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Spherical Harmonics: Difference between revisions
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(Created page with "Spherical Harmonics are a set of orthonormal basis functions ==Definition== ==Applications== ===Saliency=== * [http://duruofei.com/Research/SphericalHarmonics Ruofei's Webs...") |
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Spherical Harmonics are a set of orthonormal basis functions | Spherical Harmonics are a set of orthonormal basis functions | ||
==Background== | |||
===Harmonic Function=== | |||
[https://en.wikipedia.org/wiki/Harmonic_function Wikipedia Reference]<br> | |||
A function <math>f: \mathbb{R}^n \rightarrow \mathbb{R}</math> is a harmonic function if it satisfies Laplace's equation: | |||
* The Laplacian (or trace of the hessian) is zero. | |||
* <math>\Delta f = \frac{\partial^2f}{\partial x_1^2} + \frac{\partial^2f}{\partial x_2^2} + \cdots + \frac{\partial^2f}{\partial x_n^2} = 0</math> | |||
==Definition== | ==Definition== | ||