  Null points are important locations in vector fields, such as a magnetic
field. A new technique (a trilinear method for finding null points) is
presented for finding null points over a large grid of points, such as those
derived from a numerical experiment. The method was designed so that the null
points found would agree with any fieldlines traced using the commonly used
trilinear interpolation. It is split into three parts: reduction, analysis and
positioning, which, when combined, provide an efficient means of locating null
points to a user-defined sub-grid accuracy. We compare the results of the
trilinear method with that of a method based on the Poincare index, and discuss
the accuracy and limitations of both methods.
