Courses are taught by internationally known experts. Instructors typically include an overview of the state of the art of their topic, and highlight their own research, but also include the current work of others. It is intended to be a “course” in the traditional sense of enabling attendees to go forth and produce new results of their own, rather than simply use existing knowledge.
- Mesh intersection: down the rabbit hole
Dr. Bruno Lévy, Research Director at the Inria Saclay center and at the Orsay Mathematics Laboratory - Towards Higher-Order Simplicial Mesh Generation with Guarantees
Prof. Marcel Campen, Professor at Paderborn University, Germany - Interval-Based Continuous Collision Detection
Prof. Teseo Schneider, Assistant Professor in Computer Science at the Univerity of Victoria, Canada
Mesh intersection: down the rabbit hole
Dr. Bruno Lévy
Abstract: Why is mesh intersection so hard ? Considered from a mathematical point of view, the problem is simple: you got a bunch of triangles that may have intersections and overlaps, and what you want is another bunch of triangles that represent exactly the same shape and that has no intersection. Why don’t we have a standard implementation that everybody uses? Why is there still active research on this topic that is several decades old? In this short course, I will explain why the problem becomes hard as soon as you want to implement a solution on a computer, and I will review different techniques described in the literature and implemented in existing software packages, some well-established and some recently developed. This comprises floating-point and integer computer arithmetic, predicates, homogeneous coordinates, geometric data structures and combinatorial data structures. I will also share some “war stories” and lessons learnt during the past three years that I spent designing, implementing, testing and debugging this type of algorithm.
Biography: Bruno Lévy is Research Director at the Inria Saclay center and at the Orsay Mathematics Laboratory. He is interested in meshing and partial differential equation problems, with applications in computational physics. In the first part of his career (2000-2018), he focused on computer graphics issues, such as surface parameterization and texture mapping. With his ALICE team, which he founded in 2004, and as part of his two ERC projects, he developed a set of algorithms to optimize the representation of 3D shapes. One of these (Least Squares Conformal Maps), published at the SIGGRAPH conference in 2002, was recognized in 2023 on the occasion of SIGGRAPH’s 50th anniversary in the collection of the most significant advances in the field published over the last 25 years (seminal graphic papers). Since 2015, he has been interested in optimal transport theory in the context of computational physics, particularly cosmology, which he studies with colleagues in astrophysics and mathematics. He and his colleagues published two articles in Physical Review Letters (the most prestigious journal in Physics) on the first efficient cosmological reconstruction algorithm based on optimal transport, which makes it possible to detect a subtle signal in the initial conditions (BAOs, baryon acoustic oscillations). From 2018 to 2022, he headed the Inria Nancy Grand-Est Center / Inria Center at the University of Lorraine (20 teams, 450 people). In 2022, he worked on designing the Inria Quadrant Program (PIQ), which he has since led as Scientific Director. This national program supports high-risk research projects in the digital field, led by researchers and engineers from French higher education and research institutions. The program currently supports around twenty projects on topics ranging from quantum physics to ancient Greek, molecular biology, AI, and cybersecurity. He is committed to building bridges between disciplines and connecting fundamental and digital aspects, both in his research activities and in his research administration roles. Most of his research results are available in the Geogram open-source programming library.
Towards Higher-Order Simplicial Mesh Generation with Guarantees
Prof. Marcel Campen
Abstract: The generation of meshes consisting of linear simplices (triangle meshes, tetrahedral meshes) is a well-researched problem. Various efficient algorithms with formal guarantees, suitable for large-scale practical use, are available. For meshes consisting of non-linear, curved, higher-order elements, the situation is less ideal; algorithms often are of a best-effort kind, lacking guarantees, with consequent reliability and robustness issues in practice.
In this short course, recent research advances on this front are covered. In particular, we discuss a set of novel algorithmic ideas for the automatic generation of higher-order triangle and tetrahedral meshes. They are capable of offering guarantees regarding practically relevant properties such as boundary conformance, element injectivity, and even element quality. A common scheme in these is favoring constructive techniques over optimization-centric approaches, and incrementally reducing the hard meshing problem to simpler subproblems. Using a careful algorithmic design, even the common gap between reliability in theory and in practice (in particular due to numerical issues) can be addressed.
Biography: Marcel Campen is a professor at Paderborn University, Germany, heading the Computer Science department’s Computer Graphics & Visualization group. Former affiliations include RWTH Aachen University, New York University, and Osnabrück University. His research concerns meshing, mapping, and related geometric and algorithmic challenges, in 2D and 3D, with a particular focus on aspects of reliability and robustness. His scientific contributions have been recognized by the EUROGRAPHICS Association with the Best PhD Thesis Award and the Young Researcher Award 2020 for his contributions to the field of Geometry Processing. He serves as Associate Editor for the journals Computer Graphics Forum, Computers & Graphics, and IEEE Transactions on Visualization and Computer Graphics.
Interval-Based Continuous Collision Detection
Prof. Teseo Schneider
Abstract: Robust continuous collision detection (CCD) is a foundational component of geometry processing and physics simulation. Many existing CCD algorithms are prone to floating-point failures, often missing collisions or reporting false positives. This course introduces interval-based CCD, an inclusion method that guarantees conservative detection by relying on bounding computations and robust interval arithmetic. We explain the key insights behind interval root finding, interval arithmetics, bounding motion trajectories, implicit function tests, and conservative pruning. The session demonstrates how interval-based CCD integrates into simulation pipelines and how it compares in performance and reliability to other approaches (e.g., Newton-based CCD, conservative advancement).
Biography: Teseo Schneider is an Assistant Professor in Computer Science at the Univerity of Victoria, Canada. Teseo earned his Ph.D. in Computer Science from the Universita della Svizzera italiana (2017) with the thesis entitled “Theory and Applications of Bijective Barycentric Mappings.” He earned a PostdocMobility fellowship from the Swiss National Science Foundation (SNSF) to pursue his research at the Courant Institute of Mathematical Science at the New York University, aiming to bridge physical simulations and geometry. His research interests are finite element simulations, mathematics, discrete differential geometry, and geometry processing. Teseo is the leading developer of Polyfem, a flexible and easy-to-use Finite Element Library. He is one of the maintainers of libigl and a contributor to wild meshing, a 2D and 3D robust meshing library. In 2022, Teseo was awarded the Young Investigator Award by Shape Modelling International and the Cowie Faculty Innovation Award by the Univerity of Victoria. In 2024 he was awarded the Early Career Researcher Award from Graphics Interface.
