Spherical Harmonics: Difference between revisions
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==Definition== | ==Definition== | ||
Spherical Harmonics are a set of orthonormal basis functions defined on the sphere.<br> | |||
Below are some explicit formulas for Laplace spherical harmonics stolen from <ref name="stupidsh">Peter-Pike Sloan, [http://www.ppsloan.org/publications/StupidSH36.pdf Stupid Spherical Harmonics (SH) Tricks]</ref> | |||
==Applications== | ==Applications== | ||
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* [http://www.ppsloan.org/publications/StupidSH36.pdf Stupid SH] | * [http://www.ppsloan.org/publications/StupidSH36.pdf Stupid SH] | ||
* [https://en.wikipedia.org/wiki/Spherical_harmonics Wikipedia page] | * [https://en.wikipedia.org/wiki/Spherical_harmonics Wikipedia page] | ||
==References== | |||
<references /> | |||
Revision as of 13:51, 6 November 2019
Spherical Harmonics are a set of orthonormal basis functions
Background
Harmonic Function
Wikipedia Reference
A function \(\displaystyle f: \mathbb{R}^n \rightarrow \mathbb{R}\) is a harmonic function if it satisfies Laplace's equation:
- The Laplacian (or trace of the hessian) is zero.
- \(\displaystyle \Delta f = \frac{\partial^2f}{\partial x_1^2} + \frac{\partial^2f}{\partial x_2^2} + \cdots + \frac{\partial^2f}{\partial x_n^2} = 0\)
Definition
Spherical Harmonics are a set of orthonormal basis functions defined on the sphere.
Below are some explicit formulas for Laplace spherical harmonics stolen from [1]
Applications
Saliency
Ruofei did a project on Saliency using Spherical Harmonics as part of his PhD dissertation.
Resources
References
- ↑ Peter-Pike Sloan, Stupid Spherical Harmonics (SH) Tricks