Related papers: Coordinate Geometric Approach to Spherometer

We continue our study, initiated in our earlier paper, of Riemann surfaces with constant curvature and isolated conic singularities. Using the machinery developed in that earlier paper of extended configuration families of simple divisors,…

Coarse geometry studies metric spaces on the large scale. Our goal here is to study dynamics from a coarse point of view. To this end we introduce a coarse version of topological entropy, suitable for unbounded metric spaces, consistent…

In the process of projecting the surface of a three-dimensional object onto a two-dimensional surface, due to the perspective distortion, the image on the surface of the object will have different degrees of distortion according to the…

The kinematical setting of spherically symmetric quantum geometry, derived from the full theory of loop quantum gravity, is developed. This extends previous studies of homogeneous models to inhomogeneous ones where interesting field theory…

We prove that any compact surface with constant positive curvature and conical singularities can be decomposed into irreducible components of standard shape, glued along geodesic arcs connecting conical singularities. This is a spherical…

Modeling deformations of a real object is an important task in computer vision, biomedical engineering and biomechanics. In this paper, we focus on a situation where a three-dimensional object is rotationally deformed about a fixed axis,…

In this article, we study the complexity involved in the computation of the reach in arbitrary dimension and in particular the computation of the critical spherical curvature points of an arbitrary algebraic variety. We present properties…

We survey the classification of the Riemannian metrics on spheres with respect to which all equators are minimal hypersurfaces, and discuss problems related to these geometries.

The parameterization of open and closed anatomical surfaces is of fundamental importance in many biomedical applications. Spherical harmonics, a set of basis functions defined on the unit sphere, are widely used for anatomical shape…

I present an exact and explicit solution to the scalar (Stokes flux intensity) radio interferometer imaging equation on a spherical surface which is valid also for non-coplanar interferometer configurations. This imaging equation is…

Blending schemes based on circles provide smooth `fair' interpolations between series of points. Here we demonstrate a simple, robust set of algorithms for performing circle blends for a range of cases. An arbitrary level of G-continuity…

Sky coverage is one of the most important pieces of information about astronomical observations. We discuss possible representations, and present algorithms to create and manipulate shapes consisting of generalized spherical polygons with…

In recent years there has been a resurgence of interest in our community in the shape analysis of 3D objects represented by surface meshes, their voxelized interiors, or surface point clouds. In part, this interest has been stimulated by…

A spherical conical metric $g$ on a surface $\Sigma$ is a metric of constant curvature $1$ with finitely many isolated conical singularities. The uniformization problem for such metrics remains largely open when at least one of the cone…

The traditional study of plane and space algebraic curves by looking at their tangent vectors, curvatures and torsions provides geometric, but unfortunately not sufficient information about individual curves in order to be able to…

We give a metric characterization of the scalar curvature of a smooth Riemannian manifold, analyzing the maximal distance between $(n+1)$ points in infinitesimally small neighborhoods of a point. Since this characterization is purely in…

In this paper, we propose using the scattering surface area rather than the scattering cross section to characterize the scattering behavior of ellipsoidal rigid bodies. We examined the scattering behavior of ellipsoidal rigid bodies,…

Traditional geometry employs idealized concepts like that of a point or a curve, the operational definition of which relies on the availability of classical point particles as probes. Real, physical objects are quantum in nature though,…

High-quality time series provided by space instrumentation such as CoRoT and Kepler, allow us to measure modulations in the light curves due to changes in the surface of stars related to rotation and activity. Therefore, we are able to…

In this work, we present an adaptation of the classical stereographic projection, originally formulated for the sphere, now considering the context of the ellipsoid and the elliptic paraboloid. We begin by constructing the stereographic…