Waveshaping is known by several alternative names, including 'non-linear distortion' and 'non-linear processing'. Jean-Claude Risset is credited with the first use of the technique, in 1969, though the principle technical papers on the technique were published independently ten years later, by Daniel Arfib, James Beauchamp, and Marc Lebrun.
Recalling the structure of the basic wavetable, and assuming that it contains a sine wave, the regular increment of the instantaneous phase can be represented by a straight line. This line is the 'transfer function' applied to the wavetable. Complex timbral modification can be created by simple means, and this modification can be made amplitude-sensitive and thus reflect the behaviour of acoustic instrumental sounds. The transfer function can be drawn empirically, or it can be calculated by mathematical formulae which give precise control of the harmonics arising from the waveshaping process. (Source - Richard Dobson (1992). A Dictionary of Electronic and Computer Music Technology. Oxford University Press.)