Journal Article Existence conditions of framed curves for smooth curves

FUKUNAGA, Tomonori  ,  TAKAHASHI, Masatomo

108 ( 2 )  , pp.763 - 774 , 2017-01-28 , Springer International Publishing
A framed curve is a smooth curve in the Euclidean space with a moving frame. We call the smooth curve in the Euclidean space the framed base curve. In this paper, we give an existence condition of framed curves. Actually, we construct a framed curve such that the image of the framed base curve coincides with the image of a given smooth curve under a condition. As a consequence, polygons in the Euclidean plane can be realised as not only a smooth curve but also a framed base curve.

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