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Precomputation-Based Rendering presents a unified mathematical view of precomputation-based rendering, while discussing its motivation, history and current and future research directions. It goes back to some of the early origins of precomputation-based rendering in replaying offline solutions for image relighting. Following this, it describes the new innovations in terms of environment maps and spherical harmonic convolution that inspired the PRT method of Sloan et al. in 2002, the approach that for the first time brought precomputation-based ideas into the mainstream of real-time rendering. It goes on to discuss a number of new innovations in this field over the past six years, to all-frequency effects, changing lighting and view, reflectance editing, dynamic scenes and lighting design. Precomputation-Based Rendering is an invaluable reference for students and computer graphics researchers. It will also be of interest to professional graphics practitioners.