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In this work, we present a dense tracking and mapping system named Vox-Fusion, which seamlessly fuses neural implicit representations with traditional volumetric fusion methods. Our approach is inspired by the recently developed implicit…
A new model order reduction approach is proposed for parametric steady-state nonlinear fluid flows characterized by shocks and discontinuities whose spatial locations and orientations are strongly parameter dependent. In this method,…
We propose an unsupervised technique for implicit parameterization of data manifolds. In our approach, the data is assumed to belong to a lower dimensional manifold in a higher dimensional space, and the data points are viewed as the…
Neural fields have emerged as a powerful representation for 3D geometry, enabling compact and continuous modeling of complex shapes. Despite their expressive power, manipulating neural fields in a controlled and accurate manner --…
This paper presents a numerical method for the simulation of multiscale materials composed of an elastic matrix and slender active inclusions. The setting is motivated by the modeling of vascularized tissues and by problems arising in the…
This paper presents a reduced order approach for transient modeling of multiple moving objects in nonlinear crossflows. The Proper Orthogonal Decomposition method and the Galerkin projection are used to construct a reduced version of the…
Deep implicit surfaces excel at modeling generic shapes but do not always capture the regularities present in manufactured objects, which is something simple geometric primitives are particularly good at. In this paper, we propose a…
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…
Plasmas are highly nonlinear and multi-scale, motivating a hierarchy of models to understand and describe their behavior. However, there is a scarcity of plasma models of lower fidelity than magnetohydrodynamics (MHD), although these…
We propose a novel 3D shape correspondence method based on the iterative alignment of so-called smooth shells. Smooth shells define a series of coarse-to-fine shape approximations designed to work well with multiscale algorithms. The main…
In this paper, we propose a method for tracking structures (e.g., ventricles and myocardium) in cardiac images (e.g., magnetic resonance) by propagating forward in time a previous estimate of the structures via a new deformation estimation…
As the most common representation for 3D shapes, mesh is often stored discretely with arrays of vertices and faces. However, 3D shapes in the real world are presented continuously. In this paper, we propose to learn a continuous…
Recently, 3D Gaussian splatting has gained attention for its capability to generate high-fidelity rendering results. At the same time, most applications such as games, animation, and AR/VR use mesh-based representations to represent and…
We resolve a longstanding open problem in the computational modeling of nonlinear plates by introducing a numerical method that exactly enforces the isometry constraint, namely, that the first fundamental form of the mid-surface coincides…
Mesh models are a promising approach for encoding the structure of 3D objects. Current mesh reconstruction systems predict uniformly distributed vertex locations of a predetermined graph through a series of graph convolutions, leading to…
Existing curved-layer-based process planning methods for multi-axis manufacturing address collisions only indirectly and generate toolpaths in a post-processing step, leaving toolpath geometry uncontrolled during optimization. We present an…
A unifying moving mesh method is developed for general $m$-dimensional geometric objects in $d$-dimensions ($d \ge 1$ and $1\le m \le d$) including curves, surfaces, and domains. The method is based on mesh equidistribution and alignment…
We explore a new way to handle flux boundary conditions imposed on level sets. The proposed approach is a diffuse interface version of the shifted boundary method (SBM) for continuous Galerkin discretizations of conservation laws in…
We present a novel framework for PDE-constrained $r$-adaptivity of high-order meshes. The proposed method formulates mesh movement as an optimization problem, with an objective function defined as a convex combination of a mesh quality…
We present a novel approach for the reconstruction of dynamic geometric shapes using a single hand-held consumer-grade RGB-D sensor at real-time rates. Our method does not require a pre-defined shape template to start with and builds up the…