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Large-Scale Geometric Data Decomposition, Processing And Louisiana State University LSU Digital Commons LSU Doctoral Dissertations Graduate School 2015 Large-scale Geometric Data Decomposition, Processing and Structured Mesh Generation Wuyi Yu Louisiana State University and Agricultural and Mechanical College, [email protected] Follow this and additional works at: https://digitalcommons.lsu.edu/gradschool_dissertations Part of the Computer Sciences Commons Recommended Citation Yu, Wuyi, "Large-scale Geometric Data Decomposition, Processing and Structured Mesh Generation" (2015). LSU Doctoral Dissertations. 211. https://digitalcommons.lsu.edu/gradschool_dissertations/211 This Dissertation is brought to you for free and open access by the Graduate School at LSU Digital Commons. It has been accepted for inclusion in LSU Doctoral Dissertations by an authorized graduate school editor of LSU Digital Commons. For more information, please [email protected]. LARGE-SCALE GEOMETRIC DATA DECOMPOSITION, PROCESSING AND STRUCTURED MESH GENERATION A Dissertation Submitted to the Graduate Faculty of the Louisiana State University and Agricultural and Mechanical College in partial fulfillment of the requirements for the degree of Doctor of Philosophy in The Department of Electrical and Computer Science The Division of Computer Science Engineering by Wuyi Yu B.S., Xiamen University, 2005 May 2016 To Sibyl, Alex, Ella and Ekka ii ACKNOWLEDGEMENTS First of all, I would like to gratefully and sincerely thank my Ph.D. supervisor, Professor Xin Li, for his warm encouragement and thoughtful guidance. He is my best role model. I appreciate all his contributions of time, ideas, and funding to my Ph.D. study. I would like to thank my committee members, Bijaya Karki, Costas Busch, Robert Kooima, Hongchao Zhang and Brian Marx for their patience, discussion and collaborations. I would also like to thank all members in Geometric and Visual Computing Group at LSU. Many thanks to Shenghua Wan, Huanhuan Xu, Kang Zhang, Shuai Zheng and Celong Liu for delightful collaborations and discussions we had together. Thanks Zhao Yin, Li Wei, Wei Li, Xiao Lin, Tengfei Ye, Wei Yu and so many others for their help during the past years. Last but not least, I would like to thank my beloved wife Wenting Jing for her understanding and love. Without her support, encouragement and tolerance, all these would not have been possible. Wenting, I love you. I would like to thank my lovely son, Alexander, who brings me great joy. I would like to thank my family for their endless love and support. iii TABLE OF CONTENTS ACKNOWLEDGEMENTS ................................ iii LISTOFTABLES ..................................... vii LISTOFFIGURES .................................... ix ABSTRACT ........................................ xiii I PROBLEM STATEMENT AND BACKGROUND .............. 1 1 INTRODUCTION ................................... 2 1.1 BACKGROUND ................................. 2 1.2 CHALLENGINGISSUES ............................ 4 1.3 RELATEDWORK................................ 5 1.3.1 ShapePartitioning ............................ 6 1.3.2 Quad/HexMeshGeneration . .. .. 8 1.4 OURAPPROACH ................................ 9 II SHAPE PARTITIONING ........................ 11 2 COMPUTING 3D SHAPE GUARDING AND STAR DECOMPOSITION . 13 2.1 RELATEDWORK................................ 14 2.1.1 ShapeGuarding.............................. 14 2.1.2 ShapeDecomposition........................... 15 2.2 3DSHAPEGUARDING............................. 16 2.2.1 Visibility Detection . 17 2.2.2 GreedyandOptimalGuarding. 19 2.2.3 ProgressiveGuarding........................... 20 2.3 STARDECOMPOSITION............................ 27 2.4 APPLICATIONS ................................. 31 2.4.1 ShapeMatchingandRetrieval . 31 2.4.2 ShapeMorphing ............................. 37 2.5 CONCLUSION .................................. 39 3 GEOMETRIC-AWARE GRAPH PARTITIONING . 40 3.1 RELATEDWORK................................ 42 iv 3.1.1 DataPartitioning............................. 42 3.1.2 QuadrilateralMeshGeneration . 44 3.2 REGIONPARTITIONING ........................... 45 3.2.1 Notation.................................. 46 3.2.2 WorkloadBalance............................. 47 3.2.3 TotalSeparatorLength. .. .. 48 3.2.4 SeparatorAngleDeviation . 49 3.2.5 ConnectivityConstraints. 51 3.2.6 Our Two-Step Partitioning Algorithm . 53 3.3 QUADMESHGENERATION.......................... 58 3.3.1 Parallel Quad Meshing on Subregions . 58 3.3.2 Post-processing after Composition . 59 3.4 EXPERIMENTALRESULTS . .. .. 59 3.4.1 Partitioning Quality Comparison . 60 3.4.2 Parallel Computational Efficiency . 62 3.4.3 Meshing Quality Comparison . 65 3.5 CONCLUSION .................................. 67 III HEXAHEDRAL MESH GENERATION .................. 68 4 AUTOMATIC POLYCUBE DOMAIN CONSTRUCTION . 72 4.1 RELATEDWORK................................ 72 4.2 BASIC IDEAS AND ALGORITHM OVERVIEW . 73 4.3 PRE-DEFORMATION.............................. 74 4.4 POLYCUBE CONSTRUCTION AND OPTIMIZATION . 77 4.4.1 Polycube Extraction by Voxelization . 77 4.4.2 Polycube Shape Optimization . 80 4.5 DISCUSSIONS AND IMPLEMENTATION . 84 4.5.1 Topology Preservation in Polycube Construction . 84 4.5.2 Different Weights in Polycube Optimization . 86 4.5.3 FeaturePreserving ............................ 87 5 POLYCUBE MAPPING COMPUTATION . 89 5.1 RELATEDWORK................................ 89 5.2 POLYCUBE VOLUMETRIC PARAMETERIZATION . 90 5.2.1 PolycubeSurfaceMapping. 90 5.2.2 Volumetric Polycube Parameterization . 91 5.3 RESULTSANDCOMPARISON . .. .. 96 5.4 CONCLUSIONS ................................. 103 6 SIMULTANEOUSLY OPTIMIZING THE POLYCUBE DOMAIN AND THE PA- RAMETERIZATION.................................. 104 6.1 NOTATIONANDOVERVIEW . 104 6.2 L1 FORMULATIONOFTHEPOLYCUBE . 105 v 6.3 PARAMTERIZATION DISTORTION TERM . 106 6.4 SOLVING THE OPTIMIZATION PROBLEM . 108 6.4.1 GradientComputation . .. .. 108 6.4.2 WeightingSchedule............................ 109 6.5 SIMPLIFYING THE POLYCUBE DOMAIN . 110 6.5.1 PolyCubeEnergyFormulation. 112 6.5.2 Solving the Optimal Patch Heights using Beam Search . 114 6.6 RESULTSANDCOMPARISON . 115 6.7 CONCLUSION .................................. 120 7 CONCLUSIONANDFUTUREWORK . 121 REFERENCES....................................... 122 VITA ............................................ 131 vi LIST OF TABLES 2.1 Guarding Statistics. NV is the boundary surface vertex number. NI , NG, NP indicate the number of necessary guards computed by ILP, Greedy, and PILP approaches, respectively. t shows the computational time in seconds. Guard- ing of big models cannot be solved directly using ILP, so their statistics are notapplicable. .................................. 24 2.2 Skeletal-Nodes Guarding versus Tetrahedral-Vertices Guarding. V∂M and | | VM are numbers of boundary vertices and tetrahedral vertices, respectively; | | S is the number of nodes on extracted skeletons; GV and GS are the sizes | | | M | | | of computed guarding sets (solved by ILP) when using all tetrahedral vertices as candidates and using only skeletal nodes as candidates, respectively. 26 3.1 Partitioning on the Key and Pipe models using direct CVT versus using our CVT-GP algorithm. NS is the number of subregions, RW , RˆC , and δˆθ are the workload balance ratio, average compactness, and average separator angle deviation. ..................................... 57 3.2 Decomposition quality comparison (the key and pipe model): direct L∞-CVT, METIS, MADD and our L∞-CVT-GP method (initialized 4000 CVT Cells). NS is the number of subregions. Our method has comparable workload bal- ance and average compactness, while our δˆθ is up to about 50% and 55% smaller than the METIS method on key and pipe model respectively; our δˆθ is 20% and 15% smaller than MADD on two models respectively. Compared with L∞ method, our RW is40%smaller. ................... 61 3.3 The Runtime Table for different partitioning algorithms. NS is the number of subregions. The runtime is in minute, and includes the partitioning, meshing and relaxation time. Usually, the METIS is fastest, and our method has the secondbestefficiency. .............................. 63 vii 3.4 Mesh Quality Comparison between the sequential meshing algorithm, L∞- CVT, METIS, MADD, and our algorithm. The sequential algorithm applies the advancing front without partitioning; and it only works on small models such as the Key and Pipe. NS is the number of subregions. The four values: (1) average, (2) standard deviation, and (3) minimum of the scaled Jacobian, and (4) the number of singularities are listed to show meshing quality. The scaled Jacobian of our mesh is comparable to the sequential algorithm, but we have 20% more singularities. The average and minimal scaled Jacobians of our algorithm are 10% and 4% better than METIS and MADD, respectively. Our singularities are 40% and 20% fewer than METIS and MADD. Compared with L∞-CVT, our algorithm leads to about 4% better average and minimal scaled Jacobians and 8% fewer singularities. 66 4.1 Different Weights in Polycube Optimization. Ec is the corner number of the polycube; Eg is the accumulated distance of the vertices on surface P to surface Q. ζ¯ istheaverageScaledJacobian. 87 5.1 Runtime Table (in seconds). NV is vertex number of the input mesh S; tpre, topt, tsmap, tvmap are computational times on pre-processing, polycube con- struction/optimization, surface mapping, and volumetric mapping, respectively. 96 5.2 Comparison with other methods. # Hexes indicates the number of hex ele- ments in the final mesh. ζ¯ is the average Scaled
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