SGP Summer School Presentations

2025

Graduate School

For several years now, SGP offers a colocated Graduate School on Geometry Processing that features several lectures in various topics in the field, held by world-class experts and lead researchers in the respective discipline.

The school is typically addressed to PhD students and other postgraduate students, with an interest in Geometry Processing, but offers introductory lectures suitable for many other practitioners and researchers. All participants to SGP 2025 have access to the SGP Graduate School. Videos for lectures from previous years are available here.

Geometry, Topology and Physics of 3D Shape Generative Models

Existing 3D generative models predominantly focus on adopting cutting-edge generative models (e.g., GAN, VAE, auto-regressive models, normalizing flows, and diffusion models) under some 3D representations (e.g., mesh, voxels, implicit representations, and point clouds). Although these methods show promising visual results, they do not model and therefore do not preserve important geometric, physical, and topological priors on synthetic shapes. This lecture will teach recent advances on modeling these priors into deep neural networks, focusing on network design for 3D neural representations and regression losses for 3D shape generative models. The course is self-contained but prior knowledge about 3D neural representations is preferred.

Course materials:
[Slides]
[Video (Archive)]

Qixing Huang ( UT Austin)

Convex Relaxation Strategies for Graphics and Geometry Processing

A number of tasks in geometry processing can be conceived as critical point conditions for an optimization problem. These optimization problems, however, often involve nonlinear or nonconvex formulations that cannot be solved easily with standard tools. In this course, we will go over how convex relaxation techniques can make solving these optimization problems more efficient. In particular, we will explore how convex optimization is used to solve for shape matching, contour models, geodesic distances and PDEs, and optimal transport tasks in computer graphics. We will also cover modern convex optimization software tools. The goal of the course is to equip students with a beginner’s toolkit to apply convex optimization strategies to problems that they might encounter in their own research.

Course materials:
[Video (Archive)]

Leticia Mattos Da Silva (MIT)

Computational Knitting

Geometric representations such as 3D models have always been a popular tool in digital fabrication domains, and knitting is no exception. Due to its ability to create complex shapes with controllable material properties, as well as its popularity amongst hobbyists and industrial applications, knitting has become increasingly popular as a target for computational intervention. However, translating from high-level geometric descriptions to the precisely entangled loops of yarn that make up knitting is a challenging task that requires a host of computational techniques. This course provides a quick introduction to the fundamentals of knitting before diving into various geometric techniques that have been leveraged for computational knitting pipelines. Topics include stripe patterns and singular foliations for stitch pattern generation, quad-dominant meshes as the key to templated patterns, and the link between graph embeddings and machine knittability. We then conclude with a discussion of challenging open problems for the world of computational knitting.

Course materials:
[Slides]
[Video (Archive)]

Jenny Han Lin (University of Utah)
Benjamin Jones (MIT)
Edward Chien (Boston University)

Rendering and Geometry from 3D Gaussian Splatting

In this course, we will discuss the 3D Gaussian Splatting representation, its image formation model, and its opportunities for point-based geometry extraction. 3D Gaussian Splatting provides high performance and portability, but at the cost of several shortcuts and approximations in its rendering routine; understanding these design choices is key for converting trained models into high-quality geometry, such as meshes: A growing body of recent work discusses how triangle meshes can be extracted from the point cloud that 3D Gaussian Splatting optimizes. After revisiting the fundamentals and the impact of the approximations in 3D Gaussian Splatting, this course delves into strategies that can be used during training to encourage results that allow for high-quality mesh extraction. Finally, we provide a detailed overview of relevant recent work and research trends in this domain.

Course materials:
[Slides-Overview]
[Slides-Artifacts-Meshing]
[Video (Archive)]

Felix Windisch (TU Graz)
Bernhard Kerbl (TU Wien)
Thomas Köhler (TU Graz)
Markus Steinberger (TU Graz)

Computational Design of Metamaterials

Metamaterials are engineered materials with architectured structures that exhibit unconventional mechanical behavior, making them attractive for diverse applications. Designing these materials is challenging because their shape and topology exert a complex, nonlinear influence on their performance. This course introduces computational methods for metamaterial design, focusing on 1) computational models for efficiently simulating native-scale structures, 2) numerical homogenization techniques for characterizing mechanical properties, and 3) design methodologies—including constrained optimization, sensitivity analysis, and adjoint methods—to enable efficient, inverse design for targeted mechanical behavior. In addition to core theoretical foundations, the course provides an overview of current research trends in the characterization and design of sheet-like metamaterials such as flexible-scale materials, discrete interlocking materials, and thin-sheet metamaterials with patterned stripes.

Course materials:
[Slides]
[Video (Archive)]

Pengbin Tang (ETH Zurich)

Robust Methods for Non-Rigid Spectral Shape Matching

This course provides an overview of modern methods for non-rigid shape matching. Shape matching, or shape correspondence, is the backbone of most shape comparison approaches with applications in several fields such as medical imaging or computer graphics. This course will focus on the functional map framework, which can be seen as an extension of rigid shape alignment developed in the last decade, and which is now the main framework for unsupervised dense shape correspondence computations. A first part will introduce spectral shape analysis, functional maps and the most recent advances in the field. A second part will then present recent endeavours for unsupervised learning of shape correspondences from raw data.

Course materials:
[Video (Archive)]

Robin Magnet (INRIA Paris)

Deep Learning on Meshes and Point Clouds

Data-driven algorithms have proven valuable for many tasks, with high-profile success in image understanding and synthesis and language modelling. In this course, we look at how such algorithms can be used for data on curved surfaces. Our aim is to give researchers the required background to use such algorithms in an informed way in their own research. We consider the types of data and tasks that are relevant for mesh- and point-cloud surfaces, the requirements on our algorithms (e.g., scaling and generalization over the representation), and review the state-of-the-art for how these requirements can be met.

Course materials:
[Slides]
[Video (Archive)]

Ruben Wiersma (ETH Zurich)

DDG Methods for Geometry Processing

This lecture will explore two approaches to Discrete Differential Geometry (DDG) and its applications.
The first approach treats a mesh not just as a discretization of a shape but as a geometric object with its own intrinsic structure. Just as classical differential geometry develops theories for smooth surface parametrizations, a discrete counterpart can be formulated for meshes. This perspective can be a powerful tool in Geometry Processing: on one hand, it enables the generation of visually or structurally optimized meshes particularly relevant in architectural geometry; on the other, it allows us to design shapes with specific properties by imposing only local constraints on the mesh. For instance, a geodesic and orthogonal mesh naturally defines a developable surface.
The second approach highlights the power of Higher Geometries in Geometry Processing. For example, compared to Euclidean geometry Möbius geometry offers greater flexibility - preserving only intersection angles instead of distances. Examples we consider are conformal mappings and Möbius subdivision. Beyond Möbius geometry, we will also introduce line geometry and Laguerre geometry, discussing both their theoretical foundations and practical implementations.

Course materials:
[Slides]
[Video (Archive)]

Niklas Affolter (TU Wien)
Felix Dellinger (TU Wien)