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E-raamat: Geometric Modeling and Mesh Generation from Scanned Images

(Carnegie Mellon University, Pittsburgh, Pennsylvania, USA)
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Cutting-Edge Techniques to Better Analyze and Predict Complex Physical Phenomena

Geometric Modeling and Mesh Generation from Scanned Images shows how to integrate image processing, geometric modeling, and mesh generation with the finite element method (FEM) to solve problems in computational biology, medicine, materials science, and engineering. Based on the authors recent research and course at Carnegie Mellon University, the text explains the fundamentals of medical imaging, image processing, computational geometry, mesh generation, visualization, and finite element analysis. It also explores novel and advanced applications in computational biology, medicine, materials science, and other engineering areas.

One of the first to cover this emerging interdisciplinary field, the book addresses biomedical/material imaging, image processing, geometric modeling and visualization, FEM, and biomedical and engineering applications. It introduces image-mesh-simulation pipelines, reviews numerical methods used in various modules of the pipelines, and discusses several scanning techniques, including ones to probe polycrystalline materials.

The book next presents the fundamentals of geometric modeling and computer graphics, geometric objects and transformations, and curves and surfaces as well as two isocontouring methods: marching cubes and dual contouring. It then describes various triangular/tetrahedral and quadrilateral/hexahedral mesh generation techniques. The book also discusses volumetric T-spline modeling for isogeometric analysis (IGA) and introduces some new developments of FEM in recent years with applications.

Arvustused

"Congratulations to the first reference and textbook for a new interdisciplinary approach to image-based engineering and science. The book covers all topics ranging from imaging, image processing, geometric modeling, and mesh generation, to simulation and applications. It is an excellent textbook for both senior undergraduate and graduate students, researchers, and engineers in aerospace, biomedical, civil, materials science, and mechanical engineering." Wing Kam Liu, PhD, PE, Walter P. Murphy Professor of Mechanical and Civil Engineering, Northwestern University

"Professor Zhangs book on image-derived geometric modeling and meshing will be an indispensable resource for researchers in computational biology and medicine where mesh-generation is a critical bottle neck. The author covers state-of-the-art methods such as isogeometric analysis and T-splines while providing a thorough background and ample practical examples for interdisciplinary readership." Andrew D. McCulloch, Distinguished Professor of Bioengineering and Medicine, University of California, San Diego

"This is a wide-ranging book, bringing together a set of topics not yet covered in a single book. It will give a graduate student or advanced undergraduate a solid foundation to understand a modern pipeline, which collects data from the real world and performs an engineering analysis of it, particularly biomedical data. Topics covered include numerical methods and basic geometric computations, various different 2D and 3D image capture techniques, image preprocessing, surface and volume mesh extraction, T-splines for geometric modeling, and various finite element methods for engineering analysis. The book is to be commended in its cross-discipline approach, including topics from math, computer science, and engineering. Students often just consider each topic in isolation but are not shown how the pieces fit together to make a whole. This book will give them the big picture." Ralph Martin, Cardiff University

Preface vii
1 Introduction and Pipelines
1(6)
1.1 Introduction
1(1)
1.2 Pipelines and Five Topics
2(3)
1.3 Challenges and Advances
5(2)
2 Review of Numerical Methods
7(50)
2.1 Introduction
8(5)
2.2 Linear and Nonlinear Algebraic Equations
13(13)
2.3 Curve Fitting
26(3)
2.4 Ordinary Differential Equations
29(4)
2.5 Eigenvalue Problems
33(3)
2.6 Partial Differential Equations
36(3)
2.7 Numerical Integration
39(4)
2.8 Fourier Analysis
43(5)
2.9 Optimization
48(9)
3 Scanning Techniques and Image Processing
57(42)
3.1 Scanning Techniques
58(11)
3.2 Basic Operations
69(2)
3.3 Filtering
71(5)
3.4 Segmentation
76(9)
3.5 Registration
85(14)
4 Fundamentals to Geometric Modeling and Meshing
99(56)
4.1 Fundamentals
100(8)
4.2 Geometric Objects and Transformations
108(9)
4.3 Curves and Surfaces
117(6)
4.4 Spline-Based Modeling
123(21)
4.5 Isocontouring and Visualization
144(11)
5 Image-Based Triangular and Tetrahedral Meshing
155(38)
5.1 A Review of Unstructured Triangular and Tetrahedral Mesh Generation
156(9)
5.2 Octree-Based Triangular and Tetrahedral Mesh Generation from Images
165(9)
5.3 Resolving Topology Ambiguities
174(5)
5.4 Quality Improvement
179(14)
6 Image-Based Quadrilateral and Hexahedral Meshing
193(36)
6.1 A Review of Unstructured Quadrilateral and Hexahedral Mesh Generation
194(4)
6.2 Octree-Based Quadrilateral and Hexahedral Mesh Generation from Images
198(9)
6.3 Sharp Feature Preservation for CAD Assemblies
207(5)
6.4 Octree vs. RD-Tree Based Adaptive Hexahedral Meshing
212(4)
6.5 Quality Improvement
216(13)
7 Volumetric T-Spline Modeling
229(58)
7.1 Introduction
230(9)
7.2 Converting Unstructured Quadrilateral and Hexahedral Meshes to T-Splines
239(9)
7.3 Polycube-Based Parametric Mapping Methods
248(21)
7.4 Eigenfunction-Based Surface Parameterization
269(4)
7.5 Truncated Hierarchical Catmull--Clark Subdivision Modeling
273(4)
7.6 Weighted T-Spline and Trimmed Surfaces
277(6)
7.7 Incorporating T-Splines into Commercial Software
283(4)
8 Finite Element and Isogeometric Analysis Applications
287(18)
8.1 Introduction to Finite Element Method and Its New Developments
288(4)
8.2 Multiscale Biomolecular Modeling
292(4)
8.3 Patient-Specific Geometric Modeling for Cardiovascular Systems
296(3)
8.4 Applications in Material Sciences
299(6)
Bibliography 305(36)
Index 341
Yongjie Jessica Zhang is an associate professor in the Department of Mechanical Engineering at Carnegie Mellon University with a courtesy appointment in the Department of Biomedical Engineering. She is the co-author of more than 130 publications in peer-reviewed international journals and conference proceedings. She has been a recipient of the Presidential Early Career Award for Scientists and Engineers, NSF CAREER Award, Office of Naval Research Young Investigator Award, USACM Gallagher Young Investigator Award, Clarence H. Adamson Career Faculty Fellow in Mechanical Engineering, George Tallman Ladd Research Award, and Donald L. and Rhonda Struminger Faculty Fellow. Her research interests include computational geometry, mesh generation, computer graphics, visualization, finite element method, isogeometric analysis, and their application in computational biomedicine and engineering. She earned a PhD in computational engineering and sciences from the Institute for Computational Engineering and Sciences (ICES) at the University of Texas at Austin.