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Spherical cap harmonics revisited and their relationship to ordinary spherical harmonics
Physics and Chemistry of the Earth, Part A: Solid Earth and Geodesy, 1999Abstract The “global” representation of the geomagnetic field in terms of ordinary spherical harmonics (SHs) and its corresponding set {g,h} of coefficients has been studied extensively, but the “local” representation in terms of spherical cap harmonics (SCHs) and its corresponding set {G,H} of coefficients is not yet well understood.
De Santis, A. +2 more
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SIGGRAPH Asia 2017 Technical Briefs, 2017
Spherical Harmonics (SH) are a convenient basis for representing various signals in computer graphics, with lighting and visibility being the most common. While the inputs tend to be strictly positive, after projection the reconstructed function can be negative.
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Spherical Harmonics (SH) are a convenient basis for representing various signals in computer graphics, with lighting and visibility being the most common. While the inputs tend to be strictly positive, after projection the reconstructed function can be negative.
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On the Symmetries of Spherical Harmonics
Canadian Journal of Mathematics, 1954Letbe a finite group of transformations of three-dimensional Euclidean space, such that the distance between any two points is preserved by all transformations of the group. Such a group is a group of orthogonal linear transformations of three variables, or, geometrically speaking, a group of rotations and rotatory inversions. Thirty-two groups of this
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Advances in Applied Clifford Algebras, 2016
Let \(\Delta\) be the Laplace operator in \(\mathbb R^3\) with the coordinates \((x,y,t)\). The author is interested in the solutions of the equation \[ t \Delta v + \frac{\partial v}{\partial t} =0 \tag{1} \] which is a particular case of the equation \[ t \Delta v+ \lambda \frac{\partial v}{\partial t} =0 ,\tag{2} \] with \(\lambda\) real ...
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Let \(\Delta\) be the Laplace operator in \(\mathbb R^3\) with the coordinates \((x,y,t)\). The author is interested in the solutions of the equation \[ t \Delta v + \frac{\partial v}{\partial t} =0 \tag{1} \] which is a particular case of the equation \[ t \Delta v+ \lambda \frac{\partial v}{\partial t} =0 ,\tag{2} \] with \(\lambda\) real ...
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1988
In Chaps. 13, 14 and 15 we have studied the motion of a particle of mass m under the influence of a spherically symmetric potential V(r). With such a potential the forces act only in the direction of the line from the origin of coordinates to the position of the particle, i.e.
Erich W. Schmid +2 more
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In Chaps. 13, 14 and 15 we have studied the motion of a particle of mass m under the influence of a spherically symmetric potential V(r). With such a potential the forces act only in the direction of the line from the origin of coordinates to the position of the particle, i.e.
Erich W. Schmid +2 more
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Computation of Spherical Harmonics and Approximation by Spherical Harmonic Expansions,
1985Abstract : A technique is developed for generating spherical harmonics by exact computation (in integer mode) thereby circumventing any source of rounding errors. Essential results of the theory of spherical harmonics are recapitulated by intrinsic properties of the space of homogeneous harmonic polynomials.
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