Storage free terrain simulation

Landscape visualisation is the process of recreating a natural environment and displaying it in an interactive graphical simulation. To do this a terrain is displayed together with accompanying plant life and other objects. Present landscape visualisation software is capable in theory of displaying very detailed and large landscapes. The software is also in theory capable of simulating environments with thousands if not millions of individually structured plants. In practice though, the simulation of such landscapes requires such a large amount of storage space that it is not achievable on personal computers. Even storing small landscapes with a moderate amount plant life can be a major development problem. The extent of this problem is such that modem simulators almost always exhibit the following limitations. • When detailed landscapes are stored to the hard disk, the area of terrain covered is usually very small. • When large terrains are stored to the hard disk the detail used is usually low. • When detailed plants are used in a landscape only twenty or so plants are created and used over and over again in the landscape. This work is an original approach to solving the storage space problem that involves not storing any landscape data to the hard disk at all. In this solution, instead of the landscape simulator displaying a landscape that is stored on a hard disk, the landscape simulator displays a landscape that is randomly generated. The landscape is produced on a need-to know basis, the only landscape that exists in the simulator is the landscape that the user of the simulator can see. If the user\u27s position in the landscape alters then the newly visible areas of landscape are created, and the areas no longer visible are removed from the simulator entirely. Areas of landscape being visited for a second time are always re-created the same way as they were originally created

TetSplat: Real-time Rendering and Volume Clipping of Large Unstructured Tetrahedral Meshes

We present a novel approach to interactive visualization and exploration of large unstructured tetrahedral meshes. These massive 3D meshes are used in mission-critical CFD and structural mechanics simulations, and typically sample multiple field values on several millions of unstructured grid points. Our method relies on the pre-processing of the tetrahedral mesh to partition it into non-convex boundaries and internal fragments that are subsequently encoded into compressed multi-resolution data representations. These compact hierarchical data structures are then adaptively rendered and probed in real-time on a commodity PC. Our point-based rendering algorithm, which is inspired by QSplat, employs a simple but highly efficient splatting technique that guarantees interactive frame-rates regardless of the size of the input mesh and the available rendering hardware. It furthermore allows for real-time probing of the volumetric data-set through constructive solid geometry operations as well as interactive editing of color transfer functions for an arbitrary number of field values. Thus, the presented visualization technique allows end-users for the first time to interactively render and explore very large unstructured tetrahedral meshes on relatively inexpensive hardware

A limit field for orthogonal range searches in two-dimensional random point search trees

We consider the cost of general orthogonal range queries in random quadtrees. The cost of a given query is encoded into a (random) function of four variables which characterize the coordinates of two opposite corners of the query rectangle. We prove that, when suitably shifted and rescaled, the random cost function converges uniformly in probability towards a random field that is characterized as the unique solution to a distributional fixed-point equation. We also state similar results for $2$-d trees. Our results imply for instance that the worst case query satisfies the same asymptotic estimates as a typical query, and thereby resolve an old question of Chanzy, Devroye and Zamora-Cura [\emph{Acta Inf.}, 37:355--383, 2000]Comment: 24 pages, 8 figure