Abstract: When the boundary conditions of the two ends of the geodesic lines on the revolving
surface are given, according to the Clairant theorem, a kind of shape, number and computer
combination method is designed. To avoid the abstraction and complexity of the traditional solution
of partial differential equations, the corresponding mathematical model based on the mapping process
is established, and finally the geodesic line is drawn. The proposed method is suitable for the
revolving surface, which possesses the advantages of visual image, controllable precision, stable and
reliable.

Key words: revolving surface, geodesic line, Clairant theorem, algorithm design