nmwsharp/geometry-central
Applied 3D geometry in C++, with a focus on surface meshes. (⭐ 1285)
Telling Left from Right: Identifying Geometry-Aware Semantic Correspondence
While pre-trained large-scale vision models have shown significant promise for semantic correspondence, their features often struggle to grasp the geometry and orientation of instances. This paper identifies the importance of being geometry-aware for...
A Timeless Game: A Game-Theoretic Model of Mass-Geometry Relations
We develop a minimal, timeless game-theoretic representation of the mass-geometry relation. An "Object" (mass) and "Space" (geometry) choose strategies in a static normal-form game; utilities encode stability as mutual consistency rather than dynamic...
Asymptotic Properties of Hilbert Geometry
We show that the spheres in Hilbert geometry have the same volume growth entropy as those in the Lobachevsky space. We give the asymptotic estimates for the ratio of the volume of metric ball to the area of the metric sphere in Hilbert geometry. De...
Derived symplectic geometry
This is an invited contribution to the 2nd edition of the Encyclopedia of Mathematical Physics, that provides a very short survey of derived symplectic geometry. Derived symplectic geometry studies symplectic structures on derived stacks. Derived s...
Some open questions on anti-de Sitter geometry
We present a list of open questions on various aspects of AdS geometry, that is, the geometry of Lorentz spaces of constant curvature -1. When possible we point out relations with homogeneous spaces and discrete subgroups of Lie groups, to Teichmüll...
Polyhedral Geometry in OSCAR
OSCAR is an innovative new computer algebra system which combines and extends the power of its four cornerstone systems - GAP (group theory), Singular (algebra and algebraic geometry), Polymake (polyhedral geometry), and Antic (number theory). Assumi...
Play Dashmetry - Free Geometry Dash Like Game Online!
Play Dashmetry - Free Geometry Dash Like Game Online! Enjoy the impossibility of Geometry Dash, a rhythm-based running game, and enjoy a musical adventure that requires lightning-fast reflexes and …
On the geometry of sharply 2-transitive groups
We show that the geometry associated to certain non-split sharply 2-transitive groups does not contain a proper projective plane. For a sharply 2-transitive group of finite Morley rank we improve known rank inequalities for this geometry and conclude...
Geometry-Discovery-Project-UCI/gdp.math.uci.edu
The Geometry Discovery Project - University of California, Irvine (⭐ 7)
The geometry on the slope of a mountain
The geometry on a slope of a mountain is the geometry of a Finsler metric, called here the {\it slope metric}. We study the existence of globally defined slope metrics on surfaces of revolution as well as the geodesic's behavior. A comparison between...
On Klein's So-called Non-Euclidean geometry
In two papers titled "On the so-called non-Euclidean geometry", I and II, Felix Klein proposed a construction of the spaces of constant curvature -1, 0 and and 1 (that is, hyperbolic, Euclidean and spherical geometry) within the realm of projective g...
Geometry - Math is Fun
Geometry is all about shapes and their properties. If you like playing with objects, or like drawing, then geometry is for you!
Geometry - Wikipedia
Geometry is, along with arithmetic, one of the oldest branches of mathematics. A mathematician who works in the field of geometry is called a geometer.
RGI-Net: 3D Room Geometry Inference from Room Impulse Responses With Hidden First-Order Re…
Room geometry is important prior information for implementing realistic 3D audio rendering. For this reason, various room geometry inference (RGI) methods have been developed by utilizing the time-of-arrival (TOA) or time-difference-of-arrival (TDOA)...
Around groups in Hilbert Geometry
This is survey about action of group on Hilbert geometry. It will be a chapter of the "Handbook of Hilbert geometry" edited by G. Besson, M. Troyanov and A. Papadopoulos....
Why we live in 3 Dimensions
A Cantorian fractal spacetime, a family member of von Neumann's noncommutative geometry is introduced as a geometry underlying a new relativity theory which is similar to the relation between general relativity and Riemannian geometry. Based on thi...
"Brave New" Algebraic Geometry and global derived moduli spaces of ring spectra
We develop homotopical algebraic geometry (see math.AG/0207028) in the special context where the base symmetric monoidal model category is the category S of spectra, i.e. what might be called, after Waldhausen, ``brave new algebraic geometry''. We...
A primer on Script Geometry
This text is an exposition of a new approach into discrete differential geometry, called Script Geometry. In difference to classic approaches while scripts are based on complexes of cells we are not limited to simplicial complexes. One of the princip...
Distance Geometry for Kissing Spheres
A kissing sphere is a sphere that is tangent to a fixed reference ball. We develop in this paper a distance geometry for kissing spheres, which turns out to be a generalization of the classical Euclidean distance geometry....