Related papers: Map Projection
In computer graphics, the field of view of a camera is represented by a viewing frustum and a corresponding projection matrix, the properties of which, in the absence of restrictions on rectangular shape of the near plane and its…
A distance-squared function is one of the most significant functions in the application of singularity theory to differential geometry. Moreover, distance-squared mappings are naturally extended mappings of distance-squared functions,…
We provide a formal introduction into the classic theorems of general topology and its axiomatic foundations in set theory. In this second part we introduce the fundamental concepts of topological spaces, convergence, and continuity, as…
The primary goal of this paper is to abstract notions, results and constructions from the theory of categories to the broader setting of plots. Loosely speaking, a plot can be thought of as a non-associative non-unital category with a…
For a surface in the 3-dimensional real projective space, we define a Gauss map, which is a quadric in $\mathbb R^{4}$ and called the first-order Gauss map. It will be shown that the surface is a Demoulin surface if and only if the…
This article is devoted to the study of mappings defined in the region on the plane. Under certain conditions, the upper estimate of the distortion of the modulus of families of paths is obtained. Similarly, the upper estimate of the…
The "Brownian map" is a fundamental object in mathematics, in some sense a 2-dimensional analogue of Brownian motion. Here we briefly explain this object and a bit of its history.
On the base of symplectic quantum tomogram we define a probability distribution on the plane. The dual map transfers all observables which are polynomials of the position and momentum operators to the set of polynomials of two variables. In…
We give an estimate of the Gauss curvature for minimal surfaces in ${\mathbb R}^m$ whose Gauss map omits more than $m(m+1)/2$ hyperplanes in ${\mathbb P}^{m-1}({\mathbb C})$.
This text is a survey of derived algebraic geometry. It covers a variety of general notions and results from the subject with a view on the recent developments at the interface with deformation quantization.
The article presents a new approach to euclidean plane geometry based on projective geometric algebra (PGA). It is designed for anyone with an interest in plane geometry, or who wishes to familiarize themselves with PGA. After a brief…
Maps are arguably one of the most fundamental concepts used to define and operate on manifold surfaces in differentiable geometry. Accordingly, in geometry processing, maps are ubiquitous and are used in many core applications, such as…
We present a method for computing projective isomorphisms between rational surfaces that are given in terms of their parametrizations. The main idea is to reduce the computation of such projective isomorphisms to five base cases by…
We compute the expected value of various quantities related to the biparametric singularities of a pair of smooth centered Gaussian random fields on an n-dimensional compact manifold, such as the lengths of the critical curves and contours…
An approach to modelling the universe based on the requisites of gravitational energy. This model is explained as it relates to the stages of the universal life cycle and the continued existence of the universe as it is known today. The…
The aim of this chapter is twofold. In the first part we will provide a brief overview of the mathematical and statistical foundations of graphical models, along with their fundamental properties, estimation and basic inference procedures.…
High-resolution climate projections are essential for local decision-making. However, available climate projections have low spatial resolution (e.g. 12.5 km), which limits their usability. We address this limitation by leveraging…
We propose DeMapGS, a structured Gaussian Splatting framework that jointly optimizes deformable surfaces and surface-attached 2D Gaussian splats. By anchoring splats to a deformable template mesh, our method overcomes topological…
Cartograms are maps that rescale geographic regions (e.g., countries, districts) such that their areas are proportional to quantitative demographic data (e.g., population size, gross domestic product). Unlike conventional bar or pie charts,…
A path deviation equation in the Parameterized Absolute Parallelism (PAP) geometry is derived. This equation includes curvature and torsion terms. These terms are found to be naturally quantized. The equation represents the deviation from a…