A novel method of the surfaces mapping, namely ℝ-mapping of the interacting part surfaces is disclosed. The preliminary remarks on the developed approach is followed by an in-detail consideration of the concept underlying in the ℝ-mapping of the interacting part surfaces. Then, principal features of ℝ-mapping of a part surface P1 onto another part surface P2 are disclosed. Due to ℝ-mapping of surface returns an equation of the mapped surface in natural representation, namely, in terms of fundamental magnitudes of the first and of the second order, the derived equation of the mapped surface is required been reconstructed and been represented in a convenient reference system. This issue got a comprehensive discussion in this chapter of the monograph. Consideration in the chapter end with two examples of implementation of the discussed method of part surfaces mapping.
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