Pattern Recognition, 4th Edition

Distances between a Point and a Quadric Surface

In this section we introduce definitions in addition to those discussed in Chapter 11 concerning the distance between a point and a quadric surface.

We recall that the general equation of a quadric surface, Q, is(14.35)where A is an l × l symmetric matrix, b is an l × l vector, c is a scalar, and x = [x¹, …, x^l]^T. The A, b and c quantities are the parameters defining Q. For various choices of these quantities we obtain hyperellipses, hyperparabolas, and so on. An alternative to the Eq. (14.35) form is easily verified to be (see Problem 14.8)(14.36)whereand(14.38)with r = l(l + 1)/2 and s = r + ...