I’ll have to do a land navigation exercise tomorrow. I’ve been given a set of 6 points. One is more or less central (little below center, actually) and the others are roughly in a pentagon with two close at the bottom. The route I’ve been given has me zigzagging all over the place. I want to rework the route to make it as short as possible. I have to start at the center and end at the center (where the bus is). I can’t quite come up with an algorithm for finding it.

Right now, my idea is to connect all the outside points in a closed loop. Then I need to find some way to include the center point. I figure the best way would be to break the link between, say, A and B, and make the route go A-Center-B. Then I’d just need to find out which should be broken.

Is my method valid? Is there a better way? Are there at least nonobvious rules that say it can’t be the shortest path?

How can I easily find the best link to break? I thought about finding the biggest interior angle, but that’s no good if the triangle is short…or is it?

I’m supposed to spend 4 hours outside tomorrow in 20-something degree weather with snow/rain. I’d REALLY like to keep it down to 3 or so. Help me out, or wish me luck.

I’t’s been a long time since i did any of this but I’d say that you need to examine the terrain closely. a longer route that is easy to mark your progress on is better than a short but hard to follow route through woods, obstacles, etc. Look for terrain markers you can use.

heh heh…can’t change too much Well with no compass, no map, I’d say knowing what your stride is will be key, that way you can make a geuss at your relative position. Count your pace and good luck!

I suppose you could call that a compass, but I meant the spinny needle kind. Finding the points will be easy as pie. I just don’t want to walk very far. As I add it up now, it’s 3000 meters following the given path (screw that), which is like 1.86 miles. Not that bad as a whole, but I want it as short as possible.

In the meantime, if the outer five points are close enough to forming a regular convex pentagon that a loop is best, you want to include the center by breaking the step between points A and B for which

M(A,B) = d(center,A) + d(center,B) - d(A,B)

is smallest, where d(a,b) is the distance between points a and b, with “center” being the center. There are only five values of M to calculate, so this shouldn’t be too hard. Note that a loop is not always best, but it sounds like for your points it probably is.

Or, if you don’t want to post the real coordinates, could you post a randomly shifted version? If you do either of these, I can post the shortest route (brute force with a computer).

A very useful thing in land-nav is to constantly be looking behind you. As long as you can get back to you last waypoint, you can pretty much beat the thing to death. If you go from ‘A’ to where you think ‘B’ might be, and ‘B’ is not there; getting back to ‘A’ is critical. If you can get back, you’ve lost some time; if you can’t get to either ‘A’ or ‘B’ you’re hosed.

Turns out it didn’t matter after all. There was so much brush and very prominant hills that any distance calc took a back seat to actually being able/wanting to walk it. The lower left and right points were separated from the upper left and right points, respectively, by hills at least 200m up. No thanks, I’ll go around. When it was plotted out, it seemed intuitive enough which route was quickest. The lame one was when they gave us a bridge as our last point, but didn’t post a marker for it. I spent at least 5 minutes on the bridge going “IT’S RIGHT HERE!! WHERE IS IT?!” I eventually called back to CP to ask them and they told me to go to the CP. Well they were assuming that I was doing the points in order and thought I was done. I still had a point left. So I went after that instead. Ended up pushing, literally, through at least 20 feet of torns total over that 700m hike to the last point.