Bridging the gap between rectifying developables and tangent developables: a family of developable surfaces associated with a space curve.

ABSTRACT: There are two familiar constructions of a developable surface from a space curve. The tangent developable is a ruled surface for which the rulings are tangent to the curve at each point and relative to this surface the absolute value of the geodesic curvature κ _g of the curve equals the curvature κ. The alternative construction is the rectifying developable. The geodesic curvature of the curve relative to any such surface vanishes. We show that there is a family of developable surfaces that can be generated from a curve, one surface for each function k that is defined on the curve and satisfies |k| ≤ κ, and that the geodesic curvature of the curve relative to each such constructed surface satisfies κ _g  = k.

SUBMITTER: Seguin B 

PROVIDER: S-EPMC8317982 | biostudies-literature | 2021 Feb

REPOSITORIES: biostudies-literature