Greg Egan on Nostr: nprofile1q…7749s Bachman writes: “Here’s a more general problem: Given a 3D ...
nprofile1qy2hwumn8ghj7un9d3shjtnddaehgu3wwp6kyqpqn5m2nzhgp2ma9wxvrfzs46p34slg4pqpuhrj5uysdperw325564sf7749s (nprofile…749s) Bachman writes:
“Here’s a more general problem: Given a 3D curve in space, what shape would a rectangular strip of paper take on if it was bent so the line down its center followed the curve? (For the mathematicians: obvious conditions, such as having Gaussian curvature zero, or being a ruled surface, are not sufficient.)”
The extra condition is surely just that the centreline is a geodesic of the surface, and that *is* a solved problem:
https://www.gregegan.net/SCIENCE/PSP/PSP.html#RectifyingDevelopables
“Here’s a more general problem: Given a 3D curve in space, what shape would a rectangular strip of paper take on if it was bent so the line down its center followed the curve? (For the mathematicians: obvious conditions, such as having Gaussian curvature zero, or being a ruled surface, are not sufficient.)”
The extra condition is surely just that the centreline is a geodesic of the surface, and that *is* a solved problem:
https://www.gregegan.net/SCIENCE/PSP/PSP.html#RectifyingDevelopables