A beautiful related result is the Crofton Formula [0], which says that you can measure the length of any curve by appropriately counting the number of straight lines that intersect it.
(My co-authors and I discovered a generalization of the formula that also holds in curved space [1].)
Interesting as the paper is, please link to the arxiv abstract rather than the pdf as that's more web friendly. Reader can always click on he pdf link there.
I'm especially intrigued by the "Timelike, Spacelike, and Lightlike" diagram on Page 10 of the linked paper where "lightlike" phenomena share an endpoint. Fascinating.
https://arxiv.org/abs/1505.05515