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From: Rune Allnor <allnor@tele.ntnu.no>
Newsgroups: comp.soft-sys.matlab
Subject: Re: find distance along complicated geometric surface
Date: Tue, 18 May 2010 11:52:48 -0700 (PDT)
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On 18 Mai, 19:51, "Matt J " <mattjacREM...@THISieee.spam> wrote:
> Rune Allnor <all...@tele.ntnu.no> wrote in message <99c70f0a-1227-4506-b3a1-ab8556861...@l6g2000vbo.googlegroups.com>...
> > The *idea* is simple, assuming you already have a surface
> > consisting of edges and vertices, like in a triangulation:
> > Track the points where you cross edges, and compute the
> > distance between consecutive edge crossings (possibly also
> > accounting for path waypoints). The total distance along the
> > path will be the cumulant sum of all such edge-to-edge
> > distances.
>
> ========
>
> The difficulty though, Rune, is that you don't have the shortest-distance path a priori. It's finding the shortest path, not computing its length, which is the challenge.

I can't see how being able to compute the distance along
a genrral path isn't helpful:

1) Select an initial path
2) Compute the distance along this path
3) Modify the path in a way that likely
   might shorten the distance
4) Repeat from 2

until no significant improvements in path distance can be made.
Of course, one can only hope to find a local solution to this
problem.

Rune