Representation and Realistic Rendering of Natural Scenes with Directed Cyclic Graphs

A nice sympodial tree. It is built up with a small set of grammar symbols. One to build up the trunk, another to generate its top and a third for twigs with leaves. 
A conifer tree generated by four symbols. The tree consists of the trunk, first order branches attached to it and twigs bearing needles, which are attached to branches. They have all different growing patterns and thus are generated by the combination of four DCGs.
Another conifer tree derived from the one above by simply changing some parameters like branching angles, the distance between succeeding branching points and the growth factor of twigs.
Just another conifer tree with different branching patterns. The topology differs from the trees above. I know trees usually don't grow on icy surfaces but the scene shows that ray tracing with DCGs works very well. You can see the cast of shadow and reflections.
This palm tree shows a significant different growing pattern and is generated by only two grammar symbols. The first spherically arranges twigs at the top of the trunk, the second generates twigs. 
This bush was derived from the sympodial tree. Some parameters were modified and stochastic branching patterns were used. This is done by randomly combining slightly different topologies. Each topology is generated by a separate production. 
This scene shows several individuals of a species. One DCG was used to position the plants. Another generates all the plants. Variations among individuals are achieved by randomly selecting branching patterns and by random numbers for some parameters. 
Palms and grass grow on the pre-designed terrain of an atoll. Like for the scenes above one DCG generated all the palms with random variations.
An approximation of a Canadian National Park scene. Levels of detail were incorporated to save computation time. Conifer trees that are far away are approximated in less detail. For example twigs don't grow anymore but are represented by squashed cones. 
Here you can see three levels of detail of the conifer species used for the Canadian National Park scene. The middle and right tree have less detail. The small images beside them show the appropriate screen size for these levels of detail.

Sierpinski's Tetrahedron on the left is one of the most famous fractals. Although consisting of millions of tetrahedra, the recursive definition makes it possible to store it in a very compact form. In the same way the whole family of linear fractals can be modelled and visualized. 
This is called "Fractals in the Hausdorff Room". On the table you can see Menger's Sponge, von Koch's Dodecahedron, and again Sierpinski's Tetrahedron. The floor is paved with Menger's Carpet, which is also used for the relief on the walls and the struts connecting the table legs. Outside in the desert there are two Sierpinsky pyramids. The vase contains Barnsley's Fern.
A fractal terrain defined by the CSG-pL-system version of Carpenter's algorithm, which is also known as Random Midpoint Displacement. 
And this happens if we don't take random values for the displacement of midpoints but positive numbers that are scaled down by a certain factor in each subdivision step. The scaling factor determines the dimension of this linear fractal that is called Landsberg Surface. 

Shells and Buildings
What have shells and buildings in common besides that shells are buildings for molluscan? They can both be generated with CSG-pL-systems. Shells are a nice example for the recursive application of the substraction operator of CSG. 
Approximations of three famous skyscrapers. The tower at the Battery Park (left) and the Chrysler Building (right) both in New York City. In the middle you can see the Sears Tower from Chigago. Buildings have a highly repetitive structure though they are not fractal. 

Non Linear Transformations
A climbing plant loops around a fence and pillars. This growth pattern is efficiently simulated by recursively applying non linear transformations within DCGs. Visit Peter Wonka's site for more details. 
A non linear version of the palm tree. Non linear transformation are applied to twist and bend twigs. This yields more natural looking irregularities. 
This happens if you apply non linear transformations to classic fractals like the Sierpinsky Tetrahedron. Don't try this home alone. Visit Peter Wonka's site for more details. 

Xmas Pics
The only way to manufacture fractal Xmas decoration is by using computer graphics. The twig as well as the Xmas decoration can easily be modelled by CSG-pL-systems and rendered with DCGs.
In our Xmas 95 picture we used CSG-pL-systems not only for recursively defined objects like the tree in the middle but also for the non recursively defined snowmen. 
Modelling with (CSG)-pL-systems is not trivial and demands a lot of experience. That's why we applied genetic algorithms later in the project. However not for this picture which shows an intermediate result on the hard way to a conifer tree. 
Another stage in the development of conifer trees. It resembles the horrible meat eating Tentacle Tree growing in the mountains of the northern continent Cepaway on Krisis Prime. A lot of careless hikers from Earth were doomed. 
This is called "Attack of the Killer Beans". It was one of the early trials to let gras grow on terrain. 
Well a part of the atoll scene in development. No wait, an accurate simulation of a tanker accident that was filled with shower gel and a passing quantum singularity attracting the palm twigs. Or is it a snapshot from a French nuclear bomb test short after ignition? 
A variation of the Canadian National Park scene. In fact the Canadian National Park scene is a variation of this scene. It is a pretty realistic rendering of the bad lands of Squorn Hellish Zeta. Or just a toxic waste deposit on good old Earth? 

Institute of Computer Graphics / Visualization and Animation Group / Research Rendering / DCG Main

This page is maintained by Christoph Traxler. It was last updated on July 17, 1998.
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