For a reduction of data, but also especially for lowering the modeling effort, it is very helpful to render a large plant population by combining many equal base elements. Doing so, the region or space that a population usually inhabits, is divided into squares using a plane division method. tiling ^ On each square, i. e., each tile, a small part of the population is generated. The total population results from the combination of the squares, which are iterated over the plane. The time used for storing the data decreases hereby considerably. Aside from the representatives of the plants, now only the positions of the individual tiles must be stored.
Consequently, for rendering significantly less data needs to be processed. Also, per tile some preparatory steps can be performed to speed up image generation. To prefabricate the distribution for the use of tiles, specification and simulation methods must be adjusted. However, in a Poisson distribution, this is trivial, since the positions to be distributed randomly for the plants are simply placed into the tiles analogously to the total distribution. The tile iteration then again produces a distribution similar to a Poisson distribution.
The task becomes more intricate when creating a Poisson disk distribution. in order to yield the criteria of the circle panes, the edges of the tiles must be coordinated; this can be accomplished by using an extension of the dart-throwing method or by applying an extension of the local optimization mentioned above.
Figure 8.9
(a) Local optimization of a tile;
(b) periodic arrangement of tiles;
(c) the whole set results again in a Poisson disk distribution
The application of the already-mentioned dart throwing mechanism is problematic here due to the additional boundary conditions. It decreases the number of possible positions at the edges of the tiles, and therefore makes a uniform coverage difficult to obtain. An easier method is an extension of the adaptive production method for the Poisson disk distribution, as demonstrated in Sect. 8.1. The edges of the optimization area, which up to now were given by the population boundaries or the boundaries of the given area, are now eliminated. Instead plant locations are cyclically continued beyond the edges, meaning the plane behaves as if it was the surface of a torus.
A point that slides over the left or lower tile edge during tile iteration appears on the right or upper edge. If continued in this way, all Voronoi regions can be closed, and the iteration converges. The edges now are no longer straight lines, but instead show folded jags. Figure 8.9a illustrates the result of the optimization on the tiles. A total of 200 points were distributed here.
