Fast approximation to spherical harmonics rotation

We present a fast and simple approximation of spherical harmonic rotation which decreases the asymptotic complexity and achieves a speedup of four to six in practical applications. The rotation procedure's simplicity allows implementation in a pixel shader of standard graphics hardware. The main idea is to replace the general spherical harmonic rotation matrix by its truncated Taylor expansion, resulting in a sparse matrix. We show applications in global illumination (radiance interpolation) and GPU-based real-time shading (normal mapping on surfaces with arbitrary BRDFs illuminated by low-frequency environment lighting). Although the rotation approximation is accurate only for small rotation angles, we show this is not a serious limitation in our applications.