Graphics Reference

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Appendix A

Projection of face images in 9-D spherical harmonic

space

The multiplication of two spherical harmonic basis satisfies the following relation according

to [Cohen-Tannoudji and et al., 1977]:

where is the Clebsch-Gordan coefficients. The coefficient of

in the righthand side is non-zero if and only if

range from

to

and is even.

We then look at the second term of the righthand side in equation 6.7. Suppose

comes from and comes from the factor corresponding to lighting. For any

we have If for any we have That

proves the claim that if does not have the first four order components, the

second term of the righthand side in equation 6.7 contains components with orders equal to or

higher than 3.

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