Spherical harmonics

From DmWiki

The spherical harmonics are a set of functions defined on the sphere. Mathematically, they can be used as a basis for all real- or complex-valued functions on the sphere; because of the way spherical harmonics are defined, it is easy to approximate other functions using a finite number of harmonics. Thus, functions on the sphere are represented as a vector of coefficients with respect to the spherical-harmonic basis.

Spherical harmonics are particularly important in precomputed radiance transfer. There, the "radiance transfer function" (which represents, in a certain sense, the way an object absorbs and reflects light around it) is encoded at each vertex or at each texel using spherical harmonics. The incoming light is also represented using spherical harmonics, and the two can be multiplied using just their coefficients, yielding a spherical-harmonic representation of the light on the object's surface, which can then be evaluated by a shader.

For more information, see:

• Wikipedia: Spherical harmonics (http://en.wikipedia.org/wiki/Spherical_harmonics)

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