Critical points of vector fields are important topological features, which are
characterized by the number and order of areas of different flow behavior
around it. We present an approach to detect the different sectors around
general critical points of 3D vector fields. This approach is based on a
piecewise linear approximation of the vector fields around the critical points.
We showed examples how this approach can also treat critical points of a higher
order, and we discussed the limitation of the approach as well.