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

[Stefan de Konink]

On Sun, 18 Jun 2006, Lars Aronsson wrote:

> 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.

All the AutoCAD drawings made for the Dutch government are curves.
Although these are road 'building' instructions using functions to
describe a road reduce the data you need to save.

> 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?

Interpolating for export :)

> 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.

This is correct. But as you know you probably know Linear Algebra allows
you to transform the track from one projection to another one. I'm not
into GIS (yet), but eventually you also want to you elevation/altitude
data  to project this on a globe.

> 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.

This is correct ofcourse, but I hope you agree that for the editor it is
*way* faster to track an curve and the system interpolates nodes (if you
wish). But my data save point still stands.



Stefan