13952010
FastSplats: optimized splatting on rectilinear grids
Splatting is widely applied in many areas, including volume, point-based, and image-based rendering. Improvements to splatting, such as eliminating popping and color bleeding, occlusion-based acceleration, post-rendering classification and shading, have all been recently accomplished, These improvements share a common need for efficient framebuffer accesses. We present an optimized software splatting package, using a newly designed primitive, called FastSplat, to scan-convert footprints. Our approach does not use texture mapping hardware, but supports the whole pipeline in memory. In such an integrated pipeline, we are then able to study the optimization strategies and address image quality issues. While this research is meant for a study of the inherent trade-ofSof splatting, our renderer, purley in software, achieves 3 to 5 times speedups over a top-end texture hardware (for opaque data sets) implementation. We further propose a way of efSicient occlusion culling using a summed area table of opacity. 3 0 solid texturing and bump mapping capabilities are demonstrated to show the flexibility of such an integrated rendering pipeline. A detailed numerical error analysis, in addition to the performance and storage issues, is also presented. Our approach requires low storage and uses simple operations. Thus, it is easily implementable in hardware.
36043890
Remote Visualization by Browsing Image Based Databases with Logistical Networking
2569639
Visibility culling for time-varying volume rendering using temporal occlusion coherence
Typically there is a high coherence in data values between neighboring time steps in an iterative scientific software simulation; this characteristic similarly contributes to a corresponding coherence in the visibility of volume blocks when these consecutive time steps are rendered. Yet traditional visibility culling algorithms were mainly designed for static data, without consideration of such potential temporal coherency. We explore the use of temporal occlusion coherence (TOC) to accelerate visibility culling for time-varying volume rendering. In our algorithm, the opacity of volume blocks is encoded by means of plenoptic opacity functions (POFs). A coherence-based block fusion technique is employed to coalesce time-coherent data blocks over a span of time steps into a single, representative block. Then POFs need only be computed for these representative blocks. To quickly determine the subvolumes that do not require updates in their visibility status for each subsequent time step, a hierarchical "TOC tree" data structure is constructed to store the spans of coherent time steps. To achieve maximal culling potential, while remaining conservative, we have extended our previous POP into an optimized POP (OPOP) encoding scheme for this specific scenario. To test our general TOC and OPOF approach, we have designed a parallel time-varying volume rendering algorithm accelerated by visibility culling. Results from experimental runs on a 32-processor cluster confirm both the effectiveness and scalability of our approach.
1676234
A complete distance field representation
Distance fields are an important volume representation. A high quality distance field facilitates accurate surface characterization and gradient estimation. However, due to Nyquist's law, no existing volumetric methods based on the linear sampling theory can fully capture surface details, such as comers and edges, in 3D space. We propose a novel complete distance field representation (CDFR) that does not rely on Nyquist's sampling theory. To accomplish this, we construct a volume where each voxel has a complete description of all portions of surface that affect the local distance field. For any desired distance, we are able to extract a surface contour in true Euclidean distance, at any level of accuracy, from the same CDFR representation. Such point-based iso-distance contours have faithful per-point gradients and can be interactively visualized using splatting, providing per-point shaded image quality. We also demonstrate applying CDFR to a cutting edge design for manufacturing application involving high-complexity parts at unprecedented accuracy using only commonly available computational resources.
6888787
Distributed data management for large volume visualization
We propose a distributed data management scheme for large data visualization that emphasizes efficient data sharing and access. To minimize data access time and support users with a variety of local computing capabilities, we introduce an adaptive data selection method based on an "enhanced time-space partitioning" (ETSP) tree that assists with effective visibility culling, as well as multiresolution data selection. By traversing the tree, our data management algorithm can quickly identify the visible regions of data, and, for each region, adaptively choose the lowest resolution satisfying user-specified error tolerances. Only necessary data elements are accessed and sent to the visualization pipeline. To further address the issue of sharing large-scale data among geographically distributed collaborative teams, we have designed an infrastructure for integrating our data management technique with a distributed data storage system provided by logistical networking (LoN). Data sets at different resolutions are generated and uploaded to LoN for wide-area access. We describe a parallel volume rendering system that verifies the effectiveness of our data storage, selection and access scheme.
8122062
High quality splatting and volume synthesis
Our recent improvements to volume rendering using splatting allow for an accurate functional reconstruction and volume integration, occlusion-based acceleration, post-rendering classification and shading, 3D texture mapping, bump mapping, anti-aliasing and gaseous animation. A pure software implementation requiring low storage and using simple operations has been implemented to easily support these operations. This paper presents a unified framework and discussion of these enhancements, as well as extensions to support hypertextures efficiently. Discussions on appropriate volume models for effective usage of these techniques is also presented.
16721854
Learning from labeled and unlabeled data on a directed graph
We propose a general framework for learning from labeled and unlabeled data on a directed graph in which the structure of the graph including the directionality of the edges is considered. The time complexity of the algorithm derived from this framework is nearly linear due to recently developed numerical techniques. In the absence of labeled instances, this framework can be utilized as a spectral clustering method for directed graphs, which generalizes the spectral clustering approach for undirected graphs. We have applied our framework to real-world web classification problems and obtained encouraging results.
9961789
Interactively visualizing procedurally encoded scalar fields
While interactive visualization of rectilinear gridded volume data sets can now be accomplished using texture mapping hardware on commodity PCs, interactive rendering and exploration of large scattered or unstructured data sets is still a challenging problem. We have developed a new approach that allows the interactive rendering and navigation of procedurally-encoded 3D scalar fields by reconstructing these fields on PC class graphics processing units. Since the radial basis functions (RBFs) we use for encoding can provide a compact representation of volumetric scalar fields, the large grid/mesh traditionally needed for rendering is no longer required and ceases to be a data transfer and computational bottleneck during rendering. Our new approach will interactively render RBF encoded data obtained from arbitrary volume data sets, including both structured volume models and unstructured scattered volume models. This procedural reconstruction of large data sets is flexible, extensible, and can take advantage of the Moore's Law cubed increase in performance of graphics hardware.
400858
Toward good elimination orders for symbolic SAT solving
Fundamentally different from DPLL, a new approach to SAT has recently emerged that abandons search and enlists BDDs to symbolically represent clauses of the CNF. These BDDs are conjoined according to a schedule where some variables may be eliminated by quantification at each step to reduce the size of the intermediate BDDs. SAT solving then reduces to checking whether the final BDD is the zero constant. For this approach to be practical, finding a good quantification schedule is critical. We study the use of a variable elimination algorithm for this purpose, as well as two specific methods for the generation of good elimination orders based on CNF structure. While neither method appears to dominate, we show how one can heuristically select the better using the notion of width. We implement a symbolic SAT solver based on these techniques and evaluate its efficiency and robustness on a set of benchmarks against five other solvers, each having unique characteristics, including winners of the most recent SAT competition.
14351696
A sufficient condition for a semicomplete multipartite digraph to be Hamiltonian
Abstract A multipartite tournament is an orientation of a complete k -partite graph for some k ⩾ 2. A factor of a digraph D is a collection of vertex disjoint cycles covering all the vertices of D . We show that there is no degree of strong connectivity which together with the existence of a factor will guarantee that a multipartite tournament is Hamiltonian. Our main result is a sufficient condition for a multipartite tournament to be Hamiltonian. We show that this condition is general enough to provide easy proofs of many existing results on paths and cycles in multipartite tournaments. Using this condition, we obtain a best possible lower bound on the length of a longest cycle in any strongly connected multipartite tournament.
10979198
Weakly Hamiltonian-connected ordinary multipartite tournaments
Abstract We characterize weakly Hamiltonian-connected ordinary multipartite tournaments. Our result generalizes such a characterization for tournaments by Thomassen and implies a polynomial algorithm to decide the existence of a Hamiltonian path connecting two given vertices in an ordinary multipartite tournament and finds one, if it exists.