Some very impressive results have been obtained in the past few years in plants and trees image synthesis. Some algorithms are largely based on the irregularity and fuzziness of the objects, and use fractals, graftals or particle systems. Others focus on the branching pattern of the trees with emphasis on morphology. Our concern here is the faithfulness of the models to the botanical nature of trees and plants. We present a model which integrates botanical knowledge of the architecture of the trees: how they grow, how they occupy space, where and how leaves,flowers or fruits are located, etc. The very first interest of the model we propose is its great richness: the same procedural methods can produce "plants" as different as weeping willows, fir trees, cedar trees, frangipani trees, poplars, pine trees, wild cherry trees, herbs, etc. Another very important benefit one can deriw from the model is the integration of time which enables viewing the aging of a tree (possibility to get different pictures of the same tree at different ages, accurate simulation of the death of leaves and branches for example). The ease to integrate physical parameters such as wind, the incidence of factors such as insects attacks, use of fertilizers, plantation density, and so on makes it a useful tool for agronomy or botany.

Quadtrees constitute a hierarchical data structure which permits fast access to multidimensional data. This paper presents the analysis of the expected cost of various types of searches in quadtrees--fully specified and partial-match queries. The data model assumes random points with independently drawn coordinate values.The analysis leads to a class of "full-history" divide-and-conquer recurrences. These recurrences are solved using generating functions, either exactly for dimension d = 2, or asymptotically for higher dimensions. The exact solutions involve hypergeometric functions. The general asymptotic solutions rely on the classification of singularities of linear differential equations with analytic coefficients, and on singularity analysis techniques.These methods are applicable to the asymptotic solution of a wide range of linear recurrences, as may occur in particular in the analysis of multidimensional searching problems.

Some very impressive results have been obtained in the past few years in plants and trees image synthesis. Some algorithms are largely based on the irregularity and fuzziness of the objects, and use fractals, graftals or particle systems. Others focus on the branching pattern of the trees with emphasis on morphology. Our concern here is the faithfulness of the models to the botanical nature of trees and plants. We present a model which integrates botanical knowledge of the architecture of the trees: how they grow, how they occupy space, where and how leaves, flowers or fruits are located, etc. The very first interest of the model we propose is its great richness: the same procedural methods can produce "plants" as different as weeping willows, fir trees, cedar trees, frangipani trees, poplars, pine trees, wild cherry trees, herbs, etc. Another very important benefit one can derive from the model is the integration of time which enables viewing the aging of a tree (possibility to get different pictures of the same tree at different ages, accurate simulation of the death of leaves and branches for example). The ease to integrate physical parameters such as wind, the incidence of factors such as insects attacks, use of fertilizers, plantation density, and so on makes it a useful tool for agronomy or botany.

A precise analysis of partial match retrieval of multidimensional data is presented. The structures considered here are multidimensional search trees ( k -d-trees) and digital tries ( k -d-tries), as well as structures designed for efficient retrieval of information stored on external devices. The methods used include a detailed study of a differential system around a regular singular point in conjunction with suitable contour integration techniques for the analysis of k -d-trees, and properties of the Mellin integral transform for k -d-tries and extendible cell algorithms.

Visualization of very complex scenes can be significantly accelerated using occlusion culling. In this paper we present a visibility preprocessing method which efficiently computes potentially visible geometry for volumetric viewing cells. We introduce novel extended projection operators, which permits efficient and conservative occlusion culling with respect to all viewpoints within a cell, and takes into account the combined occlusion effect of multiple occluders. We use extended projection of occluders onto a set of projection planes to create extended occlusion maps; we show how to efficiently test occludees against these occlusion maps to determine occlusion with respect to the entire cell. We also present an improved projection operator for certain specific but important configurations. An important advantage of our approach is that we can re-project extended projections onto a series of projection planes (via an occlusion sweep), and accumulate occlusion information from multiple blockers. This new approach allows the creation of effective occlusion maps for previously hard-to-treat scenes such as leaves of trees in a forest. Graphics hardware is used to accelerate both the extended projection and reprojection operations. We present a complete implementation demonstrating significant speedup with respect to view-frustum culling only, without the computational overhead of on-line occlusion culling.