ADVANCED FLOW VISUALIZATION DISSERTATION Presented in Partial Ful¯llment of the Requirements for the Degree Doctor of Philosophy in the Graduate School of The Ohio State University By Liya Li, B.E., M.S. ***** The Ohio State University 2007 Dissertation Committee: Approved by Professor Han-Wei Shen, Adviser Professor Roger Craw¯s Adviser Professor Yusu Wang Graduate Program in Computer Science and Engineering °c Copyright by Liya Li 2007 ABSTRACT Flow visualization has been playing a substantial role in many engineering and scienti¯c applications, such as automotive industry, computational fluid dynamics, chemical processing, and weather simulation and climate modelling. Many meth- ods have been proposed in the past decade to visualize steady and time-varying flow ¯elds, in which textures-based and geometry-based visualization are widely used to explore the underlying fluid dynamics. This dissertation presents a view- dependent flow texture algorithm, an illustrative streamline placement algorithm on two-dimensional vector ¯elds, and an image-based streamline placement algorithm on three-dimensional vector ¯elds. Flow texture, generated through convolution and ¯ltering of texture values ac- cording to the local flow vectors, is a dense representation of the vector ¯eld to provide global information of the flow structure. A view-dependent algorithm for multi-resolution flow texture advection on two-dimensional structured rectilinear and curvilinear grid is presented. By using an intermediate representation of the under- lying flow ¯elds, the algorithm can adjust the resolutions of the output texture on the fly as the user zooms in and out of the ¯eld, which can avoid aliasing as well as ensure enough detail. Geometry-based methods use geometries, such as lines, tubes, or balls, to represent the motion paths advected from the vector ¯elds. It provides a sparse representation ii and an intuitive visualization of flow trajectory. For two-dimensional vector ¯elds, a streamline placement strategy is presented to generate representative and illustrative streamlines, which can e®ectively prevent the visual overload by emphasizing the essential and deemphasizing the trivial or repetitive flow patterns. A user study is performed to quantify the e®ectiveness of this visualization algorithm, and the results are provided. For three-dimensional vector ¯elds, an image-based streamline seeding algorithm is introduced to better display the streamlines and reduce visual cluttering in the output images. Various e®ects can be achieved to enhance the visual understanding of three-dimensional flow lines. iii To Tao, and my parents. iv ACKNOWLEDGMENTS I am grateful to my advisor Dr. Han-Wei Shen, who guided me expertly along the PhD study and helped me through many research di±culties. I would like to express my sincere gratitude to Dr. Roger Craw¯s, Dr. Yusu Wang, Dr. Garry McKenzie, and my other committee members. Thank you very much for your valuable time and e®ort, insightful criticism and advice. A heartfelt thanks to my colleagues Dr. Jinzhu Gao, Dr. Antonio Garcia, Teng- Yok Lee, Dr. Naeem Shareef, Dr. Chaoli Wang, and Jonathan Woodring, whose hard work and passion encouraged me. I enjoyed working with them and learning from them. I would like to extend my thanks to other members in the Computer Graphics group with whom I shared memorable experiences for the past ¯ve years. I wish you all the best in your respective research and career. My deepest gratitude is to my husband Tao Li, for everything. For love and for life. I am very grateful to my loyal friends for their encouragement. v VITA 1978 . .Born - Hubei, China 1999 . .B.E. Computer Science Beijing Institute of Technology, China 2002 . .M.S. Computer Science Beijing Institute of Technology, China 2006 . .M.S. Computer Science The Ohio State University September 2002 - August 2003 . .University Fellow The Ohio State University September 2003 - March 2004 . .Graduate Teaching Associate The Ohio State University April 2004 - August 2007 . Graduate Research Associate The Ohio State University June - September, 2005 . Research Intern The National Center for Atmospheric Research September - November, 2007 . .Intern NVIDIA vi PUBLICATIONS Refereed Papers Liya Li, Hsien-Hsi Hsieh, and Han-Wei Shen, \Illustrative Streamline Placement and Visualization". IEEE Paci¯c Visualization Symposium, March 2008. Liya Li and Han-Wei Shen, \Image-Based Streamline Generation and Rendering". IEEE Transactions on Visualization and Computer Graphics, 13(3):630-640, May 2007. Liya Li and Han-Wei Shen, \View-dependent Multi-resolutional Flow Texture Ad- vection". Visualization and Data Analysis, 2006. Chaoli Wang, Jinzhu Gao, Liya Li, and Han-Wei Shen, \A Multiresolution Volume Rendering Framework for Large-Scale Time-Varying Data Visualization". In Proceed- ings of International Workshop on Volume Graphics 2005, Stony Brook, New York, pages 11-19, June 2005. Jinzhu Gao, Chaoli Wang, Liya Li, and Han-Wei Shen, \A Parallel Multiresolution Volume Rendering Algorithm for Large Data Visualization". Parallel Computing (Special Issue on Parallel Graphics and Visualization), 31(2):185-204, February 2005. Unrefereed Papers Liya Li and Han-Wei Shen, \Image-Based Streamline Generation and Rendering". Technical Report OSU-CISRC8/06-TR71, Department of Computer Science and En- gineering, The Ohio State University, 2005. FIELDS OF STUDY Major Field: Computer Science and Engineering Studies in: Computer Graphics Professor Han-Wei Shen Computer Architecture Professor Gagan Agrawal Computer Networking Professor Dong Xuan vii TABLE OF CONTENTS Page Abstract . ii Dedication . iv Acknowledgments . v Vita . vi List of Tables . x List of Figures . xi Chapters: 1. Introduction . 1 2. Background . 9 2.1 Vector Fields . 9 2.1.1 Grids . 9 2.1.2 Integral Curves . 12 2.2 Critical Points and Flow Topology . 14 3. Related Work . 17 3.1 Flow Texture . 17 3.2 Two-dimensional Streamline Placement . 20 3.3 Simpli¯cation of Vector Fields . 23 3.4 Streamline Clustering . 25 3.5 Three-dimensional Streamline Placement . 25 3.6 Visualization Enhancement . 27 viii 4. View-dependent Multi-resolutional Flow Texture Advection . 29 4.1 Algorithm Overview . 29 4.2 Flow Field Representation . 30 4.3 Texture Advection . 31 4.4 Spatial Coherence . 34 4.5 Multi-resolutional Texture Avection . 35 4.5.1 Adjustment of Advection Step Size . 37 4.6 Results . 39 5. Illustrative Streamline Placement . 47 5.1 Algorithm Overview . 47 5.1.1 Distance Field . 49 5.1.2 Computation of Local Dissimilarity . 50 5.1.3 Influence from Multiple Streamlines . 52 5.1.4 Computation of Global Dissimilarity . 54 5.1.5 Selection of Candidate Seeds . 54 5.2 Topology-Based Enhancement . 57 5.3 Quality Analysis . 59 5.3.1 Quantitative Comparison . 59 5.3.2 User Study . 64 5.4 Results . 70 6. Image Based Streamline Generation and Rendering . 76 6.1 Algorithm Overview . 76 6.2 Image Space Streamline Placement . 78 6.2.1 Evenly-spaced Streamlines in Image Space . 79 6.2.2 Streamline Placement Strategies . 81 6.2.3 Additional Run Time Control . 90 6.3 Results . 98 7. Conclusions . 101 Bibliography . 106 ix LIST OF TABLES Table Page 4.1 Datasets used in the experiments. Note that the size for the vortex data includes all 31 time steps. The sizes are in KBytes. 39 4.2 The time for trace slice preprocessing and texture creation and loading (in seconds). .................................. 40 4.3 The size of trace slices (in MBytes) including all time steps. Note that Vortex dataset is time-varying. 44 5.1 The percentages of user rankings for each image based on the easiness to follow the underlying flow paths. ...................... 68 5.2 The percentages of user rankings for each image based on the easiness to locate the critical points by observing the streamlines. 69 5.3 The percentages of user rankings for each image based on the overall e®ec- tiveness of visualization considering the flow paths and critical points. 69 5.4 Information of four di®erent datasets, and the number of streamlines gen- erated by the algorithm. .......................... 71 5.5 Timings (in seconds) measured for generating streamlines. Each row corre- sponds to a data set listed in the same row of Table 5.4. 72 x LIST OF FIGURES Figure Page 1.1 Hand-drawn streamlines for a flow ¯eld around a cylinder. Image courtesy of Greg Turk [63]. ............................. 5 2.1 Di®erent types of grids (a) regular Cartesian grid (b) irregular Cartesian grid (c) structured grid (d) unstructured grid. 10 2.2 Classi¯cation of critical points of two-dimensional vector ¯elds. R1 and R2 denote the real part of the eigenvalues of the Jacobian matrix, while I1 and I2 denote the imaginary parts. Image courtesy of Helman and Hesselink [24]. 16 4.1 The creation of trace slices by backward advection. 32 4.2 Texture advection using two-stage texture lookups. 34 4.3 Comparison of particle position errors for travelling 1 to 10 time steps using the down-sampled trace slices and the down-sampled vortex dataset reduced from 100x100 to 50x50. X axis indicates the time steps that the particles have travelled, and Y axis indicates particle position errors compared to the accurate traces using the Euclidean distance in the ¯eld. 42 4.4 Comparison of particle position errors for travelling 1 to 10 time steps using the down-sampled trace slice and the down-sampled vortex dataset reduced from 100x100 to 25x25. X axis indicates the time steps that the particles have travelled, and Y axis indicates particle position errors compared to the accurate traces using the Euclidean distance in the ¯eld. 42 4.5 Rendering of the post dataset (a) with (b) without the multi-resolution level of detail control. .............................. 43 4.6 (a)With the correction of noise distribution, no stretched pattern can be seen (b) Rendering using LIC with the original resolution of 52x62. 44 xi 4.7 The image on the left was generated when zoomed in.