Automatic Band‐Limited Approximation of Shaders Using Mean‐Variance Statistics in Clamped Domain

In this paper, we present a new shader smoothing method to improve the quality and generality of band‐limiting shader programs. Previous work [YB18] treats intermediate values in the program as random variables, and utilizes mean and variance statistics to smooth shader programs. In this work, we extend such a band‐limiting framework by exploring the observation that one intermediate value in the program is usually computed by a complex composition of functions, where the domain and range of composited functions heavily impact the statistics of smoothed programs. Accordingly, we propose three new shader smoothing rules for specific composition of functions by considering the domain and range, enabling better mean and variance statistics of approximations. Aside from continuous functions, the texture, such as color texture or normal map, is treated as a discrete function with limited domain and range, thereby can be processed similarly in the newly proposed framework. Experiments show that compared with previous work, our method is capable of generating better smoothness of shader programs as well as handling a broader set of shader programs.