David E. Sigeti

ROAMing terrain: real-time optimally adapting meshes

Terrain visualization is a difficult problem for applications requiring accurate images of large datasets at high frame rates, such as flight simulation and ground-based aircraft testing using synthetic sensor simulation. On current graphics hardware, the problem is to maintain dynamic, view-dependent triangle meshes and texture maps that produce good images at the required frame rate. We present an algorithm for constructing triangle meshes that optimizes flexible view-dependent error metrics, produces guaranteed error bounds, achieves specified triangle counts directly and uses frame-to-frame coherence to operate at high frame rates for thousands of triangles per frame. Our method, dubbed Real-time Optimally Adapting Meshes (ROAM), uses two priority queues to drive split and merge operations that maintain continuous triangulations built from pre-processed bintree triangles. We introduce two additional performance optimizations: incremental triangle stripping and priority-computation deferral lists. ROAMs execution time is proportional to the number of triangle changes per frame, which is typically a few percent of the output mesh size; hence ROAMs performance is insensitive to the resolution and extent of the input terrain. Dynamic terrain and simple vertex morphing are supported.

Exponential decay of power spectra at high frequency and positive Lyapunov exponents

Abstract It is generally accepted that power spectra of time-series taken from continuous-time dynamical systems exhibiting deterministic chaos will decay exponentially at high frequency. The exponential decay constant, μ, is an inverse time-scale that is an invariant of the dynamics of the system and that is unique to deterministic chaos. Theoretical arguments are presented that suggest that μ should be related to the positive Lyapunov exponents. Numerical results are presented from four models with attractor dimensions ranging from 2.009 to 20.28 which suggest that μ is roughly proportional to the sum of the positive Lyapunov exponents, Σλi+. For these models, the ratio of μ to Σλi+ lies between the values 0.639 and 2.46 and shows no systematic change with attractor dimension.

MULTIRESOLUTION REPRESENTATION OF DATASETS WITH MATERIAL INTERFACES

We present a new method for constructing multiresolution representations of data sets that contain material interfaces. Material interfaces embedded in the meshes of computational data sets are often a source of error for simplification algorithms because they represent discontinuities in the scalar or vector field over mesh elements. By representing material interfaces explicitly, we are able to provide separate field representations for each material over a single cell. Multiresolution representations utilizing separate field representations can accurately approximate datasets that contain discontinuities without placing a large percentage of cells around the discontinuous regions. Our algorithm uses a multiresolution tetrahedral mesh supporting fast coarsening and refinement capabilities; error bounds for feature preservation; explicit representation of discontinuities within cells; and separate field representations for each material within a cell.

The bispectral aliasing test: a clarification and some key examples

Controversy regarding the correctness of a test for aliasing proposed by Hinich and Wolinsky (1988) has been surprisingly long-lived. Two factors have prolonged this controversy. One factor is the presence of deep-seated intuitions that such a test is fundamentally impossible. Perhaps the most compelling objection is that, given a set of discrete-time samples, one can construct an unaliased continuous-time series which exactly fits those samples. Therefore, the samples alone can not show that the original time series was aliased. The second factor prolonging the debate has been an inability of its proponents to unseat those objections. In fact, as is shown here, all objections can be met and the test as stated is correct. In particular, the role of stationarity as prior knowledge in addition to the sample values turns out to be crucial. Under certain conditions, including those addressed by the bispectral aliasing test, the continuous-time signals reconstructed from aliased samples are nonstationary. Therefore detecting aliasing in (at least some) stationary continuous-time processes both makes sense and can be done. The merits of the bispectral test for practical use are addressed, but our primary concern here is its theoretical soundness.

Pu239 Cross-Section Variations Based on Experimental Uncertainties and Covariances

Algorithms and software have been developed for producing variations in plutonium 239 neutron cross sections based on experimental uncertainties and covariances. The varied cross- section sets may be produced as random samples from the multi- variate normal distribution defined by an experimental mean vector and covariance matrix, or they may be produced as Latin- Hypercube/Orthogonal-Array samples (based on the same means and covariances) for use in parametrized studies. The variations obey two classes of constraints that are obligatory for cross-section sets and which put related constraints on the mean vector and covariance matrix that detemine the sampling. Because the experimental means and covariances do not obey some of these constraints to sufficient precision, imposing the constraints requires modifying the experimental mean vector and covariance matrix. Modification is done with an algorithm based on linear algebra that minimizes changes to the means and covariances while insuring that the operations that impose the different constraints do not conflict with each other.