We present an algorithm for real-time level of detail reduction and display of high-complexity polygonal surface data. The algorithm uses a compact and e cient regular grid representation, and employs a variable screen-space threshold to bound the maximum error of the projected image. The appropriate level of detail is computed and generated dynamically in real-time, allowing for smooth changes of resolution across areas of the surface. The algorithm has been implemented for approximating and rendering digital terrain models and other height elds, and consistently performs at interactive frame rates with high image quality. T ypically, the number of rendered polygons per frame can be reduced by t w o orders of magnitude while maintaining image quality such that less than 5 of the resulting pixels di er from a full resolution image.

Current compression schemes for floating-point data commonly take fixed-precision values and compress them to a variable-length bit stream, complicating memory management and random access. We present a fixed-rate, near-lossless compression scheme that maps small blocks of 4(d) values in d dimensions to a fixed, user-specified number of bits per block, thereby allowing read and write random access to compressed floating-point data at block granularity. Our approach is inspired by fixed-rate texture compression methods widely adopted in graphics hardware, but has been tailored to the high dynamic range and precision demands of scientific applications. Our compressor is based on a new, lifted, orthogonal block transform and embedded coding, allowing each per-block bit stream to be truncated at any point if desired, thus facilitating bit rate selection using a single compression scheme. To avoid compression or decompression upon every data access, we employ a software write-back cache of uncompressed blocks. Our compressor has been designed with computational simplicity and speed in mind to allow for the possibility of a hardware implementation, and uses only a small number of fixed-point arithmetic operations per compressed value. We demonstrate the viability and benefits of lossy compression in several applications, including visualization, quantitative data analysis, and numerical simulation.

Large scale scientific simulation codes typically run on a cluster of CPUs that write/read time steps to/from a single file system. As data sets are constantly growing in size, this increasingly leads to I/O bottlenecks. When the rate at which data is produced exceeds the available I/O bandwidth, the simulation stalls and the CPUs are idle. Data compression can alleviate this problem by using some CPU cycles to reduce the amount of data needed to be transfered. Most compression schemes, however, are designed to operate offline and seek to maximize compression, not throughput. Furthermore, they often require quantizing floating-point values onto a uniform integer grid, which disqualifies their use in applications where exact values must be retained. We propose a simple scheme for lossless, online compression of floating-point data that transparently integrates into the I/O of many applications. A plug-in scheme for data-dependent prediction makes our scheme applicable to a wide variety of data used in visualization, such as unstructured meshes, point sets, images, and voxel grids. We achieve state-of-the-art compression rates and speeds, the latter in part due to an improved entropy coder. We demonstrate that this significantly accelerates I/O throughput in real simulation runs. Unlike previous schemes, our method also adapts well to variable-precision floating-point and integer data.

We introduce the notion of image-driven simplification, a framework that uses images to decide which portions of a model to simplify. This is a departure from approaches that make polygonal simplification decisions based on geometry. As with many methods, we use the edge collapse operator to make incremental changes to a model. Unique to our approach, however, is the use of comparisons between images of the original model against those of a simplified model to determine the cost of an edge collapse. We use common graphics rendering hardware to accelerate the creation of the required images. As expected, this method produces models that are close to the original model according to image differences. Perhaps more surprising, however, is that the method yields models that have high geometric fidelity as well. Our approach also solves the quandary of how to weight the geometric distance versus appearance properties such as normals, color, and texture. All of these trade-offs are balanced by the image metric. Benefits of this approach include high fidelity silhouettes, extreme simplification of hidden portions of a model, attention to shading interpolation effects, and simplification that is sensitive to the content of a texture. In order to better preserve the appearance of textured models, we introduce a novel technique for assigning texture coordinates to the new vertices of the mesh. This method is based on a geometric heuristic that can be integrated with any edge collapse algorithm to produce high quality textured surfaces.

We present an algorithm for out-of-core simplification of large polygonal datasets that are too complex to fit in main memory. The algorithm extends the vertex clustering scheme of Rossignac and Borrel [13] by using error quadric information for the placement of each cluster's representative vertex, which better preserves fine details and results in a low mean geometric error. The use of quadrics instead of the vertex grading approach in [13] has the additional benefits of requiring less disk space and only a single pass over the model rather than two. The resulting linear time algorithm allows simplification of datasets of arbitrary complexity.In order to handle degenerate quadrics associated with (near) flat regions and regions with zero Gaussian curvature, we present a robust method for solving the corresponding underconstrained leastsquares problem. The algorithm is able to detect these degeneracies and handle them gracefully. Key features of the simplification method include a bounded Hausdorff error, low mean geometric error, high simplification speed (up to 100,000 triangles/second reduction), output (but not input) sensitive memory requirements, no disk space overhead, and a running time that is independent of the order in which vertices and triangles occur in the mesh.