Geometric Modeling and Mesh Generation from Scanned Images

Introduction and Pipelines
Introduction
Pipelines and Five Topics
Challenges and Advances

Review of Numerical Methods
Introduction
Linear and Nonlinear Algebraic Equations Curve Fitting
Ordinary Differential Equations
Eigenvalue Problems
Partial Differential Equations
Numerical Integration
Fourier Analysis
Optimization

Scanning Techniques and Image Processing
Scanning Techniques
Basic Operations
Filtering
Segmentation
Registration

Fundamentals to Geometric Modeling and Meshing
Fundamentals
Geometric Objects and Transformations
Curves and Surfaces
Spline-Based Modeling
Isocontouring and Visualization

Image-Based Triangular and Tetrahedral Mesh Generation
A Review of Unstructured Triangular and Tetrahedral Meshing
Octree-Based Triangular and Tetrahedral Meshing from Images
Resolving Topology Ambiguities
Quality Improvement

Image-Based Quadrilateral and Hexahedral Mesh Generation
A Review of Unstructured Quadrilateral and Hexahedral Meshing
Octree-Based Quadrilateral and Hexahedral Meshing from Images
Sharp Feature Preservation for CAD Assemblies
Octree vs RD-Tree Based Adaptive Hexahedral Meshing
Quality Improvement

Volumetric T-Spline Modeling
Introduction
Converting Unstructured Quadrilateral and Hexahedral Meshes to T-Splines
Polycube-Based Parametric Mapping Methods
Eigenfunction-Based Surface Parameterization
Truncated Hierarchical Catmull-Clark Subdivision Modeling
Weighted T-Spline and Trimmed Surfaces
Incorporating T-Splines into Commercial Software

Finite Element and Isogeometric Analysis Applications
Introduction to Finite Element Method and Its New Developments
Multiscale Biomolecular Modeling
Patient-Specific Geometric Modeling for Cardiovascular Systems
Applications in Materials Science

Biography

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.

"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 Zhang’s 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