Re: Contour plots

[Hans-Bernhard B. <br...@ph...>]

Daniel J Sebald wrote:
> Hans-Bernhard Broeker wrote:

>> If it's closed, it doesn't really have a starting point, does it?

> Not mathematically, but in the plotting routine it has to start 
> somewhere.

Yes.  But that point is essentially just a random pick.  It has no
geometrical or mathematical relevance.

> But I'm sure the starting point for drawing the curve isn't 
> necessarily the best position.

Exactly.  Actually, it would only ever be so by strong coincidence.

Even a biassed choice like "if in doubt, place the label on the
uppermost point of a closed contour" would be better than the arbitrary
point where the linear list of points is stitched together to form a
closed loop.

> Of course, the optimum thing to do is to pick the location on the 
> level curve that is furthest from it's neighboring level curves.  It 
> has to work on general data, so gradient or such would be out.  

But the discrete gradient wouldn't be.

Remember that contours are based on a grid dataset, which actually has 
been cut into triangles in the x/y plane.  The contour curve is made 
from edges cutting through such triangles.  The gradient of the triangle 
can be used as a reasonable approximation of the surface gradient.