Abstract: The discretization and analysis principle of conjugating surfaces for adaptive synthesis is proposed in order to construct computer software of conjugating surfaces. Taking the generating process of conjugating surfaces into account, the surface∑1, and the surface∑2 are regarded as two point sets, and the surface∑1, is regarded as the whole image of vestiges of the points, which satisfy the conjugating condition, on the surface ∑2 while moving in coordinate S1. So the mathematical model derived from the equivalent transformation of conjugating condition in differential geometry is suitable for the conjugation of the computers discrete calculation and the analytical solutions of conjugating surfaces. This method, which can solve not only the solutions of analytical conjugating surfaces, but also the solutions of discrete conjugating surfaces, makes the solutions of conjugating surfaces intelligent and automatic.

Key words: Adaptive synthesis, Conjugating surfaces, Discretization and analysis