Computationally efficient methods of approximations of the S-shape functions for image processing and computer graphics tasks

The paper describes a number of methods for approximation of the S-shape functions, frequently used in computer graphics or image processing. The main focus is on efficient software and hardware implementations. We present original code for the high and low level languages which implement different approximations of the S-shape functions. Additionally we introduce the FixedFor <> template class which fills the gap of efficient representation of different length fixed-point data formats in C++.