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Bridging the gap between rectifying developables and tangent developables: a family of developable surfaces associated with a space curve
- Source :
- Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences. 477:20200617
- Publication Year :
- 2021
- Publisher :
- The Royal Society, 2021.
-
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 .
- Subjects :
- Physics
Developable surface
Bridging (networking)
Ruled surface
General Mathematics
ComputingMethodologies_IMAGEPROCESSINGANDCOMPUTERVISION
General Engineering
General Physics and Astronomy
Tangent
020207 software engineering
Geometry
02 engineering and technology
ruled surface
Space (mathematics)
rectifying developable
geodesic curvature
020303 mechanical engineering & transports
0203 mechanical engineering
0202 electrical engineering, electronic engineering, information engineering
Point (geometry)
Mathematics::Differential Geometry
Tangent developable
tangent developable
ComputingMethodologies_COMPUTERGRAPHICS
Geodesic curvature
Subjects
Details
- ISSN :
- 14712946 and 13645021
- Volume :
- 477
- Database :
- OpenAIRE
- Journal :
- Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
- Accession number :
- edsair.doi.dedup.....c809c92f7c6469611bb888258853e3b0