Abstract: Based on the developable curved surface theory of differential geometry, the
method to construct the developable tangent curved surface passed a curve on a curved surface is
put forward, the expression form and type division of the developable tangent curved surface is
given, the overall and partial mapping analysis between two surfaces is realized through
establishing the mapping relationship of them and the deformation of surface is grasped
accurately. The method is validated by example and can be applied to the design and approximate
development of curved surface and surface texture mapping.

Key words: geometry calculation, developable tangent curved surface, mapping between
surfaces, deformation analysis