/S { L R } def

to travel straight.

]]>OK, I’ll keep this secret between you, me and the internet. :)

I like the dual formula; probably the analog is easier to interpret in spherical geometry.

]]>There is also a curious non-differential formula for volume one may glean from this approach. The area of a 2-dimensional cross-section is ∑(π-\theta) – 2π, so one gets a formula which is C ∑(π-\theta_e)l_e -2π Vol(P*), where P* is the dual polyhedron of all 2-planes that meet P, and C is some constant.

]]>math……….. ]]>

One can look at two recent surveys by Crovisier: http://arxiv.org/pdf/1405.0305.pdf

Or Bonatti https://hal.archives-ouvertes.fr/hal-00463421/document or the longer treaty by Crovisier: http://arxiv.org/PS_cache/arxiv/pdf/0912/0912.2896v1.pdf (Chapter 1) for how this concept is quite used in the study of smooth dynamics (from a C1-generic viewpoint).