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This paper presents a novel basis function, called spherical piecewise constant basis function (SPCBF), for precomputed radiance transfer. SPCBFs have several desirable properties: rotatability, ability to represent all-frequency signals, and support for efficient multiple product. By smartly partitioning the illumination sphere into a set of subregions, and associating each subregion with an SPCBF valued 1 inside the region and 0 elsewhere, we precompute the light coefficients using the resulting SPCBFs. Efficient rotation of the light representation in SPCBFs is achieved by rotating the domain of SPCBFs. We run-time approximate the BRDF and visibility coefficients using the set of SPCBFs for light, possibly rotated, through fast lookup of summed-area-table (SAT) and visibility distance table (VDT), respectively. SPCBFs enable new effects such as object rotation in all-frequency rendering of dynamic scenes and on-the-fly BRDF editing under rotating environment lighting. With graphics hardware acceleration, our method achieves real-time frame rates.
Computer Graphics, Color, Shading, shadowing, and texture, Real-time Rendering, Precomputed Radiance Transfer, Spherical Piecewise Constant Basis Functions

Y. Jia, S. Hu, K. Xu, C. Tai and H. Fu, "Spherical Piecewise Constant Basis Functions for All-Frequency Precomputed Radiance Transfer," in IEEE Transactions on Visualization & Computer Graphics, vol. 14, no. , pp. 454-467, 2007.
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