On the euclidean distance from a point to a conic
Victoria Hernández Mederos Victoria Hernández Mederos, Jorge Estrada Sarlabous, Pablo Barrera Sánchez · Universidad Industrial de Santander · 1997
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.