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We propose an end-to-end deep learning architecture that produces a 3D shape in triangular mesh from a single color image. Limited by the nature of deep neural network, previous methods usually represent a 3D shape in volume or point cloud,…
Computational fluid dynamics is both a thriving research field and a key tool for advanced industry applications. The central challenge is to simulate turbulent flows in complex geometries, a compute-power intensive task due to the large…
Writing an uncomplicated, robust, and scalable three-dimensional convex hull algorithm is challenging and problematic. This includes, coplanar and collinear issues, numerical accuracy, performance, and complexity trade-offs. While there are…
Existing auto-regressive mesh generation approaches suffer from ineffective topology preservation, which is crucial for practical applications. This limitation stems from previous mesh tokenization methods treating meshes as simple…
Sumset estimates, which provide bounds on the cardinality of sumsets of finite sets in a group, form an essential part of the toolkit of additive combinatorics. In recent years, probabilistic or entropic analogs of many of these…
We propose an end-to-end pipeline to robustly generate high-quality, high-order and coarse quadrilateral meshes on CAD models. This kind of mesh enables the use of high-order analysis techniques such as high-order finite element methods or…
We develop and test high-order methods for integration on surface point clouds. The task of integrating a function on a surface arises in a range of applications in engineering and the sciences, particularly those involving various integral…
We present a simple set of data structures, and a collection of methods for constructing and updating the structures, designed to support the use of cohesive elements in simulations of fracture and fragmentation. Initially all interior…
We present a novel methodology for deriving high-order volume elements (HOVE) designed for the integration of scalar functions over regular embedded manifolds. For constructing HOVE we introduce square-squeezing --a homeomorphic multilinear…
We develop a new optimisation technique that combines multiresolution subdivision surfaces for boundary description with immersed finite elements for the discretisation of the primal and adjoint problems of optimisation. Similar to wavelets…
We formalize and study the natural approach of designing convex surrogate loss functions via embeddings, for problems such as classification, ranking, or structured prediction. In this approach, one embeds each of the finitely many…
We present a flexible discretization technique for computational models of thin tubular networks embedded in a bulk domain, for example a porous medium. These systems occur in the simulation of fluid flow in vascularized biological tissue,…
Although polygon meshes have been a standard representation in geometry processing, their irregular and combinatorial nature hinders their suitability for learning-based applications. In this work, we introduce a novel learnable mesh…
We propose a robust and scalable procedure for general optimization and inference problems on manifolds leveraging the classical idea of `median-of-means' estimation. This is motivated by ubiquitous examples and applications in modern data…
We present a novel formulation for the dynamics of geometrically exact Timoshenko beams and beam structures made of viscoelastic material featuring complex, arbitrarily curved initial geometries. An $\textrm{SO}(3)$-consistent and…
The inverse design of optical metasurfaces is a rapidly emerging field that has already shown great promise in miniaturizing conventional optics as well as developing completely new optical functionalities. Such a design process relies on…
Intrinsic volumes are fundamental geometric invariants generalizing volume, surface area, and mean width for convex bodies. We establish a unified Laplace-Grassmannian representation for intrinsic and dual volumes of convex polynomial…
In order to reduce the computational cost of the simulation of electromagnetic responses in geophysical settings that involve highly heterogeneous media, we develop a multiscale finite volume method with oversampling for the quasi-static…
Many tasks in geometry processing are modeled as variational problems solved numerically using the finite element method. For solid shapes, this requires a volumetric discretization, such as a boundary conforming tetrahedral mesh.…
We present a computational framework for simulating filaments interacting with rigid bodies through contact. Filaments are challenging to simulate due to their codimensionality, i.e., they are one-dimensional structures embedded in…