This paper discusses a numerical technique that approximates an implicit surface with a polygonal representation. The implicit function is adaptively sampled as it is surrounded by a spatial partitioning. The partitioning is represented by an octree, which may either converge to the surface or track it. A piecewise polygonal representation is derived from the octree.

this paper, such as the global distribution of radiative energy in the tree crowns, which affects the amount of light reaching the leaves and the local temperature of plant organs. The presented framework itself is also open to further research. To begin, the precise functional specification of the environment, implied by the design of the modeling framework, is suitable for a formal analysis of algorithms that capture various environmental processes. This analysis may highlight tradeoffs between time, memory, and communication complexity, and lead to programs matching the needs of the model to available system resources in an optimal manner. A deeper understanding of the spectrum of processes taking place in the environment may lead to the design of a mini-language for environment specification. Analogous to the language of L-systems for plant specification, this mini-language would simplify the modeling of various environments, relieving the modeler from the burden of low-level programming in a general-purpose language. Fleischer and Barr's work on the specification of environments supporting collisions and reaction-diffusion processes [20] is an inspiring step in this direction. Complexity issues are not limited to the environment, but also arise in plant models. They become particularly relevant as the scope of modeling increases from individual plants to groups of plants and, eventually, entire plant communities. This raises the problem of selecting the proper level of abstraction for designing plant models, including careful selection of physiological processes incorporated into the model and the spatial resolution of the resulting structures. The complexity of the modeling task can be also addressed at the level of system design, by assigning various components o...

This paper describes a biologically motivated method of texture synthesis called reaction-diffusion and demonstrates how these textures can be generated in a manner that directly matches the geometry of a given surface. Reaction-diffusion is a process in which two or more chemicals diffuse at unequal rates over a surface and react with one another to form stable patterns such as spots and stripes. Biologists and mathematicians have explored the patterns made by several reaction-diffusion systems. We extend the range of textures that have previously been generated by using a cascade of multiple reaction-diffusion systems in which one system lays down an initial pattern and then one or more later systems refine the pattern. Examples of patterns generated by such a cascade process include the clusters of spots on leopards known as rosettes and the web-like patterns found on giraffes. In addition, this paper introduces a method by which reaction-diffusion textures are created to match the geometry of an arbitrary polyhedral surface. This is accomplished by creating a mesh over a given surface and then simulating the reactiondiffusion process directly on this mesh. This avoids the often difficult task of assigning texture coordinates to a complex surface. A mesh is generated by evenly distributing points over the model using relaxation and then determining which points are adjacent by constructing their Voronoi regions. Textures are rendered directly from the mesh by using a weighted sum of mesh values to compute surface color at a given position. Such textures can also be used as bump maps.

The reflection of light from most materials consists of two major terms: the specular and the diffuse. Specular reflection may be modeled from first principles by considering a rough surface consisting of perfect reflectors, or micro-facets. Diffuse reflection is generally considered to result from multiple scattering either from a rough surface or from within a layer near the surface. Accounting for diffuse reflection by Lambert's Cosine Law, as is universally done in computer graphics, is not a physical theory based on first principles. This paper presents

This article introduces new techniques for non-distorted texture mapping on complex triangulated meshes. Texture coordinates are assigned to the vertices of the triangulation by using an iterative optimization algorithm, honoring a set of constraints minimizing the distortions. As compared to other global optimization techniques, our method allows the user to specify the surface zones where distortions should be minimized in order of preference. The modular approach described in this paper results in a highly flexible method, facilitating a customized mapping construction. For instance, it is easy to align the texture on the surface with a set of user defined isoparametric curves. Moreover, the mapping can be made continuous through cuts, allowing to parametrize in one go complex cut surfaces. It is easy to specify other constraints to be honored by the so-constructed mappings, as soon as they can be expressed by linear (or linearizable) relations. This method has been integrated successfully within a widely used C.A.D. software dedicated to geosciences. In this context, applications of the method comprise numerical computations of physical properties stored in fine grids within texture space, unfolding geological layers and generating grids that are suitable for finite element analysis. The impact of the method could be also important for 3D paint systems.

Interaction with the environment is a key factor affecting the development of plants and plant ecosystems. In this paper we introduce a modeling framework that makes it possible to simulate and visualize a wide range of interactions at the level of plant architecture. This framework extends the formalism of Lindenmayer systems with constructs needed to model bi-directional information exchange between plants and their environment. We illustrate the proposed framework with models and simulations that capture the development of tree branches limited by collisions, the colonizing growth of clonal plants competing for space in favorable areas, the interaction between roots competing for water in the soil, and the competition within and between trees for access to light. Computer animation and visualization techniques make it possible to better understand the modeled processes and lead to realistic images of plants within their environmental context. CR categories: F.4.2 [Mathematical Logi...

The paper extends Lindenmayer systems in a manner suitable for simulating the interaction between a developing plant and its environment. The formalism is illustrated by modeling the response of trees to pruning, which yields synthetic images of sculptured plants found in topiary gardens.

In this paper we present a method for modeling herbaceous plants, suit-able for generating realistic plant images and animating developmental processes. The idea is to achieve realism by simulating mechanisms which control plant growth in nature. The developmental approach to the modeling of plant architecture is extended to the modeling of leaves and flowers. The method is expressed using the formalism of L-systems.

Parallel projection z-buffer images are precomputed for a number of preset viewing directions on the unit sphere. Using the depth information, we can reconstruct a 3-D point from each image pixel. Then parallel or perspective views can be found from any other viewpoint by rotating the 3-D points from the nearest three or four precomputed views into the proper position and projecting them onto an output z-buffer. A temporary z-buffer image, constructed in the same way for a viewpoint at the light source, is used for a z-buffer shadow algorithm.

We integrate into plant models three elements of plant representation identified as important by artists: posture (manifested in curved stems and elongated leaves), gradual variation of features, and the progression of the drawing process from overall silhouette to local details. The resulting algorithms increase the visual realism of plant models by offering an intuitive control over plant form and supporting an interactive modeling process. The algorithms are united by the concept of expressing local attributes of plant architecture as functions of their location along the stems.