Geometry of Surfaces pp 35-64 | Cite as

# On a Possibility of Classification of Part Surfaces

## Abstract

This chapter is devoted to the analysis of a possibility of classification of part surfaces. Irrespective of no scientific classification of smooth regular surfaces in global sense is feasible in nature, local part surface patches can be classified. For the investigation of geometry of local part surface patches planar characteristic images are employed. In this analysis Dupin indicatrix, curvature indicatrix, and circular diagrams at a part surface point are covered in detail. Base on the obtained results of the analysis two more circular charts are developed. One of them employs the part surface curvature indicatrices, while another one is based on the properties of circular diagrams at a current part surface point. This section of the book ends with a brief consideration of one more useful characteristic curve, which can be helpful for analytical description of geometry of a part surface locally.

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