Related papers: The Kinematics of Completely-Faceted Surfaces

Triangulated meshes have become ubiquitous discrete-surface representations. In this paper we address the problem of how to maintain the manifold properties of a surface while it undergoes strong deformations that may cause topological…

Accurate representation of interfaces and flux exchange is vital for coupled multiphysics simulations across a broad range of applications. Currently, coupling approaches are limited by the underlying discretization or to specific physical…

We construct algorithms and topological invariants that allow us to distinguish the topological type of a surface, as well as functions and vector fields for their topological equivalence. In the first part (arXiv:2501.15657), we discused…

Swept volume computation, the determination of regions occupied by moving objects, is essential in graphics, robotics, and manufacturing. Existing approaches either explicitly track surfaces, suffering from robustness issues under complex…

Reconstructing the surfaces of deformable objects from correspondences between a 3D template and a 2D image is well studied under Shape-from-Template (SfT) methods; however, existing approaches break down when topological changes accompany…

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…

In this article, a new method for segmentation and restoration of images on two-dimensional surfaces is given. Active contour models for image segmentation are extended to images on surfaces. The evolving curves on the surfaces are…

Living systems exhibit complex yet organized behavior on multiple spatiotemporal scales. To investigate the nature of multiscale coordination in living systems, one needs a meaningful and systematic way to quantify the complex dynamics, a…

We describe a hidden surface removal algorithm for two-dimensional layered scenes built from arbitrary primitives, particularly suited to interaction and animation in rich scenes (for example, in illustration). The method makes use of a…

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…

This paper proposes an approach to learn generic multi-modal mesh surface representations using a novel scheme for fusing texture and geometric data. Our approach defines an inverse mapping between different geometric descriptors computed…

The advent of high resolution imaging has made data on surface shape widespread. Methods for the analysis of shape based on landmarks are well established but high resolution data require a functional approach. The starting point is a…

We develop a computational framework that leverages the features of sophisticated software tools and numerics to tackle some of the pressing issues in the realm of earth sciences. The algorithms to handle the physics of multiphase flow,…

Topological surgery occurs in natural phenomena where two points are selected and attracting or repelling forces are applied. The two points are connected via an invisible `thread'. In order to model topologically such phenomena we…

This paper is part of a program that aims to understand the connection between the emergence of chaotic behaviour in dynamical systems in relation with the multi-valuedness of the solutions as functions of complex time $\tau$. In this work…

Recovering point clouds involves the sequential process of sampling and restoration, yet existing methods struggle to effectively leverage both topological and geometric attributes. To address this, we propose an end-to-end architecture…

We present a simple yet general and efficient approach to representation of computational meshes. Meshes are represented as sets of mesh entities of different topological dimensions and their incidence relations. We discuss a…

We give a new algorithm of slow continued fraction expansion related to any real cubic number field as a 2-dimensional version of the Farey map. Using our algorithm, we can find the generators of dual substitutions (so-called tiling…

In this paper we combine a survey of the most important topological properties of kinematic maps that appear in robotics, with the exposition of some basic results regarding the topological complexity of a map. In particular, we discuss…

Deformable objects present a formidable challenge for robotic manipulation due to the lack of canonical low-dimensional representations and the difficulty of capturing, predicting, and controlling such objects. We construct compact…