相关论文: Mode Surfaces of Symmetric Tensor Fields: Topologi…

Nodal noncentrosymmetric superconductors have topologically nontrivial properties manifested by protected zero-energy surface states. Specifically, it was recently found that zero-energy surface flat bands of topological origin appear at…

Metasurfaces are subwavelength structured thin films consisting of arrays of units that allow the controls of polarization, phase and amplitude of light over a subwavelength thickness. The recent developments in topological photonics have…

In this paper we develop a generalization of foliated manifolds in the context of metric spaces. In particular we study dendritations of surfaces that are defined as maximal atlases of compatible upper semicontinuous local decompositions…

Topological transitions of isofrequency surfaces of a composite magnetic-semiconductor structure influenced by an external static magnetic field are studied in the long-wavelength approximation. For the lossless case, the topological…

We discuss (2+1)D topological phases on non-orientable spatial surfaces, such as M\"obius strip, real projective plane and Klein bottle, etc., which are obtained by twisting the parent topological phases by their underlying pairty…

Topological data analysis (TDA) allows us to explore the topological features of a dataset. Among topological features, lower dimensional ones have recently drawn the attention of practitioners in mathematics and statistics due to their…

Symmetry-resolved entanglement is a useful tool for characterizing symmetry-protected topological states. In two dimensions, their entanglement spectra are described by conformal field theories but the symmetry resolution is largely…

We propose 3Deformer, a general-purpose framework for interactive 3D shape editing. Given a source 3D mesh with semantic materials, and a user-specified semantic image, 3Deformer can accurately edit the source mesh following the shape…

Shape manipulation is a central research topic in computer graphics. Topology editing, such as breaking apart connections, joining disconnected ends, and filling/opening a topological hole, is generally more challenging than geometry…

Signed distance fields (SDFs) are a widely used implicit surface representation, with broad applications in computer graphics, computer vision, and applied mathematics. To reconstruct an explicit triangle mesh surface corresponding to an…

Stable fold maps are fundamental tools in a generalization of the theory of Morse functions on smooth manifolds and its application to studies of geometric properties of smooth manifolds. Round fold maps were introduced as stable fold maps…

Various line fields naturally arise on surfaces in both physical and biological contexts, and generic singularities frequently appear in the form of 1-prong (thorn-like) and 3-prong (tripod-like) configurations, which can be modeled by…

A non associative, noncommutative algebra is defined that may be interpreted as a set of vector modules over a noncommutative surface of rotation. Two of these vector modules are identified with the analogues of the tangent and cotangent…

Models for fluid deformable surfaces provide valid theories to describe the dynamics of thin fluidic sheets of soft materials. To use such models in morphogenesis and development requires to incorporate active forces. We consider active…

Scientific research and engineering practice often require the modeling and decomposition of nonlinear systems. The Dynamic Mode Decomposition (DMD) is a novel Koopman-based technique that effectively dissects high-dimensional nonlinear…

Continuum lattice grid structures which consist of joined elastic beams subject to flexural deformations are ubiquitous. In this work, we establish a theoretical framework of the topological dynamics of continuum lattice grid structures,…

The aim of this paper is to investigate the sufficient condition for the invariance of a normal curve on a smooth immersed surface under isometry. We also find the the deviations of the tangential and normal components of the curve with…

This research uses deep learning to estimate the topology of manifolds represented by sparse, unordered point cloud scenes in 3D. A new labelled dataset was synthesised to train neural networks and evaluate their ability to estimate the…

Accurately restoring topology is both challenging and crucial in tubular structure extraction tasks, such as blood vessel segmentation and road network extraction. Diverging from traditional approaches based on pixel-level classification,…

Spatially localized deformation components are very useful for shape analysis and synthesis in 3D geometry processing. Several methods have recently been developed, with an aim to extract intuitive and interpretable deformation components.…