Abstract: The general theory and method to construct the developable tangent curved
surface of rotary surface and mapping analysis between them are put forward systematically, the
mathematical model and mapping relationship of the developable tangent cylinder and
developable tangent cone of rotary surface are established. The differential equations of the
extreme value mapping curve and equidistant mapping curve are put forward according to the
theory of differential length ratio between the rotary surface and its developable tangent curved
surface. The deformation of mapping will be grasped accurately by the whole and local
deformation analysis.

Key words: geometry calculation, rotary surface, developable tangent curved surface;
mapping analysis