  The aim in this note is to define an algorithm to carry out minimal curvature
spherical harmonics interpolation, which is then used to calculate the
Laplacian for multi-electrode EEG data analysis. The approach taken is to
respect the data. That is, we implement a minimal curvature condition for the
interpolating surface subject to the constraints determined from the
multi-electrode data. We implement this approach using spherical harmonics
interpolation. In this elegant example we show that minimization requirement
and constraints complement each other to fix all degrees of freedom
automatically, as occurs in gauge theories. That is, the constraints are
respected, while only the orthogonal subspace minimization constraints are
enforced. As an example, we discuss the application to interpolate control data
and calculate the temporal sequence of laplacians from an EEG Mismatch
Negativity (MMN) experiment (using an implementation of the algorithm in IDL).
