Flat Approximations of Surfaces Along Curves

Demonstratio mathematica

article

Shyuichi Izumiya¹  Saki Otani² 

[1] DEPARTMENT OF MATHEMATICS HOKKAIDO UNIVERSITY SAPPORO 060-0810;KYORITSU SHUPPAN CO. LTD KOHINATA BUNKYO-KU

关键词: flat approximations;    curves on surfaces;    contour generators;    developable surfaces;   

DOI  :  10.1515/dema-2015-0018

学科分类：外科医学

来源: De Gruyter

【 摘 要 】

We consider a developable surface tangent to a surface along a curve on the surface. We call it an osculating developable surface along the curve on the surface. We investigate the uniqueness and the singularities of such developable surfaces. We discover two new invariants of curves on a surface which characterize these singularities. As a by-product, we show that a curve is a contour generator with respect to an orthogonal projection or a central projection if and only if one of these invariants constantly equal to zero.

【 授权许可】

CC BY