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Flexible slender structures such as rods, ribbons, plates, and shells exhibit extreme nonlinear responses bending, twisting, buckling, wrinkling, and self contact, that defy conventional simulation frameworks. Discrete Differential Geometry…
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…
The task of finding an extension to a given partial drawing of a graph while adhering to constraints on the representation has been extensively studied in the literature, with well-known results providing efficient algorithms for…
Many iterative methods in applied mathematics can be thought of as fixed-point iterations, and such algorithms are usually analyzed analytically, with inequalities. In this paper, we present a geometric approach to analyzing contractive and…
In this work, we propose a geometric framework for analyzing mechanical manipulation, for instance, by a robotic agent. Under the assumption of conservative forces and quasi-static manipulation, we use energy methods to derive a metric. In…
Deep learning has enabled remarkable improvements in grasp synthesis for previously unseen objects from partial object views. However, existing approaches lack the ability to explicitly reason about the full 3D geometry of the object when…
Generating realistic 3D faces is of high importance for computer graphics and computer vision applications. Generally, research on 3D face generation revolves around linear statistical models of the facial surface. Nevertheless, these…
Although shape correspondence is a central problem in geometry processing, most methods for this task apply only to two-dimensional surfaces. The neglected task of volumetric correspondence--a natural extension relevant to shapes extracted…
We propose in this paper a Proper Generalized Decomposition (PGD) approach for the solution of problems in linear elastodynamics. The novelty of the work lies in the development of weak formulations of the PGD problems based on the…
Understanding the contact dynamics of nonspherical particles beyond the microscale is crucial for accurately modeling colloidal and granular systems, where shape anisotropy dictates structural organization and transport properties. In this…
What is the best representation for doing euclidean geometry on computers? These notes from a SIGGRAPH 2019 short course entitled "Geometric algebra for computer graphics" introduce projective geometric algebra (PGA) as a modern framework…
Field-guided parametrization methods have proven effective for quad meshing of surfaces; these methods compute smooth cross fields to guide the meshing process and then integrate the fields to construct a discrete mesh. A key challenge in…
Automatic mesh-based shape generation is of great interest across a wide range of disciplines, from industrial design to gaming, computer graphics and various other forms of digital art. While most traditional methods focus on primitive…
3D Gaussian Splatting (3DGS) has recently emerged as a pioneering approach in explicit scene rendering and computer graphics. Unlike traditional neural radiance field (NeRF) methods, which typically rely on implicit, coordinate-based models…
The problem of 3D reconstruction from posed images is undergoing a fundamental transformation, driven by continuous advances in 3D Gaussian Splatting (3DGS). By modeling scenes explicitly as collections of 3D Gaussians, 3DGS enables…
We present a form of algebraic reasoning for computational objects which are expressed as graphs. Edges describe the flow of data between primitive operations which are represented by vertices. These graphs have an interface made of…
Particles bound to an interface interact because they deform its shape. The stresses that result are fully encoded in the geometry and described by a divergence-free surface stress tensor. This stress tensor can be used to express the force…
Geometric Algebra and Calculus are mathematical languages encoding fundamental geometric relations that theories of physics seem to respect. We propose criteria given which statistics of expressions in geometric algebra are computable in…
Deep Learning (DL) has attracted a lot of attention for its ability to reach state-of-the-art performance in many machine learning tasks. The core principle of DL methods consists in training composite architectures in an end-to-end…
This paper examines stability properties of distance-based formation control when the underlying topology consists of a rigid graph and a flex node addition. It is shown that the desired equilibrium set is locally asymptotically stable but…