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The interest in matching non-rigidly deformed shapes represented as raw point clouds is rising due to the proliferation of low-cost 3D sensors. Yet, the task is challenging since point clouds are irregular and there is a lack of intrinsic…
We consider the problem of category-level 6D pose estimation from a single RGB image. Our approach represents an object category as a cuboid mesh and learns a generative model of the neural feature activations at each mesh vertex to perform…
Parametric boundary representation models (B-Reps) are the de facto standard in CAD, graphics, and robotics, yet converting them into valid meshes remains fragile. The difficulty originates from the unavoidable approximation of high-order…
We present a single-image head mesh reconstruction framework that addresses the longstanding challenge of simultaneously preserving facial identity and producing industry-grade topology. Our framework adopts a coarse-to-fine optimization…
A new topography adapted mesh generation process tailored to simulate Atmospheric Boundary Layer (ABL) flows on complex terrains is presented. The mesher is fully automatic given: the maximum and minimum surface mesh size, the size of the…
Meshes are ubiquitous in visual computing and simulation, yet most existing machine learning techniques represent meshes only indirectly, e.g. as the level set of a scalar field or deformation of a template, or as a disordered triangle soup…
About a decade ago Thurston proved that a vast collection of 3-manifolds carry metrics of constant negative curvature. These manifolds are thus elements of {\em hyperbolic geometry}, as natural as Euclid's regular polyhedra. For a closed…
The triangulation of images has become an active research area in recent years for its compressive representation and ease of image processing and visualization. However, little work has been done on how to faithfully recover image…
With the advancement in 3D scanning technology, there has been a surge of interest in the use of point clouds in science and engineering. To facilitate the computations and analyses of point clouds, prior works have considered…
Recent advances in learning 3D shapes using neural implicit functions have achieved impressive results by breaking the previous barrier of resolution and diversity for varying topologies. However, most of such approaches are limited to…
The goal of this paper is to study the geometry of cusped complex hyperbolic manifolds through their compactifications. We characterize toroidal compactifications with non-nef canonical divisor. We derive effective very ampleness results…
Computational modeling of aerodynamics is a key problem in aerospace engineering, often involving flows interacting with solid objects such as airfoils. Deep surrogate models have emerged as purely data-driven approaches that learn direct…
We consider the problem of 3D shape reconstruction from multi-modal data, given uncertain calibration parameters. Typically, 3D data modalities can be in diverse forms such as sparse point sets, volumetric slices, 2D photos and so on. To…
An important new trend in additive manufacturing is the use of optimization to automatically design industrial objects, such as beams, rudders or wings. Topology optimization, as it is often called, computes the best configuration of…
Topological surgery in dimension $3$ is intrinsically connected with the classification of $3$-manifolds and with patterns of natural phenomena. In this expository paper, we present two different approaches for understanding and visualizing…
We study a notion of strict pseudoconvexity in the context of topologically (often unsmoothably) embedded 3-manifolds in complex surfaces. Topologically pseudoconvex (TPC) 3-manifolds behave similarly to their smooth analogues, cutting out…
Geometrical Volume-of-Fluid (VoF) methods mainly support structured meshes, and only a small number of contributions in the scientific literature report results with unstructured meshes and three spatial dimensions. Unstructured meshes are…
We present a novel topology-preserving 3D medial axis computation framework based on volumetric restricted power diagram (RPD), while preserving the medial features and geometric convergence simultaneously, for both 3D CAD and organic…
Reliable 3D segmentation is critical for understanding complex scenes with dense layouts and multi-scale objects, as commonly seen in industrial environments. In such scenarios, heavy occlusion weakens geometric boundaries between objects,…
Point clouds have gained prominence across numerous applications due to their ability to accurately represent 3D objects and scenes. However, efficiently compressing unstructured, high-precision point cloud data remains a significant…