相关论文: Coordinate Geometric Generalization of the Spherom…
This gives some information about the conformal point and the calibrating conic, and their relationship one to the other. These concepts are useful for visualizing image geometry, and lead to intuitive ways to compute geometry, such as…
This research work aims to explore the distortions in distance in equidistant cylindrical projection. The horizontal bending that occurs in the projection process can be assessed by performing a geometric analysis using Tissot's…
This paper presents a novel technique for camera calibration using a single view that incorporates a spherical mirror. Leveraging the distinct characteristics of the sphere's contour visible in the image and its reflections, we showcase the…
A spherical n-gon is a bordered surface homeomorphic to a closed disk, with n distinguished boundary points called corners, equipped with a Riemannian metric of constant curvature 1, except at the corners, and such that the boundary arcs…
We introduce an arbitrary order, computationally efficient method to smooth corners on curves in the plane, as well as edges and vertices on surfaces in $\mathbb R^3$. The method is local, only modifying the original surface in a…
Trigonometry is the study of circular functions, which are functions defined on the unit circle $x^2+y^2 =1$, where distances are measured using the Euclidean norm. When distances are measured using the $L_p$-norm, we get generalized…
In this paper, studying the inverse problem, we establish a curvature compatibility condition on a spherically symmetric Finsler metric. As an application, we characterize the spherically symmetric metrics of scalar curvature. We construct…
A canal surface is the envelope of a moving sphere with varying radius, defined by the trajectory C(t) (spine curve) of its center and a radius function r(t). In this paper, we investigate when parameter curves of the canal surface are also…
This article provides an overview of the techniques related to classification of spherical and more general objects within triangulated categories, and its relationship with algebraic geometry, representation theory and symplectic geometry.…
See http://www.youtube.com/watch?v=izbGXdjvK_I for a YouTube video showing part of the results in this paper.We will consider surfaces whose mean curvature at a point is a linear function of the square of the distance from that point to the…
The research field of spatial scientometrics is dedicated to measuring and analyzing science with spatial components (e.g., location, place, mapping). Because of the dynamic nature of this field, researchers from multidisciplinary domains…
Formulas about the side lengths, diagonal lengths or radius of the circumcircle of a cyclic polygon in Euclidean geometry, hyperbolic geometry or spherical geometry can be unified.
An all-spherical catadioptic system made of glass of one type is proposed for the monitoring of large sky areas. We provide an example of such a system with the aperture of diameter 400 mm and the curved field of 30 degree in diameter.
In this paper we study the geometry of metric spheres in the curve complex of a surface, with the goal of determining the "average" distance between points on a given sphere. Averaging is not technically possible because metric spheres in…
Geometric metrology includes one or two-dimensional (1D or 2D) distance or plane measurements, as well as the three-dimensional (3D) scanning. The 1D or 2D measuring system is unable to obtain advanced 3D feature, while the 3D scanning…
A simple mechanical device is introduced, the parallelometer, that can be used to measure curvatures of surfaces. The device can be used as a practical illustration of parallel transport of a vector and to study Berry phase shift when it is…
We present a novel orbit parameterization in spherical coordinates. This parameterization enables the mixing of varying and invariant orbital parameters, and clarifies the physics of the orbit. It also simplifies the process of placing…
A spherical quadrilateral is a bordered surface homeomorphic to a closed disk, with four distinguished boundary points called corners, equipped with a Riemannian metric of constant curvature 1, except at the corners, and such that the…
Grazing incidence interferometry has been applied to rough planar and cylindrical surfaces. As suitable beam splitters diffractive optical phase elements are quite common because these allow for the same test sensitivity for all surface…
We provide a comprehensive overview of metric-affine geometries with spherical symmetry, which may be used in order to solve the field equations for generic gravity theories which employ these geometries as their field variables. We discuss…