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This paper presents a new set of hemispherical basis functions dedicated to hemispherical data representation. These functions are derived from associated Legendre polynomials. We demonstrate the usefulness of this basis for representation of surface reflectance functions, rendering using environment maps and for efficient global illumination computation using radiance caching. We show that our basis is more appropriate for hemispherical functions than spherical harmonics. This basis can be efficiently combined with spherical harmonics in applications involving both hemispherical and spherical data.