In this paper, we propose a novel external-memory algorithm to support view-dependent
Key time steps selection is essential for effective and efficient scientific visualization of large-scale time-varying datasets. We present a novel approach that can decide the number of most representative time steps while selecting them to minimize the difference in the amount of information from the original data. We use linear interpolation to reconstruct the data of intermediate time steps between selected time steps. We propose an evaluation of selected time steps by computing the difference in the amount of information (called information difference) using variation of information (VI) from information theory, which compares the interpolated time steps against the original data. In the one-time preprocessing phase, a dynamic programming is applied to extract the subset of time steps that minimize the information difference. In the run-time phase, a novel chart is used to present the dynamic programming results, which serves as a storyboard of the data to guide the user to select the best time steps very efficiently. We extend our preprocessing approach to a novel out-of-core approximate algorithm to achieve optimal I/O cost, which also greatly reduces the in-core computing time and exhibits a nice trade-off between computing speed and accuracy. As shown in the experiments, our approximate method outperforms the previous globally optimal DTW approach [TLS12] on out-of-core data by significantly improving the running time while keeping similar qualities, and is our major contribution.
In this paper, we propose a novel technique for constructing multiple levels of a tetrahedral volume dataset whilepreserving the topologies of all isosurfaces embedded in the data. Our simplification technique has two majorphases. In the segmentation phase, we segment the volume data into topological‐equivalence regions, that is, thesub‐volumes within each of which all isosurfaces have the same topology. In the simplification phase, we simplifyeach topological‐equivalence region independently, one by one, by collapsing edges from the smallest to the largesterrors (within the user‐specified error tolerance, for a given error metrics), and ensure that we do not collapseedges that may cause an isosurface‐topology change. We also avoid creating a tetrahedral cell of negative volume(i.e., avoid the fold‐over problem). In this way, we guarantee to preserve all isosurface topologies in the entiresimplification process, with a controlled geometric error bound. Our method also involves several additionalnovel ideas, including using the Morse theory and the implicit fully augmented contour tree, identifying typesof edges that are not allowed to be collapsed, and developing efficient techniques to avoid many unnecessary orexpensive checkings, all in an integrated manner. The experiments show that all the resulting isosurfaces preservethe topologies, and have good accuracies in their geometric shapes. Moreover, we obtain nice data‐reductionrates, with competitively fast running times.
The design and implementation of theoretically-sound robot motion planning algorithms is challenging. Within the framework of resolution-exact algorithms, it is possible to exploit soft predicates for collision detection. The design of soft predicates is a balancing act between easily implementable predicates and their accuracy/effectivity. In this paper, we focus on the class of planar polygonal rigid robots with arbitrarily complex geometry. We exploit the remarkable decomposability property of soft collision-detection predicates of such robots. We introduce a general technique to produce such a decomposition. If the robot is an m-gon, the complexity of this approach scales linearly in m. This contrasts with the O(m 3) complexity known for exact planners. It follows that we can now routinely produce soft predicates for any rigid polygonal robot. This results in resolution-exact planners for such robots within the general Soft Subdivision Search (SSS) framework. This is a significant advancement in the theory of sound and complete planners for planar robots. We implemented such decomposed predicates in our open-source Core Library. The experiments show that our algorithms are effective, perform in real time on non-trivial environments, and can outperform many sampling-based methods.
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