Optimal Spherical Harmonics Projection
نویسنده
چکیده
We introduce the reader to the mathematics behind projection of n-dimensional vectors into a basis on n-dimensional space, where n can be anything upto and including infinity. We show how ideally one wants to project into the duals of a basis if this basis is not orthonormal, and provide the mathematics to formulate this operation in matrix form. The second part of the article discusses spherical harmonics projection of real-valued scalar functions on S2, used in realtime global illumination applications and conclude that projection into the dual basis is equal to calculating a least-squares solution.
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