A surface spherical harmonic expansion of gravity anomalies with respect to a geodetic reference ellipsoid can be used to model the global gravity field and reveal its spectral properties. In this paper, a direct and rigorous transformation between solid spherical harmonic coefficients of the Earth’s disturbing potential and surface spherical harmonic coefficients of gravity anomalies in ellips...

Various problems in Computer Vision become difficult due to a strong influence of lighting on the images of an object. Recent work showed analytically that the set of all images of a convex, Lambertian object can be accurately approximated by the low-dimensional linear subspace constructed using spherical harmonic functions. In this paper we present two major contributions: first, we extend pre...

The spherical harmonics are the angular portion of the solution to the Laplace equation in spherical coordinates and provide a frequency-basis for representing functions on the sphere. The spherical harmonic lighting, as defined by Robin Green at Sony Computer Entertainment in 2003, is a family of real-time rendering techniques that may produce certain realistic shading and shadowing with relat...

The harmonic projection (HP), which is implicit in the numerous harmonic transforms between physical and spectral spaces, is responsible for the reliability of the spectral method for modeling geophysical phenomena. As currently configured, the HP consists of a forward transform from physical to spectral space (harmonic analysis) immediately followed by a harmonic synthesis back to physical spa...

The real spherical harmonics have been used extensively in computer graphics, but the conventional representation is in terms of spherical coordinates and involves expensive trigonometric functions. While the polynomial form is often listed for low orders, directly evaluating the basis functions independently is inefficient. This paper will describe in detail how recurrence relations can be use...

A collection of MATLAB classes for computing and using spherical harmonic transforms is presented. Methods of these classes compute differential operators on the sphere and are used to solve simple partial differential equations in a spherical geometry. The spectral synthesis and analysis algorithms using fast Fourier transforms and Legendre transforms with the associated Legendre functions are...

A complete discrete set of spherical single-particle wave functions for studies of weakly-bound many-body systems is proposed. The new basis is obtained by means of a local-scale point transformation of the spherical harmonic os-cillator wave functions. Unlike the harmonic oscillator states, the new wave functions decay exponentially at large distances. Using the new basis, characteristics of w...

We carry out the harmonic analysis on four Platonic spherical three-manifolds with different topologies. Starting out from the homotopies (Everitt 2004), we convert them into deck operations, acting on the simply connected three-sphere as the cover, and obtain the corresponding variety of deck groups. For each topology, the three-sphere is tiled into copies of a fundamental domain under the cor...