基于SpanSpace划分的海量数据等值面提取算法关键技术研究
|
摘要
科学计算可视化技术是分析处理海量科学数据的重要手段,目前针对海量数据的可视化仍然面临诸多难题,如需要更长的预处理时间、难于实施交互绘制等问题,因此目前对海量数据的可视化依然是国际上的研究难点与热点。
本文针对目前海量数据处理过程中区间二叉树与BBIO树存在的问题,采用自适应构建四叉树以及构建区间包围盒的方式对两种树形结构进行了改进,进一步完成了相关理论分析与实验,同时完成了海量数据处理相关算法的系统框架实现。本文的主要工作及取得的主要研究成果包括:
(1)提出了四叉树自适应划分的区间二叉树节点构造算法。实践发现,对于海量数据集的meta-cell构建区间二叉树时,往往出现胖节点的情况。胖节点将严重影响海量数据预处理效率,使得预处理时间无法控制。针对胖节点问题,提出使用四叉树自适应划分的方法取代原有两次全局排序的方法,在降低了预处理时间开销的同时,保持原有最优搜索活动单元效率。通过实验证明,采用自适应划分算法构造四叉树较传统方法构造时间缩短50%左右,在搜索活动meta-cell方面与最优方法相比相差不到0.2s。
(2)提出了基于节点包围盒的BBIO树构造算法。针对传统BBIO树搜索效率低的问题,采用节点内区间分组做包围盒的方式对BBIO树节点进行了重新构建,有效提高了BBIO树节点内搜索活动meta-cell的效率,实验表明改进后的节点包围盒算法比传统BBIO树算法搜索效率提升近20%。
(3)设计实现了集成自适应划分区间二叉树和节点包围盒BBIO树的海量数据可视化框架。整合本文所提出的两种海量数据组织改进方法,合并相同的数据读取、meta-cell划分以及等值面提取阶段,将海量数据组织阶段抽象为对象接口,在更高抽象层次上实现了完整的海量数据可视化流程。设计依照现代面向对象软件工程原则,综合考虑系统框架的功能可扩展性、有效性和模块可重用性,设计实现了优秀的易于扩展、易于维护的海量数据可视化框架。
Visualization has been played an important role for analyzing and processing large-scale datasets. However, visualizing large-scale datasets still suffers lots of difficulties, such as preprocessing time is too long, rendering time is too long or consuming too much space. How to realize the real-time and interactive visualization of large scale dataset has become a hot topic of visualization.
In this paper, we will discuss some large-scale datasets visualization methods. Aiming at the problems of current large-scale datasets visualization, we make use of quad tree based adaptive partition and bounding box based node construction methods to improve traditional binary interval tree and BBIO tree. The theory analysis and experiments show that our approaches are much efficient for large-scale datasets visualization. The contributions and relevant work in the paper are as follows.
Firstly, we introduce an adaptive quad tree partition method for binary interval tree. In large-scale datasets visualization process, fat nodes will block the pre-processing efficiency and make visualization time uncontrollable. We use adaptive quad tree partition strategy to reform the construction of binary interval tree, and it not only reduce pre-processing time but also maintain the efficiency of searching active meta-cell. The experiments demonstrate that the adaptive quad tree method is faster than the traditional construction method, and will reduce the pre-processing time almost 50%, the difference between two methods in active meta-cell searching is only less 0.2s;
Secondly, we propose a BBIO tree node construction method based on bounding box. We improve the traditional low efficiency of BBIO tree construction, and leverage Span Space bounding box to reform the layout of BBIO tree nodes, the experiments proved that our algorithm is more efficient than the traditional and will achieve 20% speed up for detecting active meta-cell;
Finally,for solving the problems of large-scale dataset visualization, we have combined all approaches which is proposed in this paper, and integrated all techniques to a large-scale datasets isosurface extraction framework. We defined all interfaces and model functions well-formed and design a scalable, reusable visualization frame work. At last, we analysis the framework in modern software engineering angle, and in abstract level, we complete all integration work for our framework, and have built an excellent large-scale datasets visualization software framework.
本文针对目前海量数据处理过程中区间二叉树与BBIO树存在的问题,采用自适应构建四叉树以及构建区间包围盒的方式对两种树形结构进行了改进,进一步完成了相关理论分析与实验,同时完成了海量数据处理相关算法的系统框架实现。本文的主要工作及取得的主要研究成果包括:
(1)提出了四叉树自适应划分的区间二叉树节点构造算法。实践发现,对于海量数据集的meta-cell构建区间二叉树时,往往出现胖节点的情况。胖节点将严重影响海量数据预处理效率,使得预处理时间无法控制。针对胖节点问题,提出使用四叉树自适应划分的方法取代原有两次全局排序的方法,在降低了预处理时间开销的同时,保持原有最优搜索活动单元效率。通过实验证明,采用自适应划分算法构造四叉树较传统方法构造时间缩短50%左右,在搜索活动meta-cell方面与最优方法相比相差不到0.2s。
(2)提出了基于节点包围盒的BBIO树构造算法。针对传统BBIO树搜索效率低的问题,采用节点内区间分组做包围盒的方式对BBIO树节点进行了重新构建,有效提高了BBIO树节点内搜索活动meta-cell的效率,实验表明改进后的节点包围盒算法比传统BBIO树算法搜索效率提升近20%。
(3)设计实现了集成自适应划分区间二叉树和节点包围盒BBIO树的海量数据可视化框架。整合本文所提出的两种海量数据组织改进方法,合并相同的数据读取、meta-cell划分以及等值面提取阶段,将海量数据组织阶段抽象为对象接口,在更高抽象层次上实现了完整的海量数据可视化流程。设计依照现代面向对象软件工程原则,综合考虑系统框架的功能可扩展性、有效性和模块可重用性,设计实现了优秀的易于扩展、易于维护的海量数据可视化框架。
Visualization has been played an important role for analyzing and processing large-scale datasets. However, visualizing large-scale datasets still suffers lots of difficulties, such as preprocessing time is too long, rendering time is too long or consuming too much space. How to realize the real-time and interactive visualization of large scale dataset has become a hot topic of visualization.
In this paper, we will discuss some large-scale datasets visualization methods. Aiming at the problems of current large-scale datasets visualization, we make use of quad tree based adaptive partition and bounding box based node construction methods to improve traditional binary interval tree and BBIO tree. The theory analysis and experiments show that our approaches are much efficient for large-scale datasets visualization. The contributions and relevant work in the paper are as follows.
Firstly, we introduce an adaptive quad tree partition method for binary interval tree. In large-scale datasets visualization process, fat nodes will block the pre-processing efficiency and make visualization time uncontrollable. We use adaptive quad tree partition strategy to reform the construction of binary interval tree, and it not only reduce pre-processing time but also maintain the efficiency of searching active meta-cell. The experiments demonstrate that the adaptive quad tree method is faster than the traditional construction method, and will reduce the pre-processing time almost 50%, the difference between two methods in active meta-cell searching is only less 0.2s;
Secondly, we propose a BBIO tree node construction method based on bounding box. We improve the traditional low efficiency of BBIO tree construction, and leverage Span Space bounding box to reform the layout of BBIO tree nodes, the experiments proved that our algorithm is more efficient than the traditional and will achieve 20% speed up for detecting active meta-cell;
Finally,for solving the problems of large-scale dataset visualization, we have combined all approaches which is proposed in this paper, and integrated all techniques to a large-scale datasets isosurface extraction framework. We defined all interfaces and model functions well-formed and design a scalable, reusable visualization frame work. At last, we analysis the framework in modern software engineering angle, and in abstract level, we complete all integration work for our framework, and have built an excellent large-scale datasets visualization software framework.
引文
[1] Y.-J. Chiang and C. T. Silva. I/O Optimal Isosurface Extraction[C]//Los Alamitos:IEEE Computer Society Press. IEEE Visualization ,1997: 293–300.
[2] Aggarwal, J. S. Vitter. The Input/Output Complexity of Sorting and Related Problems[J]. Communications of the ACM, 1988, 31(9): 1116–1127.
[3] Y.-J. Chiang, C. T. Silva, and W. J. Schroeder. Interactive Out-Of-Core Isosurface Extraction[C]//Los Alamitos:IEEE Computer Society Press. IEEE Visualization 1998: 167–174.
[4] P. Cignoni, P. Marino, C. Montani, E. Puppo, R. Scopigno. Speeding Up Isosurface Extraction Using Interval Trees[J].IEEE Transactions on Visualization and Computer Graphics, 1997, 3(2):158-170.
[5] Y.-J. Chiang and C. T. Silva. External Memory Techniques for Isosurface Extraction in Scientific Visualization[J]. External Memory Algorithms and Visualization, DIMACS Series, 1999,50:247–277.
[6] L. Arge and J. S. Vitter. Optimal Interval Management in External Memory. Proc. 37th Annu[C]//Los Alamitos:IEEE Computer Society Press. IEEE Sympos Found Comput Sci, 1996:560–569.
[7] Qin.Wang, Joseph.JaJa, Amitabh Varshney. An efficient and scalable parallel algorithm for out-of-core isosurface, extraction and rendering[J]. Journal of Parallel and Distributed Computing, J. Parallel Distrib. Comput. 2007, 67:592-603.
[8] P. C. Kanellakis, S. Ramaswamy, D. E. Vengroff, and J. S. Vitter. Indexing for Data Models with Constraints and Classes[J]. Journal of Computer and System Sciences, , 1996,52(3):589–612.
[9] Yarden Livnat, Han-Wei Shen, Christopher R. Johnson. A Near Optimal IsoSurface Extraction Algorithm Using the Span Space[J]. IEEE Transactions on Visualization and Computer Graphics, 1996, 2(1):73-84.
[10] J. Wilhelms and A. van Gelder. Octrees for faster isosurface generation[J]. ACM Transactions on Graphics, , 1992,11(3):201–227.
[11] P. Sutton, C. Hansen. Accelerated isosurface extraction in time-varying fields[J]. IEEE Trans. on Visualization, 2001, 6(2):98-107.
[12] Q. Shi, J. JaJa. Isosurface extraction and spatial ?ltering using Persistent OcTree (POT)[J]. IEEE Transactions On Visualization And Computer Graphics, 2006 ,12(5):1283-1290.
[13] Cong Wang, Yi-Jen Chiang. Isosurface Extraction and View- Dependent Filtering from Time-Varying Fields Using Persistent Time-Octree (PTOT)[J]. IEEE Transaction on Visualization and Computer Graphics. 2009, 15(6):1367-1374.
[14] Jusub Kim, Joseph JaJa. A Novel Information-Aware Octree for theVisualization of Large Scale Time-varying Data[R]. (Technical Report CS-TR-4778 and UMIACS-TR-2006-03)
[15] Zhiyan Du, Yi-Jen Chiang, Han-Wei Shen. Out-of-core volume rendering for time-varying fields using a space-partitioning time (SPT) tree. Visualization Symposium, 2009. PacificVis '09. IEEE Pacific. 73 - 80
[16] ParaView. http://www.paraview.org
[17] Shaffer E, Garland M. A multiresolution representation for massive meshes[J]. IEEE Transactions on Visualization and Computer Graphics, 2005, 11(2):139-148.
[18]熊华,面向并行环境的绘制加速技术研究[D].浙江:浙江大学,2008.
[19] Chaoli Wang, Jinzhu Gao, Liya Li, Han-Wei Shen. A Multiresolution Volume Rendering Framework for Large-Scale Time-Varying Data Visualization[J]. Volume Graphics, 2005, 6(21): 11 - 223
[20] Kenneth Moreland, Brian Wylie, Constantine Pavlakos. Sort-Last Parallel Rendering for Viewing Extremely Large Data Sets on Tile Displays. 2001.8(6):85-154
[21] Chaoli Wang, Han-Wei Shen. LOD Map - A Visual Interface for Navigating Multiresolution Volume Visualization. IEEE Trans Vis Comput Graph. 2006.12(5):1029-1036.
[22] LAMAR E., PASCUCCI V. A multi-layered image cache for scienti?c visualization In Parallel and Large-Data Visualization and Graphics 2003. PVG 2003:61–67.
[23] Pascucci V, Laney D. E, Frank R. J, Scorzelli G, Linsen L., Hamann B., Gygi F. Real-time monitoring of large scienti?c simulations. InSAC’03: Proceedings of the 2003 ACM symposium on Applied computing, 2003:194–198.
[24] Jinzhu Gao, Han-Wei Shen, Jian Huang, James Arthur Kohl. Visibility Culling for Time-Varying Volume Rendering Using Temporal Occlusion Coherence[C]//Los Alamitos:IEEE Computer Society Press. IEEE Visualization 2004:147–154.
[25] S. Molnar, M. Cox, D. Ellsworth, and H. Fuchs. A Sorting Classification of Parallel Rendering[J]. IEEE Computer Graphics and Algorithms, 1994:23-32
[26] Humphrey G, Houston M, Ng R. Chromuim: A stream-processing framework for interactive rendering on clusters[C]// New York:ACM Press. Proceeding of ACM SIGGRAPH, San Antonio, 2002; 693-702.
[27] Yang J. AnyGL: A Large scale hybrid distributed graphics system[D]. Ph.D. Thesis. Hangzhou: Zhejiang University, 2002.
[28] Li K, Chen H, Chen Y Q, et al. Early experiences and challenges in building and using a scalable display wall system[C]//Los Alamitos:IEEE Computer Society Press. IEEE Computer Graphics and Application, 2000, 20(4): 671-680.
[29] VTK. http://www.vtk.org
[30] Praveen Bhaniramka, Philippe C.D. Robert, Stefan Eilemann. OpenGL Multipipe SDK: A Toolkit for Scalable Parallel Rendering. IEEE Visualization, 2005:119-126
[31] Kwan-Liu Ma, Jame S. Painter, Charles D. Hansen, Michael F. Krogh. Parallel Volume Rendering Using Binary-Swap Compositing.Computer Graphics and Applications, 1994, 14(4):59– 68.
[32] Stefan Eilemann, Renato Pajarola. Direct Send Compositing for Parallel Sort-Last Rendering. SIGGRAPH Asia '08 ACM. 2008: 15-24.
[33] VisIt. http://www.llnl.org/visit
[34] Hongfeng Yu, Chaoli Wang, Kwan-Liu Ma. Massively Parallel Volume Rendering Using 2-3 Swap Image Compositing. High Performance Computing, Networking, Storage and Analysis, 2008. SC 2008:1 - 11
[35] W.E. Lorensen, H.E. Cline. Marching cubes: a high resolution 3D surface construction algorithm, Computer Graphics (SIGGRAPH’87 Proceedings), 1987, 7(21):161-169.
[36] Doi A, Koide.A. An Efficient Method of Triangulating Equi-Value Surfaces By Using Tetrahedra[J]. IEICE. Transactions, 1991(1):214-224.
[37] Yarden Livnat, Han-Wei Shen, Christopher R. Johnson. A Near Optimal IsoSurface Extraction Algorithm Using the Span Space[J]. IEEE Transactions on Visualization and Computer Graphics, 1996, 2(1):73-84.
[38] Dana A. Jacobsen, Julien C. Thibault, Inanc Senocak. An MPI-CUDA Implementation for Massively Parallel Incompressible Flow computations on Multi-GPU Clusters[C]//New York:WIT Press.2010 AIAA, 2010:1-15
[39] C. C. Law, K. M. Martin, W. J. Schroeder, J. E. Temkin. A multithreaded streaming pipeline architecture for large structured data sets[C]//Los Alamitos:IEEE Computer Society Press. IEEE Visualization. 1999:225-232.
[40] J. Ahrens, K. M. Martin, B. Geveci, C.Law. Large-scale data visualization using parallel data streaming[J]. IEEE Computer Graphics and, Applications, 2001,21(4):34-41
[41] Thomas Fogal, Hank Childs, Siddharth Shankar, Jens Krüger, R. Daniel Bergeron and Philip Hatcher. Large Data Visualization on Distributed Memory Multi-GPU Clusters[C]//New York:ACM Press. 2010 High Performance Graphics, 2010:20-26
[42] Antonio Garcia, Han-Wei Shen. Asynchronous Rendering of Time-Variant Workload-Based Data Shuffling.Proceedings of High Performance 2005. 2005:12-19
[43] Luke J. Gosink, John C. Anderson, E. Wes Bethel, Kenneth I. Joy, Query-Driven Visualization of Time-Varying Adaptive Mesh Refinement Data[J], IEEE Transactions on Visualization and Computer Graphics, 2008,11(14):1715-1722.
[44] Nielson G M, Hamann B. The Asymptotic Decider: Resolving the Ambiguity in Marching Cubes. IEEE Proceedings of Visualization, 1991:83-91
[45]周勇,唐圣泽.三维数据可视化技术的研究与实现[D].清华大学博士学位论文,1995.6:1-5
[46] NVIDIA CUDA. http://www.nvidia.com/object/cuda.html
[47] OpenCL. http://www.khronos.org/opencl
[48] Klein, T.; Stegmaier, S.; Ertl, T. Hardware-accelerated reconstruction of polygonal isosurface representations on unstructured grids. Computer Graphics and Applications, 2004[C]//Los Alamitos:IEEE Computer Society Press. Proceedings. 12th Pacific Conference. 2004:35-42
[49] Gunnar Johansson, Hamish Carr. Accelerating Marching Cubes with Graphics Hardware[C]//Los Alamitos:IEEE Computer Society Press. Proceedings of the 2006 conference of the Center for Advanced Studies on Collaborative research. 2006:33-37.
[50] Frank Goetz, Theodor Junklewitz and Gitta Domik. Real-Time Marching Cubes on the Vertex Shader[C]//Aire-la-Ville:Eurographics Association Press. Proceedings of Eurographics 2005:15-21.
[51] CUDA SDK:http://www.nvidia.com/object/cuda.html
[52] Erich Gamma, Richard Helm, Ralph Johnson, John Vlissides.设计模式——可复用面向对象软件的基础[M].北京:机械工业出版社, 1994:20-35
[53]谭庆平,齐治昌,宁洪.软件工程(第二版)[M].北京:高等教育出版社,2004:11-19
[2] Aggarwal, J. S. Vitter. The Input/Output Complexity of Sorting and Related Problems[J]. Communications of the ACM, 1988, 31(9): 1116–1127.
[3] Y.-J. Chiang, C. T. Silva, and W. J. Schroeder. Interactive Out-Of-Core Isosurface Extraction[C]//Los Alamitos:IEEE Computer Society Press. IEEE Visualization 1998: 167–174.
[4] P. Cignoni, P. Marino, C. Montani, E. Puppo, R. Scopigno. Speeding Up Isosurface Extraction Using Interval Trees[J].IEEE Transactions on Visualization and Computer Graphics, 1997, 3(2):158-170.
[5] Y.-J. Chiang and C. T. Silva. External Memory Techniques for Isosurface Extraction in Scientific Visualization[J]. External Memory Algorithms and Visualization, DIMACS Series, 1999,50:247–277.
[6] L. Arge and J. S. Vitter. Optimal Interval Management in External Memory. Proc. 37th Annu[C]//Los Alamitos:IEEE Computer Society Press. IEEE Sympos Found Comput Sci, 1996:560–569.
[7] Qin.Wang, Joseph.JaJa, Amitabh Varshney. An efficient and scalable parallel algorithm for out-of-core isosurface, extraction and rendering[J]. Journal of Parallel and Distributed Computing, J. Parallel Distrib. Comput. 2007, 67:592-603.
[8] P. C. Kanellakis, S. Ramaswamy, D. E. Vengroff, and J. S. Vitter. Indexing for Data Models with Constraints and Classes[J]. Journal of Computer and System Sciences, , 1996,52(3):589–612.
[9] Yarden Livnat, Han-Wei Shen, Christopher R. Johnson. A Near Optimal IsoSurface Extraction Algorithm Using the Span Space[J]. IEEE Transactions on Visualization and Computer Graphics, 1996, 2(1):73-84.
[10] J. Wilhelms and A. van Gelder. Octrees for faster isosurface generation[J]. ACM Transactions on Graphics, , 1992,11(3):201–227.
[11] P. Sutton, C. Hansen. Accelerated isosurface extraction in time-varying fields[J]. IEEE Trans. on Visualization, 2001, 6(2):98-107.
[12] Q. Shi, J. JaJa. Isosurface extraction and spatial ?ltering using Persistent OcTree (POT)[J]. IEEE Transactions On Visualization And Computer Graphics, 2006 ,12(5):1283-1290.
[13] Cong Wang, Yi-Jen Chiang. Isosurface Extraction and View- Dependent Filtering from Time-Varying Fields Using Persistent Time-Octree (PTOT)[J]. IEEE Transaction on Visualization and Computer Graphics. 2009, 15(6):1367-1374.
[14] Jusub Kim, Joseph JaJa. A Novel Information-Aware Octree for theVisualization of Large Scale Time-varying Data[R]. (Technical Report CS-TR-4778 and UMIACS-TR-2006-03)
[15] Zhiyan Du, Yi-Jen Chiang, Han-Wei Shen. Out-of-core volume rendering for time-varying fields using a space-partitioning time (SPT) tree. Visualization Symposium, 2009. PacificVis '09. IEEE Pacific. 73 - 80
[16] ParaView. http://www.paraview.org
[17] Shaffer E, Garland M. A multiresolution representation for massive meshes[J]. IEEE Transactions on Visualization and Computer Graphics, 2005, 11(2):139-148.
[18]熊华,面向并行环境的绘制加速技术研究[D].浙江:浙江大学,2008.
[19] Chaoli Wang, Jinzhu Gao, Liya Li, Han-Wei Shen. A Multiresolution Volume Rendering Framework for Large-Scale Time-Varying Data Visualization[J]. Volume Graphics, 2005, 6(21): 11 - 223
[20] Kenneth Moreland, Brian Wylie, Constantine Pavlakos. Sort-Last Parallel Rendering for Viewing Extremely Large Data Sets on Tile Displays. 2001.8(6):85-154
[21] Chaoli Wang, Han-Wei Shen. LOD Map - A Visual Interface for Navigating Multiresolution Volume Visualization. IEEE Trans Vis Comput Graph. 2006.12(5):1029-1036.
[22] LAMAR E., PASCUCCI V. A multi-layered image cache for scienti?c visualization In Parallel and Large-Data Visualization and Graphics 2003. PVG 2003:61–67.
[23] Pascucci V, Laney D. E, Frank R. J, Scorzelli G, Linsen L., Hamann B., Gygi F. Real-time monitoring of large scienti?c simulations. InSAC’03: Proceedings of the 2003 ACM symposium on Applied computing, 2003:194–198.
[24] Jinzhu Gao, Han-Wei Shen, Jian Huang, James Arthur Kohl. Visibility Culling for Time-Varying Volume Rendering Using Temporal Occlusion Coherence[C]//Los Alamitos:IEEE Computer Society Press. IEEE Visualization 2004:147–154.
[25] S. Molnar, M. Cox, D. Ellsworth, and H. Fuchs. A Sorting Classification of Parallel Rendering[J]. IEEE Computer Graphics and Algorithms, 1994:23-32
[26] Humphrey G, Houston M, Ng R. Chromuim: A stream-processing framework for interactive rendering on clusters[C]// New York:ACM Press. Proceeding of ACM SIGGRAPH, San Antonio, 2002; 693-702.
[27] Yang J. AnyGL: A Large scale hybrid distributed graphics system[D]. Ph.D. Thesis. Hangzhou: Zhejiang University, 2002.
[28] Li K, Chen H, Chen Y Q, et al. Early experiences and challenges in building and using a scalable display wall system[C]//Los Alamitos:IEEE Computer Society Press. IEEE Computer Graphics and Application, 2000, 20(4): 671-680.
[29] VTK. http://www.vtk.org
[30] Praveen Bhaniramka, Philippe C.D. Robert, Stefan Eilemann. OpenGL Multipipe SDK: A Toolkit for Scalable Parallel Rendering. IEEE Visualization, 2005:119-126
[31] Kwan-Liu Ma, Jame S. Painter, Charles D. Hansen, Michael F. Krogh. Parallel Volume Rendering Using Binary-Swap Compositing.Computer Graphics and Applications, 1994, 14(4):59– 68.
[32] Stefan Eilemann, Renato Pajarola. Direct Send Compositing for Parallel Sort-Last Rendering. SIGGRAPH Asia '08 ACM. 2008: 15-24.
[33] VisIt. http://www.llnl.org/visit
[34] Hongfeng Yu, Chaoli Wang, Kwan-Liu Ma. Massively Parallel Volume Rendering Using 2-3 Swap Image Compositing. High Performance Computing, Networking, Storage and Analysis, 2008. SC 2008:1 - 11
[35] W.E. Lorensen, H.E. Cline. Marching cubes: a high resolution 3D surface construction algorithm, Computer Graphics (SIGGRAPH’87 Proceedings), 1987, 7(21):161-169.
[36] Doi A, Koide.A. An Efficient Method of Triangulating Equi-Value Surfaces By Using Tetrahedra[J]. IEICE. Transactions, 1991(1):214-224.
[37] Yarden Livnat, Han-Wei Shen, Christopher R. Johnson. A Near Optimal IsoSurface Extraction Algorithm Using the Span Space[J]. IEEE Transactions on Visualization and Computer Graphics, 1996, 2(1):73-84.
[38] Dana A. Jacobsen, Julien C. Thibault, Inanc Senocak. An MPI-CUDA Implementation for Massively Parallel Incompressible Flow computations on Multi-GPU Clusters[C]//New York:WIT Press.2010 AIAA, 2010:1-15
[39] C. C. Law, K. M. Martin, W. J. Schroeder, J. E. Temkin. A multithreaded streaming pipeline architecture for large structured data sets[C]//Los Alamitos:IEEE Computer Society Press. IEEE Visualization. 1999:225-232.
[40] J. Ahrens, K. M. Martin, B. Geveci, C.Law. Large-scale data visualization using parallel data streaming[J]. IEEE Computer Graphics and, Applications, 2001,21(4):34-41
[41] Thomas Fogal, Hank Childs, Siddharth Shankar, Jens Krüger, R. Daniel Bergeron and Philip Hatcher. Large Data Visualization on Distributed Memory Multi-GPU Clusters[C]//New York:ACM Press. 2010 High Performance Graphics, 2010:20-26
[42] Antonio Garcia, Han-Wei Shen. Asynchronous Rendering of Time-Variant Workload-Based Data Shuffling.Proceedings of High Performance 2005. 2005:12-19
[43] Luke J. Gosink, John C. Anderson, E. Wes Bethel, Kenneth I. Joy, Query-Driven Visualization of Time-Varying Adaptive Mesh Refinement Data[J], IEEE Transactions on Visualization and Computer Graphics, 2008,11(14):1715-1722.
[44] Nielson G M, Hamann B. The Asymptotic Decider: Resolving the Ambiguity in Marching Cubes. IEEE Proceedings of Visualization, 1991:83-91
[45]周勇,唐圣泽.三维数据可视化技术的研究与实现[D].清华大学博士学位论文,1995.6:1-5
[46] NVIDIA CUDA. http://www.nvidia.com/object/cuda.html
[47] OpenCL. http://www.khronos.org/opencl
[48] Klein, T.; Stegmaier, S.; Ertl, T. Hardware-accelerated reconstruction of polygonal isosurface representations on unstructured grids. Computer Graphics and Applications, 2004[C]//Los Alamitos:IEEE Computer Society Press. Proceedings. 12th Pacific Conference. 2004:35-42
[49] Gunnar Johansson, Hamish Carr. Accelerating Marching Cubes with Graphics Hardware[C]//Los Alamitos:IEEE Computer Society Press. Proceedings of the 2006 conference of the Center for Advanced Studies on Collaborative research. 2006:33-37.
[50] Frank Goetz, Theodor Junklewitz and Gitta Domik. Real-Time Marching Cubes on the Vertex Shader[C]//Aire-la-Ville:Eurographics Association Press. Proceedings of Eurographics 2005:15-21.
[51] CUDA SDK:http://www.nvidia.com/object/cuda.html
[52] Erich Gamma, Richard Helm, Ralph Johnson, John Vlissides.设计模式——可复用面向对象软件的基础[M].北京:机械工业出版社, 1994:20-35
[53]谭庆平,齐治昌,宁洪.软件工程(第二版)[M].北京:高等教育出版社,2004:11-19