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In differential geometry, a smooth surface in three dimensions has a ridge point when a line of curvature has a local maximum or minimum of principal curvature. The set of ridge points form curves on the surface called ridges. The ridges of a given surface fall into two families, typically designated ''red'' and ''blue'', depending on which of the two principal curvatures has an extremum. At umbilical points the colour of a ridge will change from red to blue. There are two main cases: one has three ridge lines passing through the umbilic, and the other has one line passing through it. Ridge lines correspond to cuspidal edges on the focal surface. ==References== * Ian R. Porteous (2001) ''Geometric Differentiation'', Chapter 11 Ridges and Ribs, pp 182–97, Cambridge University Press ISBN 0-521-00264-8 . 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Ridge (differential geometry)」の詳細全文を読む スポンサード リンク
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