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Sparse zonal harmonic factorization for efficient sh rotation.
| Content Provider | CiteSeerX |
|---|---|
| Author | Nowrouzezahrai, Derek Simari, Patricio Fiume, Eugene |
| Abstract | We present a sparse analytic representation for spherical functions, including those expressed in a spherical harmonic (SH) expansion, that is amenable to fast and accurate rotation on the GPU. Exploiting the fact that each band-l SH basis function can be expressed as a weighted sum of 2l+1 rotated band-l zonal harmonic (ZH) lobes, we develop a factorization that significantly reduces this number. We investigate approaches for promoting sparsity in the change-of-basis matrix, and also introduce lobe sharing to reduce the total number of unique lobe directions used for an order-N expansion from N 2 to 2N −1. Our representation does not introduce approximation error, is suitable for any type of spherical function (e.g., lighting or transfer), and requires no offline fitting procedure; only a (sparse) matrix multiplication is required to map to/from SH. We provide code for our rotation algorithms, and apply them to several real-time rendering applications. |
| File Format | |
| Access Restriction | Open |
| Subject Keyword | Sparse Zonal Harmonic Factorization Efficient Sh Rotation Spherical Function Approximation Error Sparse Analytic Representation Order-n Expansion Spherical Harmonic Weighted Sum Change-of-basis Matrix Several Real-time Rendering Application Total Number Rotation Algorithm Matrix Multiplication Band-l Sh Basis Function Band-l Zonal Harmonic Offline Fitting Procedure Unique Lobe Direction |
| Content Type | Text |
