Related papers: Morphology-Preserving Remeshing Approach to Partic…
Many computational algorithms applied to geometry operate on discrete representations of shape. It is sometimes necessary to first simplify, or coarsen, representations found in modern datasets for practicable or expedited processing. The…
This paper describes an interdisciplinary approach to geometry modeling of geospatial boundaries. The objective is to extract surfaces from irregular spatial patterns using differential geometry and obtain coherent directional predictions…
We propose a three-dimensional nonlinear diffusion method to implement the similar autofocusing function of multiple micro-objects and simultaneously remove the defocused images, which can distinguish the locations of certain sized…
A prerequisite for many biomechanical simulation techniques is discretizing a bounded volume into a tetrahedral mesh. In certain contexts, such as cortical surface simulations, preserving input surface connectivity is critical. However,…
Micromechanical constitutive parameters are important for many engineering materials, typically in microelectronic applications and material design. Their accurate identification poses a three-fold experimental challenge: (i) deformation of…
We propose a new, efficient multi-scale method to decompose a map (or signal in general) into components maps that contain structures of different sizes. In the widely-used wave transform, artifacts containing negative values arise around…
We use spherical cap harmonic (SCH) basis functions to analyse and reconstruct the morphology of scanned genus-0 rough surface patches with open edges. We first develop a novel one-to-one conformal mapping algorithm with minimal area…
Many nano and quantum devices, with their sizes often spanning from millimeters down to sub-nanometer, have intricate low-dimensional, non-uniform, or hierarchical structures on surfaces and interfaces. Since their functionalities are…
We consider image denoising using a nonlinear diffusion process, where we solve unsteady partial differential equations with nonlinear coefficients. The noised image is given as an initial condition, and nonlinear coefficients are used to…
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 reduction and reconstruction procedures for the solutions of symmetric stochastic differential equations, similar to those available for ordinary differential equations. Additionally, we use the local tangent-normal…
Persistence-based topological optimization deforms a point cloud $X \subset \mathbb{R}^d$ by minimizing objectives of the form $L(X) = \ell(\mathrm{Dgm}(X))$, where $\mathrm{Dgm}(X)$ is a persistence diagram. In practice, optimization is…
The plasticity of amorphous solids undergoing shear is characterized by quasi-localized rearrangements of particles. While many models of plasticity exist, the precise relationship between plastic dynamics and the structure of a particle's…
Simulating the deformation of fractured media requires the coupling of different models for the deformation of fractures and the formation surrounding them. We consider a cell-centered finite-volume approach, termed the multipoint stress…
High mesh quality plays a crucial role in maintaining the stability of solutions in geometric flow problems. Duan and Li [Duan & Li, SIAM J. Sci. Comput. 46 (1) (2024) A587-A608] applied the minimal deformation (MD) formulation to propose…
Nowadays, three-dimensional reconstruction is used in various fields like computer vision, computer graphics, mixed reality and digital twin. The three-dimensional reconstruction of cultural heritage objects is one of the most important…
This paper addresses the limitations of neural rendering-based multi-view surface reconstruction methods, which require an additional mesh extraction step that is inconvenient and would produce poor-quality surfaces with mesh aliasing,…
In this paper we suggest a simple analytical method for description of electromagnetic properties of a geometrically regular two-dimensional subwavelength arrays (metasurfaces) formed by particles with randomly fluctuating polarizabilities.…
We introduce a smoothing algorithm for triangle, quadrilateral, tetrahedral and hexahedral meshes whose centerpiece is a simple geometric triangle transformation. The first part focuses on the mathematical properties of the element…
Multiscale techniques have been widely shown to potentially overcome the limitation of homogenization schemes in representing the microscopic failure mechanisms in heterogeneous media as well as their influence on their structural response…