Interactive Modeling of Plants

environment. They dominate outdoor scenes and most interior scenes as well. So why do we only have a few satisfactory plant models? We think it’s because, so far, creating plants is a job for experts who can handle the large structural and geometrical complexity of these models. In this article we present a modeling method that allows easy generation of many branching objects including flowers, bushes, trees, and even nonbotanical things. A set of components describing structural and geometrical elements of plants maps to a graph that forms the description of a specific plant and generates the geometry. Users get immediate feedback on what they’ve created—geometrical parameters, tropisms, and free-form deformations can control the overall shape of a plant. We’ll demonstrate that our method handles the complexity of most real plants. Before we discuss related work on interactive aspects of plant modeling systems, we want to stress that plant modeling aims to achieve two distinct goals. One is biologically motivated—people try to simulate the development of natural plants. The other seeks to generate only visually correct shapes of plants. This reflects the need for good geometric models in many computer graphics applications. Our method focuses on the second goal and tries to give users as much modeling power as possible for creating different plants. In the beginning, work on plant generation was biologically motivated. Pioneering work by Lindenmayer and later by Prusinkiewicz described the structure of plants by string rewriting systems (L-systems) operating on a set of rules. The approach includes context sensitivity as well as stochastic behavior and was recently extended to let plants adapt to environmental effects. L-systems specify plants in terms of local growth rules. This may be intuitive for biologists, but from the modeling point of view we’re interested in dealing directly with the global characteristics of plants. Lindenmayer and Prusinkiewicz created a virtual laboratory for L-systems that lets users customize the models by specifying simulation parameters graphically. However, controlling the global aspects of the shape directly still proves difficult. Also, users get no direct feedback because they must rerun the simulation after changing the parameters. To provide more intuitive parameters and to ease control over the models, others have developed customizable procedural plant models. Oppenheimer presented a fractal tree model where, in each branch, users can specify parameters like branching angle, the size ratio between the main stem and branch, or the number of branches per stem. De Reffye et al. developed a procedural model based on the birth and death of growing buds that lets users control the generation of plants by some parameters. AMAP, a commercial library of plants (particularly trees) and generation procedures, builds on this idea (see http://www.cirad.fr/amap/amap.html). The user edits a plant type’s parameters and runs the simulation to produce the desired geometry. Holton’s procedural model of trees assigns a strand to any path from the root to a tree’s leaves. The number of strands in a fork determines the branches’ fork angle, length, and taper. This lets the models be parameterized on the level of various tropisms that control growth. After specifying the parameters, the models are rendered—a time-consuming process that makes interaction difficult. While the authors listed above concentrated on finding efficient descriptions that fit into botanical principles, Weber and Penn focused on the second goal of generating a visually favorable geometry without adhering strictly to botanical laws—they put special emphasis on modeling the overall shape of a tree. Specifying the shape geometrically and restricting the model to grow within the bounds of the shape accomplished this. A set of textually edited parameters described the geometry for each branching level of the tree. Onyx Computing’s TreeMaker (http://www.onyxtree. Bernd Lintermann Center for Media Arts and Technology Karlsruhe