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[Xianfeng David Gu]
[Xianfeng David Gu]
Department of Computer Science, State University of New York at Stony Brook, USA
Dr. David Xianfeng Gu is a New York Empire Innovation Professor at the Department of Computer Science, Stony Brook University. David received his Ph.D degree from the Department of Computer Science, Harvard University in 2003, supervised by the Fields medalist Prof. Shing-Tung Yau, and B.S. degree from Tsinghua University, Beijing, China in 1994. David's research focuses on applying modern topology and geometry theories in engineering and medical fields. With his collaborators, David systematically develops discrete theories and computational algorithms in the interdisciplinary field: Computational Conformal Geometry, and applies them for real problems, such as global surface parameterization based on Hodge decomposition theorem in graphics, deformable shape registration based on Teichmuller map in vision, structured mesh generation based on Abel-Jacobi theorem in solid modeling, curvature convergence analysis in geometric processing, explainable generative models based on geometric optimal transportation in deep learning, brain mapping and virtual colonoscopy in medical imaging and so on. Recently, David and his collaborators have proved the discrete surface uniformization theorem using surface Ricci flow, the Alexandrov theorem and Minkowski theorem using geometric optimal transportation, the singularity configuration of structured quad-mesh using Abel-Jacobi theorem. David has broad collaborations with companies in CAD industry, including Simens, Cadence and Ansys. David is a recipient of Morningside Gold Medal of Applied Mathematics in 2013; National Science Foundation Faculty Early Career Award, 2005.
Title: Structured Mesh Generation
Abstract： Structured surface quadrilateral mesh generation and volume hexahedral mesh generation are crucial for geometric modeling and processing. But the structured meshing problem is intrinsically challenging. This talk focuses on the recent development to tackle these challenges based on modern topological and geometric theories.
It is well known that a closed torus does not admit a quad-mesh with only two singularities, whose valences are 3 and 5 respectively. But the theoretic proof is highly non-trivial. Although it seems to be a combinatorial problem, it has deep roots in the characteristic class theory of holomorphic line bundles, especially the Abel-Jacobi theorem. This discovery leads to the governing equations of the configurations of quad-mesh singularities. By solving these equations using Hodge theory and surface Ricci flow, the high quality, automatic quad-mesh generation algorithms can be developed.
The singularity configuration of volumetric hex-meshes becomes more complicated, due to the fact that the fundamental group of the manifold of crosses is non-Abelian, hence the classical topological obstruction theory for fiber bundles can not be applied. Instead, the recent breakthrough of the proof of Thurston's virtual Haken conjecture offers novel insights to the problem, by using the cube-complex theory it is promising to conquer the problem with theoretic guarantees.
[Hanan Samet]
[Hanan Samet]
Department of Computer Science, University of Maryland, USA
Hanan Samet (http://www.cs.umd.edu/~hjs/) is a Distinguished University Professor of Computer Science at the University of Maryland, College Park and is a member of the Institute for Computer Studies. He is also a member of the Computer Vision Laboratory at the Center for Automation Research where he leads a number of research projects on the use of hierarchical data structures for database applications, geographic information systems, computer graphics, computer vision, image processing, solid modeling, games, robotics, and search. He received the B.S. degree in engineering from UCLA, and the M.S. Degree in operations research and the M.S. and Ph.D. degrees in computer science from Stanford University. His doctoral dissertation dealt with proving the correctness of translations of LISP programs which was the first work in translation validation and the related concept of proof-carrying code. He is the author of the recent book "Foundations of Multidimensional and Metric Data Structures" (http://www.cs.umd.edu/~hjs/multidimensional-book-flyer.pdf) published by Morgan-Kaufmann, an imprint of Elsevier, in 2006, an award winner in the 2006 best book in Computer and Information Science competition of the Professional and Scholarly Publishers (PSP) Group of the American Publishers Association (AAP), and of the first two books on spatial data structures "Design and Analysis of Spatial Data Structures", and "Applications of Spatial Data Structures: Computer Graphics, Image Processing, and GIS", both published by Addison-Wesley in 1990. He is the Founding Editor-In-Chief of the ACM Transactions on Spatial Algorithms and Systems (TSAS), the founding chair of ACM SIGSPATIAL, a recipient of a Science Foundation of Ireland (SFI) Walton Visitor Award at the Centre for Geocomputation at the National University of Ireland at Maynooth (NUIM), 2009 UCGIS Research Award, 2010 CMPS Board of Visitors Award at the University of Maryland, 2011 ACM Paris Kanellakis Theory and Practice Award, 2022 SMA Bezier Award, 2014 IEEE Computer Society Wallace McDowell Award, and a Fellow of the ACM, IEEE, AAAS, IAPR (International Association for Pattern Recognition), UCGIS (University Consortium for Geographic Science), and SMA. He received best paper awards in the 2007 Computers & Graphics Journal, the 2008 ACM SIGMOD and SIGSPATIAL ACMGIS (also 10 year impact award) Conferences, the 2012 SIGSPATIAL MobiGIS Workshop, and the 2013 SIGSPATIAL GIR Workshop, as well as best demo paper awards at the 2011 and 2016 SIGSPATIAL ACMGIS Conferences. His paper at the 2009 IEEE International Conference on Data Engineering (ICDE) was selected as one of the best papers for publication in the IEEE Transactions on Knowledge and Data Engineering. He was elected to the ACM Council as the Capitol Region Representative for the term 1989-1991, and was an ACM Distinguished Speaker for the 2008-2015 and 2018-terms.
Title: Sorting in space
Abstract： The representation of spatial data is an important issue in computer graphics, solid modeling, computer vision, geographic information systems, and robotics. A wide number of representations is currently in use. Recently, there has been much interest in hierarchical data structures such as quadtrees, octrees, R-trees, etc. The key advantage of these representations is that they provide a way to index into space. In fact, they are little more than multidimensional sorts. They are compact and, depending on the nature of the spatial data, they save space as well as time and also facilitate operations such as search. In particular, they act like dimension-reducing devices which makes them useful in solid modeling as well as imaging. In this talk we give a brief overview of hierarchical spatial data structures and related research results such as k-instantiation vs: bucketing where the decomposition process is decoupled from the aggregation process and nearest neighbor finding is with respect to data drawn from a spatial network with dramatic savings stemming from using the dimension-reducing property of quadtrees. In addition, we point out the VASCO JAVA applet which illustrate these methods (found at http://www.cs.umd.edu/~hjs/quadtree/index.html).
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