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We introduce a novel neural network architecture for encoding and synthesis of 3D shapes, particularly their structures. Our key insight is that 3D shapes are effectively characterized by their hierarchical organization of parts, which…
We propose a new representation for encoding 3D shapes as neural fields. The representation is designed to be compatible with the transformer architecture and to benefit both shape reconstruction and shape generation. Existing works on…
Scalable spatial GPs for massive datasets can be built via sparse Directed Acyclic Graphs (DAGs) where a small number of directed edges is sufficient to flexibly characterize spatial dependence. The DAG can be used to devise fast algorithms…
We analyze the performance of a reduced-order simulation of geometric meta-materials based on zigzag patterns using a simplified representation. As geometric meta-materials we denote planar cellular structures which can be fabricated in 2d…
Using a geometric formalism of elasticity theory we develop a systematic theoretical method for controlling and manipulating the mechanical response of slender solids to external loads. We formally express global mechanical properties…
Chemical, mechanical, thermal and/or electronic properties of bulk or low-dimensional materials can be engineered by introducing structural defects to form novel functionalities. When using particles irradiation, these defects can be…
One of the key advantages of 3D rendering is its ability to simulate intricate scenes accurately. One of the most widely used methods for this purpose is Gaussian Splatting, a novel approach that is known for its rapid training and…
We present a method for balancing between the Local and Global Structures (LGS) in graph embedding, via a tunable parameter. Some embedding methods aim to capture global structures, while others attempt to preserve local neighborhoods. Few…
This paper proposes some efficient and accurate adaptive two-grid (ATG) finite element algorithms for linear and nonlinear partial differential equations (PDEs). The main idea of these algorithms is to utilize the solutions on the $k$-th…
This paper presents the design and implementation of a Grid-enabled physics analysis environment for handheld and other resource-limited computing devices as one example of the use of mobile devices in eScience. Handheld devices offer great…
Enhanced Geothermal Systems (EGS) can provide constant, reliable electricity and heat with minimal emissions, but high drilling costs and uncertain cost reductions leave their future unclear. We explore scenarios for the future adoption of…
In an EPG-representation of a graph $G$ each vertex is represented by a path in the rectangular grid, and $(v,w)$ is an edge in $G$ if and only if the paths representing $v$ an $w$ share a grid-edge. Requiring paths representing edges to be…
In this article we introduce a family of elastic metrics on the space of parametrized surfaces in 3D space using a corresponding family of metrics on the space of vector valued one-forms. We provide a numerical framework for the computation…
Algebraic multigrid (AMG) is conventionally applied in a black-box fashion, agnostic to the underlying geometry. In this work, we propose that using geometric information -- when available -- to assist with setting up the AMG hierarchy is…
Many applications of geometry modeling and computer graphics necessite accurate curvature estimations of curves on the plane or on manifolds. In this paper, we define the notion of the discrete geodesic curvature of a geodesic polygon on a…
Within periodic materials and structures, wave scattering and dispersion occur across constituent material interfaces leading to a banded frequency response. In an earlier paper, the elastodynamics of one-dimensional periodic materials and…
Gaussian Splatting (GS) has demonstrated impressive quality and efficiency in novel view synthesis. However, shape extraction from Gaussian primitives remains an open problem. Due to inadequate geometry parameterization and approximation,…
We study the behavior of thin elastic sheets that are bent and strained under the influence of weak, smooth confinement. We show that the emerging shapes exhibit the coexistence of two types of domains that differ in their characteristic…
Advancements in 3D Gaussian Splatting have significantly accelerated 3D reconstruction and generation. However, it may require a large number of Gaussians, which creates a substantial memory footprint. This paper introduces GES (Generalized…
Regrasping on fixtures is a promising approach to reduce pose uncertainty in robotic assembly, but conventional rigid fixtures lack adaptability and require dedicated designs for each part. To overcome this limitation, we propose a soft jig…