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All are welcome at the Symposium on Geometry Processing 2021.
Attendees, presenters, volunteers and sponsors are subject to the SGP 2021 Code of Conduct.


Bradley Rothenberg
CEO, nTopology

Engineering-driven design: a new foundation

nTopology (nTop) solves some of the most difficult problems in shape design, especially those emerging due to additive manufacturing. In doing so, nTop enables new processes for design -- it empowers engineers to design parts that are impossible with older software. To achieve these goals, we use some interesting technologies that are new to engineering software -- specifically basing our modeling tech on Signed Distance Fields (SDFs). This talk describes the new design problems that engineers today face and the software we have developed for solving them.

Bradley Rothenberg is the founder and CEO of nTopology, an engineering software company based in New York City built to enable engineers to design transformative products. nTopology's breakthrough technology unifies geometry and physics into finely tuned digital models, supporting engineers as they collaborate to develop lightweight, optimized parts with the requirements built right in. Bradley studied architecture at Pratt Institute in Brooklyn, New York, and has been developing computational design tools for advanced manufacturing for the last 10-plus years.

Geoffrey Hinton
University of Toronto/Google Research

How to represent part-whole hierarchies in a neural net

I will present a single idea about representation which allows advances made by several different groups to be combined into an imaginary system called GLOM. The advances include transformers, neural fields, contrastive representation learning, distillation and capsules. GLOM answers the question: How can a neural network with a fixed architecture parse an image into a part-whole hierarchy which has a different structure for each image? The idea is simply to use islands of identical vectors to represent the nodes in the parse tree. The talk will discuss the many ramifications of this idea. If GLOM can be made to work, it should significantly improve the interpretability of the representations produced by transformer-like systems when applied to vision or language.

Geoffrey Hinton received his BA in Experimental Psychology from Cambridge in 1970 and his PhD in Artificial Intelligence from Edinburgh in 1978. He did postdoctoral work at Sussex University and the University of California San Diego and spent five years as a faculty member in the Computer Science department at Carnegie-Mellon University. He then became a fellow of the Canadian Institute for Advanced Research and moved to the Department of Computer Science at the University of Toronto. He spent three years from 1998 until 2001 setting up the Gatsby Computational Neuroscience Unit at University College London and then returned to the University of Toronto where he is now an emeritus distinguished professor. From 2004 until 2013 he was the director of the program on "Neural Computation and Adaptive Perception" which is funded by the Canadian Institute for Advanced Research. Since 2013 he has been working half-time for Google in Mountain View and Toronto. Geoffrey Hinton is a fellow of the Royal Society, the Royal Society of Canada, and the Association for the Advancement of Artificial Intelligence. He is an honorary foreign member of the American Academy of Arts and Sciences and the National Academy of Engineering, and a former president of the Cognitive Science Society. He has received honorary doctorates from the University of Edinburgh, the University of Sussex, and the University of Sherbrooke. He was awarded the first David E. Rumelhart prize (2001), the IJCAI award for research excellence (2005), the Killam prize for Engineering (2012) , The IEEE James Clerk Maxwell Gold medal (2016), and the NSERC Herzberg Gold Medal (2010) which is Canada's top award in Science and Engineering. Geoffrey Hinton designs machine learning algorithms. His aim is to discover a learning procedure that is efficient at finding complex structure in large, high-dimensional datasets and to show that this is how the brain learns to see. He was one of the researchers who introduced the back-propagation algorithm and the first to use backpropagation for learning word embeddings. His other contributions to neural network research include Boltzmann machines, distributed representations, time-delay neural nets, mixtures of experts, variational learning, products of experts and deep belief nets. His research group in Toronto made major breakthroughs in deep learning that have revolutionized speech recognition and object classification.

Lining Yao
Carnegie Mellon University

Computing Morphing Matter: the Marriage of Geometry and Hidden Forces

Morphing Matter is an interplay of geometry and hidden forces. Lining Yao, the director of Morphing Matter Lab, will share her team's experiences of computing, designing, and fabricating morphing mechanisms that leverage both geometrical and physical knowledge of materials. Lining will unfold a few marriages of geometry and forces in the talk: a conformal map interconnecting beams shrinking and fighting for the lowest entropy, a frustum-shaped groove interfering disks swelling with differential diffusion rate, and a triangulated filler path affecting spacer fabric deforming with biased shear forces. Novel morphing mechanisms and applications also come from these marriages, such as self-assembling furniture, crawling soft robots, and morphing pasta.

Lining Yao is an Assistant Professor of Human-Computer Interaction Institute at Carnegie Mellon University (CMU), School of Computer Science, directing the Morphing Matter Lab. Lining also holds courtesy appointments at Mechanical Engineering and Material Sciences and Engineering at CMU. Morphing Matter lab develops processes, materials, tools, and applications of adaptive, dynamic, and intelligent morphing matter from nano to macro scales. Research often combines material science, computational fabrication, and creative design practices. The mission is to advance both science and society with the design of morphing matter. Lining and her lab work anti-disciplinarily, publishing and exhibiting across science, engineering, design, and art. Lining gained her Ph.D. from the MIT Media Lab. She is a Wired UK fellow, CMU Provost's Inclusive Teaching Fellow, and a recipient of the NSF CAREER Award.

Graduate School

Shape approximation and applications

Shape approximation methods aim at generating a light weight proxy from high resolution surfaces, such as 3D scans. The proxy can then be used a convenient substitute to the actual shape for various compute-intensive tasks such as retrieval, physics simulation, freeform modeling, level-of-detail rendering, performance capture reverse engineering and more. Depending on the application, the nature and desired properties of the proxy may vary. Often, its efficient yet controllable generation remains an open problem. In this course, we will discuss a variety of approaches to shape approximation, including mesh simplification, shape recognition, mathematical morphology and probabilistic models. We will also review mechanisms to link a proxy to the original shape, establishing ways to propagate information from one to the other. Last, we'll discuss applications and some research directions in this space that could be fruitful for computer graphics and beyond.

Projective Dynamics/Simulation

Physically-based simulations have been used more and more in recent interactive applications. In this talk, we will cover the key ideas we have been using to accelerate our simulations, utilizing the geometric information of the simulated objects. We will start from Projective Dynamics, an acceleration method to simulate mass-spring systems, and some simple finite element models such as the as-rigid-as-possible model. We show that Projective Dynamics can be seen as a quasi-Newton method that approximates the Hessian matrix of the elastic potential with a topological-aware Laplacian matrix. Other than assembling the Laplacian matrices, we can also use the mesh topology to propagate information throughout the entire simulated mesh. We will then show an efficient unstructured Galerkin multigrid algorithm using this idea. We summarize these strategies we used as localizing the nonlinearity and grouping the similars. During this course, we use these strategies as an example of how we use geometric information to accelerate simulations. And we look forward to seeing more geometric-based ideas in accelerated physically-based simulations.

Geometric Computing with Python

In this course, we present an easy-to-use Python-based workflow for applications in geometric computing and visualization. Our libraries have a shallow learning curve while also enable programmers to accomplish a wide variety of complex tasks. Furthermore, we adopt NumPy arrays as a common interface, which greatly simplifies serialization and interoperability with existing scientific computing packages. Finally, our libraries are performant, with most computations in C++ and a minimal overhead interface to Python. In addition, we present a demo on using the libraries to implement a geometry processing algorithm with ease. By the end of the course, attendees will have exposure to a set of simple, composable, and high-performance tools for geometric computing.

Maps Between Surfaces

Maps between the surfaces of two or more 3D models are a core building block in many geometry processing tasks. They allow transferring data (e.g. textures, labels, annotations, animations) from one object to another, they are used to establish correspondence within a data set (e.g. for machine learning purposes), and they are required when algorithms process multiple shapes at once (e.g. in co-analysis contexts or in co-processing scenarios like compatible remeshing). In this course we dive into theoretical as well as practical aspects of such maps from a computational point of view. Our main focus will be on homeomorphisms: maps that satisfy strict continuity and bijectivity criteria. These avoid any kind of undesirable tears or folds and thus provide a well-defined foundation for reliable algorithms. In three blocks, we will learn (1) how to computationally represent maps, (2) how to initially construct valid maps, in particular homeomorphisms, and (3) how to improve their quality via continuous optimization. In each chapter, we will work our way up from the well-studied case of maps in the plane to the more challenging case of maps between discrete curved surfaces.

Deep Learning on Meshes

The irrefutable success of deep learning on structured data (such as images and text) has sparked significant interest in its applicability to problems in geometry processing. In this talk, we will discuss the key challenges and current solutions for using mesh convolutional neural networks on the unstructured mesh representation for problems in geometry processing. We will outline the design choices and implications of (1) learning on different mesh elements (vertices, faces, edges); (2) invariance to rigid transformations; (3) invariance and equivariance to the order of mesh elements; (4) input features, among others. We discuss existing applications of mesh convolutional neural networks, as well as potential promising future directions.

Directional Field Processing

Directional fields are core objects of geometry processing. They represent movement, flow, alignment, or geometric transformations. Their applications range from fluid simulation, through architectural design, to mesh generation. We will discuss the theoretical and empirical challenges in representing and discretizing directional fields on surfaces and in volumes, and some of their desired properties with relation to the applications; namely, smoothness, integrability, constrained size or symmetry, and more. We will further discuss how recent approaches optimized for these properties. Finally, we will demonstrate some of the common design paradigms for directional fields using the software library Directional.

Digital Geometry

Digital Geometry is about the processing of topological and geometrical objects defined in regular lattices (e.g. collection of voxels in 3d). Whereas representing quantities on regular, hierarchical or adaptive grids is a classical approach to spatially discretize a domain, processing the geometry of such objects requires us to revisit classical results from continuous or discrete mathematics. In this course, we will review tools and results that have been designed specifically to the geometry processing in Z^d. More precisely, we will present how processing regularly spaced data with integer coordinate embeddings may impact computational geometry algorithms, and how stability results (multigrid convergence) of differential quantities estimators (curvature tensor, Laplace-Beltrami,..) on boundaries of digital objects can be designed. Finally, we will present some elements of discrete calculus on digital surfaces. Lastly, we will briefly give a demo of the DGtal library ( which contains a wide class of algorithms dedicated to the processing of such specific data.

An Introduction to Geometry Processing Programming in MATLAB with gptoolbox

It is easy and convenient to use MATLAB for research and teaching in geometry processing. In this tutorial we will teach you the very basics of geometry processing in MATLAB using the simple library gptoolbox, which implements a plethora of standard geometry processing algorithms. We will show you how to do basic linear algebra operations in MATLAB, how to manipulate geometric objects, how to display surfaces, and how to do some popular geometry processing operations in MATLAB's powerful interactive environment.

A Quick Introduction to the Laplacian and Bilaplacian Through the Theory of Partial Differential Equations

In this course we will learn about the Laplacian and Bilaplacian operator, and develop mathematical tools for discussing these two popular operators in geometry processing. We will approach Laplacian and Bilaplacian from the point of view of the mathematical theory of partial differential equations and numerical analysis of finite elements. We will start with a solid mathematical foundation for the definition of Laplacian and Bilaplacian, as well as their associated partial differential equations, and discuss their solvability. Then we will discretize these operators using the finite element and mixed finite element methods, and superficially investigate their convergence. Having implemented the discrete Bilaplacian for triangle meshes, we will explore the application of this discrete operator to a variety of geometry processing problems, from smoothing and surface animation to distance computation. After completing this course you will be able to define Laplacian and Bilaplacian as operators on Sobolev spaces, comment on their solvability, discretize them with the mixed finite element method, and know of some of the interesting applications for which the Bilaplacian can be used.

Technical Papers

Proceedings on EG Digital Library

Virtual USB Key (1.1GB)

Data & Acquisition chaired by Qingnan Zhou

  • A Benchmark Dataset for Repetitive Pattern Recognition on Textured 3D Surfaces
    Stefan Lengauer
    Ivan Sipiran
    Reinhold Preiner
    Tobias Schreck
    Benjamin Bustos
  • SimJEB: Simulated Jet Engine Bracket Dataset
    Eamon Whalen
    Azariah Beyene
    Caitlin Mueller
  • A Robust Multi-View System for High-Fidelity Human Body Shape Reconstruction
    Qitong Zhang
    Lei Wang
    Linlin Ge
    Shan Luo
    Taihao Zhu
    Feng Jiang
    Jimmy Ding
    Jieqing Feng
  • Estimating Garment Patterns from Static Scan Data invited from Computer Graphics Forum
    Seungbae Bang
    Maria Korosteleva
    Sung-Hee Lee

Shape Synthesis & Editing chaired by Yotam Gingold

  • Gauss Stylization: Interactive Artistic Mesh Modeling based on Preferred Surface Normals
    Maximilian Kohlbrenner
    Ugo Finnendahl
    Tobias Djuren
    Marc Alexa
  • Normal-Driven Spherical Shape Analogies
    Hsueh-Ti Derek Liu
    Alec Jacobson
  • Roominoes: Generating Novel 3D Floor Plans From Existing 3D Rooms
    Kai Wang
    Xianghao Xu
    Leon Lei
    Selena Ling
    Natalie Lindsay
    Angel Xuan Chang
    Manolis Savva
    Daniel Ritchie
  • Blending of hyperbolic closed curves
    Aziz Ikemakhen
    Taoufik Ahanchaou

Shape matching chaired by Edward Chien

  • Discrete Optimization of Shape Matching
    Jing Ren
    Simone Melzi
    Peter Wonka
    Maks Ovsjanikov
  • A Data-Driven Approach to Functional Map Construction and Bases Pursuit
    Omri Azencot
    Rongjie Lai
  • Globally Injective Geometry Optimization with Non-Injective Steps
    Matthew Overby
    Danny Kaufman
    Rahul Narain

Surface Reconstruction chaired by Raphaelle Chaine

  • Delaunay Meshing and Repairing of Defect-laden NURBS Models
    Xiao Xiao
    Pierre Alliez
    Laurent Busé
    Laurent Rineau
  • Progressive Discrete Domains for Implicit Surface Reconstruction
    Tong Zhao
    Pierre Alliez
    Jean-Marc Thiery
    Tamy Boubekeur
    Laurent Busé
  • Scalable Surface Reconstruction with Delaunay-Graph Neural Networks
    Raphael Sulzer
    loic landrieu
    Renaud Marlet
    Bruno Vallet

Direction fields & quads chaired by Chengcheng Tang

  • Simpler Quad Layouts using Relaxed Singularities
    Max Lyon
    Marcel Campen
    Leif Kobbelt
  • Learning Direction Fields for Quad Mesh Generation
    Alexander Dielen
    Isaak Lim
    Max Lyon
    Leif Kobbelt
  • Surface Map Homology Inference
    Janis Born
    Patrick Schmidt
    Marcel Campen
    Leif Kobbelt

Differential operators chaired by Philipp Herholz

  • Stable and efficient differential estimators on oriented point clouds
    Thibault Lejemble
    David Coeurjolly
    Loïc Barthe
    Nicolas Mellado
  • The Diamond Laplace for Polygonal and Polyhedral Meshes
    Astrid Bunge
    Mario Botsch
    Marc Alexa
  • Frame Field Operators
    David Palmer
    Oded Stein
    Justin Solomon

Distances chaired by Nicholas Sharp

  • Geodesic Distance Computation via Virtual Source Propagation
    Philip Trettner
    David Bommes
    Leif Kobbelt
  • Practical Computation of the Cut Locus on Discrete Surfaces
    Claudio Mancinelli
    Marco Livesu
    Enrico Puppo
  • On Landmark Distances in Polygons
    Craig Gotsman
    Kai Hormann

Fabrication chaired by Daniele Panozzo

  • Developable Approximation via Gauss Image Thinning
    Alexandre Binninger
    Floor Verhoeven
    Philipp Herholz
    Olga Sorkine-Hornung
  • Wearable 3D machine knitting invited from IEEE TVCG
    Kui Wu
    Marco Tarini
    Cem Yuksel
    James Mccann
    Xifeng Gao
  • Fabrication-Aware Reverse Engineering for Carpentry
    James Noeckel
    Haisen Zhao
    Brian Curless
    Adriana Schulz