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Engineering simulations for analysis of structural and fluid systems require information of contacts between various 3-D surfaces of the geometry to accurately model the physics between them. In machine learning applications, 3-D surfaces…

Given a triangulated surface, a polyhedral metric could be constructed by gluing Euclidean triangles edge-to-edge. We carefully describe the construction and prove that such a polyhedral metric is the only intrinsic metric on the glued…

Most 3D shape analysis methods use triangular meshes to discretize both the shape and functions on it as piecewise linear functions. With this representation, shape analysis requires fine meshes to represent smooth shapes and geometric…

We propose a sharp and conservative 3D numerical method for simulating moving contact lines on complex geometries, developed within a coupled geometric Volume-of-Fluid (VOF) and embedded boundary framework. The first major contribution is a…

Cortical surface reconstruction (CSR) from MRI is key to investigating brain structure and function. While recent deep learning approaches have significantly improved the speed of CSR, a substantial amount of runtime is still needed to map…

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…

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…

Deep generative models have shown success in generating 3D shapes with different representations. In this work, we propose Neural Volumetric Mesh Generator(NVMG) which can generate novel and high-quality volumetric meshes. Unlike the…

We introduce TetSphere Splatting, a Lagrangian geometry representation designed for high-quality 3D shape modeling. TetSphere splatting leverages an underused yet powerful geometric primitive -- volumetric tetrahedral meshes. It represents…

We introduce DMTet, a deep 3D conditional generative model that can synthesize high-resolution 3D shapes using simple user guides such as coarse voxels. It marries the merits of implicit and explicit 3D representations by leveraging a novel…

Implicit Neural Representations (INRs) have been demonstrated to achieve state-of-the-art compression of a broad range of modalities such as images, videos, 3D surfaces, and audio. Most studies have focused on building neural counterparts…

This paper introduces a new learning-based method, NASM, for anisotropic surface meshing. Our key idea is to propose a graph neural network to embed an input mesh into a high-dimensional (high-d) Euclidean embedding space to preserve…

Utilizing patch-based transformers for unstructured geometric data such as polygon meshes presents significant challenges, primarily due to the absence of a canonical ordering and variations in input sizes. Prior approaches to handling 3D…

The human cochlea is a remarkable device, able to discern extremely small amplitude sound pressure waves, and discriminate between very close frequencies. Simulation of the cochlea is computationally challenging due to its complex geometry,…

This paper proposes a novel discretization workflow for contact problems in which the discretization of the contact interface is decoupled from that of the bulk domain. This separation enables independently tailored meshes for the contact…

Meshes are commonly used as 3D maps since they encode the topology of the scene while being lightweight. Unfortunately, 3D meshes are mathematically difficult to handle directly because of their combinatorial and discrete nature. Therefore,…

We introduce radiance meshes, a technique for representing radiance fields with constant density tetrahedral cells produced with a Delaunay tetrahedralization. Unlike a Voronoi diagram, a Delaunay tetrahedralization yields simple triangles…

Approximate convex decomposition aims to decompose a 3D shape into a set of almost convex components, whose convex hulls can then be used to represent the input shape. It thus enables efficient geometry processing algorithms specifically…

A family of quadratic finite volume method (FVM) schemes are constructed and analyzed over tetrahedral meshes. In order to prove stability and error estimate, we propose the minimum V-angle condition on tetrahedral meshes, and the surface…

Accurate segmentation of vascular networks is essential for computer-aided tools designed to address cardiovascular diseases. Despite more than thirty years of research, it remains a challenge to obtain vascular segmentation results that…