A NEW ALGORITHM TO COMPUTE THE EUCLIDEAN DISTANCE FROM A POINT TO A CONIC

Abstract

In this paper a new algorithm to compute the Euclidean distance from a point to a conic is presented. This algorithm provides good approximations for the Euclidean distance, even when the point is not very close to the given conic. Furthermore, the approximations may be improved iteratively to attain a prescribed accuracy. 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 conic are computed. This particular feature permits to obtain a noteworthy accuracy without increasing too much the computational cost.