I know one can define a least-squares-fit plane as a point and normal using the centroid of a set of points and the singular vector associated with its least singular value.
However, in doing that, is it possible to compute the residual point-to-plane distance error without simply summing all the point-to-plane distances? That is, as SVD can give the least-squares results, is there any part of the process (a singular value, or some matrix product, perhaps) that quickly produces the value of the minimized error?