[OSM-dev] Least squares to trace curved GPS data as segments

[Lars Aronsson]

Stefan de Konink wrote:

> What I would like to suggest is a to automatically trace the 
> points using Least Squares to curves. 
> http://en.wikipedia.org/wiki/Least_squares

(Today I'm going to be the old-school GIS guy, for a change.)

These are the traditional arguments against your suggestions:

No geographic information system (GIS) has ever used curved line 
segments or splines.  All use straight line segments and curves 
are represented by inserting more points.  Even for "straight" 
lines, there should be a maximum length of line segments.

Drawing a nice map on the OSM website can be one thing, but the 
purpose of OSM is to generate free geographic data that can be 
used in other applications, including traditional GIS software.  
These can handle straight line segments, but not curved ones. How 
were you going to export the curved segments?

Any curve drawing function becomes dependent on the chosen map 
projection.  What looks like a straight line in one projection, 
can be a curve in another.  The border between the northwestern 
United States and Canada runs along the latitude 49 degrees north 
of the equator, so you only need two endpoints and a long line. 
But if you try to drive a car along this line, you will constantly 
be turning.  If it was 89 degrees north, it would be more clear 
that you are indeed driving in a circle around the pole.

While this problem also appears with straight line segments, the 
solution is to make each segment short enough that this bending 
error becomes smaller than the precision of the coordinates.  And 
if you are using short enough segments, you can just as well do 
with straight line segments.


-- 
  Lars Aronsson (lars at aronsson.se)
  Aronsson Datateknik - http://aronsson.se