Are there arc-length parametrization functions hidden somewhere in Sage? I have some 3D parametric curves (smooth) of length L
along which I would like to put n
dots at regular intervals. What I've been doing so far is using numerical integration to find the arc length parameter, and then using find_root
to find the positions of the dots (spaced by arc length L/n
).
This is pretty slow, and has the further limitation that I need to specify a region on which find_root
should work. If the parametrization is really uneven, it's tough to develop a good initial estimate for where to look.
So, does anyone have other ideas for doing this? Thanks!