# [R] NOT R SPECIFIC The mean of a group of lines

Bob Sandefur rls at pincock.com
Mon Nov 19 15:24:13 CET 2001

```Hi-

Suppose I  have a group of lines which are similar given as serial points (assuming the individual points on the lines are close enough spaced that the straight line between points is the true line). (These are called polylines in Autocad). Examples include:
1. Different contour lines on a single topographic map.
2. Topographic contour maps of the same area from different surveys.
3. GPS logs of the driving to work by the same route daily over several years. (X Y Z position at 1 second intervals)
4. Redigitization of the same contour line on a map.
Can anyone suggest methods or references on how to compare two or more lines? For just two polylines, resampling at a fixed step and doing vector nearest distance to the other line and then doing dx dy dz (or (dx^2+dy^2)^0.5 dz) statistics seems a reasonable approach, but I so far have not found a reference for finding the "mean" of several lines. One way of finding the mean of several lines would seem to be to find then mean of two lines as the midpoint of resampled nearest distance; Make this a new line and then add the next line and find the "mean" of this and the first two by weighting the distance by 1/3 and 2/3; add the next line and weight by 1/4 3/4 and so on to get the "mean" line; after finding the "mean" then statistics of the dx dy dz to each line from the mean might be appropriate.

Thanx

Robert (Bob) L Sandefur
Principal Geostatistician
Pincock Allen & Holt (A Hart Crowser Company)
International Minerals Consultants
274 Union Suite 200
Lakewood CO 80228
USA
303 914-4467  v
303 987-8907 f
rls at pincock.com

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