Daniel M. Tracy

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We introduce a parallel approximation of an Over-determined Laplacian Partial Differential Equation solver (ODETLAP) applied to the compression and restoration of terrain data used for Geographical Information Systems (GIS). ODETLAP can be used to reconstruct a compressed elevation map, or to generate a dense regular grid from airborne Light Detection and(More)
Linear Algebra and its Applications xxx (2007)xxx–xxx Abstract 6 The LLL algorithm has received a lot of attention as an effective numerical tool for preconditioning 7 an integer least squares problem. However, the workings of the algorithm are not well understood. In this 8 paper, we present a new way to look at the LLL reduction, which leads to a new(More)
We describe a surface compression technique to lossily compress elevation datasets. Our approach first approximates the uncompressed terrain using an over-determined system of linear equations based on the Laplacian partial differential equation. Then the approximation is refined with respect to the uncompressed terrain using an error metric. These two(More)
We present the GeoStar project at RPI, which researches various terrain (i.e., elevation) representations and operations thereon. This work is motivated by the large amounts of hi-res data now available. The purpose of each representation is to lossily compress terrain while maintaining important properties. Our ODETLAP representation generalizes a(More)
We examine a smugglers and border guards scenario. We place observers on a terrain so as to optimize their visible coverage area. Then we compute a path that a smuggler would take so as to avoid detection, while also minimizing the path length. We also examine how our results are affected by using a lossy representation of the terrain instead. We propose(More)
We extend Laplacian PDE by adding a new equation to form an over-determined system so that we can control the relative importance of smoothness and accuracy in the reconstructed surface. Benefits of the method include the ability to process isolated, scattered elevation points and the fact that reconstructed surface could generate local maxima, which is not(More)
We report on variants of the ODETLAP lossy terrain compression method where the reconstructed terrain has accurate slope as well as elevation. Slope is important for applications such as mobility, visibility and hydrology. One variant involves selecting a regular grid of points instead of selecting the most important points, requiring more points but which(More)
We present a new form of terrain compression to preserve the hydrological information that is lost using standard terrain simplification techniques. First, we compute the drainage by using a system of linear equations to determine the amount of water flowing into each cell. The flow is then computed on the inverted terrain which provides an approximation of(More)
Accurate terrain representation with appropriate preservation of important terrain characteristics, especially slope steepness, is becoming more crucial and fundamental as the geographical models are becoming more complex. Based on our earlier success with Overdetermined Laplacian Partial Differential Equations (ODETLAP), which allows for compact yet(More)
We present a better algorithm for path planning on complex terrain in the presence of observers and define several metrics related to path planning to evaluate the quality of various terrain compression strategies. The path-planning algorithm simulates a smugglers and border guards scenario. First, we place observers on a terrain so as to optimize their(More)