CSIAM GDC Symposium on Geometric Computing

“几何计算前沿”国际研讨会

Introduction

CSIAM GDC Symposium on Geometric Computing is the premier venue for disseminating new research ideas and cutting-edge results in geometric design, processing and computing. In this symposium, concepts from mathematics and computer science are studied and applied to offer new insights and design efficient algorithms for acquisition, modeling, analysis, manipulation, simulation, fabrication and other types of processing of 3D models and shape collections.

The symposium is organized by Prof. Ligang Liu of the GCL lab (http://gcl.ustc.edu.cn) and will be held at USTC on June 11, 2024. We will invite three distinguished international researchers, including Denis Zorin from New York University, USA, Justin Solomon from MIT, USA, and Eitan Grinspun from University of Toronto, Canada, and seven young researchers from USTC GCL to give talks at this symposium, covering topics including conformal parameterizations, developable approximation, subdivision surfaces, 3D reconstruction, Delaunay triangulation, spectral segmentation, computational fabrication, mechanical systems, and digital human. For non-USTC participants, please fill in the registration form and send it to us by June 9, 2024.

• Date: Tuesday, June 11, 2024

• Venue: Room 5101, East Campus, USTC

Program

Speakers and Talks

• Title: Differentiable physical simulation for computational fabrication


• Speaker: Denis Zorin, New York University, USA


• Abstract: Differentiable physical solvers along with the solution of a problem, compute gradients of an objective or a set of objectives with respect to the simulation parameters. This type of solvers can be used for efficient optimization in many contexts. In this talk, I will describe our work on developing a general differentiable solver for time-dependent deformation problems with contact and friction. Our approach uses a finite element discretization with a high-order time integrator coupled with the recently proposed incremental potential contact method for handling contact and friction forces to solve PDE-constrained optimization problems on scenes with a complex geometry, and support gradients with respect to almost all physical parameters involved in the physical problem description: shape, material parameters, friction parameters, and initial conditions. Our formulation is very efficient, with typical additional cost for gradient computation of less than 10% of the simulation itself. One of the important applications of differentiable simulation is engineering design, computational fabrication in particular. I will describe several applications including designing lattice structures with target material properties, friction-based assembly optimization, and pneumatic actuators in robotics.


• Short bio: Denis Zorin is Silver Professor of Computer Science and Mathematics and the Chair of the Computer Science Department at the Courant Institute of Mathematical Sciences. Prior to joining Courant, he was a postdoc at Stanford University, and completed his PhD thesis at California Institute of Technology. Denis’s primary interests span the domains of geometric modeling, geometry processing and scientific computing. His main contributions are in the theory and practical algorithms for subdivision surfaces, efficient algorithms for deformation and parameterization, msshing, computational methods for integral equations, and computational fabrication. His awards include ACM Fellow, SIGGRAPH Computer Graphics Achievement Award and SIGGRAPH Academy membership, ACM Gordon Bell Prize, Sloan Foundation Fellowship, NSF Career award, and several IBM Partnership awards. He served on many program committees and editorial boards, and his former students and postdocs hold faculty positions at many universities, including Stanford, University of Toronto, University of Texas and University of Michigan.


• Homepage: https://cims.nyu.edu/gcl/denis.html


• E-mail: dzorin@cs.nyu.edu

• Title: Alternative Function Representations for Geometry Processing


• Speaker: Justin Solomon, MIT, USA


• Abstract: Geometry processing for computer graphics often yields numerical problems that are slow to solve and prone to local optima. In this talk, I will share how change-of-variables strategies can make geometry processing problems far more tractable. In particular, we will show how optimizing for Riemannian metrics and deformation tensors can facilitate classical mesh-based tasks like parameterization and skinning weights computation, and we will show how new neural network representations facilitate optimization of classical tasks in geometry processing like computation of generalized barycentric coordinates.


• Short bio: Justin Solomon is an Associate Professor of Electrical Engineering and Computer Science and a member of the Computer Science and Artificial Intelligence Laboratory (CSAIL) at MIT, where he leads the Geometric Data Processing Group. Prior to joining the MIT faculty, Solomon was an NSF Mathematical Sciences Postdoctoral Research Fellow in Princeton's Program in Applied and Computational Mathematics. He received his PhD in computer science from Stanford University in 2015, where he also received an MS in computer science (2012) and a BS in mathematics and computer science (2010). During his PhD, Solomon was supported by the National Defense Science and Engineering Graduate Fellowship (NDSEG), the Hertz Fellowship, and the NSF Graduate Research Fellowship Program (GRFP). Solomon also has worked at Pixar Animation Studios (2007-2012) and MITRE Corporation (2005-2007). His textbook Numerical Algorithms covers numerical methods for geometry, graphics, robotics, and other computational applications.


• Homepage: https://people.csail.mit.edu/jsolomon/


• E-mail: jsolomon@mit.edu

• Title: Adventures in Discretization of Mechanical Systems


• Speaker: Eitan Grinspun, The University of Toronto, Canada


• Abstract: The connections between geometry and mechanics have been explored for centuries. How these connections shape computation is a question we are just beginning to explore. Fundamental to answering this question is to understand the role of discretization, the act of transforming a description of a physical system from the language of smooth differential geometry to the finite and discrete language understood by computers.
  
  Our group has been exploring two views on discretization.
  
  Our work on Discrete Differential Geometry (DDG) considers discretization perhaps the most important aspect of the modeling process. DDG seeks to build a discrete geometric model of the physical system from the ground up, mimicking the axioms, structures, and symmetries of the smooth setting. The result has been readily computable models of elastic rods, thin shells, liquid threads, droplets, and soap films, that preserve qualitative aspects of the system, such as invariants and conservation laws. These models have been applied by others to film, medicine, engineering, robotics and condensed matter research.
  
  More recently, we have begun to explore the idea of being independent of discretization. Methods that are agnostic to a specific discretization have the potential to provide flexibility to mix and match mesh resolutions, connectivity, and type (tetrahedral, hexahedral) in simulations. We have been developing a flexible, discretization-agnostic approach to reduced-order modeling (ROM), which simplifies complex simulations by approximating the behavior of a system using a simplified kinematic representation. Unlike earlier ROM works, our ROM may be trained on multiple geometries undergoing multiple loading conditions, with multiple discretizations. This opens the door to novel applications of reduced order modeling. We can now accelerate simulations that modify the geometry at runtime, for instance via cutting, hole punching, and even swapping the entire mesh.


• Short bio: Eitan Grinspun is Associate Chair, Academic Recruiting at the Department of Computer Science at the University of Toronto, where he is also a Professor of Computer Science and Mathematics. He was previously the Director of the Columbia Computer Graphics Group at Columbia University (2004–2021), Professeur d'Université Invité at l'Université Pierre et Marie Curie in Paris (2009), a Research Scientist at New York University's Courant Institute (2003–2004), a graduate student at the California Institute of Technology (1997–2003), and an undergraduate in Engineering Science at the University of Toronto (1993–1997). He has been an NVIDIA Fellow (2001), Everhart Distinguished Lecturer (2003), NSF CAREER Awardee (2007), Alfred P. Sloan Research Fellow (2010-2012), Popular Science magazine's "Brilliant Ten Scientists" (2011), and Fast Company magazine's "Most Creative People in Business" (2013). Technologies developed by his lab are used in products such as Adobe Photoshop & Illustrator, at major film studios, and in soft matter physics and engineering research. He has been profiled in The New York Times, Scientific American, New Scientist, and mentioned in Variety. His film credits include The Hobbit, Rise of the Planet of the Apes, and Steven Spielberg's The Adventures of Tintin.


• Homepage: https://www.dgp.toronto.edu/~eitan/


• E-mail: eitan@cs.toronto.edu

• Title: Rigid and Non-rigid Registration for 3D Reconstruction


• Speaker: Juyong Zhang, USTC


• Abstract: Efficient and high quality 3D reconstruction is a key research problem in computer graphics and 3D vision. Among them, rigid and non-rigid registration between geometric data is a very important step in the entire 3D reconstruction process, and the registration accuracy will directly determine the final 3D reconstruction accuracy. In this talk, I will report on our series of geometric registration research works on the correspondence construction, the registration energy design, and its corresponding numerical optimization algorithms.


• Short bio: Juyong Zhang is a professor in the School of Mathematical Sciences at University of Science and Technology of China. He received the BS degree from the University of Science and Technology of China in 2006, and the Ph.D degree from Nanyang Technological University, Singapore. He mainly conducts research at the intersection of Vision, Graphics, and AI with a special focus on capturing, modeling and synthesizing objects, humans and large-scale scenes. He is an associate editor of IEEE Transactions on Multimedia and IEEE Computer Graphics and Applications.


• Homepage: http://staff.ustc.edu.cn/~juyong/


• E-mail: jjuyong@ustc.edu.cn

• Title: Non-uniform subdivision: recent development


• Speaker: Xin Li, USTC


• Abstract: This talk review our recent decelopment on non-uniform subdivision, which is an important technology to generalize non-uniform rational B-splines to arbitrary topology.


• Short bio: Li Xin is a professor and doctoral supervisor at the School of Mathematical Sciences, University of Science and Technology of China. He has successively won the National Excellent Doctoral Dissertation, the Second Prize in Science and Technology of the Ministry of Education, the Young Scholar Award of the Chinese Society of Industry and Applied Mathematics, and was selected as an Excellent Member of the First Innovation Promotion Association of the Chinese Academy of Sciences. His main research areas are computer-aided design and isogeometric analysis, with a particular focus on the underlying geometric representation theory in CAD geometry engines and related technologies for integrated design and analysis. The related achievements have been directly applied in multiple domestic and foreign enterprises.


• Homepage: http://staff.ustc.edu.cn/~lixustc/


• E-mail: lixustc@ustc.edu.cn

• Title: A Spectral Segmentation Method for Large Meshes


• Speaker: Weihua Tong, USTC


• Abstract: Mesh segmentation is a fundamental and critical task in mesh processing, and it has been studied extensively in computer graphics and geometric modeling communities. However, current methods are not well suited for segmenting large meshes which are now common in many applications. This paper proposes a new spectral segmentation method specifically designed for large meshes inspired by multi-resolution representations. Building on edge collapse operators and progressive mesh representations, we first devise a feature-aware simplification algorithm that can generate a coarse mesh which keeps the same topology as the input mesh and preserves as many features of the input mesh as possible. Then, using the spectral segmentation method proposed in Tong et al. (IEEE Trans Vis Comput Graph 26(4):1807–1820, 2020), we perform partition on the coarse mesh to obtain a coarse segmentation which mimics closely the desired segmentation of the input mesh. By reversing the simplification process through vertex split operators, we present a fast algorithm which maps the coarse segmentation to the input mesh and therefore obtain an initial segmentation of the input mesh. Finally, to smooth some jaggy boundaries between adjacent parts of the initial segmentation or align with the desired boundaries, we propose an efficient method to evolve those boundaries driven by geodesic curvature flows. As demonstrated by experimental results on a variety of large meshes, our method outperforms the state-of-the-art segmentation method in terms of not only speed but also usability.


• Short bio: Weihua Tong is an associate professor of School of Mathematical Sciences at University of Science and Technology of China(USTC). He earned his Bachelor's degree in Information and Computation Sciences from USTC in 1999, followed by a Ph.D. in Computational Mathematics from the same institution in 2005. He visited Internet Graphics Group at Microsoft Research Asia in 2004, did postdoctoral studies at Seoul National University (Korea) and Nanyang Technological University (Singapore) in 2007 and 2010 respectively, and was a visiting scholar in Courant Institute of Mathematical Sciences at New York University (USA) during 2013 and 2014. His current interests include sparse representation and optimization, surface reconstruction, mesh segmentation, parameterization, geometric continuous spline surfaces, deep learning method for digital geometry processing, et al. He has published many papers in some international journals, such as Computer-Aided Design, Computer Aided Geometric Design, Computer Methods in Applied Mechanics and Engineering, Communications in Mathematics and Statistics, Journal of Computational Mathematics, Graphical Models, ACM Transactions on Graphics, IEEE Transactions on Visualization and Computer Graphics.


• Homepage: http://staff.ustc.edu.cn/~tongwh/


• E-mail: tongwh@ustc.edu.cn

• Title: Parallel 3D Delaunay triangulation


• Speaker: Renjie Chen, USTC


• Abstract: We propose a fully GPU parallel algorithm for constructing the Delaunay triangulation of a given point set in R3. We extend the Local Delaunay Lemma of Chen & Gotsman to R3, allowing to localize the Delaunay neighbors within a confined region around each point. By leveraging this lemma, we efficiently construct the Delaunay triangulation via half-space intersection, allowing it to surpass the state-of-the-art by a factor of three.


• Short bio: Renjie Chen is a professor at the University of Science and Technology of China (USTC). He obtained his Ph.D. degree in Applied Mathematics from Zhejiang University in 2010. Before joining USTC, he had worked at the Technion and UNC Chapel Hill as a postdoctoral researcher and at the Max Planck Institute for Informatics as a senior researcher. His research interest include geometric processing and modeling, computational geometry, and glasses-free 3D displays.


• Homepage: http://staff.ustc.edu.cn/~renjiec/


• E-mail: renjiec@ustc.edu.cn

• Title: Piecewise Developable Approximations for Triangular Meshes


• Speaker: Xiao-Ming Fu， USTC


• Abstract: Shape modeling is fundamental for many computer graphics, engineering, and architecture applications. In manufacturing-related applications, modeling a shape with developable surfaces provides an opportunity to reduce manufacturing and construction costs because only flat pieces of material need to be folded, bent, or rolled. Since most shapes are not globally developable, we discuss how to automatically model shapes with piecewise developable patches. In this talk, I will introduce our latest progress in piecewise developable approximations of triangular meshes.


• Short bio: Xiao-Ming Fu is an associate professor at the School of Mathematical Sciences, University of Science and Technology of China. He received a BSc degree in 2011 and a PhD degree in 2016 from University of Science and Technology of China. His research interests include geometric processing and computer-aided geometric design. His research work can be found at his research website: https://ustc-gcl-f.github.io/.


• Homepage: https://ustc-gcl-f.github.io/


• E-mail: fuxm@ustc.edu.cn

• Title: Generating Sparse Cone Singularities for Conformal Parameterizations


• Speaker: Qing Fang, USTC


• Abstract: Conformal parameterizations are widely applicable in geometry processing due to their property of angle preservation. They are relatively easy to compute, but can significantly distort areas. Introducing cone singularities, i.e. points with non­zero Gaus­sian curvature can effectively reduce this area distortion. However, determining high­-quality cone configurations (number, placement, and angle) is a notoriously difficult problem.
  
  In this talk, I will present our recent progress in the sparse cone generation algorithms, which focuses on placing the minimal number of cones required to reduce the area distortion of the conformal parameterization within a given bound. Further applications of cones and the corresponding challenges will also be discussed.


• Short bio: Qing Fang is a Postdoctoral Researcher in the School of Mathematical Sciences, University of Science and Technology of China, supervised by Ligang Liu and Xiao-Ming Fu. His research interests include geometric processing and computational fabrication. He received his Ph.D. in 2021 from University of Science and Technology of China.


• Homepage: https://qingfang1208.github.io/


• E-mail: fq1208@mail.ustc.edu.cn

• Title: Efficient Digital Human Modeling with Generative Priors


• Speaker: Yudong Guo, USTC


• Abstract: Efficient and high-quality modeling of hyper-realistic 3D digital humans remains a critical technical challenge. Recently, diffusion models have achieved remarkable breakthroughs in portrait generation and editing. However, due to the scarcity of high-quality data, 3D digital human generation still lags behind traditional image generation models. In this presentation, I will introduce our latest research on leveraging generative priors to rapidly create naturally drivable and editable 3D digital humans that are virtually indistinguishable from real individuals, using simple inputs like monocular videos or single images.


• Short bio: Yudong Guo is an Associate Researcher at the University of Science and Technology of China (USTC). He received his Ph.D. degree in 2021 and his Bachelor's degree in 2015, both from USTC. His research lies at the intersection of computer vision and graphics, particularly in cutting-edge techniques for digital human modeling. His research achievements have been applied to programming at organizations including China Central Television (CCTV) and Hangzhou TV Station.


• Homepage: https://yudongguo.github.io/


• E-mail: yudongguo@mail.ustc.edu.cn

组织机构

• 主办单位：中国工业与应用数学学会(CSIAM)

• 协办单位：CSIAM几何设计与计算专业委员会(GDC)

• 承办单位：中国科学技术大学图形计算与感知交互安徽省重点实验室