Related papers: An Interface Preserving Moving Mesh in Multiple Sp…

Moving mesh methods are designed to redistribute a mesh in a regular way. This applied problem can be considered to overlap with the problem of finding a diffeomorphic mapping between density measures. In applications, an off-the-shelf grid…

3D representations of highly deformable 3D models, such as dynamic 3D meshes, have recently become very popular due to their wide applicability in various domains. This trend inevitably leads to a demand for storage and transmission of…

Despite recent advances in geometric modeling, 3D mesh modeling still involves a considerable amount of manual labor by experts. In this paper, we introduce Mesh Draping: a neural method for transferring existing mesh structure from one…

In this paper, we present a general approach to obtain numerical schemes with good mesh properties for problems with moving boundaries, that is for evolving submanifolds with boundaries. This includes moving domains and surfaces with…

Implicit neural representations (INRs) have been successfully used to compress a variety of 3D surface representations such as Signed Distance Functions (SDFs), voxel grids, and also other forms of structured data such as images, videos,…

One challenge that remains open in 3D deep learning is how to efficiently represent 3D data to feed deep networks. Recent works have relied on volumetric or point cloud representations, but such approaches suffer from a number of issues…

We study the steady state structure and dynamics of a 2-d Ising interface placed in an inhomogeneous external field with a sigmoidal profile which moves with velocity $v_{e}$. In the strong coupling limit the problem maps onto an…

We present a new fixed mesh algorithm for solving a class of interface inverse problems for the typical elliptic interface problems. These interface inverse problems are formulated as shape optimization prob- lems whose objective…

Frequently, the design of physicochemical processes requires screening of large numbers of alternative designs with complex geometries. These geometries may result in conformal meshes which introduce stability issues, significant…

We present a novel shape-approximating anisotropic re-meshing algorithm as a geometric generalization of the adaptive moving mesh method. Conventional moving mesh methods reduce the interpolation error of a mesh that discretizes a given…

Normal integration reconstructs 3D surfaces from normal maps obtained e.g. by photometric stereo. These normal maps capture surface details down to the pixel level but require large computational resources for integration at high…

Triangular meshes are the most popular representations of 3D objects, but many mesh surfaces contain topological singularities that represent a challenge for displaying or further processing them properly. One such singularity is the…

We present a method for reconstructing triangle meshes from point clouds. Existing learning-based methods for mesh reconstruction mostly generate triangles individually, making it hard to create manifold meshes. We leverage the properties…

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 work, we focus on the task of learning and representing dense correspondences in deformable object categories. While this problem has been considered before, solutions so far have been rather ad-hoc for specific object types (i.e.,…

We propose connectivity-preserving geometry images (CGIMs), which map a three-dimensional mesh onto a rectangular regular array of an image, such that the reconstructed mesh produces no sampling errors, but merely round-off errors. We…

Reconstruction of object or scene surfaces has tremendous applications in computer vision, computer graphics, and robotics. In this paper, we study a fundamental problem in this context about recovering a surface mesh from an implicit field…

We consider an open, bounded, simply connected (Lipschitz) domain in $\mathbb{R}^d$, which contains a closed polyhedral surface or polygonal contour, referred to as the interface. From this interface, forces are exerted in the normal…

We investigate the steady-state organisation of active particles residing on an interface. Particle activity induces interface deformations, while the local shape of the interface guides particle movement. We consider multiple species of…

Meshes composed of well-centered simplices have nice orthogonal dual meshes (the dual Voronoi diagram). This is useful for certain numerical algorithms that prefer such primal-dual mesh pairs. We prove that well-centered meshes also have…