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Designs generated by density-based topology optimization (TO) exhibit jagged and/or smeared boundaries, which forms an obstacle to their integration with existing CAD tools. Addressing this problem by smoothing or manual design adjustments…

Topological defects are ubiquitous on surfaces with orientational order fields. Here, we study equilibrium states generated by the feedback between geometry and nematic order on fluid membranes with an integer topological defect. When the…

Topological edge states in electromagnetic systems feature a set of attracting fundamental properties and unveil prospective applications based on disorder robustness and tailored localization. Despite active efforts in implementing…

High fidelity representation of shapes with arbitrary topology is an important problem for a variety of vision and graphics applications. Owing to their limited resolution, classical discrete shape representations using point clouds, voxels…

Computational topology is an area that revisits topological problems from an algorithmic point of view, and develops topological tools for improved algorithms. We survey results in computational topology that are concerned with graphs drawn…

The interaction of multiple fluids through a heterogeneous pore space leads to complex pore-scale flow dynamics, such as intermittent pathway flow. The non-local nature of these dynamics, and the size of the 4D datasets acquired to capture…

Our goal in this paper is to apply the topological signal processing (TSP) framework to the analysis of 3D Point Clouds (PCs) represented on simplicial complexes. Building on Discrete Exterior Calculus (DEC) theory for vector fields, we…

Within the context of 5-axis free-form machining, CAM software offers various ways of tool-path generation, depending on the geometry of the surface to be machined. Therefore, as the manufactured surface quality results from the choice of…

Topological defects (TDs) are crucial for understanding important physical properties of crystalline materials including mechanical failure, ion transport, and two-dimensional melting. This concept has not translated to disordered materials…

A method evaluating the sensitivity of a given parameter to topological changes is proposed within the method of moments paradigm. The basis functions are used as degrees of freedom which, when compared to the classical pixeling technique,…

The goal of this study is to provide a method for computing the following: Given a network of curves in 3d (satisfying a condition at the intersection points), compute efficiently a smooth surface such that the curves are geodesics on it.…

Segmentation is often an essential intermediate step in image analysis. A volume segmentation characterizes the underlying volume image in terms of geometric information--segments, faces between segments, curves in which several faces…

Two-dimensional (2D) topological electronic insulators are known to give rise to gapless edge modes, which underlie low energy dynamics, including electrical and thermal transport. This has been thoroughly investigated in the context of…

Deep learning-based medical image segmentation and surface mesh generation typically involve a sequential pipeline from image to segmentation to meshes, often requiring large training datasets while making limited use of prior geometric…

Given a 3D surface defined by an elevation function on a 2D grid as well as non-spatial features observed at each pixel, the problem of surface segmentation aims to classify pixels into contiguous classes based on both non-spatial features…

Accurate surface geometry representation is crucial in 3D visual computing. Explicit representations, such as polygonal meshes, and implicit representations, like signed distance functions, each have distinct advantages, making efficient…

Although topological surface states are known to be robust against non-magnetic surface perturbations, their band dispersions and spatial distributions are still sensitive to the surface defects. Take Bi2Se3 as an example, we demonstrated…

Topological mechanics can realize soft modes in mechanical metamaterials in which the number of degrees of freedom for particle motion is finely balanced by the constraints provided by interparticle interactions. However, solid objects are…

This paper surveys recent numerical advances in the phase field method for geometric surface evolution and related geometric nonlinear partial differential equations (PDEs). Instead of describing technical details of various numerical…

In this paper, we investigate topological modes of different physical systems defined on arbitrary two-dimensional curved surfaces. We consider the shallow water equations, inhomogeneous Maxwell's equations, Jackiw-Rebbi model and show how…