Related papers: A Spline-based Volumetric Data Modeling Framework …

This paper addresses the linear independence of T-splines that correspond to refinements of three-dimensional tensor-product meshes. We give an abstract definition of analysis-suitability, and prove that it is equivalent to…

The biological membrane, which compartmentalizes the cell and its organelles, exhibit wide variety of macroscopic shapes of varying morphology and topology. A systematic understanding of the relation of membrane shapes to composition,…

We introduce an algorithmic framework based on tensor networks for computing fluid flows around immersed objects in curvilinear coordinates. We show that the tensor network simulations can be carried out solely using highly compressed…

Soft slender structures are ubiquitous in natural and artificial systems and can be observed at scales that range from the nanometric to the kilometric, from polymers to space tethers. We present a practical numerical approach to simulate…

Recent advancements in visualizing deep neural networks provide insights into their structures and mesh extraction from Continuous Piecewise Affine (CPWA) functions. Meanwhile, developments in neural surface representation learning…

In this work, a polygonal Reissner-Mindlin plate element is presented. The formulation is based on a scaled boundary finite element method, where in contrast to the original semi-analytical approach, linear shape functions are introduced…

This paper provides a tutorial and survey for a specific kind of illustrative visualization technique: feature lines. We examine different feature line methods. For this, we provide the differential geometry behind these concepts and adapt…

In this paper, phase field models are developed for multi-component vesicle membranes with different lipid compositions and membranes with free boundary. These models are used to simulate the deformation of membranes under the elastic…

Tensor, a multi-dimensional data structure, has been exploited recently in the machine learning community. Traditional machine learning approaches are vector- or matrix-based, and cannot handle tensorial data directly. In this paper, we…

Smooth joins of simplex Bernstein-B\'ezier polynomials have been studied extensively in the past. In this paper a new method is proposed to define continuity conditions for tensor-product Bernstein polynomials on a class of mixed grids that…

Multivariate spatial data plays an important role in computational science and engineering simulations. The potential features and hidden relationships in multivariate data can assist scientists to gain an in-depth understanding of a…

General skinning techniques aim to deform the surface of an articulated model following the pose change of a skeleton. Their rapidity makes them ideal tools for real-time animation purposes. However, popular skinning algorithms are simple,…

Meshes are ubiquitous in visual computing and simulation, yet most existing machine learning techniques represent meshes only indirectly, e.g. as the level set of a scalar field or deformation of a template, or as a disordered triangle soup…

A complex system comprises multiple interacting entities whose interdependencies form a unified whole, exhibiting emergent behaviours not present in individual components. Examples include the human brain, living cells, soft matter, Earth's…

The paper presents a new method for shape and topology optimization based on an efficient and scalable boundary integral formulation for elasticity. To optimize topology, our approach uses iterative extraction of isosurfaces of a…

The proliferation of 3D representations, from explicit meshes to implicit neural fields and more, motivates the need for simulators agnostic to representation. We present a data-, mesh-, and grid-free solution for elastic simulation for any…

Developing deep learning techniques for geometric data is an active and fruitful research area. This paper tackles the problem of sphere-type surface learning by developing a novel surface-to-image representation. Using this representation…

This paper presents a general framework for calculating the dimension of spline spaces over arbitrary rectilinear partitions using the smoothing cofactor method. The approach extends existing dimension theory for polynomial splines over…

Fluid flows containing dilute or dense suspensions of thin fibers are widespread in biological and industrial processes. To describe the motion of a thin immersed fiber, or to describe the forces acting on it, it is convenient to work with…

We present a novel approach enabling interactive visualization of volumetric Locally Refined B-splines (LR-splines). To this end we propose a highly efficient algorithm for direct visualization of scalar and vector fields given by an…