### 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