Travel planning - Finding farthest points of a polygon

Question

I’d like to organize a tour around the lake with 2 objectives:

maximise the length of shores to view
minimise travel distance

In order to do so I can:

Pick 2 most remote points on the lake in terms of travelling distance
Define ‘left’ and ‘right’ shores of the lake
Travel at equal distance between shores from A to B

What is the best way to find these 2 points?

UPDATE ON ORIGINAL Q:

The approach I am using is to place multiple random points and calculate Euclidean minimum spanning tree.

Iterate trough all pairs of points/nodes in order to find a couple with longest distance. Picture shows distance where destination is point at the North. It works but a bit cumbersome, so I am looking for ideas. Raster or vector will do.

This is about never ending discussion re polygon length.

score 2 · Accepted Answer · edited Apr 13 '17 at 12:33

2

Non-Convex Polygon

You should draw the Medial Axis Transform (skeleton or center-line) of the polygon. Options to do this:

Create Centerlines
use CGAL with arcobjects

Then utilize the centerlines calculate network based distanced between any two points and find the farthest ones.

Convex Polygon

The simplest, albeit not the most efficient way is to calculate (arcpy) pair-wise distances between each vertices of your polygon feature (Lake) and extract the greatest one. The complexity would be o(n^2), with n the number of vertices, for each polygon.

If you don't want to do coding (python), create a model with:

Feature To Point GP tool
DISTANCE BETWEEN POINTS TOOL (from Hawth's Analysis Tool)

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edited Apr 13 '17 at 12:33

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answered Sep 30 '15 at 23:45

Farid Cheraghi

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I think this will need a raster rather than vector solution, and so I would look at Cost Path first. – PolyGeo Sep 30 '15 at 23:55
@Farid Cher This will pick point B and most southern point – FelixIP Oct 01 '15 at 00:10
+1 @PolyGeo Although I am using vector approach to this, do you think I have to update my post with it? – FelixIP Oct 01 '15 at 00:31
My bad. I didn't notice non-convexity of your example. – Farid Cheraghi Oct 01 '15 at 00:32
@FelixIP My preference is usually a vector approach for accuracy, but this looks like a problem that needs a more pragmatic raster solution. Whichever you seek (at least in the first instance), I think you should say explicitly in your question. – PolyGeo Oct 01 '15 at 00:37
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@FlexiIP You need to calculate the medial axis (skeleton) of the polygon (see updated answer) – Farid Cheraghi Oct 01 '15 at 01:01

Travel planning - Finding farthest points of a polygon

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