Related papers: Determining the Qibla Direction by Astronomical an…
Cosmology can be viewed as geodesic motion in an appropriate metric on an `augmented' target space; here we obtain these geodesics from an effective relativistic particle action. As an application, we find some exact (flat and curved)…
This paper provides an overview of modern digital geometry and topology through mathematical principles, algorithms, and measurements. It also covers recent developments in the applications of digital geometry and topology including image…
In this paper I present a kind of proof for classical Euclidean geometric problems which relies on both synthetic and analytic geometry. Using the elementary tools of polynomial algebra and multivariate calculus we manage to reduce the…
Geometric algebra was initiated by W.K. Clifford over 130 years ago. It unifies all branches of physics, and has found rich applications in robotics, signal processing, ray tracing, virtual reality, computer vision, vector field processing,…
Despite the large budgets spent annually on astronomical research equipment such as telescopes, instruments and supercomputers, the general trend is to analyse and view the resulting datasets using small, two-dimensional displays. We report…
Geometric calibration of cameras and projectors is an essential step that must be performed before any imaging system can be used. There are many well-known geometric calibration methods for calibrating systems comprised of multiple…
In the last two decades, Bayesian inference has become commonplace in astronomy. At the same time, the choice of algorithms, terminology, notation, and interpretation of Bayesian inference varies from one sub-field of astronomy to the next,…
In this paper, we investigate the gravitational bending angle due to the Casimir wormholes, which consider the Casimir energy as the source. Furthermore, some of these Casimir wormholes regard Generalized Uncertainty Principle (GUP)…
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.…
I apply the algebraic framework developed in [1] to study geometry of hyperbolic spaces in 1, 2, and 3 dimensions. The background material on projectivised Clifford algebras and their application to Cayley-Klein geometries is described in…
The field of numerical algebraic geometry consists of algorithms for numerically solving systems of polynomial equations. When the system is exact, such as having rational coefficients, the solution set is well-defined. However, for a…
Astrometry at centimeter wavelengths using Very Long Baseline Interferometry is approaching accuracies of ~1 uas for the angle between a target and a calibrator source separated by <1 degree on the sky. The BeSSeL Survey and the Japanese…
In the present paper a general setup for determination of imperfect geometry of radiotherapeutic devices has been proposed that base on geometric algebra framework. To account for this imperfect geometry, two methods of a calibration were…
There is a very extensive literature dealing with convex polytopes from the standpoints of combinatorics and numerical analysis. By contrast, the current paper adopts an alternative viewpoint that regards a polytope as an autonomous space…
We consider the problem of determining the length of the shortest paths between points on the surfaces of tetrahedra and cubes. Our approach parallels the concept of Alexandrov's star unfolding but focuses on specific polyhedra and uses…
This paper presents a complete Pascal interpolation scheme for use in the plane geometry mapping applied in association with numerical methods. The geometry of a domain element is approximated by a complete Pascal polynomial. The…
The geometric distortion of CCD field of view has direct influence on the positional measurements of CCD observations. In order to obtain high precision astrometric results, the geometric distortion should be derived and corrected…
Projective geometry provides the preferred framework for most implementations of Euclidean space in graphics applications. Translations and rotations are both linear transformations in projective geometry, which helps when it comes to…
This is a paper about triangle cubics and conics in classical geometry with elements of projective geometry. In recent years, N.J. Wildberger has actively dealt with this topic using an algebraic perspective. Triangle conics were also…
Geometric quantization is an attempt at using the differential-geometric ingredients of classical phase spaces regarded as symplectic manifolds in order to define a corresponding quantum theory. Generally, the process of geometric…