive positioned behind it surpasses a threshold defined by the user.
These values can either be defined in the coordinate system of the camera or can be read out directly from the depth buffer... >
As discussed at the beginning of this chapter, in the past diverse attempts were made in which trees were illustrated as skeletons with a number of different objects representing the leaves or leaf clusters.
This idea can be generalized with the introduction of so-called “abstract drawing primitives”. These are polygons always facing the viewer, similar to the already-discussed billboards. The polygons reflect here an outline of a leaf or of a group of leaves. The drawing of the entire tree then consists of a drawn version of the tree skeleton and the appropriate rendering of these primitive objects.
For the variation of the detail, which was identified as an essential forming element, depth buffers are used analogously to the works of Saito und Takahashi... >
There is a large number of different illustration styles for plants. At the beginning of Chap. 9 some examples were shown that only let us anticipate in how many different styles a tree can be drawn. A comprehensive demonstration of all the methods is not possible within the context of this book. However, different approaches are illustrated in the following by means of several hundred plant drawings made by different authors. The illustrations mainly originate from Evans . He offers a collection of models prefabricated specially for architecture. Additional tree illustrations can be found in the literature; see, for example, [123, 198].
A first classification of the illustrations is oriented on the use of light. While
many illustrations from botany and landscaping ... >
A number of works on nonphotorealistic rendering were introduced by the David Salesin’s group at the University of Washington. Instead of defining lines individually with the path-and-stroke metaphor, so-called “stroke textures” are introduced. Here, a texture consisting of strokes is generated for various gray scales and viewing angles. This texture can be applied for automatic rendering [232, 233] as well as in the context of interactive drawing programs [182, 183, 184].
In  a tree sketch is modeled with this method. Hereby the directions of the foliage and trunk silhouette are modified by a given vector field, and by an additional gray value image. Figure 11.2 shows the tree sketch as well as the applied data... >
Not only the production of synthetic plant sketches, but also the entire area of nonphotorealistic rendering will be continuously investigated during the years to come. The subject has been in discussion since the 1990s, and today the second phase in investigating the problems has been reached, with some notable attempts to systemize the area (see ) and to classify the related approaches.
Aside from the purely scientific interest, a starting point for the investigation of such representational forms is the realization that many illustrations in books and other traditional print media are not photographs, but rather abstract drawings, sketches, and illustrations . This might be due to technical reasons such as low printing costs... >
In contrast to photorealistic landscape images, the rendering of synthetic plant and landscape sketches has undergone little research so far. However, the already-addressed areas of application in architecture and landscaping require this kind of rendering. Currently, prefabricated images, which are combined via computer, most often must suffice. In addition, there are several collections of images  that incorporate lots of plant images in different styles and scales. These images can be copied and added to the drawings.
Aside from the enormous manual effort that is needed to combine the images, this method, of course, is only applicable for single images. New media, however, permit entirely new forms of presentation... >
As already discussed, in our system the vegetation is represented by plant models and ecosystem data files. To deal with the extremely large geometric complexity of entire landscapes, in two ways hierarchical data structures were implemented: firstly for the handling of complex single plants, and secondly for the representation of large amounts of small plants.
The rendering and the LOD treatment of a plant are controlled by Eqns. (10.2), (10.6) and (10.7). These supply in each case the decision for the entire plant, a fact that on the one hand speeds up the production, but on the other hand has also disadvantages... >
Each plant is divided into two subgeometries, one is represented by points, the other by lines. The decision on what approximation to use is currently provided by the user. In the future, however, this will be determined automatically through geometric analysis of the model structure. As a further step, the user determines the visual importance of each subgeometry. This is necessary, since some plant parts are visually more important than others. If this effect is exploited, a high visual quality can be obtained with an enormous reduction of the data.
The decision with regard to the kind of approximation as well as the visual importance of the plant parts is done once per plant model... >
All point-based methods have in common the need to change their representation at one point back to a polygonal model, which can result in visual artifacts. Rossignac and Borrel  try to solve this problem by merging closely positioned vertices within a set of surfaces without being concerned about whether or not they belong to the same surface. This procedure is acceptable for foliage, although the lighting conditions are changing, which leads to artifacts. Nevertheless, the advantage here is the fact that it is still a representation produced with polygons.
A similar approach modifies the geometric description of the foliage without changing the shape of the individual leaves or branches... >
A method that does not need special knowledge of the model, and which is not only applicable to trees or plants, is presented by Shade et al. [195, 196]. They solve the problem of the earlier-mentioned occluded pixels and resulting holes by storing all occluded pixels during the production of a source image for the
image-based description. To yield a satisfactory result, a raytracing algorithm is applied and, thus, the method can only be applied to computer-generated models.
Starting from the center, rays are directed through each surface of a unit cube, which surrounds the center. Each of the six surfaces is used just like the projection surface for obtaining a conventional raytracing image, and has accordingly a number of pixels that are penetrated by the rays from the center... >