On the euclidean distance from a point to a conic

Abstract

In this paper a new algorithm to compute thc cuclidean distance from
a point to a conie is presented. This algorithm provides good approximation..<;
for the euclidcan distancc, even when the point is not very c10se
to the given conie. Furthermore, the approximations may be improved
iteratively to attain a preseribed ac.curaey. Unlike the most commonly
known methods to approximate the euclidean distance, in the proposed
method the coordinates of the footpoint for the orthogonal projection of
the point on the conie are computed. This particular fcature permits to
obtain a noteworthy accuracy without increasing too mueh the oomputational
costo
A pracedure to fit a conic section to a seattered set of points inside a
triangle is discussed. The proeedure is based on minimizing the sum of
squared orthogonal distanee of data points from the canie. The approximate
orthogonal distances are computed using the previous algorithm.

Keywords. Canies, approximare distance, implicit canic section fitting,
least squares. MSC: 65Y25, 51N35.