相关论文: Analytical calculation of the solid angle defined …

We derive analytical expressions for the solid angle subtended by a right circular cylinder at a point source with cosine angular distribution in the case where the source and the cylinder axes are mutually orthogonal.

We derive analytical expressions for the solid angle subtended by a circular disc at a point source with cosine angular distribution ($f(\mu)=\mu/\pi$)under the sole condition that the disc lies in the half-space illuminated by the source…

The solid angle subtended by a right circular cylinder at a point source located at an arbitrary position generally consists of a sum of two terms: that defined by the cylindrical surface ($\Omega_{cyl}$) and the other by either of the end…

Closed form solutions for the computation of the solid angle from polygonal cross-sections are well known, however similar formulae for computation of projected solid angle are not generally available. Formulae for computing the projected…

This paper addresses the computation of normalized solid angle measure of polyhedral cones. This is well understood in dimensions two and three. For higher dimensions, assuming that a positive-definite criterion is met, the measure can be…

This paper presents formulae for calculation the solid angle of intersecting spherical caps, conical surfaces and polyhedral cones.

A concise derivation of the "Joel equations", which allow for the determination of the axis angle 2V from measurements of extinction directions on a spindle stage, is provided starting from the wave-equation. Only analytic methods and no…

This paper studies the problem of identifying directions of axial symmetry in multivariate distributions. Theoretical results are derived on how the measure or cardinality of the set of symmetry directions relates to spherical symmetry. The…

This paper aims to develop the mathematical representation of a surface generated by elliptical arcs joining the sides of a regular polygon to a point lying vertically upward on the central axis of the polygon. The volume of the…

The intersection of two orthogonal cylinders represents a classical problem in computational geometry with direct applications to engineering design, manufacturing, and numerical simulation. While analytical solutions exist for the fully…

Design details of a 127 degree electrostatic cylindrical spectrometer equipped with a position-sensitive micro-channel plate detector for measuring the sputtered ions in collisions of highly charged ions with solid surface is described. The…

We give a new characterization of pseudoconvex point, and of finite type point, using analytic discs.

Partially coherent electromagnetic sources with cylindrical symmetry and infinite extent radiating outwards are introduced. Their 3x3 cross-spectral density matrix is given through expansions of the field components in terms of basis…

An ill-posed problem of synthesis of the Pierce electrodes for a cylindrical beam with a polygonal cross-section is considered. It is assumed that a beam of charged particles is extracted from a space-charge-limited planar diode and the…

In positron emission tomography (PET), a clear theoretical model describing how system sensitivity varies as a source is moved trans-axially within the field of view (FOV) is lacking. The current understanding and practical intuition often…

Optimal search strategies where targets are observed at several different angles are found. Targets are assumed to exhibit rectangular symmetry and have a uniformly-distributed orientation. By rectangular symmetry, it is meant that one side…

In this paper, we begin by giving a necessary and sufficient condition of existence for the quadrature surfaces problem in the case where the term source is a uniform density supported by a segment. Then, we use the Steiner continuous…

Generalized diffusion type equations are considered and point symmetry analysis is applied to them. The equations with extremal order point symmetry algebras are described. Some old geometrical results are rederived in connection with…

A new method to calculate the electric field inside a spherical shell with surface charge in terms of solid angle is presented. The integral can be readily carried out without invoking special functions typically used for this classical…

Here we analyze three dimensional analogues of the classical Crofton's formula for planar compact convex sets. In this formula a fundamental role is played by the visual angle of the convex set from an exterior point. A generalization of…