Yi-Jen Chiang

Dynamic algorithms in computational geometry

Dynamic algorithms and data structures in the area of computational geometry are surveyed. The work has a twofold purpose: it introduces the area to the nonspecialist and reviews the state of the art for the specialist. Fundamental data structures, such as balanced search trees and general techniques for dynamization, are reviewed. Range searching, intersections, point location, convex hull, and proximity are discussed. Problems that do not fall into these categories are also discussed. Open problems are given. >

Interactive out-of-core isosurface extraction

We present a novel out-of-core technique for the interactive computation of isosurfaces from volume data. Our algorithm minimizes the main memory and disk space requirements on the visualization workstation, while speeding up isosurface extraction queries. Our overall approach is a two-level indexing scheme. First, by our meta-cell technique, we partition the original dataset into clusters of cells, called meta-cells. Secondly, we produce meta-intervals associated with the meta-cells, and build an indexing data structure on the meta-intervals. We separate the cell information, kept only in meta-cells on disk, from the indexing structure, which is also on disk and only contains pointers to meta-cells. Our meta-cell technique is an I/O-efficient approach for computing a k-d-tree-like partition of the dataset. Our indexing data structure, the binary blocked I/O interval tree, is a new I/O-optimal data structure to perform stabbing queries that report from a set of meta-intervals (or intervals) those containing a query value q. Our tree is simpler to implement, and is also more space-efficient in practice than existing structures. To perform an isosurface query, we first query the indexing structure, and then use the reported meta-cell pointers to read from disk the active meta-cells intersected by the isosurface. The isosurface itself can then be generated from active meta-cells. Rather than being a single cost indexing approach, our technique exhibits a smooth trade-off between query time and disk space.

External Memory View-Dependent Simplification

In this paper, we propose a novel external‐memory algorithm to support view‐dependent simplification for datasets much larger than main memory. In the preprocessing phase, we use a new spanned sub‐meshes simplification technique to build view‐dependence trees I/O‐efficiently, which preserves the correct edge collapsing order and thus assures the run‐time image quality. We further process the resulting view‐dependence trees to build the meta‐node trees, which can facilitate the run‐time level‐of‐detail rendering and is kept in disk. During run‐time navigation, we keep in main memory only the portions of the meta‐node trees that are necessary to render the current level of details, plus some prefetched portions that are likely to be needed in the near future. The prefetching prediction takes advantage of the nature of the run‐time traversal of the meta‐node trees, and is both simple and accurate. We also employ the implicit dependencies for preventing incorrect foldovers, as well as main‐memory buffer management and parallel processes scheme to separate the disk accesses from the navigation operations, all in an integrated manner. The experiments show that our approach scales well with respect to the main memory size available, with encouraging preprocessing and run‐time rendering speeds and without sacrificing the image quality.

I/O optimal isosurface extraction

The authors give I/O-optimal techniques for the extraction of isosurfaces from volumetric data, by a novel application of the I/O-optimal interval tree of Arge and Vitter (1996). The main idea is to preprocess the data set once and for all to build an efficient search structure in disk, and then each time one wants to extract an isosurface, they perform an output-sensitive query on the search structure to retrieve only those active cells that are intersected by the isosurface. During the query operation, only two blocks of main memory space are needed, and only those active cells are brought into the main memory, plus some negligible overhead of disk accesses. This implies that one can efficiently visualize very large data sets on workstations with just enough main memory to hold the isosurfaces themselves. The implementation is delicate but not complicated. They give the first implementation of the I/O-optimal interval tree, and also implement their methods as an I/O filter for Vtks isosurface extraction for the case of unstructured grids. They show that, in practice, the algorithms improve the performance of isosurface extraction by speeding up the active-cell searching process so that it is no longer a bottleneck. Moreover, this search time is independent of the main memory available. The practical efficiency of the techniques reflects their theoretical optimality.

Simple and optimal output-sensitive construction of contour trees using monotone paths

Contour trees are used when high-dimensional data are preprocessed for efficient extraction of isocontours for the purpose of visualization. So far, efficient algorithms for contour trees are based on processing the data in sorted order. We present a new algorithm that avoids sorting of the whole dataset, but sorts only a subset of so-called component-critical points. They form only a small fraction of the vertices in the dataset, for typical data that arise in practice. The algorithm is simple, achieves the optimal output-sensitive bound in running time, and works in any dimension. Our experiments show that the algorithm compares favorably with the previous best algorithm.

Geometric algorithms for conflict detection/resolution in air traffic management

We consider the problems of conflict detection and resolution in air traffic management (ATM) from the perspective of computational geometry and give algorithms for solving these problems efficiently. For conflict resolution, we propose a simple method that can route multiple aircraft, conflict-free, through a cluttered airspace, using a prioritized routing scheme in space-time. Our algorithms have been implemented into a simulation system that tracks a large set of flights, having multiple conflicts, and proposes modified routes to resolve them. We report on the preliminary results from an extensive set of experiments that are under may to determine the effectiveness of our methods.

A unified infrastructure for parallel out-of-core isosurface extraction and volume rendering of unstructured grids

We present a unified infrastructure for parallel out-of-core isosurface extraction and volume rendering of large unstructured grids on distributed-memory parallel machines. We parallelize the out-of-core isosurface extraction algorithm of Chiang et al. (1998) and the out-of-core ZSweep technique (Farias and Silva, 2001) for direct volume rendering, using the meta-cell technique as a unified underlying building block. Our one-time preprocessing first partitions the dataset into meta-cells that are stored in disk. From the meta-cells, we build a BBIO tree in disk, which can be used to speed up isosurface extraction, and a bounding-box file in disk, which is used for direct volume rendering. At run-time, we use a simple self-scheduling scheme to achieve load balancing among the processors. We perform several experiments on a sixteen-node cluster of PCs connected by a gigabit Ethernet, using datasets as large as 6.6 million cells. For the larger datasets, we have found that both our isosurface extraction and direct volume rendering approaches are perfectly scalable up to sixteen nodes.

Progressive Simplification of Tetrahedral Meshes Preserving All Isosurface Topologies

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.

Experiments on the Practical I/O Efficiency of Geometric Algorithms: Distribution Sweep vs. Plane Sweep

We present an extensive experimental study comparing the performance of four algorithms for the orthogonal segment intersection problem. The algorithms under evaluation are distribution sweep, which has optimal I/O cost, and three variations of plane sweep, which is optimal in terms of internal computation. We generate the test data by using a random number generator while producing some interesting properties that are predicted by our theoretical analysis. The sizes of the test data range from 250 thousand segments to 2.5 million segments. The experiments provide detailed quantitative evaluation of the performance of the four algorithms. This is the first experimental work comparing the practical performance between external-memory algorithms and conventional algorithms with large-scale test data.

Multiple-description geometry compression for networked interactive 3D graphics

An existing technique for robust streaming of 3D graphics contents over lossy networks is multi-resolution coding of 3D geometry. An advantage of this approach is that it uses refinement layers and therefore multiple clients with different bandwidths can be served by a single unified code stream. However, there is a dependency between refinement layers, called prefix condition. Decoding of a given layer requires the knowledge of all the previous layers. A problem in the base layer reception interrupts the streaming all together and voids the remaining layers even though they are received perfectly. To overcome this drawback, this paper proposes an alternative approach to multi-resolution geometry coding, called multiple-description coding of 3D geometry. Instead of organizing code stream into embedded layers, MDC generates several separate descriptions of a geometric object, called co-descriptions. Each co-description of MDC can be independently decoded without any knowledge of other co-descriptions. Each extra successfully received co-description improves the fidelity of reconstructed geometry regardless of what has been received so far or in what order.