Re: Finding the point on a conic, closest to an arbitrary point.

> I still don't understand what you're
> you're calculating, but it seems to
> involve something other than Euclidean distances.
>
> Ken Pledger.

The problem was, neither was I. I placed the d_alg distance in a wrong context. I'll explain the matter, as I took some of your time as well ;)

As I said somewhere before, I'm looking at this with the goal of 'fitting' a conic on scattered data. In this context, d_alg is an easy-to-compute alternative to the eucledian distance.

In http://lumumba.uhasselt.be/~danjal/conicanalog.gif you can see d_alg(X,C)^2 = d_x^2 + d_y^2. As you can see, d_geo <= d_x and d_geo <= d_y. Also this measure is not geometrically or statistically meaningfull, but provides a good initialization.

This basicly means that my assumption of being able to search for roots was wrong, hence the rest of the derivation is bogus.

The upside of the matter is that I can now solve this with Lagrange multipliers, which were previously unknown to me.

Thanks to all for the input, it's well appreciated!

- Chris
.