Marco Livesu, CNR IMATI
Tuesday, November 19th, 2024
Time: 10:15
Location: E8, room 109
Title: Stripe Embedding: Efficient Maps with Exact Numeric Computation
Abstract:
In this talk, I will consider the fundamental problem of bijectively mapping a surface mesh with disk topology onto a boundary constrained convex polygon. Starting from the basic observation that mapping a strip of triangles onto a rectangular shape yields a valid embedding, I will propose a straightforward algorithm, called Stripe Embedding, that operates by decomposing the input mesh into a set of triangle strips and then embeds each strip into the target domain by means of linear interpolation between two previously embedded vertices. Thanks to its simplicity, Stripe Embedding is extremely efficient and permits to switch to an exact implementation without almost increasing its running times. Stripe Embedding is up to three orders of magnitude faster than the Tutte embedding for the same numerical model and, even when implemented with costly rational numbers, it is faster than any floating point implementation of prior methods at any scale. In the final part of the presentation, I will discuss the possibility to extend this construction to the volumetric setting, to generate provably bijective volume maps to convex polyhedra.
Bio:
Marco Livesu is a Senior Researcher at the Institute for Applied Mathematics and Information Technologies of the National Research Council of Italy (CNR IMATI). He obtained his PhD at the University of Cagliari in 2014, after which he was post doctoral researcher at the University of British Columbia, University of Cagliari and CNR IMATI. His main research interests involve geometry processing, with applications in 3D shape modeling, digital manufacturing, and mesh generation/optimization. He is the creator and lead developer of CinoLib, a C++ library for processing polygonal and polyhedral meshes, and co-creator of the HexaLab project, a web-based visualization tool for hexahedral meshes as well as a dataset of hexmeshes produced with state of the art methods. For both these projects he received an SGP Award, in 2024 and 2021, respectively.
Ningfeng Zhou, ETH
Thursday, June 20th, 2024
Time: 11:15
Location: E8, room 109
Title: Computation Smocking through Fabric-Thread Interaction
Abstract:
We formalize Italian smocking, an intricate embroidery technique that gathers flat fabric into pleats along meandering lines of stitches, resulting in pleats that fold and gather where the stitching veers. Italian smocking permits the fabric to move freely along the stitched threads following curved paths, resulting in complex and unpredictable pleats with highly diverse, irregular structures, achieved simply by pulling on the threads. We introduce a novel method for digital previewing of Italian smocking results, given the thread stitching path as input. Our method uses a coarse-grained mass-spring system to simulate the interaction between the threads and the fabric. This configuration guides the fine-level fabric deformation through an adaptation of the state-of-the-art simulator, C-IPC. Our method models the general problem of fabric-thread interaction. We compare our results to baseline approaches and physical fabrications to demonstrate the accuracy of our method.
Pierre Alliez, Inria Sophia Antipolis
Monday, April 15th, 2024
Time: 10:15
Location: E8, room 111
Title: Quadric error metrics for variational reconstruction and neural mesh representation
Abstract:
I will first present a contribution published at ACM SIGGRAPH 2023. Inspired by the strengths of quadric error metrics initially designed for mesh decimation, we propose a concise mesh reconstruction approach for 3D point clouds. Our approach proceeds by clustering the input points enriched with quadric error metrics, where the generator of each cluster is the optimal 3D point for the sum of its quadric error metrics. This approach favors the placement of generators on sharp features, and tends to equidistribute the error among clusters.
I will then present a very recent work to appear at CVPR 2024. In this work, we introduce a novel learnable mesh representation through a set of local 3D sample Points and their associated Normals and Quadric error metrics (QEM) w.r.t. the underlying shape, which we denote PoNQ. A global mesh is directly derived from PoNQ by efficiently leveraging the knowledge of the local quadric errors. Besides marking the first use of QEM within a neural shape representation, our contribution guarantees both topological and geometrical properties by ensuring that a PoNQ mesh does not self-intersect and is always the boundary of a volume.
Ana Dodik, MIT
Thursday, December 21th, 2023
Time: 14:15
Location: E8, room 107
Title: Mesh-Free Skinning Weights
Abstract:
A common approach to computer animation relies on reduced deformation models such as deformation cages or skeletons. As part of this process, artists have to manually specify how an animated object deforms as a result of the cage or skeleton being deformed. This process is known as skinning and the relationship between the cage or skeleton and the shape itself is dictated by so-called skinning weights.
Numerous methods have been proposed to automate this process, yet their adoption in practice remains limited. We argue that this is in part due to a lack of robustness and artistic control. In this talk, we explore recent and upcoming work on mesh-free automatic painting of skinning weights and their subclass known as generalized barycentric coordinates. Similar to previous work, we formulate this as a constrained variational problem, but approach it in a notably different way, namely by building upon physics informed neural networks (PINNs) and Lagrangian representations. We explore ways of building hard constraints into these models, allowing for flexibility in the optimization objective. Our theoretical and practical results demonstrate this to be a promising future direction. The talk will cover a recent SIGGRAPH Asia publication, as well as additional directions.
Tim Felle Olsen, Technical University of Denmark
Thursday, October 28th, 2021
Time: 16:30
Location: N10, room 302
Title: Synthesis of Frame Field-aligned Multi-Laminar Structures
Abstract:
In the field of topology optimization, the homogenization approach has been revived as an important alternative to the established, density-based methods because it can represent the microstructural design at a much finer length-scale than the computational grid. The optimal microstructure for a single load case is an orthogonal rank-3 laminate. A rank-3 laminate can be described in terms of frame fields, which are also an important tool for mesh generation in both 2D and 3D. We propose a method for generating multi-laminar structures from frame fields. Rather than relying on integrative approaches that find a parametrization based on the frame field, we find stream surfaces, represented as point clouds aligned with frame vectors, and we solve an optimization problem to find well-spaced collections of such stream surfaces. The stream surface tracing is unaffected by the presence of singularities outside the region of interest. Neither stream surface tracing nor selecting well-spaced surface rely on combed frame fields. We demonstrate our methods on several frame fields produced using the homogenization approach for topology optimization, boundary-aligned, algebraic frame fields, and frame fields computed from closed-form expressions.
Our current work
In the examples of our paper, we realized that if all layers in the structure is active, we see a hexahedral structure appear. This lead to our collaboration here where we want to explore this further.
Pierre Allexandre Beaufort, Université Catholique de Louvain, Belgium
Wednesday, March 4th, 2020
Time: 11:00
Location: N10, room 302
Title: Crossfields from the Renormalized Energy
Abstract: Crossfields are auxiliary tools for quadrangular mesh generation. Their computation is crucial for the quality of the corresponding mesh. It has been lately proposed to minimize the Ginzburg-Landau functional in order to compute crossfields [Beaufort et al. 2017, Viertel et al. 2018]. This functional corresponds to an energy of the computed crossfield, which is called the Renormalized Energy [Bethuel et al. 1994]. The Renormalized Energy yields complete information about singularities of the computed crossfield, i.e. their index and location. We show how to compute the Renormalized Energy from a set of singularities and how to recover the corresponding crossfield in the planar case. We therefore derive relationships between crossfields and their so-called integrability. The extension to 2-manifolds is discussed, and insight of crossfield computation based on the Renormalized Energy is detailed.
Maxance Reberol, Université Catholique de Louvain, Belgium
Wednesday, March 4th, 2020
Time: 14:00
Location: N10, room 302
Title: 3D Frame Fields and Block Decomposition of CAD models
Abstract: Automatic generation of block-structured hexahedral meshes remains a very open and challenging research subject. In the last decade, encouraging progress has been made thanks to the democratization of surface cross field and 3D frame fields. In this talk, we discuss potential ways to leverage frame field information to build block decompositions and we focus on some issues with the current frame-field formulation, namely non hex-meshable singularities and boundary condition limitations, which prevent the generalization of surface techniques to the 3D case.
In particular, we describe a dual approach where we circumvent the difficulties and field defects around singularities by building dual sheets inside the volume, thus forming a initial (non-hex) decomposition, which can be subdivided into hex blocks (similarly to [Zheng et al. 2018, Livesu et al. 2019]). While having some success on simple models, it remains very dependent on the frame field quality (sufficient resolution and topological correctness) and application to CAD models with complicated features is definitively not straightforward.
Max Lyon, RWTH Aachen University, Germany
Friday, Feb. 21st
Time: 10:00
Location: N10, room 302
Title: Parametrization Quantization with Free Boundaries for Trimmed Quad Meshing
Abstract: The generation of quad meshes based on surface parametrization techniques has proven to be a versatile approach. These techniques quantize an initial seamless parametrization so as to obtain an integer grid map implying a pure quad mesh. State-of-the-art methods following this approach have to assume that the surface to be meshed either has no boundary, or has a boundary which the resulting mesh is supposed to be aligned to. In a variety of applications this is not desirable and non-boundary-aligned meshes or grid-parametrizations are preferred. We thus present a technique to robustly generate integer grid maps which are either boundary-aligned, non-boundary-aligned, or partially boundary-aligned, just as required by different applications. We thereby generalize previous work to this broader setting. This enables the reliable generation of trimmed quad meshes with partial elements along the boundary, preferable in various scenarios, from tiled texturing over design and modeling to fabrication and architecture, due to fewer constraints and hence higher overall mesh quality and other benefits in terms of aesthetics and flexibility.Valentin Nigolian
October 1, 2019
Valentin Nigolian visited our group and gave a talk about his research project titled:INVANER: INteractive VAscular Network Editing and Repair