ON THE DISTANCE FROM A POINT TO A QUADRIC SURFACE

Abstract

n this paper we present a new algorithm to compute the Euclidean distance from a point to a quadric surface. In some sense, this algorithm is a generalization of a previous work of V. Hernández, J. Estrada and P. Barrera, where an effective algorithm to compute the Euclidean distance from a point to a plane conic is developed. It provides good approximations of the Euclidean distance from a point to a conic, as well as of the coordinates of its orthogonal projection (footpoint), even when the point is not close to the conic. In fact, the current algorithm uses the previous one and shares with it the desirable features of working well if the point may not be assumed to be very close to the quadric surface and permitting to improve iteratively the approximations, up to obtain a prescribed accuracy.