Related papers: Algebraic 3D Graphic Statics: reciprocal construct…
Molecular property prediction is an important problem in drug discovery and materials science. As geometric structures have been demonstrated necessary for molecular property prediction, 3D information has been combined with various graph…
This work presents a generative adversarial architecture for generating three-dimensional shapes based on signed distance representations. While the deep generation of shapes has been mostly tackled by voxel and surface point cloud…
Real-world robotic grasping can be done robustly if a complete 3D Point Cloud Data (PCD) of an object is available. However, in practice, PCDs are often incomplete when objects are viewed from few and sparse viewpoints before the grasping…
In this paper, we propose a novel approach to the problem of augmenting distance-based formation controllers with a secondary constraint for the purpose of preventing 3D formation ambiguities. Specifically, we introduce three controlled…
Contact-based grasp generation plays a crucial role in various applications. Recent methods typically focus on the geometric structure of objects, producing grasps with diverse hand poses and plausible contact points. However, these…
In our previous paper, we presented the combinatorial theory for minimal isostatic pinned frameworks - Assur graphs - which arise in the analysis of mechanical linkages. In this paper we further explore the geometric properties of Assur…
We develop a Fourier--analytic framework for establishing spectral reciprocity formulas linking $\mathrm{GL}_3$ and $\mathrm{GL}_2$ automorphic spectra over number fields. The method applies uniformly to cuspidal and non-cuspidal…
The abundance of data has given machine learning considerable momentum in natural sciences and engineering, though modeling of physical processes is often difficult. A particularly tough problem is the efficient representation of geometric…
Graph Generating Dependencies (GGDs) informally express constraints between two (possibly different) graph patterns which enforce relationships on both graph's data (via property value constraints) and its structure (via topological…
Embedding diagrams prove to be quite useful when learning general relativity as they offer a way of visualizing spacetime curvature through warped two dimensional (2D) surfaces. In this manuscript we present a different 2D construct that…
We give complete presentations for the dagger-compact props of affine Lagrangian and coisotropic relations over an arbitrary field. This provides a unified family of graphical languages for both affinely constrained classical mechanical…
3D shape creation and modeling remains a challenging task especially for novice users. Many methods in the field of computer graphics have been proposed to automate the often repetitive and precise operations needed during the modeling of…
Many statistical models are algebraic in that they are defined by polynomial constraints or by parameterizations that are polynomial or rational maps. This opens the door for tools from computational algebraic geometry. These tools can be…
We discuss a link between graph theory and geometry that arises when considering graph dynamical systems with odd interactions. The equilibrium set in such systems is not a collection of isolated points, but rather a union of manifolds,…
Geometric modeling by constraints, whose applications are of interest to communities from various fields such as mechanical engineering, computer aided design, symbolic computation or molecular chemistry, is now integrated into standard…
A model of simplicial quantum gravity in three dimensions(3D) was investigated numerically based on the technique of dynamical triangulation (DT). We are concerned with the genus of surfaces appearing on boundaries (i.e., sections) of a 3D…
To enumerate 3-manifold triangulations with a given property, one typically begins with a set of potential face pairing graphs (also known as dual 1-skeletons), and then attempts to flesh each graph out into full triangulations using an…
Partial differential equations can be solved on general polygonal and polyhedral meshes, through Polytopal Element Methods (PEMs). Unfortunately, the relation between geometry and analysis is still unknown and subject to ongoing research in…
While orthogonal drawings have a long history, smooth orthogonal drawings have been introduced only recently. So far, only planar drawings or drawings with an arbitrary number of crossings per edge have been studied. Recently, a lot of…
3D grasp synthesis generates grasping poses given an input object. Existing works tackle the problem by learning a direct mapping from objects to the distributions of grasping poses. However, because the physical contact is sensitive to…