In this paper, we propose a new method for threedimensional object indexing based on D.A.M.C-S.H.C descriptor (Direct and Analytical Method for Calculating the Spherical Harmonics Coefficients). For this end, we propose a direct calculation of the coefficients of spherical harmonics with perfect precision. The aims of the method are to minimize, the processing time on the 3D objects database an...

We describe and compare two types of microwave sky simulations which are good for small angular scales. The first type uses expansions in spherical harmonics, and the second one is based on plane waves and the Fast Fourier Transform. The angular power spectrum is extracted from maps corresponding to both types of simulations, and the resulting spectra are appropriately compared. In this way, th...

Spherical harmonics are often used for compact description of incident radiance in low-frequency but distant lighting environments. For interaction with nearby emitters, computing the incident radiance at the center of an object only is not sufficient. Previous techniques then require expensive sampling of the incident radiance field at many points distributed over the object. Our technique all...

The first part of this talk is dedicated to the introduction of the nonlinear Galerkin method applied to the Navier-Stokes equation on the rotating sphere. The Navier-Stokes equation plays a fundamental role in meteorology by modelling meso-scale (stratified) atmospherical flows. The nonlinear Galerkin method is implemented by using type three vector spherical harmonics, and convergence is sket...

Spherical harmonics are widely used in 3D image processing due to their compactness and rotation properties. For example, it is quite easy to obtain rotation invariance by taking the magnitudes of the representation, similar to the power spectrum known from Fourier analysis. We propose a novel approach extending the spherical harmonic representation to tensors of higher order in a very efficien...

Nonlinear thermal convection in a spherical fluid layer in the presence of spherically symmetric gravity, spherical RayleighBénard convection, is investigated. At the onset of spherical Rayleigh-Bénard convection, there exists the (2l+1)-fold degeneracy of the linear solution, where l is the degree of a spherical harmonics. Nonlinear convection is studied through fully three-dimensional numeric...

We present a 3D shape retrieval methodology based on the theory of spherical harmonics. Using properties of spherical harmonics, scaling and axial flipping invariance is achieved. Rotation normalization is performed by employing the continuous principal component analysis along with a novel approach which applies PCA on the face normals of the model. The 3D model is decomposed into a set of sph...

We present a spectral method for solving elliptic equations which arise in general relativity, namely three-dimensional scalar Poisson equations, as well as generalized vectorial Poisson equations of the type ∆ ~ N + λ~ ∇(~ ∇ · ~ N) = ~ S with λ 6= −1. The source can extend in all the Euclidean space R, provided it decays at least as r−3 (scalar case) or r−4 (vectorial case). A multi-domain app...

We establish a precise relationship between spherical harmonics and Fourier basis functions over a hypercube randomly embedded in the sphere. In particular, we give a bound on the expected Boolean noise sensitivity of a randomly rotated function in terms of its “spherical sensitivity,” which we define according to its evolution under the spherical heat equation. As an application, we prove an a...